https://fsunuc.physics.fsu.edu/wiki/api.php?action=feedcontributions&feedformat=atom&user=Bk20buFSU Fox's Lab Wiki - User contributions [en]2026-04-09T13:37:06ZUser contributionsMediaWiki 1.39.0https://fsunuc.physics.fsu.edu/wiki/index.php?title=Weekly_Tandem_Maintenance&diff=2649Weekly Tandem Maintenance2025-08-18T15:04:20Z<p>Bk20bu: </p>
<hr />
<div><br />
Name: <br />
<br />
Date:<br />
<br />
----<br />
Preliminary:<br />
Use your best judgment to determine if a particular step is not appropriate for today's maintenance!<br />
Photo-Checklist located here: [[Tandem Maintenance Checklist Photos]]<br />
<br />
# Determine whether or not the tandem or ion sources are currently operating.<br />
# Begin filling the 500 L liquid nitrogen dewar at the linac hall fill station. <br />
# Cheek the previous week's maintenance sheet for uncorrected problems.<br />
----<br />
Checklist: Circle and explain all items on this list, which could not be checked. <br />
{<br />
# On the back side of this sheet, record the control room Penning gauge vacuum readings.<br />
# Record the control room tank pressure ____ and temperature ___<br />
# Record propane tank levels. (Located outside by helium tanks.) #1____ #2____<br />
# Check the generator oil and water levels: start the generator and allow it to run until list is complete.<br />
# Check that the Air Compressor Room Exhaust Fan is running ( south wall exterior, room west of emergency generator ) If not, notify staff immediately.<br />
# Record the drop across the lab water filter located south of the LE tandem vault entrance. <br />
# Check the SNICS source deionized cooling water level.<br />
# Check the SNICS source backing pump oil level and two drive belts.<br />
# Check the pressure in the SNICS source argon cylinder; replace if less than 100 psi _____<br />
# Record the SNICS source vacuum gauge readings on the back of this sheet.<br />
# Drain the water from the airline trap (NOT THE OILER) on west side of SNICS source.<br />
# Record the LE cryopump temperature.<br />
# Record the beam line LE Vacuum (Penning gauge) on the back of this sheet. <br />
# Actuate the LE cryopump gate valve.<br />
# There is an unpumped section of beam line between the LE valve and the SNICS source exit valve. If either valve is open, cycle the LE beam line gate valve.<br />
# If the tandem is not running, actuate (close and immediately open) both gas security ball valves. <br />
# Drain the line water trap (NOT THE OILER).<br />
# Ensure that the LE faraday cup rotates and the indicator lights flash.<br />
# Record the Pelletron chain run time hours: #1_____ #2_____<br />
# Record the Scott Airpack pressure _____ (At HE end of the tandem in yellow case.)<br />
# Record the tandem pressure and temperature shown on gauges at HE end of tandem.<br />
# Record the HE cryopump temperature. <br />
# Record the HE pumping station vacuums on the back of this sheet.<br />
# Actuate the HE pumping station gate valve.<br />
# Actuate the HE beamline gate valve.<br />
# Ensure that the HE faraday cup rotates and the indicator lights flash.<br />
# Drain the HE air line water trap (NOT THE OILER).<br />
# Drain the compressor oil from the tandem 90 degree magnet image slits trap.<br />
# Ensure that the faraday cup 2 rotates and the indicator lights flash.<br />
# Record the target room 1-90 degree magnet vacuum on the back of this sheet.<br />
# Record the linac beam line vacuum and actuate entrance gate valve if vacuum permits.<br />
# Record the target room 1-90 degree magnet cryopump temperature back of this sheet.<br />
# Record the target room 1-90 degree magnet pumping station vacuums on the back of this sheet.<br />
# Actuate the target mom 1-90 degree magnet pumping station gate valve.<br />
# Record the switching magnet pumping station vacuums on the back of this sheet.<br />
# Ignore this step until new pump installed: Actuate the switching magnet pumping station gate valve.<br />
# Ensure that all necessary switches are active on the tandem beam line valve status panel and that each item is in the protect mode at the individual device's control box or panel.<br />
# Drain the switching magnet water trap (NOT THE OILER).<br />
# Ensure that the 4 radiation warning signs are lit. Lamps are only lit if tandem or preaccelerator is on.<br />
# Record the emergency generator temperature ___ oil pressure ___ and output voltages.<br />
## 1 _____ 2 _____ 3_____<br />
# Turn off the generator and set switch to REMOTE position.<br />
# Record any problems found and corrected during this maintenance on the back of this sheet. <br />
# Drain the water traps located in the gas handling mom on the north and south walls.<br />
# If no experiment running: Close the Tandem Source - Tandem Vault - TR1 and TR2 doors, then verify the corresponding status lights on the Control Room interlock panel. <br />
# Activate the audible alarm in the control room and break the interlock by opening the TR1 door. Verify that alarm is audible. <br />
# Verify that the LE Cup can not be retracted at the cup control panel while door is open.<br />
# If Tandem is running: Verify the operation of lit signs at the TR1 and TR2 entries, near the film badge rack and the lit sign outside the loading dock. <br />
<br />
'''IN CONTROL ROOM'''<br />
HE Penning gauge: ________ TORR <br />
LE Penning gauge: ________ TORR <br />
SNICS Penning gauge: _____ TORR<br />
Polarized Ion Source: ____ TORR<br />
<br />
'''IN TANDEM VAULT SOURCE AREA'''<br />
SNICS Backing Line Thermocouple __________________ μ<br />
<br />
SNICS Diffusion Pump Thermocouple ________________ μ<br />
<br />
SNICS Channel 2 Source Box Thermocouple __________ μ<br />
<br />
'''IN TANDEM VAULT: LOW ENERGY END'''<br />
LE Cryopump: Head Temperature _____ K <br />
<br />
LE Vacuum: Penning Gauge ____ TORR<br />
<br />
'''IN TANDEM VAULT: HIGH ENERGY END'''<br />
<br />
HE Cryopump:Head Temperature _______ K<br />
<br />
HE Vacuum: Penning Gauge 1 ______ TORR, Penning Gauge 2 ______ TORR<br />
<br />
TR 1-90 degree Magnet Penning gauge: _________ TORR <br />
TR 1-90 degree Magnet Cryopump: Head Temperature _________ K<br />
<br />
Linac Beam Line Penning gauge: __________ TORR<br />
Switching Magnet Penning gauge ________ TORR <br />
<br />
Additional Notes:</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Tandem_Maintenance_Checklist_Photos&diff=2648Tandem Maintenance Checklist Photos2025-08-18T15:02:58Z<p>Bk20bu: </p>
<hr />
<div>Attached on this page is a pdf version of the weekly maintenance checklist, with various photos/locations showing where the checklist items are located in/around Fox Lab<br />
<br />
Last updated summer of 2024, locations may change, this should just serve as rough guide to where things reside within Fox Lab. If there are any questions always double check with Lagy, Brian, or Ingo.<br />
<br />
PDF should be viewable/downloadable from online -- B. Kelly<br />
<br />
[[File:Weekly Tandem Maintenance Locator2024.pdf|thumb]]</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Tandem_Maintenance_Checklist_Photos&diff=2647Tandem Maintenance Checklist Photos2025-08-18T15:00:18Z<p>Bk20bu: Created page with "Attached on this page is a pdf version of the weekly maintenance checklist, with various photos/locations showing where the checklist items are located in/around Fox Lab thumb"</p>
<hr />
<div>Attached on this page is a pdf version of the weekly maintenance checklist, with various photos/locations showing where the checklist items are located in/around Fox Lab<br />
<br />
[[File:Weekly Tandem Maintenance Locator2024.pdf|thumb]]</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=FSU_Fox%27s_Lab_Wiki&diff=2646FSU Fox's Lab Wiki2025-08-18T14:58:17Z<p>Bk20bu: /* Other Resources */</p>
<hr />
<div><br />
= Introduction =<br />
<br />
*This is the wiki for all details about FSU [[John D Fox]]' Lab for nuclear physics.<br />
*The original manual can be found in [[:File:FoxManual20200415.pdf]].<br />
*This wiki is <b><span style="color:red">OPEN TO PUBLIC</span></b>. Any confidential material should be put in <b>[http://elog.physics.fsu.edu elog]</b> or use internal pages.<br />
*For [https://www.lsu.edu/physics/research/nuclear-physics.php Louisiana State University] users, please see [https://fsunuc.physics.fsu.edu/elog/2022_04_SPS_Blocker/2 this elog] for acessing the [[Fox's Lab Network]].<br />
*New account may like to see the wiki syntax in [[Wiki_Edit_Cheat_Sheet | here]].<br />
<br />
= Accelerator Operation Procedures =<br />
● [[Radiation Safety]]<br />
<br />
= Hardware = <br />
{|style="width: 100%;"<br />
|● [[Tandem Accelerator]] || ● [[LINAC]]<br />
|-<br />
|● [[SF6 Gas Handling System]] || ● [[Vacuum Systems]]<br />
|-<br />
|● [[Water Cooling System]] || ● [[He refrigerator]]<br />
|-<br />
|● [[Computers Network]] || ● [[Hardware/Cable Changes for Switching Target Rooms]]<br />
|-<br />
|● [[Ion Sources]]: This includes the [[Ion Sources#Sputter Source|Sputter Source]] and [[Ion Sources#RF Source|RF Source]] || ● [[Target Lab]]<br />
|-<br />
|● [[RESOLUT]]: In-flight radioactive beam facility<br />
|-<br />
|● [[Triton Beam Project]]: Multi-SNICS with Tritium Cathodes<br />
|}<br />
<br />
== Detector stations ==<br />
<br />
{|style="width: 100%;"<br />
|● [[ANASEN]] || ● [[CATRiNA]]<br />
|-<br />
|● [[Clarion2]] || ● [[ENCORE]]<br />
|-<br />
|● [[Gamma Station]] || ● [[RESONEUT]]<br />
|-<br />
|● [[Split-Pole Spectrograph]]<br />
|-<br />
|● [[Penning Trap]]<br />
|}<br />
<br />
== DAQ systems==<br />
{|style="width: 100%;"<br />
|● [[Pixie16 digitizer]] || ● [[CAEN digitizer]] (for 1st-gen)<br />
|-<br />
|● [[NSCL DAQ]] / [[NSCL SpecTcl]] || ● [[FSU SOLARIS DAQ]] (for CAEN 2nd-gen)<br />
|-<br />
|● [[Mesytec]] || <br />
|}<br />
<br />
= Software & Resources = <br />
<br />
{|style="width: 100%;"<br />
|◆[[Online Resources]]: Web server, Elog, Grafana, Wiki, InfluxDB || ◆[[Data Server]]<br />
|-<br />
|◆[https://fsunuc.physics.fsu.edu/git/explore/repos Git repository] by Gitea || ◆[[Github repositories]] <br />
|-<br />
|◆[[SSH tunneling]] || ◆[[VNC viewer]]<br />
|-<br />
|◆[[Slack Channel]] || ◆[[gnuscope]]<br />
|-<br />
|◆[[SolidWorks]] || ◆[[Online Analysis]]<br />
|-<br />
| ◆[[Raspberry Pi Camera]] || ◆[[Python Iseg HV controller]] <br />
|-<br />
|◆[https://fsunuc.physics.fsu.edu/research/publication_list/ List of Publications] || ◆[[Ptolmey GUI]] <br />
|}<br />
<br />
= Layout of the Laboratory =<br />
{|<br />
|[[File:Lab Model.png|450px|frameless|none]] || [[File:JohnDFoxLayout.png|550px|frameless|none]] <br />
|}<br />
<!--[[File:NRBbasement.png|1000px|thumb|none]]--><br />
<br />
= External Collaborations = <br />
<br />
* [[LSU Collaboration]]<br />
* [[ORNL Collaboration]]<br />
* [[TRIUMF Collaboration]]<br />
* [[FRIB FDSi e21062]]<br />
* [[FRIB SOLARIS Collaboration]]<br />
* [[ANL MUSIC Collaboration]]<br />
<br />
= Past Experiments =<br />
<br />
[[List of Past Experiments]]<br />
<br />
= Other Resources =<br />
<br />
* [[Journal Club]]<br />
<br />
* [[Help Call List for Evenings, Weekends, Holidays]]<br />
<br />
* [[Laboratory Infrastructure]]<br />
<br />
* [[Wiki Edit Cheat Sheet]]<br />
<br />
* [[Guide for using this wiki]]<br />
<br />
* [https://www.qr-code-generator.com/ QR code generator]<br />
<br />
* [[Weekly Tandem Maintenance]]<br />
<br />
* [[Tandem Maintenance Checklist Photos]]<br />
<br />
* [[Source Sign Out Sheet]]<br />
<br />
* [[Xilinx FPGA]]<br />
<br />
* [[Gamma Calibration Sources]]<br />
<br />
= Contacts = <br />
<br />
{|<br />
| for accelerator ||: Lagy Baby mailto:lbaby@fsu.edu <br>: Ingo Wiedenhoever mailto:iwiedenhoever@fsu.edu<br />
|-<br />
| for vacuum ||: Powell Barber mailto:pbarber@fsu.edu<br />
|-<br />
| for ion sources || : Brian Schmidt mailto:bschmidt@fsu.edu<br />
|-<br />
| for LINAC || : David Spinger mailto: dspingler@fsu.edu<br />
|-<br />
| for IT and DAQ ||: Ryan Tang mailto:rtang@fsu.edu<br />
|-<br />
|}</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Weekly_Tandem_Maintenance&diff=2645Weekly Tandem Maintenance2025-08-18T14:54:48Z<p>Bk20bu: </p>
<hr />
<div><br />
Name: <br />
<br />
Date:<br />
<br />
----<br />
Preliminary:<br />
Use your best judgment to determine if a particular step is not appropriate for today's maintenance!<br />
<br />
# Determine whether or not the tandem or ion sources are currently operating.<br />
# Begin filling the 500 L liquid nitrogen dewar at the linac hall fill station. <br />
# Cheek the previous week's maintenance sheet for uncorrected problems.<br />
----<br />
Checklist: Circle and explain all items on this list, which could not be checked. <br />
{<br />
# On the back side of this sheet, record the control room Penning gauge vacuum readings.<br />
# Record the control room tank pressure ____ and temperature ___<br />
# Record propane tank levels. (Located outside by helium tanks.) #1____ #2____<br />
# Check the generator oil and water levels: start the generator and allow it to run until list is complete.<br />
# Check that the Air Compressor Room Exhaust Fan is running ( south wall exterior, room west of emergency generator ) If not, notify staff immediately.<br />
# Record the drop across the lab water filter located south of the LE tandem vault entrance. <br />
# Check the SNICS source deionized cooling water level.<br />
# Check the SNICS source backing pump oil level and two drive belts.<br />
# Check the pressure in the SNICS source argon cylinder; replace if less than 100 psi _____<br />
# Record the SNICS source vacuum gauge readings on the back of this sheet.<br />
# Drain the water from the airline trap (NOT THE OILER) on west side of SNICS source.<br />
# Record the LE cryopump temperature.<br />
# Record the beam line LE Vacuum (Penning gauge) on the back of this sheet. <br />
# Actuate the LE cryopump gate valve.<br />
# There is an unpumped section of beam line between the LE valve and the SNICS source exit valve. If either valve is open, cycle the LE beam line gate valve.<br />
# If the tandem is not running, actuate (close and immediately open) both gas security ball valves. <br />
# Drain the line water trap (NOT THE OILER).<br />
# Ensure that the LE faraday cup rotates and the indicator lights flash.<br />
# Record the Pelletron chain run time hours: #1_____ #2_____<br />
# Record the Scott Airpack pressure _____ (At HE end of the tandem in yellow case.)<br />
# Record the tandem pressure and temperature shown on gauges at HE end of tandem.<br />
# Record the HE cryopump temperature. <br />
# Record the HE pumping station vacuums on the back of this sheet.<br />
# Actuate the HE pumping station gate valve.<br />
# Actuate the HE beamline gate valve.<br />
# Ensure that the HE faraday cup rotates and the indicator lights flash.<br />
# Drain the HE air line water trap (NOT THE OILER).<br />
# Drain the compressor oil from the tandem 90 degree magnet image slits trap.<br />
# Ensure that the faraday cup 2 rotates and the indicator lights flash.<br />
# Record the target room 1-90 degree magnet vacuum on the back of this sheet.<br />
# Record the linac beam line vacuum and actuate entrance gate valve if vacuum permits.<br />
# Record the target room 1-90 degree magnet cryopump temperature back of this sheet.<br />
# Record the target room 1-90 degree magnet pumping station vacuums on the back of this sheet.<br />
# Actuate the target mom 1-90 degree magnet pumping station gate valve.<br />
# Record the switching magnet pumping station vacuums on the back of this sheet.<br />
# Ignore this step until new pump installed: Actuate the switching magnet pumping station gate valve.<br />
# Ensure that all necessary switches are active on the tandem beam line valve status panel and that each item is in the protect mode at the individual device's control box or panel.<br />
# Drain the switching magnet water trap (NOT THE OILER).<br />
# Ensure that the 4 radiation warning signs are lit. Lamps are only lit if tandem or preaccelerator is on.<br />
# Record the emergency generator temperature ___ oil pressure ___ and output voltages.<br />
## 1 _____ 2 _____ 3_____<br />
# Turn off the generator and set switch to REMOTE position.<br />
# Record any problems found and corrected during this maintenance on the back of this sheet. <br />
# Drain the water traps located in the gas handling mom on the north and south walls.<br />
# If no experiment running: Close the Tandem Source - Tandem Vault - TR1 and TR2 doors, then verify the corresponding status lights on the Control Room interlock panel. <br />
# Activate the audible alarm in the control room and break the interlock by opening the TR1 door. Verify that alarm is audible. <br />
# Verify that the LE Cup can not be retracted at the cup control panel while door is open.<br />
# If Tandem is running: Verify the operation of lit signs at the TR1 and TR2 entries, near the film badge rack and the lit sign outside the loading dock. <br />
<br />
'''IN CONTROL ROOM'''<br />
HE Penning gauge: ________ TORR <br />
LE Penning gauge: ________ TORR <br />
SNICS Penning gauge: _____ TORR<br />
Polarized Ion Source: ____ TORR<br />
<br />
'''IN TANDEM VAULT SOURCE AREA'''<br />
SNICS Backing Line Thermocouple __________________ μ<br />
<br />
SNICS Diffusion Pump Thermocouple ________________ μ<br />
<br />
SNICS Channel 2 Source Box Thermocouple __________ μ<br />
<br />
'''IN TANDEM VAULT: LOW ENERGY END'''<br />
LE Cryopump: Head Temperature _____ K <br />
<br />
LE Vacuum: Penning Gauge ____ TORR<br />
<br />
'''IN TANDEM VAULT: HIGH ENERGY END'''<br />
<br />
HE Cryopump:Head Temperature _______ K<br />
<br />
HE Vacuum: Penning Gauge 1 ______ TORR, Penning Gauge 2 ______ TORR<br />
<br />
TR 1-90 degree Magnet Penning gauge: _________ TORR <br />
TR 1-90 degree Magnet Cryopump: Head Temperature _________ K<br />
<br />
Linac Beam Line Penning gauge: __________ TORR<br />
Switching Magnet Penning gauge ________ TORR <br />
<br />
Additional Notes:</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Weekly_Tandem_Maintenance&diff=2644Weekly Tandem Maintenance2025-08-18T14:53:59Z<p>Bk20bu: </p>
<hr />
<div><br />
Name: <br />
<br />
Date:<br />
<br />
----<br />
Preliminary:<br />
Use your best judgment to determine if a particular step is not appropriate for today's maintenance!<br />
A pdf of the checklist items locations in the lab: [[File:Weekly Tandem Maintenance Locator2024.pdf|thumb]]<br />
<br />
# Determine whether or not the tandem or ion sources are currently operating.<br />
# Begin filling the 500 L liquid nitrogen dewar at the linac hall fill station. <br />
# Cheek the previous week's maintenance sheet for uncorrected problems.<br />
----<br />
Checklist: Circle and explain all items on this list, which could not be checked. <br />
{<br />
# On the back side of this sheet, record the control room Penning gauge vacuum readings.<br />
# Record the control room tank pressure ____ and temperature ___<br />
# Record propane tank levels. (Located outside by helium tanks.) #1____ #2____<br />
# Check the generator oil and water levels: start the generator and allow it to run until list is complete.<br />
# Check that the Air Compressor Room Exhaust Fan is running ( south wall exterior, room west of emergency generator ) If not, notify staff immediately.<br />
# Record the drop across the lab water filter located south of the LE tandem vault entrance. <br />
# Check the SNICS source deionized cooling water level.<br />
# Check the SNICS source backing pump oil level and two drive belts.<br />
# Check the pressure in the SNICS source argon cylinder; replace if less than 100 psi _____<br />
# Record the SNICS source vacuum gauge readings on the back of this sheet.<br />
# Drain the water from the airline trap (NOT THE OILER) on west side of SNICS source.<br />
# Record the LE cryopump temperature.<br />
# Record the beam line LE Vacuum (Penning gauge) on the back of this sheet. <br />
# Actuate the LE cryopump gate valve.<br />
# There is an unpumped section of beam line between the LE valve and the SNICS source exit valve. If either valve is open, cycle the LE beam line gate valve.<br />
# If the tandem is not running, actuate (close and immediately open) both gas security ball valves. <br />
# Drain the line water trap (NOT THE OILER).<br />
# Ensure that the LE faraday cup rotates and the indicator lights flash.<br />
# Record the Pelletron chain run time hours: #1_____ #2_____<br />
# Record the Scott Airpack pressure _____ (At HE end of the tandem in yellow case.)<br />
# Record the tandem pressure and temperature shown on gauges at HE end of tandem.<br />
# Record the HE cryopump temperature. <br />
# Record the HE pumping station vacuums on the back of this sheet.<br />
# Actuate the HE pumping station gate valve.<br />
# Actuate the HE beamline gate valve.<br />
# Ensure that the HE faraday cup rotates and the indicator lights flash.<br />
# Drain the HE air line water trap (NOT THE OILER).<br />
# Drain the compressor oil from the tandem 90 degree magnet image slits trap.<br />
# Ensure that the faraday cup 2 rotates and the indicator lights flash.<br />
# Record the target room 1-90 degree magnet vacuum on the back of this sheet.<br />
# Record the linac beam line vacuum and actuate entrance gate valve if vacuum permits.<br />
# Record the target room 1-90 degree magnet cryopump temperature back of this sheet.<br />
# Record the target room 1-90 degree magnet pumping station vacuums on the back of this sheet.<br />
# Actuate the target mom 1-90 degree magnet pumping station gate valve.<br />
# Record the switching magnet pumping station vacuums on the back of this sheet.<br />
# Ignore this step until new pump installed: Actuate the switching magnet pumping station gate valve.<br />
# Ensure that all necessary switches are active on the tandem beam line valve status panel and that each item is in the protect mode at the individual device's control box or panel.<br />
# Drain the switching magnet water trap (NOT THE OILER).<br />
# Ensure that the 4 radiation warning signs are lit. Lamps are only lit if tandem or preaccelerator is on.<br />
# Record the emergency generator temperature ___ oil pressure ___ and output voltages.<br />
## 1 _____ 2 _____ 3_____<br />
# Turn off the generator and set switch to REMOTE position.<br />
# Record any problems found and corrected during this maintenance on the back of this sheet. <br />
# Drain the water traps located in the gas handling mom on the north and south walls.<br />
# If no experiment running: Close the Tandem Source - Tandem Vault - TR1 and TR2 doors, then verify the corresponding status lights on the Control Room interlock panel. <br />
# Activate the audible alarm in the control room and break the interlock by opening the TR1 door. Verify that alarm is audible. <br />
# Verify that the LE Cup can not be retracted at the cup control panel while door is open.<br />
# If Tandem is running: Verify the operation of lit signs at the TR1 and TR2 entries, near the film badge rack and the lit sign outside the loading dock. <br />
<br />
'''IN CONTROL ROOM'''<br />
HE Penning gauge: ________ TORR <br />
LE Penning gauge: ________ TORR <br />
SNICS Penning gauge: _____ TORR<br />
Polarized Ion Source: ____ TORR<br />
<br />
'''IN TANDEM VAULT SOURCE AREA'''<br />
SNICS Backing Line Thermocouple __________________ μ<br />
<br />
SNICS Diffusion Pump Thermocouple ________________ μ<br />
<br />
SNICS Channel 2 Source Box Thermocouple __________ μ<br />
<br />
'''IN TANDEM VAULT: LOW ENERGY END'''<br />
LE Cryopump: Head Temperature _____ K <br />
<br />
LE Vacuum: Penning Gauge ____ TORR<br />
<br />
'''IN TANDEM VAULT: HIGH ENERGY END'''<br />
<br />
HE Cryopump:Head Temperature _______ K<br />
<br />
HE Vacuum: Penning Gauge 1 ______ TORR, Penning Gauge 2 ______ TORR<br />
<br />
TR 1-90 degree Magnet Penning gauge: _________ TORR <br />
TR 1-90 degree Magnet Cryopump: Head Temperature _________ K<br />
<br />
Linac Beam Line Penning gauge: __________ TORR<br />
Switching Magnet Penning gauge ________ TORR <br />
<br />
Additional Notes:</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=File:Weekly_Tandem_Maintenance_Locator2024.pdf&diff=2643File:Weekly Tandem Maintenance Locator2024.pdf2025-08-18T14:53:06Z<p>Bk20bu: </p>
<hr />
<div>Photo-descriptions of where weekly checklist items are located in Fox Lab</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1819Split-Pole Spectrograph2023-07-24T15:38:39Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb| Solid Works drawing of the fully planned array, which will consist of 13 CeBr<sub>3</sub> detectors.]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a γ-ray detector array designed to be used in conjunction with the SE-SPS. Comprised of low-background CeBr<sub>3</sub> scintillators with Hamamatsu photomultipliers. There are currently 7 commissioned detectors in the array with varying size crystals (2-1x1 inch, 4-2x2 inch, and 1-3x4 inch crystal detectors; a schematic for the full array on is shown on the right). The goal of CeBrA is to establish coincident events with the light-ions detected in the focal plane detector of the SE-SPS and the corresponding γ-rays from the excited recoiling nucleus, which are called particle-gamma coincidences. The scattering chamber used for CeBrA differs from the usual sliding-seal chamber that is used with the SE-SPS. With a hemisphere shape, it sits at a fixed 35<sup>o</sup> angle relative to the SE-SPS and allows for a more detailed study of the electromagnetic transitions from nuclei excited in reactions using the SE-SPS.<br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:Current_array.jpg | 400px|frameless|]] <br />
|-<br />
|Current array setup for CeBrA as it was used in the Summer 2023 REU experiments studying the <sup>52</sup>Cr(d,pγ)<sup>53</sup>Cr and <sup>34</sup>S(d,pγ)<sup>35</sup>S reactions, which was a follow up from the previous REU from 2022.<br />
|}<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1811Split-Pole Spectrograph2023-07-12T22:33:06Z<p>Bk20bu: /* SABRE */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb| Solid Works drawing of the fully planned array, which will consist of 13 CeBr<sub>3</sub> detectors.]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a γ-ray detector array designed to be used in conjunction with the SE-SPS. Comprised of low-background CeBr<sub>3</sub> scintillators with Hamamatsu photomultipliers, there are currently 7 commissioned detectors in the array with varying size crystals (2-1x1 inch, 4-2x2 inch, and 1-3x4 inch crystal detectors; a schematic for the full array on is shown on the right). The goal of CeBrA is to establish coincident events with the light-ions detected in the focal plane detector of the SE-SPS and the corresponding γ-rays from the excited recoiling nucleus, which are called particle-gamma coincidences. The scattering chambering used for CeBrA differs from the usual sliding-seal chamber that is used with the SE-SPS. With a hemisphere shape, it sits at a fixed 35<sup>o</sup> angle relative to the SE-SPS and allows for a more detailed study of the electromagnetic transitions from nuclei excited in reactions using the SE-SPS.<br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:Current_array.jpg | 400px|frameless|]] <br />
|-<br />
|Current array setup for CeBrA as it was used in the Summer 2023 REU experiments studying the <sup>52</sup>Cr(d,pγ)<sup>53</sup>Cr and <sup>34</sup>S(d,pγ)<sup>35</sup>S reactions, which was a follow up from the previous REU from 2022.<br />
|}<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1810Split-Pole Spectrograph2023-07-12T22:30:17Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
[[File:Current array.jpg|thumb]]<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb| Solid Works drawing of the fully planned array, which will consist of 13 CeBr<sub>3</sub> detectors.]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a γ-ray detector array designed to be used in conjunction with the SE-SPS. Comprised of low-background CeBr<sub>3</sub> scintillators with Hamamatsu photomultipliers, there are currently 7 commissioned detectors in the array with varying size crystals (2-1x1 inch, 4-2x2 inch, and 1-3x4 inch crystal detectors; a schematic for the full array on is shown on the right). The goal of CeBrA is to establish coincident events with the light-ions detected in the focal plane detector of the SE-SPS and the corresponding γ-rays from the excited recoiling nucleus, which are called particle-gamma coincidences. The scattering chambering used for CeBrA differs from the usual sliding-seal chamber that is used with the SE-SPS. With a hemisphere shape, it sits at a fixed 35<sup>o</sup> angle relative to the SE-SPS and allows for a more detailed study of the electromagnetic transitions from nuclei excited in reactions using the SE-SPS.<br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:Current_array.jpg | 400px|frameless|]] <br />
|-<br />
|Current array setup for CeBrA as it was used in the Summer 2023 REU experiments studying the <sup>52</sup>Cr(d,pγ)<sup>53</sup>Cr and <sup>34</sup>S(d,pγ)<sup>35</sup>S reactions, which was a follow up from the previous REU from 2022.<br />
|}<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1809Split-Pole Spectrograph2023-07-12T21:58:02Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
[[File:Current array.jpg|thumb]]<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb|test here]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a gamma-ray detector array designed to be used in conjunction with the SE-SPS.<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1808Split-Pole Spectrograph2023-07-12T21:57:51Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
[[File:Current array.jpg|thumb]]<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb|test here]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a gamma-ray detector array designed to be used in conjunction with the SE-SPS.<br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:Current array.jpg | 400px|frameless| ]] <br />
|-<br />
|Another test here| }<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1807Split-Pole Spectrograph2023-07-12T21:57:19Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
[[File:Current array.jpg|thumb]]<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb|test here]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a gamma-ray detector array designed to be used in conjunction with the SE-SPS.<br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:Current array.jpg | 400px|frameless| ]] <br />
|-<br />
|Another test here }<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=File:Current_array.jpg&diff=1806File:Current array.jpg2023-07-12T21:56:12Z<p>Bk20bu: </p>
<hr />
<div>Current working array</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1805Split-Pole Spectrograph2023-07-12T20:35:23Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb|test here]]<br />
<br />
The Cerium Bromide Array (CeBrA) is a gamma-ray detector array designed to be used in conjunction with the SE-SPS.<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1804Split-Pole Spectrograph2023-07-12T20:30:49Z<p>Bk20bu: /* CeBrA */</p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
= CeBrA =<br />
<br />
<br />
<br />
The Cerium Bromide Array (CeBrA) is a gamma-ray detector array designed to be used in conjunction with the SE-SPS.<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=Split-Pole_Spectrograph&diff=1803Split-Pole Spectrograph2023-07-12T20:28:58Z<p>Bk20bu: </p>
<hr />
<div><br />
{| align="right" style="width:30%;"<br />
|-<br />
| [[File:SPS Pictue Annotated.png|thumb|Annotated picture of the SE-SPS, An plain picture is here : [[:File:SPS Magnet.png]]]] || [[File:SPS Picture ray.png|thumb| SE-SPS COSY simulation. An plain picture is here [[:File:SPS Sketch With Cosy.png]]]]<br />
|}<br />
<br />
{{Notice | Need a picture of SPS }}<br />
<br />
The '''Super Enge Split-Pole Spectrograph''' <br />
<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref><br />
<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref><br />
is a magnet spectrometer to measure the spectrum of nuclear reactions. The concept and design were developed by [https://en.wikipedia.org/wiki/Harald_A._Enge Harald A. Enge]<ref>J. E. Spencer and H. A. Enge, NIM '''49''', 181 (1967) https://doi.org/10.1016/0029-554X(67)90684-2 </ref> at 1967, aimed to have a broad-momentum range spectrograph with <math> p_{max}/p_{min} \approx 2.8 </math> or <math> E_{max}/E_{min} \approx 8 </math>. The spectrometer was originally located at the Wright Nuclear Structure Laboratory (closed at 2013), at Yale University. It was moved to FSU in the fall of 2013. It consists of a reaction chamber, a '''split-pole magnetic spectrograph''', a '''position-sensitive ionization drift chamber''', and a '''plastic scintillator'''. It has an angular acceptance of 128 msr (vertical ±40 mrad, horizontal ±80 mrad). The maximum B-field is 1.63 T with a radius of curvature from 511 mm to 920 mm. The mean radius is 600 mm. The advantage of the split-pole instead of a single-pole magnet is the aberration (x|θ<sup>2</sup>) and (x|φ<sup>2</sup>) are almost zero <ref name="Enge1979" />. <br />
<br />
The '''Super''' Enge Split-Pole Spectrograph is an upgrade of the Yale Enge SPS. The major change is the redesign of the backward silicon detector array to the [[Split-Pole_Spectrograph#SABRE|SABRE]].<br />
<br />
= Magnet =<br />
[[File:Design of a Split-pole spectrograph.png|thumb|Design of a Split-pole spectrograph. Take from Ref. <ref name="Enge1979"/>]]<br />
<br />
The primary goal of a spectrograph is resolving momentum. A general discussion of magnetic spectrographs can be found at Ref. <ref name="Enge1979" /> and Ref. <ref> H. A. Enge, Physics Today '''20''', 65 (1967) https://doi.org/10.1063/1.3034401 </ref>. There are many designs from a simple single dipole to a combination of multiple dipoles and quadrupoles. <br />
<br />
The SPS magnet was designed for a large solid angle, large resolving power, and correction of kinematic broadening. Using two-directional focusing and second-order focusing spectrograph can achieve a large sold angle and resolving power. Second-order focusing means the second-order terms in the acceptance angles vanish, i.e. no aberration.<br />
<br />
The SPS contains 2 separate poles enveloped by a single coil. The split provides second-order double focusing over a broad range of momenta. The magnet can be rotated from 0 to 55 degrees in the lab. The magnetic field has an upper limit of 1.63 T (or 16.3 kG).<br />
<br />
{| class="wikitable"<br />
|+ This table is taken from B.P. Kay Ph.D thesis (2007)<br />
! Property !! Symbol !! Value<br />
|-<br />
| Orbital radius || <math> \rho </math> || 511 to 920 mm<br />
|-<br />
|Resolving power || <math> p/\Delta p </math> || 1st order of <math> (x|\theta) </math>4290 (at <math>\theta = \pm 80 </math> mrad) <br />
|- <br />
|rowspan="2"| Acceptance || Horizontal || 160 mrad<br />
|-<br />
| Vertical || 80 mrad<br />
|-<br />
| Dispersion || <math> D=(x|\delta) </math> || 1.96<br />
|-<br />
|rowspan="2" | Magnification || <math> M_x = (x|x)</math> || 0.39<br />
|-<br />
| <math> M_y = (y|y)</math> || 2.9<br />
|-<br />
| Maximum field || <math> B </math> || 1.63 T<br />
|}<br />
<br />
== Transfer matrix and COSY INFINITY simulation ==<br />
[[File:Schematics of ion-beam optical element.png|thumb|An illustration of the coordinate of an optical element. This is taken from H.A. Enge NIM 162, 161 (1979).]]<br />
{{Notice | need to fill up. Any 1st few orders transfer matrixes?}}<br />
<br />
The entrance coordinates of the beam are <math> x_1, y_1, \theta_1, \phi_1 </math> wiht momentum <math> \delta = p/p_0 </math>, and coordinate at exit are <math> x_2, y_2, \theta_2, \phi_2 </math>. The entrance and exit coordinates are related by <br />
<br />
<math> x_2 = f_x(x_1, y_1, \theta_1, \phi_1, \delta) </math><br />
<br />
using Taylor expansion:<br />
<br />
<math> \frac{x_2}{\rho} = (x|x) \frac{x_1}{\rho} + (x|\theta) \theta_1 + (x|\delta) \delta + (x|\theta^2) \theta_1^2 + ... </math><br />
<br />
In the above expansion, the term <math> (x|x) </math> is the '''magnification''' in the x-direction. <math> (x|\delta) </math> is the '''dispersion''', and <math> (x|\theta^2) </math> is '''aberration'''. The '''focal plane''' is the z-position that <math> (x|\theta) = 0 </math>, i.e. the exit <math> x_2 </math> does not depend on the entrance angle. <br />
<br />
=== Kinematic broadening ===<br />
[[File:Kinematic correction of spectrometer.png|thumb|Kinematic correction of spectrometer. Taken from H. A. Enge NIM 162, 161 (1979)]]<br />
<br />
Kinematic broadening is the broadening of focus for the same reaction state. After a reaction, the angle and momentum of the recoil particle are related that the entrance angle <math> \theta_1 = f(\delta)</math> is a function of momentum. For each energy state, the relation between the angle and momentum is unique. For example, in a 2-body transfer reaction, the momentum vector is <br />
<br />
<math> ( p_x, p_z ) = ( k \sin(\theta), \gamma \beta \sqrt{m^2-k^2} + \gamma k \cos(\theta) ) </math><br />
<br />
where <math> k, \theta</math> are the momentum and the scattering angle at the CM frame, <math> \gamma, \beta </math> are the Lorentz factor from Lab frame to CM frame, and <math> m </math> is the mass of the particle. All 5 coefficients are constant for a fixed energy state. And the different state is characterized by <math> k </math>. Defined the kinematic factor K:<br />
<br />
<math> K = \frac{1}{p} \frac{dp}{d\theta_1} = \frac{\beta E \sin(\theta)}{ k + \beta \sqrt{m^2 - k^2} \cos(\theta)} </math><br />
<br />
The kinematic broadening can be corrected by shifting the focal plane by <br />
<br />
<math> \Delta z = - D M \rho K, D = (x|\delta), M = (x|x) </math><br />
<br />
= Focal plane detector =<br />
[[File:Focal plane detector.png|400px|thumb|right|Front view of the opened camerabox. The SPS focal plane detector with the front window removed is at the bottom.]]<br />
<br />
[[File:Side Cross section view of the SPS focal plane detector.png|400px|thumb|Side Cross section view of the SPS focal plane detector. Taken from B.P. Kay Ph.D. thesis (2007).]]<br />
<br />
[[File:PID EDE annoteted.png|400px|thumb]]<br />
<br />
{{Notice | The drift ion chamber was repaired in summer 2018 }}<br />
<br />
The focal plane detector <br />
<ref> C. Marshal ''et. al'', IEEE Tran. Inst. and Meas. '''68''', 533 (2018) https://doi.org/10.1109/TIM.2018.2847938</ref><br />
<ref name="Markham1975"> R. G. Markham and R. G. H. Robertson, NIM '''129''', 131 (1975) https://doi.org/10.1016/0029-554X(75)90122-6 </ref><br />
consists of an ion drift chamber with a set of delay lines to detect the position of a particle along the focal plane and a plastic scintillator to detect the energy of the incoming particle. Using the energy loss of the particle through the ion chamber with the energy deposited in the scintillator, particles of different charges and masses can be identified.<br />
<br />
The typical pressure of the drift chamber is 70 to 300 Torr of isobutane gas [HC(CH3)3]. The pressure controls the density of the gas and affects the bias voltage, it further affects the drift velocity.<br />
<br />
{|class='wikitable'<br />
|+ Table of pressure and bias voltages. Data was taken from the Ph.D. thesis of Erin Good (2020)<br />
! Gas pressure (Torr) !! Anode bias (V) !! Cathode plate bias (V) <br />
|-<br />
| 70 || +1050 to +1035 || -550 to -500<br />
|-<br />
| 80 || +1150 || -550<br />
|-<br />
| 100 || +1250 || -600<br />
|-<br />
| 110 || +1200 to 1320 || -620 to -600<br />
|-<br />
| 125 || +1425 || -650<br />
|-<br />
| 130 || +1360 || -725<br />
|-<br />
| 150 || +1500 || -700<br />
|-<br />
|}<br />
<br />
From bottom to top, the cathode plate, drift region (contains four biased field-shaping wire grids), Frisch grid (grounded), three anode wires, and pickup pads (which are with the delay lines). Electrons induced by any radiation will drift upward, pass the Frisch grid, are accelerated by the anodes, and hit the pickup pads. The pickup pads are strips with 45° against the anode wires, almost parallel to the particle trajectories<ref name="Markham1975" />. Each pickup strip is 0.09" (2.286 mm) wide and 1.4" (35.56 mm) long, and spaced 0.01" (0.245 mm). A total of 440 lead-coated copper strips with a 5 ns delay per strip results in a nominal total delay of 2.2 μs. Every 10 strips share a delay chip. The position of the hit position can then be determined by the time difference at the end of the delay line.<br />
<br />
There are two position-sensitive delay lines (separated by 42.8625 mm) in the focal plane detector. By reconstructing the particle trajectory using the position information of both delay lines, the resolution can be enhanced by correcting for the kinematic shift of the reaction.<br />
<br />
After passing the drift chamber, the particles will be stopped and detected in a plastic scintillator with a photomultiplier tube (PMT) at each end. Together with the energy loss, obtained by the cathode in the drift chamber, a ΔE-E particle identification can be done.<br />
<br />
<br />
== Outline of the algorithm ==<br />
<br />
There are 9 readouts channels from the focal plane detector: <br />
{| class="wikitable"<br />
! readout !! type of signal <br />
|-<br />
| cathode || energy loss<br />
|-<br />
| Front delay line Left || timing<br />
|-<br />
| Front delay line Right || timing<br />
|-<br />
| Front anode || energy loss<br />
|-<br />
| Rear delay line Left || timing<br />
|-<br />
| Rear delay line Right || timing<br />
|-<br />
| Rear anode || energy loss<br />
|-<br />
| PMT Left || energy loss<br />
|-<br />
| PMT Right || energy loss<br />
|}<br />
<br />
The PID is usually using one of the PMT energy and either the cathode or anode energy. <br />
<br />
The coordinate at the Focal Plane is the conventional one, where z-axis is perpendicular to the focal plane detector, y-axis is the vertical, and x-axis is the z-axis cross y-axis. The positions of the front and Rear planes are constructed by the timestamp. Suppose the timestamp is in ns. <br />
<br />
<math> <br />
x_1 = \frac{t_{FL} - t_{FR}}{2} \frac{1}{2.1} ; ~~~ x_2 = \frac{t_{BL} - t_{BR}}{2} \frac{1}{1.98}<br />
</math><br />
<br />
The position at the center of the focal plane is <br />
<br />
<math><br />
x_{avg} = x_1 + x_2 <br />
</math><br />
<br />
However, for different reactions, there is a z-offset, so that the focal plane is shifted<br />
<br />
<math><br />
x_{avg} = \left(\frac{1}{2} - \frac{z_{o}}{D} \right) x_1 + \left(\frac{1}{2} + \frac{z_{o}}{D} \right) x_2 <br />
</math><br />
<br />
where <math> D = 42.8625~[\textrm{mm}] </math> is the distance between the front and rear delay lines.<br />
<br />
=== Calculation of the z-offset ===<br />
<br />
The z-offset depends on the reaction, the angle <math> \theta </math>, and the magnetic field of the spilt-pole. Suppose we know the KE <math> T_b </math> and momentum <math> P </math> of the ejectile or the interested particle that goes into the split-pole, The reaction is denoted as a(A,B)b, where a is the beam (projectile), A is the target, B is the heavy recoil (residual),and b is the recoil (ejectile).<br />
<br />
<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math><br />
<br />
<math> \rho = \frac{P}{c Z B}~[\textrm{m}] </math>, where <math> c = 299.792458 </math>, <math>Z</math> is the charge number, and <math>B</math> is the magnetic field in Tesla.<br />
<br />
<math> k = \frac{v \sin(\theta)}{ m_b + m_B - v \cos(\theta)},~~~ v = \sqrt{\frac{m_a m_B T_a}{T_b}}</math><br />
<br />
<math> z_o = -\rho \delta_x M_x k [\textrm{m}]</math><br />
<br />
where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.<br />
<br />
== Kinematic correction of the focal plane == <br />
<br />
As pointed out before, the [[Split-Pole_Spectrograph#Kinematic_broadening | kinematic broadening]] can be corrected. In SPS, the dispersion D is 1.96, magnification is 0.39. <br />
<br />
{|class='wikitable'<br />
| style="width: 400px;"| [[File:AnnotatedFocalPlaneRay.png | 400px|frameless| ]] <br />
| style="width: 400px;"| [[File:FPShift.gif|frame|]]<br />
|-<br />
|Simulated rays near the focal plane. || An animation on the shift of the focal panel. An optimum is reached at FP = -42 mm.<br />
|}<br />
<br />
[[File:XavgDiagram.png|thumb| construction of Xavg (X-average) on the virtual focal plan (a liner plane in this case). Need to redraw the picture, the Y-axis should be Z-axis, and it should be rotated 180 degree, so the particle is from bottom to top.]]<br />
A parallel shift of the focal plane maybe not be enough. Suppose the best focal plan is given by a function <math> z = f(x) </math>. The 2 positions extracted from the front and rear delay lines are <math> x_1, x_2 </math>, and the distance between the front and rear delay lines is <math> d</math>. The X-avg is the solution of the equation:<br />
<br />
<math> f(x) = \frac{x_2 - x_1}{d} \left( x - \frac{x_2 + x_1}{2} \right) </math><br />
<br />
For a linear tilted plane <math> f(x) = m x + z_0 </math>, the X-avg is <br />
<br />
<math> X_{avg} = \frac{x_1^2 - x_2^2 - 2d z_0 }{2 (d m + x_1 - x_2) } </math><br />
<br />
<br />
<!--[[File:TwoBodyKinematics.png|thumb]]--><br />
<br />
= SABRE =<br />
<br />
[[File:SABER installing particle shield.png|thumb|right|Installing particle shield on SABRE (photo taken on May 5, 2022)]]<br />
<br />
SABRE is a '''S'''ilicon '''A'''rray for '''B'''ranching '''R'''atio '''E'''xperiments <br />
<ref> E. C. Good ''et. al'', NIM A '''1003''', 165299 (2021) https://www.sciencedirect.com/science/article/pii/S0168900221002837</ref> <br />
with the SPS. Its predecessor is the Yale Lamp Shade Array (YLSA). SABRE sits at backward angles from the target and covers roughly 30% of 4π. SABRE has both thick and thin dead-layer detectors, with the thin dead-layer detectors capable of reaching ~200 keV thresholds for protons and deuterons.<br />
<br />
= CeBrA =<br />
<br />
[[File:CeBrA array diagram.png|thumb|right|Fully planned array for CeBrA consisting of 13 CeBr_3 detectors.]<br />
<br />
The Cerium Bromide Array (CeBrA) is a gamma-ray detector array designed to be used in conjunction with the SE-SPS.<br />
<br />
= SPS Experiment Guide =<br />
[[Media:SPS_Experiment_Guide.pdf]]<br />
<br />
= SPS Operating Procedures =<br />
I created this section as a place to store procedures for the chamber swaps, however, I expect there are other things we might want to document here. -p<br />
* [[Target Chamber Swaps]]<br />
<br />
= Repositories =<br />
https://github.com/sesps<br />
<br />
= Contact =<br />
* Jeff Blackmon mailto:blackmon@lsu.edu<br />
* Ingo <br />
* <span style=color:red">who should be contacted? </span><br />
<br />
= References =</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=File:CeBrA_array_diagram.png&diff=1802File:CeBrA array diagram.png2023-07-12T20:26:50Z<p>Bk20bu: </p>
<hr />
<div>The fully planned array for CeBrA consisting of 13 CeBr_3 detectors</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=List_of_Past_Experiments&diff=1420List of Past Experiments2022-09-26T19:10:23Z<p>Bk20bu: </p>
<hr />
<div>{| class='wikitable'<br />
! Start Date !! End Date !! Beam !! PI !! Device !! Reaction !! Elog Link !! Raw data Location !! Git/Analysis code<br />
|-<br />
| 2022-Sep-26 || TBA || d || Spieker-Group (FSU) || [[CeBrA]] || 12C(d,pg); 49Ti(d,pg); 61Ni(d,pg) || [https://fsunuc.physics.fsu.edu/elog/2022_09_10_CeBrA/ ] || spieker-group computer || SPS_CEBRA_EventBuilder ||<br />
|-<br />
| 2022-Sep-06 || 2022-Sep-14 || d || Ashton Morelock (FSU) || [[CATRiNA]] || 16O(d,n) || || Hades ||<br />
|-<br />
| 2022-Jul-07 || 2022-Jul-08|| d || Anthony Kuchera (Davidson Colleges) || [[Split-Pole Spectrograph]] || 34S(d,p)35S || [https://fsunuc.physics.fsu.edu/elog/2022_07_REU_dp/ 2022_07_REU_dp] || pauli:/mnt/data0/2022_06_REU_dp ||<br />
|-<br />
| 2022-Jun-22 || 2022-Jun-30 || d || Paul (FSU) + other people from colleges || [[Split-Pole Spectrograph]] || 52Cr, 34S, 51V (d,p) || || pauli:/mnt/data0/2022_06_REU_dp ||<br />
|-<br />
| 2022-Jun-13 || 2022-Jun-17 || 14N || Jeff (LSU) || [[ANASEN]] || || || ||<br />
|-<br />
| 2022-Jun-07 || 2022-Jun-10 || || Mitch Allmond (ORNL) || [[Clarion2]] || || || || <br />
|-<br />
| 2022-May-31 || 2022-Jun-6 || 7Li || Eliens Lopez Saavedra (FSU) || [[Split-Pole Spectrograph]] || (7Li, t) || [https://fsunuc.physics.fsu.edu/elog/2022_06_11B_alpha_transfer/ 2022_06_11B_alpha_transfer] || pauli:/mnt/data0/2022_06_11B ||<br />
|-<br />
| 2022-May-23 || 2022-May-25 || 3He, d || Gemma Wilson (LSU) || [[Split-Pole Spectrograph]] || (3He,d) and (d,p) reaction to populate mirror nuclei || [https://fsunuc.physics.fsu.edu/elog/2022_05_mirror_transfer/ 2022_05_mirror_transfer] || pauli:/mnt/data0/2022_05_LSU_dp ||<br />
|-<br />
| 2022-May-10 || 2022-May-19 || Cock-tail || Vandana || FRIB || [[FRIB_FDSi_e21062]] || [https://fsunuc.physics.fsu.edu/elog/2022_05_e21062_FRIB/ 2022_05_e21062_FRIB/ ] || pauli:/mnt/data0/2022_05_e21062 || [https://fsunuc.physics.fsu.edu/git/rtang/FRIB_e21062 FRIB_e21062]<br />
|-<br />
| 2022-May-9 || 2022-May-13|| || Gordon McCann || [[Split-Pole Spectrograph]] || || [https://fsunuc.physics.fsu.edu/elog/2022_05-06_3He_2H/ 2022_05-06_3He_2H ] || pauli:/mnt/data0/2022_05_10B_3Hea_gwn17 || <br />
|-<br />
|2022 || 2022 || || Catherine Deibel (LSU) || [[Split-Pole Spectrograph]] || || [https://fsunuc.physics.fsu.edu/elog/2022_04_SPS_Blocker/ 2022_04_SPS_Blocker] || ||<br />
|- <br />
|2022- || 2022 || || Eli Temanson|| [[RESOLUT ]] || || [https://fsunuc.physics.fsu.edu/elog/2022_12Cdn13N/ 2022_12Cdn13N] || pauli:/mnt/2022_04_12C_dn_est18c ||<br />
|- <br />
|2022-Mar-8 || 2022-Mar-18 || 7Li || Soumik Bhattacharya || [[Clarion2]] || 64Ni(7Li, pn)69Zn || [https://fsunuc.physics.fsu.edu/elog/202203_64Ni_7Li/ 202203_64Ni_7Li] || ||<br />
|-<br />
|2022 || 2022 || || Mitch Allmond (ORNL) || [[Clarion2]] || || || ||<br />
|-<br />
|2022 || 2022 || || Catur Wibisono || [[Clarion2]] || 16O(18O, p)32P || || nucx8:/data1/202112_16O_clarion2 ||<br />
|-<br />
| || || || || || || || nucx8:/data1/ZnMar2022 ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Dec2021_16O|| <br />
|-<br />
| || || || || || || || nucx8:/data1/Clarion2_calib ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Aug2021_16O ||<br />
|-<br />
| || || || || || || || nucx8:/data1/NOv2021_Li7 ||<br />
|-<br />
| || || || || || || || nucx8:/data1/40K_decay ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Apr2020_11B ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Aug2021_13C ||<br />
|-<br />
| || || || || || || || nucx8:/data1/248CmFission ||<br />
|-<br />
| || || || || || || || nucx8:/data1/A127adSi29 ||<br />
|}</div>Bk20buhttps://fsunuc.physics.fsu.edu/wiki/index.php?title=List_of_Past_Experiments&diff=1419List of Past Experiments2022-09-26T18:57:08Z<p>Bk20bu: </p>
<hr />
<div>{| class='wikitable'<br />
! Start Date !! End Date !! Beam !! PI !! Device !! Reaction !! Elog Link !! Raw data Location !! Git/Analysis code<br />
|-<br />
| 2022-Sep-26 || TBA || d || Spieker-Group (FSU) || [[CeBrA]] || 47Ti(d,pg) || [https://fsunuc.physics.fsu.edu/elog/2022_09_10_CeBrA/ ] || spieker-group computer || SPS_CEBRA_EventBuilder ||<br />
|-<br />
| 2022-Sep-06 || 2022-Sep-14 || d || Ashton Morelock (FSU) || [[CATRiNA]] || 16O(d,n) || || Hades ||<br />
|-<br />
| 2022-Jul-07 || 2022-Jul-08|| d || Anthony Kuchera (Davidson Colleges) || [[Split-Pole Spectrograph]] || 34S(d,p)35S || [https://fsunuc.physics.fsu.edu/elog/2022_07_REU_dp/ 2022_07_REU_dp] || pauli:/mnt/data0/2022_06_REU_dp ||<br />
|-<br />
| 2022-Jun-22 || 2022-Jun-30 || d || Paul (FSU) + other people from colleges || [[Split-Pole Spectrograph]] || 52Cr, 34S, 51V (d,p) || || pauli:/mnt/data0/2022_06_REU_dp ||<br />
|-<br />
| 2022-Jun-13 || 2022-Jun-17 || 14N || Jeff (LSU) || [[ANASEN]] || || || ||<br />
|-<br />
| 2022-Jun-07 || 2022-Jun-10 || || Mitch Allmond (ORNL) || [[Clarion2]] || || || || <br />
|-<br />
| 2022-May-31 || 2022-Jun-6 || 7Li || Eliens Lopez Saavedra (FSU) || [[Split-Pole Spectrograph]] || (7Li, t) || [https://fsunuc.physics.fsu.edu/elog/2022_06_11B_alpha_transfer/ 2022_06_11B_alpha_transfer] || pauli:/mnt/data0/2022_06_11B ||<br />
|-<br />
| 2022-May-23 || 2022-May-25 || 3He, d || Gemma Wilson (LSU) || [[Split-Pole Spectrograph]] || (3He,d) and (d,p) reaction to populate mirror nuclei || [https://fsunuc.physics.fsu.edu/elog/2022_05_mirror_transfer/ 2022_05_mirror_transfer] || pauli:/mnt/data0/2022_05_LSU_dp ||<br />
|-<br />
| 2022-May-10 || 2022-May-19 || Cock-tail || Vandana || FRIB || [[FRIB_FDSi_e21062]] || [https://fsunuc.physics.fsu.edu/elog/2022_05_e21062_FRIB/ 2022_05_e21062_FRIB/ ] || pauli:/mnt/data0/2022_05_e21062 || [https://fsunuc.physics.fsu.edu/git/rtang/FRIB_e21062 FRIB_e21062]<br />
|-<br />
| 2022-May-9 || 2022-May-13|| || Gordon McCann || [[Split-Pole Spectrograph]] || || [https://fsunuc.physics.fsu.edu/elog/2022_05-06_3He_2H/ 2022_05-06_3He_2H ] || pauli:/mnt/data0/2022_05_10B_3Hea_gwn17 || <br />
|-<br />
|2022 || 2022 || || Catherine Deibel (LSU) || [[Split-Pole Spectrograph]] || || [https://fsunuc.physics.fsu.edu/elog/2022_04_SPS_Blocker/ 2022_04_SPS_Blocker] || ||<br />
|- <br />
|2022- || 2022 || || Eli Temanson|| [[RESOLUT ]] || || [https://fsunuc.physics.fsu.edu/elog/2022_12Cdn13N/ 2022_12Cdn13N] || pauli:/mnt/2022_04_12C_dn_est18c ||<br />
|- <br />
|2022-Mar-8 || 2022-Mar-18 || 7Li || Soumik Bhattacharya || [[Clarion2]] || 64Ni(7Li, pn)69Zn || [https://fsunuc.physics.fsu.edu/elog/202203_64Ni_7Li/ 202203_64Ni_7Li] || ||<br />
|-<br />
|2022 || 2022 || || Mitch Allmond (ORNL) || [[Clarion2]] || || || ||<br />
|-<br />
|2022 || 2022 || || Catur Wibisono || [[Clarion2]] || 16O(18O, p)32P || || nucx8:/data1/202112_16O_clarion2 ||<br />
|-<br />
| || || || || || || || nucx8:/data1/ZnMar2022 ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Dec2021_16O|| <br />
|-<br />
| || || || || || || || nucx8:/data1/Clarion2_calib ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Aug2021_16O ||<br />
|-<br />
| || || || || || || || nucx8:/data1/NOv2021_Li7 ||<br />
|-<br />
| || || || || || || || nucx8:/data1/40K_decay ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Apr2020_11B ||<br />
|-<br />
| || || || || || || || nucx8:/data1/Aug2021_13C ||<br />
|-<br />
| || || || || || || || nucx8:/data1/248CmFission ||<br />
|-<br />
| || || || || || || || nucx8:/data1/A127adSi29 ||<br />
|}</div>Bk20bu