Split-Pole Spectrograph - Revision history

Jce18: 12.8 msr not 128msr

2026-02-16T22:28:16Z

12.8 msr not 128msr

← Older revision		Revision as of 18:28, 16 February 2026
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	<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref>		<ref name="Enge1979">H.A. Enge, NIM '''162''', 161 (1979) https://doi.org/10.1016/0029-554X(79)90711-0</ref>
	<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref>		<ref>H. A. Enge, NIM '''187''', 1 (1981) https://doi.org/10.1016/0029-554X(81)90465-1 </ref>
	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" />.		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 12.8 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" />.

	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]].		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]].

Iwiedenhoever: /* Simplification of the z-offset calculation (IW) */

2024-06-20T19:52:42Z

Simplification of the z-offset calculation (IW)

← Older revision		Revision as of 15:52, 20 June 2024
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	<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,		<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,

	which only depends on the beam momentum and masses and the spectrograph B, theta.		which only depends on the beam momentum and masses and the spectrograph B and <math> \theta </math>.
	The second order correction (tilt of focal plane) is included in the denominator through the <math> \rho <\math> dependence.		The second order correction (tilt of focal plane) is included in the denominator through the <math> \rho </math> dependence.

	== Kinematic correction of the focal plane ==		== Kinematic correction of the focal plane ==

Iwiedenhoever: /* Simplification of the z-offset calculation (IW) */

2024-06-20T19:49:14Z

Simplification of the z-offset calculation (IW)

← Older revision		Revision as of 15:49, 20 June 2024
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	<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,		<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,

	which only depends on the beam momentum, spectrograph ~~angle and~~ B ~~and~~ the ~~corresponding masses~~.		which only depends on the beam momentum and masses and the spectrograph B, theta.
			The second order correction (tilt of focal plane) is included in the denominator through the <math> \rho <\math> dependence.

	== Kinematic correction of the focal plane ==		== Kinematic correction of the focal plane ==

Iwiedenhoever: /* Simplification of the z-offset calculation (IW) */

2024-06-20T19:44:53Z

Simplification of the z-offset calculation (IW)

← Older revision		Revision as of 15:44, 20 June 2024
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	<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,		<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,

			which only depends on the beam momentum, spectrograph angle and B and the corresponding masses.

	== Kinematic correction of the focal plane ==		== Kinematic correction of the focal plane ==

Iwiedenhoever: /* Calculation of the z-offset */

2024-06-20T19:42:31Z

Calculation of the z-offset

← Older revision		Revision as of 15:42, 20 June 2024
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	=== Calculation of the z-offset ===		=== Calculation of the z-offset ===

	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).		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).

	<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}]</math>		<math> P^2 = (m_b+T_b)^2 - m_b^2 = T_b(T_b + 2m_b)~[\textrm{MeV/c}^2]</math>

	<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.		<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.
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	where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.		where <math> \delta_x = 1.96 </math> is the x-dispersion and <math> M_x = 0.39</math> is the x-magnification.

			=== Simplification of the z-offset calculation (IW) ===

			The Kinematic Factor k can be re-written as a function of the beam and ejectile momenta:

			<math> k = \frac{(p_a/p_b) \sin(\theta)}{ 1 + m_B/m_b - (p_a/p_b) \cos(\theta)} </math>

			Inserting that into the offset formula and using <math> p_b = B \rho q_b </math> gives

			<math> z_o = - \delta_x M_x \frac{(p_a/B q_b) \sin(\theta) }{ 1 + m_B/m_b - (p_a/(B \rho q_b)) \cos(\theta)} </math>,

	== Kinematic correction of the focal plane ==		== Kinematic correction of the focal plane ==

Rtang at 05:49, 27 February 2024

2024-02-27T05:49:27Z

← Older revision		Revision as of 01:49, 27 February 2024
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			[[File:Sideview of the split-pole spectrometer.jpg\|none\| 800px \| Side view of the spilt-pole spectrometer]]

	{\| align="right" style="width:30%;"		{\| align="right" style="width:30%;"
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	\| [[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]]]]		\| [[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]]]]
	\|}		\|}

	~~[[File:Sideview of the split-pole spectrometer.jpg\|none\| 800px \| Side view of the spilt-pole spectrometer]]~~

	The '''Super Enge Split-Pole Spectrograph'''		The '''Super Enge Split-Pole Spectrograph'''

Rtang at 18:41, 17 November 2023

2023-11-17T18:41:46Z

← Older revision		Revision as of 14:41, 17 November 2023
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	~~[[File:Sideview of the split-pole spectrometer.jpg\|thumb\| 600px \| Side view of the spilt-pole spectrometer]]~~

	{\| align="right" style="width:30%;"		{\| align="right" style="width:30%;"
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	\|}		\|}

	~~{{Notice~~ \| ~~Need a picture~~ of ~~SPS }}~~		[[File:Sideview of the split-pole spectrometer.jpg\|none\| 800px \| Side view of the spilt-pole spectrometer]]

	The '''Super Enge Split-Pole Spectrograph'''		The '''Super Enge Split-Pole Spectrograph'''

Rtang at 18:40, 17 November 2023

2023-11-17T18:40:30Z

← Older revision		Revision as of 14:40, 17 November 2023
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	[[File:Sideview of the split-pole spectrometer.jpg\|thumb\|~~right\| 400px~~ \| Side view of the spilt-pole spectrometer]]		[[File:Sideview of the split-pole spectrometer.jpg\|thumb\| 600px \| Side view of the spilt-pole spectrometer]]

	{\| align="right" style="width:30%;"		{\| align="right" style="width:30%;"

Rtang at 18:39, 17 November 2023

2023-11-17T18:39:54Z

← Older revision		Revision as of 14:39, 17 November 2023
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	[[File:Sideview of the split-pole spectrometer.jpg\|thumb\|~~left~~\|Side view of the spilt-pole spectrometer]]		[[File:Sideview of the split-pole spectrometer.jpg\|thumb\|right\| 400px \| Side view of the spilt-pole spectrometer]]

	{\| align="right" style="width:30%;"		{\| align="right" style="width:30%;"

Rtang at 18:39, 17 November 2023

2023-11-17T18:39:35Z

← Older revision		Revision as of 14:39, 17 November 2023
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			[[File:Sideview of the split-pole spectrometer.jpg\|thumb\|left\|Side view of the spilt-pole spectrometer]]

	{\| align="right" style="width:30%;"		{\| align="right" style="width:30%;"