improved angular scattering

calculations.cpp

@@ -477,22 +477,26 @@ double energy_straggling_firsov(double z1,double energy, double z2, double m2){
     return factor*beta2/fine_structure/fine_structure;
     }
 
-double angular_scattering_variance(const Projectile &p, const Target &t){
+double angular_scattering_power(const Projectile &p, const Target &t, double Es2){
     if(p.T<=0)return 0.0;
     double e=p.T;
     double _p = p_from_T(e,p.A);
     double beta = _p/((e+atomic_mass_unit)*p.A);
     double lr = radiation_length(t.Z,t.A);
-    return 198.81 * pow(p.Z,2)/(lr*pow(_p*beta,2));
+    //constexpr double Es2 = 198.81;
+    //constexpr double Es2 =2*PI/fine_structure* electron_mass * electron_mass;
+    return Es2 * pow(p.Z,2)/(lr*pow(_p*beta,2));
 }
 
-double angular_scattering_variance(const Projectile &p, const Material &mat){
+double angular_scattering_power(const Projectile &p, const Material &mat, double Es2){
     if(p.T<=0)return 0.0;
     double e=p.T;
     double _p = p_from_T(e,p.A);
     double beta = _p/((e+atomic_mass_unit)*p.A);
     double X0 = radiation_length(mat);
-    return 198.81 * pow(p.Z,2)/(X0*pow(_p*beta,2));
+    //constexpr double Es2 = 198.81;
+    //constexpr double Es2 =2*PI/fine_structure* electron_mass * electron_mass;
+    return Es2 * pow(p.Z,2)/(X0*pow(_p*beta,2));
 }
 
 /// radiation lengths are taken from Particle Data Group 2014
@@ -632,6 +636,7 @@ double z_effective(const Projectile &p,const Target &t, const Config &c){
         return z_eff_Schiwietz(p.Z, beta, t.Z);
     }
     else{
+        assert("unknown effective charge config");
         return 0.0;
     }
 }

calculations.h

@@ -100,9 +100,9 @@ namespace catima{
       */ 
     double sezi_dedx_e(const Projectile &p, const Material &mat, const Config &c=default_config);
 
-
+    constexpr double Es2_FR =2*PI/fine_structure* electron_mass * electron_mass;
-    double angular_scattering_variance(const Projectile &p, const Target &t);
+    double angular_scattering_power(const Projectile &p, const Target &t, double Es2=Es2_FR);
-    double angular_scattering_variance(const Projectile &p, const Material &material);
+    double angular_scattering_power(const Projectile &p, const Material &material, double Es2=Es2_FR);
 
     /**
       * returns radiation length of the (M,Z) material

catima.cpp

@@ -58,7 +58,16 @@ double domega2dx(const Projectile &p, const Material &mat, const Config &c){
 }
 
 double da2dx(const Projectile &p, const Material &mat, const Config &c){
-    return angular_scattering_variance(p,mat);    
+    //double Es2 = Es2_FR;
+    //if(c.scattering == scattering_types::atima_scattering){        
+    //        Es2 = 198.81;
+    //}    
+    const double Es2 = 198.81;
+    return angular_scattering_power(p,mat, Es2);    
+}
+
+double da2de(const Projectile &p, const Material &mat, const Config &c){
+    return da2dx(p,mat,c)/dedx(p,mat,c);    
 }
 
 
@@ -113,19 +122,42 @@ double domega2de(const Projectile &p, double T, const Material &t, const Config
     spline_type range_straggling_spline = get_range_straggling_spline(data);
     return range_straggling_spline.derivative(T);
 }
-
+/*
 double da2de(const Projectile &p, double T, const Material &t, const Config &c){
     auto& data = _storage.Get(p,t,c);
     //Interpolator angular_variance_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
     spline_type angular_variance_spline = get_angular_variance_spline(data);
     return angular_variance_spline.derivative(T);
 }
+*/
 
-double angular_straggling_from_E(const Projectile &p, double T, double Tout, const Material &t, const Config &c){
+double angular_variance(Projectile p, const Material &t, const Config &c){
+    const double T = p.T;
+    auto& data = _storage.Get(p,t,c);    
+    spline_type range_spline = get_range_spline(data);
+    auto fx0p = [&](double x)->double{         
+        double e =energy_out(T,x,range_spline);        
+        //double l = x/radiation_length(t);
+        //double f = 0.97*(1+log(l)/20.7) + (1+log(l)/22.7);
+        constexpr double f = 1;
+	    return f*da2dx(p(e), t, c);
+            };
+    double f = 1.0;  
+    double range = range_spline(T);
+    double rrange = std::min(range, t.thickness());
+    return f*integrator.integrate(fx0p,0, rrange);
+}
+
+double angular_straggling(Projectile p, const Material &t, const Config &c){
+    return sqrt(angular_variance(p,t,c));
+}
+
+double angular_straggling_from_E(const Projectile &p, double T, double Tout, Material t, const Config &c){
     auto& data = _storage.Get(p,t,c);
-    //Interpolator angular_straggling_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
+    spline_type range_spline = get_range_spline(data);    
-    spline_type angular_variance_spline = get_angular_variance_spline(data);
+    double th = range_spline(T)-range_spline(Tout);
-    return sqrt(angular_variance_spline(T) - angular_variance_spline(Tout));
+    t.thickness(th);    
+    return angular_straggling(p,t,c);
 }
 
 double energy_straggling_from_E(const Projectile &p, double T, double Tout,const Material &t, const Config &c){
@@ -213,73 +245,88 @@ Result calculate(Projectile p, const Material &t, const Config &c){
     if(T<catima::Ezero && T<catima::Ezero-catima::numeric_epsilon){return res;}
     auto& data = _storage.Get(p,t,c);
 
+    bool use_angular_spline = false;
+    if(c.scattering == scattering_types::atima_scattering){
+        use_angular_spline = true;
+    }
+
     //Interpolator range_spline(energy_table.values,data.range.data(),energy_table.num);
     spline_type range_spline = get_range_spline(data);
+    spline_type range_straggling_spline = get_range_straggling_spline(data);    
 
     res.Ein = T;
     res.range = range_spline(T);
-    res.dEdxi = p.A/range_spline.derivative(T);
+    res.dEdxi = p.A/range_spline.derivative(T);   
-    res.Eout = energy_out(T,t.thickness(),range_spline);
+    res.sigma_r = sqrt(range_straggling_spline(T));        
 
-    //Interpolator range_straggling_spline(energy_table.values,data.range_straggling.data(),energy_table.num);
+    if(t.thickness()==0){
-    spline_type range_straggling_spline = get_range_straggling_spline(data);
+        res.dEdxo = res.dEdxi;
-    spline_type angular_variance_spline = get_angular_variance_spline(data);
+        return res;
+    }
+    
+    res.Eout = energy_out(T,t.thickness(),range_spline);
+    res.Eloss = (res.Ein - res.Eout)*p.A;
+        
     if(res.Eout<Ezero){
         res.dEdxo = 0.0;
         res.sigma_a = 0.0;
         res.tof = 0.0;
         res.sigma_E = 0.0;
-    }
+    }    
-    else{
+    else{        
+        spline_type angular_variance_spline = get_angular_variance_spline(data);
         res.dEdxo = p.A/range_spline.derivative(res.Eout);        
         #ifdef THIN_TARGET_APPROXIMATION
         if(thin_target_limit*res.Ein<res.Eout){
-            double edif = (res.Ein-res.Eout);
+            double edif = (res.Ein-res.Eout);            
             double s1 = range_straggling_spline.derivative(T);
             double s2 = range_straggling_spline.derivative(res.Eout);
             res.sigma_E = res.dEdxo*sqrt(edif*0.5*(s1+s2))/p.A;
-            s1 = angular_variance_spline.derivative(T);
+            if(use_angular_spline){
-            s2 = angular_variance_spline.derivative(res.Eout);
+                s1 = angular_variance_spline.derivative(T);
-            res.sigma_a = sqrt(0.5*(s1+s2)*edif);
+                s2 = angular_variance_spline.derivative(res.Eout);
+                res.sigma_a = sqrt(0.5*(s1+s2)*edif);
+            }        
         }
         else{
             res.sigma_E = res.dEdxo*sqrt(range_straggling_spline(T) - range_straggling_spline(res.Eout))/p.A;            
-            res.sigma_a = sqrt(angular_variance_spline(T) - angular_variance_spline(res.Eout));    
+            if(use_angular_spline){
-        }
+                res.sigma_a = sqrt(angular_variance_spline(T) - angular_variance_spline(res.Eout));
-        
+            }
+            
+        }        
         #else
         res.sigma_E = res.dEdxo*sqrt(range_straggling_spline(T) - range_straggling_spline(res.Eout))/p.A;
-        //Interpolator angular_variance_spline(energy_table.values,data.angular_variance.data(),energy_table.num);
+        if(use_angular_spline){
-        spline_type angular_variance_spline = get_angular_variance_spline(data);
+            res.sigma_a = sqrt(angular_variance_spline(T) - angular_variance_spline(res.Eout));
-        res.sigma_a = sqrt(angular_variance_spline(T) - angular_variance_spline(res.Eout));
+        }        
         #endif
-        if( t.thickness()>0){
+        if( (!use_angular_spline) && res.range>t.thickness()){ // do not calculate angle scattering when stopped inside material        
-            //auto tofdata = calculate_tof(p,t,c);
+            res.sigma_a = angular_straggling(p(T),t,c);
-            //Interpolator tof_spline(energy_table.values, tofdata.data(), energy_table.num,interpolation_t::linear);
+        }
-            //res.tof = tof_spline(res.Ein) - tof_spline(res.Eout);
+        //Interpolator tof_spline(energy_table.values, tofdata.data(), energy_table.num,interpolation_t::linear);
-            res.tof = calculate_tof_from_E(p,res.Eout,t);
+        //res.tof = tof_spline(res.Ein) - tof_spline(res.Eout);
-            }
+        res.tof = calculate_tof_from_E(p,res.Eout,t);
-    }
+            
-    res.sigma_r = sqrt(range_straggling_spline(T));    
+    } //end of else for non stopped case
-    res.Eloss = (res.Ein - res.Eout)*p.A;
     
+    // position straggling in material
     double rrange = std::min(res.range/t.density(), t.thickness_cm());
     auto fx2p = [&](double x)->double{ 
         double e =energy_out(T,x*t.density(),range_spline);
 	    return (rrange-x)*(rrange-x)*da2dx(p(e), t, c)*t.density();
             };           
     
-    //res.sigma_x = integrator_adaptive.integrate(fx2p,0, rrange,1e-3, 1e-3,1);    
+    res.sigma_x = integrator_adaptive.integrate(fx2p,0, rrange,1e-3,1e-6);    
-    res.sigma_x = integrator_adaptive.integrate(fx2p,0, rrange);    
     res.sigma_x = sqrt(res.sigma_x);
 
+    // position vs angle covariance, needed later for final position straggling
     auto fx1p = [&](double x)->double{ 
         double e =energy_out(T,x*t.density(),range_spline);        
 	    return (rrange-x)*da2dx(p(e), t, c)*t.density();
             };
-    
+    res.cov = integrator.integrate(fx1p,0, rrange);    
-    //res.cov = integrator_adaptive.integrate(fx1p,0, t.thickness_cm(), 1e-3, 1e-3,1);
+
-    res.cov = integrator.integrate(fx1p,0, rrange);
     #ifdef REACTIONS
     res.sp = nonreaction_rate(p,t,c);
     #endif
@@ -341,6 +388,9 @@ DataPoint calculate_DataPoint(Projectile p, const Material &t, const Config &c){
     auto fomega = [&](double x)->double{
             return domega2dx(p(x),t,c)/catima::power(dedx(p(x),t,c),3);
             };
+    auto ftheta = [&](double x)->double{
+          return da2de(p(x),t,c);
+          };
 
     //double res=0.0;
     //calculate 1st point to have i-1 element ready for loop
@@ -354,12 +404,14 @@ DataPoint calculate_DataPoint(Projectile p, const Material &t, const Config &c){
     //res = integrator.integrate(fomega,Ezero,energy_table(0));
     //res = p.A*res;
     dp.range_straggling[0]=0.0;
-    //p.T = energy_table(0);
+    //p.T = energy_table(0);    
     for(int i=1;i<max_datapoints;i++){
         double res = p.A*integrator.integrate(fdedx,energy_table(i-1),energy_table(i));
         dp.range[i] = res + dp.range[i-1];
-        res = da2dx(p(energy_table(i)),t)*res;
+        //res = da2dx(p(energy_table(i)),t)*res;
-        dp.angular_variance[i] = res + dp.angular_variance[i-1];
+        //dp.angular_variance[i] = res + dp.angular_variance[i-1];        
+        dp.angular_variance[i] = p.A*integrator.integrate(ftheta,energy_table(i-1),energy_table(i))
+                                + dp.angular_variance[i-1];
 
         res = integrator.integrate(fomega,energy_table(i-1),energy_table(i));
         res = p.A*res;

catima.h

@@ -113,6 +113,23 @@ namespace catima{
       */
     double da2de(const Projectile &p, double T, const Material &t, const Config &c=default_config);
 
+    /**
+      * returns the planar RMS angular straggling in rad
+      * @param p - Projectile
+      * @param t - Material class
+      * @param c - Config class
+      * @return angular RMS straggling in rad
+      */
+    double angular_straggling(Projectile p, const Material &t, const Config &c=default_config);
+    /**
+      * returns the planar RMS angular variance in rad
+      * @param p - Projectile
+      * @param t - Material class
+      * @param c - Config class
+      * @return angular RMS variance in rad
+      */
+    double angular_variance(Projectile p, const Material &t, const Config &c=default_config);
+
     /**
       * calculates angular scattering in the material from difference of incoming a nd outgoing energies
       * @param p - Projectile
@@ -121,7 +138,7 @@ namespace catima{
       * @param mat - Material
       * @return angular straggling
       */
-    double angular_straggling_from_E(const Projectile &p, double T, double Tout,const Material &t, const Config &c=default_config);
+    double angular_straggling_from_E(const Projectile &p, double T, double Tout,Material t, const Config &c=default_config);
 
     /**
       * calculates Energy straggling in the material from difference of incoming a nd outgoing energies
@@ -132,7 +149,7 @@ namespace catima{
       * @return angular straggling
       */
     double energy_straggling_from_E(const Projectile &p, double T, double Tout,const Material &t, const Config &c=default_config);
-
+    
     /**
       * calculates outcoming energy from range spline
       * @param T - incoming energy

config.h

@@ -45,6 +45,14 @@ namespace catima{
         srim_95 = 1,
     };
 
+    /**
+      * enum to select angular scattering
+      */
+    enum scattering_types:unsigned char{
+        fermi_rossi = 0,
+        atima_scattering = 255,
+    };
+
     /**
       * structure to store calculation configuration
       */
@@ -57,7 +65,8 @@ namespace catima{
 
         unsigned char corrections = 0;
         unsigned char calculation = 1;
-        unsigned char low_energy = 0;
+        unsigned char low_energy = low_energy_types::srim_85;
+        unsigned char scattering = scattering_types::atima_scattering;
     };
 
 

integrator.h

@@ -62,7 +62,7 @@ using integrator_type = IntegratorGSL;
 #else
 using integrator_type = GaussLegendreIntegration<8>;
 #endif
-using integrator_adaptive_type = GaussKronrodIntegration<15>;
+using integrator_adaptive_type = GaussKronrodIntegration<21>;
 
 extern integrator_type integrator;
 extern integrator_adaptive_type integrator_adaptive;

material_database.cpp

@@ -158,6 +158,7 @@ namespace catima{
 		 case material::C21H24O4:	 return Material({{0,6,21},{0,1,24},{0,8,4}},1.18);
 		 case material::CoRe_Alloy:	 return Material({{0,27,17},{0,75,23},{0,24,1}},11.5);
 		 case material::LLZO_electrolyte:	 return Material({{0,3,7},{0,57,3},{0,40,2},{0,8,12}},5.1);
+		 case material::Nylon:	 return Material({{0,6,6},{0,1,11},{0,7,1},{0,8,1}},1.14);
             default:break;
              }
         return Material();

material_database.h

@@ -150,7 +150,8 @@ namespace catima{
 		 Iodonaphthalene = 343,
 		 C21H24O4 = 344,
 		 CoRe_Alloy = 345,
-		 LLZO_electrolyte = 346
+		 LLZO_electrolyte = 346,
+		 Nylon = 347
         };
 
       Material get_compound(material m);

pymodule/pycatima.cpp

@@ -11,11 +11,8 @@
 namespace py = pybind11;
 using namespace catima;
 
-void catima_info(){
+std::string catima_info(){
-    printf("CATIMA version = 1.5\n");
+    return "CATIMA version = 1.54\n";
-    printf("number of energy points = %d\n",max_datapoints);
-    printf("min energy point = 10^%lf MeV/u\n",logEmin);
-    printf("max energy point = 10^%lf MeV/u\n",logEmax);
 }
 
 std::string  material_to_string(const Material &r){
@@ -239,6 +236,11 @@ PYBIND11_MODULE(pycatima,m){
     py::enum_<low_energy_types>(m,"low_energy_types")
             .value("srim_85", low_energy_types::srim_85)
             .value("srim_95", low_energy_types::srim_95);
+            
+    py::enum_<scattering_types>(m,"scattering_types")
+            .value("fermi_rossi", scattering_types::fermi_rossi)
+            .value("atima_scattering", scattering_types::atima_scattering);
+            
 
     py::enum_<material>(m,"material")
             .value("Plastics", material::Plastics)
@@ -262,7 +264,13 @@ PYBIND11_MODULE(pycatima,m){
             .value("Suprasil", material::Suprasil)
             .value("HAVAR", material::HAVAR)
             .value("Steel", material::Steel)
-            .value("CO2", material::CO2);
+            .value("CO2", material::CO2)
+            .value("Methane", material::Methane)
+            .value("Methanol", material::Methanol)
+            .value("Nylon", material::Nylon)
+            .value("Polystyrene", material::Polystyrene)
+            .value("Polycarbonate", material::Polycarbonate)
+            .value("Teflon", material::Teflon);
 
 
     py::class_<Config>(m,"Config")
@@ -271,12 +279,14 @@ PYBIND11_MODULE(pycatima,m){
             .def_readwrite("corrections", &Config::corrections)
             .def_readwrite("calculation", &Config::calculation)
             .def_readwrite("low_energy", &Config::low_energy)
+            .def_readwrite("scattering", &Config::scattering)
             .def("get",[](const Config &r){
                py::dict d;
                d["z_effective"] = r.z_effective;
                d["corrections"] = r.corrections;
                d["calculation"] = r.calculation;
                d["low_energy"] = r.low_energy;
+               d["scattering"] = r.scattering;
                return d;
                })
             .def("__str__",[](const Config &r){
@@ -285,9 +295,12 @@ PYBIND11_MODULE(pycatima,m){
                 s += ", corrections = "+std::to_string(r.corrections);
                 s += ", calculation = "+std::to_string(r.calculation);
                 s += ", low_energy = "+std::to_string(r.low_energy);
+                s += ", scattering = "+std::to_string(r.scattering);
                 return s;
             });
 
+    m.def("angular_scattering_power",py::overload_cast<const Projectile&, const Material&, double>(&angular_scattering_power),"angular scattering power in rad^2/g/cm^2",py::arg("projectile"),py::arg("material"),py::arg("Es2")=Es2_FR);
+    m.def("radiation_length",py::overload_cast<const Material&>(radiation_length));
     m.def("srim_dedx_e",&srim_dedx_e);
     m.def("sezi_dedx_e",&sezi_dedx_e, "sezi_dedx_e",  py::arg("projectile"), py::arg("material"), py::arg("config")=default_config);
     m.def("calculate",py::overload_cast<Projectile, const Material&, const Config&>(&calculate),"calculate",py::arg("projectile"), py::arg("material"), py::arg("config")=default_config);

tests/test_calculations.cpp

@@ -185,10 +185,22 @@ using namespace std;
       CHECK( fabs(dif) < 0.01);
     }
     TEST_CASE("angular scattering"){
+      catima::Config conf;
       catima::Projectile p{1,1,1,158.6};
       catima::Material cu = catima::get_material(29);
-          
+      catima::Material water = catima::get_material(catima::material::Water);      
-      
+
+      p.T = 158.6;
+
+      for(double th = 0.01;th<3;th+=0.02){
+        cu.thickness(th);
+        conf.scattering = catima::scattering_types::fermi_rossi;
+        auto r1 = catima::calculate(p,cu,conf);
+        conf.scattering = catima::scattering_types::atima_scattering;
+        auto r2= catima::calculate(p,cu, conf);  
+        CHECK( r2.sigma_a == approx(r1.sigma_a).R(1e-3));
+      }
+
       cu.thickness_cm(0.02963);
       auto res = catima::calculate(p,cu);
       CHECK( 1000*res.sigma_a == approx(7.2,0.5));
@@ -259,7 +271,7 @@ using namespace std;
         water.thickness_cm(29.4/n);
         for(int i=0;i<n;i++)lll.add(water);        
         res2 = catima::calculate(p(215),lll);
-        CHECK(res2.total_result.sigma_x == approx(res29.sigma_x).R(0.01));
+        CHECK(res2.total_result.sigma_x == approx(res29.sigma_x).R(0.025));
         }
       
 
@@ -334,7 +346,7 @@ using namespace std;
         CHECK(res1.tof == res2.tof);
 
         auto ra = catima::angular_straggling_from_E(p,res1.Ein,res1.Eout,graphite);
-        CHECK(res1.sigma_a == ra);
+        CHECK(res1.sigma_a == approx(ra).R(1e-3));
 
         auto re = catima::energy_straggling_from_E(p,res1.Ein,res1.Eout,graphite);
         CHECK(res1.sigma_E == re);