API tools faq
paste
Advertisement
phystota

excitation_radiative_decay_added

phystota
Apr 19th, 2025
175
0
Never
Add comment
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
C++ 43.76 KB | None | 0 0
raw download clone embed print report
  1. #include <iostream>
  2. #include <random>
  3. #include <fstream>
  4. #include <assert.h>
  5.  
  6. #include <math.h>
  7. #include <time.h>
  8. #include <iomanip>  // For std::fixed and std::setprecision
  9.  
  10. #include <algorithm>  // For std::shuffle
  11. #include <numeric>    // For std::iota
  12.  
  13. //physical constants
  14.  
  15. #define m_e 9.1093837E-31 // electron mass in kg
  16. #define M_n 6.6464731E-27 // Helium atom mass
  17. #define k_b 1.380649E-23 // Boltzmann constant
  18. #define q 1.602176634E-19 // elementary charge    - eV -> J transfer param
  19. #define Coulomb_log 15.87 // Coulomb logarithm
  20. #define epsilon_0 8.854188E-12 // Vacuum permittivity
  21. #define Coulomb_const pow(q,4)/(pow(4.0*M_PI*epsilon_0,2)) // e^4/(4*pi*eps0)^2
  22. #define thresh1 19.82 // threshold energy excitation tripet state
  23. #define thresh2 20.61 // threshold energy excitation singlet state
  24. #define tau_singlet 0.0195
  25.  
  26. // simulation parameters
  27.  
  28. #define n_e 50000
  29. // #define N_He 1000000 // Helium neutrals number
  30. #define T_n 2.0 // Helium neutral temperature in eV
  31. #define T_e 5.0    // electron Maxwell initial distribution
  32. #define Emin 0.0
  33. #define Emax 3000.0
  34. #define Volume 1.0E-12 // Volume to calculate netral density and collision frequency
  35. #define time 1.0E-3 // 500 microsec time to equalibrate the system
  36. #define dopant 1.0E-5 // addition to avoid zero
  37. #define E_reduced 0.0 // constant electrin field along z-axis
  38.  
  39. #define bin_width 0.05 // keep energy step ~ this to maintain cross-section clarity (Ramsauer minimum etc)
  40. #define N ( (int)((Emax-Emin)/bin_width) + 1) // add 1 to include E_max if needed?
  41.  
  42. // handling final energy bin
  43.  
  44. #define bin_width_smooth 0.05 // energy bin for smooth final distribution
  45. #define N_smooth ( (int)((Emax-Emin)/bin_width_smooth) )
  46.  
  47.  
  48.  
  49. double solve_A(double s) { // Netwon method solver
  50.  
  51.     if (s > 3) {
  52.         return 3*exp(-s);
  53.     }
  54.     if (s < 0.01) {
  55.         return 1.0/s;
  56.     }
  57.    
  58.     double A0 = 0.01; // initial guess
  59.     double A = A0;  //starting with initial guess
  60.     double tol = 1.0E-7; // accuracy
  61.  
  62.              
  63.     for (int i = 0; i < 1000; i++){
  64.  
  65.         double tanhA = tanh(A);
  66.         // Avoid division by an extremely small tanh(A)
  67.         if (fabs(tanhA) < 1e-12) {
  68.             std::cerr << "tanh(A) too small, returning fallback at iteration " << i << "\n";
  69.             return 1.0E-7;
  70.         }        
  71.  
  72.         double f = 1.0 / tanhA - 1.0 / A - exp(-s);
  73.         if (fabs(f) < tol)
  74.             break;
  75.  
  76.         double sinhA = sinh(A);
  77.         if (fabs(sinhA) < 1e-12) {
  78.             std::cerr << "sinh(A) too small, returning fallback at iteration " << i << "\n";
  79.             return 1.0E-5;
  80.         }
  81.  
  82.         double dfdA = -1.0/(sinh(A)*sinh(A)) + 1.0/(A*A);
  83.  
  84.         // Check if derivative is too close to zero to avoid huge updates
  85.         if (fabs(dfdA) < 1e-12) {
  86.             std::cerr << "dfdA is too small at iteration " << i << ", returning fallback\n";
  87.             if (s < 0.01) {
  88. //                std::cout << "Small s! Huge A!" << "\n";
  89.                 return 1.0/s;
  90.             }
  91.             if (s > 3) {
  92.                 return 3.0*exp(-s);
  93.             }
  94.         }        
  95.  
  96.         A -= f/dfdA;
  97.  
  98.         // Early check for numerical issues
  99.         if (std::isnan(A) || std::isinf(A)) {
  100.             std::cerr << "Numerical error detected, invalid A at iteration " << i << "\n";
  101.             return (A > 0) ? 1.0E-5 : -1.0E-5;  // Fallback value based on sign
  102.         }        
  103.  
  104.  
  105.     }
  106.  
  107.     return A;
  108. }
  109.  
  110. struct Electron {
  111.  
  112.     //velocity components
  113.     double vx = 0.0;
  114.     double vy = 0.0;
  115.     double vz = 0.0;
  116.     //energy in eV
  117.     double energy = 0.0;
  118.     //Collision flag
  119.     bool collided_en = false;
  120.     bool collided_ee = false;
  121.  
  122.     // initializing Maxwell-Boltzmann distribution with T_e
  123.     void initialize(std::mt19937& gen, std::uniform_real_distribution<double>& dis, std::gamma_distribution<double>& maxwell) {
  124.  
  125.         double R = dis(gen);
  126.  
  127.         // velocity angles in spherical coordinates
  128.         double phi = 2*M_PI*dis(gen);
  129.         double cosTheta = 2.0*dis(gen) - 1.0;
  130.         double sinTheta = sqrt(1.0 - cosTheta*cosTheta);
  131.  
  132.            
  133.         energy = maxwell(gen); // neutrals energies sampled as Maxwell distribution in eV
  134.            
  135.         double speed = sqrt(2*energy*q/m_e);
  136.  
  137.         //velocity components of neutrals in m/s
  138.         vx = speed * sinTheta * cos(phi);
  139.         vy = speed * sinTheta * sin(phi);
  140.         vz = speed * cosTheta;
  141.     }
  142.  
  143.  
  144. };
  145.  
  146. struct CrossSection {
  147.     double energy;
  148.     double sigma;
  149. };
  150.  
  151. double interpolate (double energy, const std::vector<CrossSection>& CS) {
  152.  
  153.  
  154.     if (energy < CS.front().energy) {
  155. //        std::cout << " required energy value lower than range of cross-section data at energy: " << energy << "\n";
  156.         return 0.0;
  157.     }
  158.     if (energy > CS.back().energy) {
  159. //        std::cout << " required energy value higher than range of cross-section data" << "\n";
  160.         return 0.0;        
  161.     }
  162.  
  163.     int step = 0;  
  164.         while (step < CS.size() && energy > CS[step].energy) {
  165.             step++;
  166.         }
  167.  
  168.     double k = (CS[step].sigma - CS[step-1].sigma)/(CS[step].energy - CS[step-1].energy);
  169.     double m = CS[step].sigma - k*CS[step].energy;
  170.    
  171.     return k*energy + m;
  172. }
  173.  
  174.  
  175. struct NeutralParticle {
  176.  
  177.     double energy = 0.0;
  178.     double vx = 0.0;
  179.     double vy = 0.0;
  180.     double vz = 0.0;
  181.  
  182.     void initialize(std::mt19937& gen, std::uniform_real_distribution<double>& dis, std::gamma_distribution<double>& maxwell) {
  183.  
  184.         double R = dis(gen);
  185.  
  186.         // velocity angles in spherical coordinates
  187.         double phi = 2*M_PI*dis(gen);
  188.         double cosTheta = 2.0*dis(gen) - 1.0;
  189.         double sinTheta = sqrt(1.0 - cosTheta*cosTheta);
  190.  
  191.            
  192.         energy = maxwell(gen); // neutrals energies sampled as Maxwell distribution in eV
  193.            
  194.         double speed = sqrt(2*energy*q/M_n);
  195.  
  196.         //velocity components of neutrals in m/s
  197.         vx = speed * sinTheta * cos(phi);
  198.         vy = speed * sinTheta * sin(phi);
  199.         vz = speed * cosTheta;
  200.     }
  201.    
  202. };
  203.  
  204. struct Excited_neutral {
  205.  
  206.     double energy;
  207.     double vx;
  208.     double vy;
  209.     double vz;
  210.    
  211. };
  212.  
  213.  
  214.  
  215. int main() {
  216.  
  217.     clock_t start = clock();
  218.  
  219.     int N_He = 10000000;
  220.  
  221.     std::vector<Electron> electrons(n_e); // better to use vector instead of simple array as it's dynamically allocated (beneficial for ionization)
  222. //    std::vector<NeutralParticle> neutrals(N_He); // I don't need a vector of neutrals bcs it's like a backhround in MCC-simulation
  223.  
  224.     std::vector<int> histo_random(N, 0); // initialize N size zero-vector for random (initial) histogram
  225.     std::vector<int> histo_maxwell(N, 0); // initialize N size zero-vector for maxwellian histogram
  226.     std::vector<int> histo_neutral(N, 0); // initialize N size zero-vector for neutral distribution histogram
  227.     std::vector<int> histo_excited(N, 0); // initialize N size zero-vector for excited He distribution histogram
  228.  
  229.     std::vector<double> elastic_vec(N, 0); // precompiled elastic cross-section-energy vector
  230.     std::vector<double> inelastic1_vec(N, 0); // precompiled inelastic(triplet excitation) cross-section-energy vector
  231.     std::vector<double> inelastic2_vec(N, 0); // precompiled inelastic(singlet excitation) cross-section-energy vector    
  232.     std::vector<double> superelastic1_vec(N, 0); // precompiled superelastic(triplet de-excitation) cross-section-energy vector
  233.     std::vector<double> superelastic2_vec(N, 0); // precompiled superelastic(triplet de-excitation) cross-section-energy vector
  234.  
  235.     std::random_device rd;
  236.     std::mt19937 gen(rd());
  237.     std::uniform_real_distribution<double> dis(0.0, 1.0);
  238.     std::gamma_distribution<double> maxwell_neutral(1.5, T_n);
  239.     std::gamma_distribution<double> maxwell_electron(1.5, T_e);
  240.  
  241.     std::ifstream elastic_cs_dat("cross_sections/elastic.dat");
  242.     if (!elastic_cs_dat.is_open()) {
  243.         std::cerr << "Error opening elastic cross-sections file!" << std::endl;
  244.         return 1;
  245.     }    
  246.  
  247.     std::ifstream excitation1_cs_dat("cross_sections/inelastic_triplet.dat");
  248.     if (!excitation1_cs_dat.is_open()) {
  249.         std::cerr << "Error opening inelastic triplet cross-sections file!" << std::endl;
  250.         return 1;
  251.     }
  252.  
  253.     std::ifstream excitation2_cs_dat("cross_sections/inelastic_singlet.dat");
  254.     if (!excitation2_cs_dat.is_open()) {
  255.         std::cerr << "Error opening inelastic singlet cross-sections file!" << std::endl;
  256.         return 1;
  257.     }
  258.  
  259.     // --- starts reading cross section datafiles
  260.  
  261. //-----------------elastic---------------------------//
  262.     std::vector<CrossSection> elastic_CS_temp;
  263.  
  264.     double energy, sigma;
  265.  
  266.     while (elastic_cs_dat >> energy >> sigma) {
  267.         elastic_CS_temp.push_back({energy, sigma});
  268.     }    
  269.     elastic_cs_dat.close();
  270.  
  271.     energy = 0.0;
  272.     sigma = 0.0;
  273. //-----------------triplet excitation---------------------------//
  274.     std::vector<CrossSection> inelastic1_CS_temp;
  275.  
  276.     while (excitation1_cs_dat >> energy >> sigma) {
  277.         inelastic1_CS_temp.push_back({energy, sigma});
  278.     }    
  279.     excitation1_cs_dat.close();    
  280. //-----------------singlet excitation---------------------------//
  281.     energy = 0.0;
  282.     sigma = 0.0;
  283.  
  284.     std::vector<CrossSection> inelastic2_CS_temp;
  285.  
  286.     while (excitation2_cs_dat >> energy >> sigma) {
  287.         inelastic2_CS_temp.push_back({energy, sigma});
  288.     }    
  289.     excitation2_cs_dat.close();    
  290.  
  291.     // --- finish reading cross-section datafiles  
  292.  
  293.     std::ofstream file0("output_files/velocities.dat");    
  294.     std::ofstream file1("output_files/energies.dat");        
  295.     std::ofstream file2("output_files/energies_final.dat");    
  296.     std::ofstream file3("output_files/histo_random.dat");    
  297.     file3 << std::fixed << std::setprecision(10);
  298.    
  299.     std::ofstream file4("output_files/histo_maxwell.dat");
  300.     file4 << std::fixed << std::setprecision(10);          
  301.    
  302.     std::ofstream file5("output_files/neutral_distribution.dat");    
  303.     std::ofstream file6("output_files/E*f(E).dat");    
  304.     std::ofstream file7("output_files/nu_max.dat");
  305.     std::ofstream file8("output_files/electron_mean_energy.dat");
  306.     std::ofstream file9("output_files/nu_elastic_average_initial.dat");
  307.     std::ofstream file10("output_files/nu_inelastic1_average_initial.dat");
  308.     std::ofstream file11("output_files/nu_elastic_average_final.dat");
  309.     std::ofstream file12("output_files/nu_inelastic1_average_final.dat");
  310.     std::ofstream file13("output_files/log_output.dat");  
  311.     std::ofstream file14("output_files/excited_energies.dat");      
  312.     std::ofstream file15("output_files/excited_histo.dat");            
  313.     std::ofstream file_temp("output_files/collision_rates.dat");
  314.     std::ofstream file16("output_files/energy_gain.dat");  
  315.  
  316.     // Initialize all electrons
  317.     for (auto& e : electrons) {
  318.         e.initialize(gen, dis, maxwell_electron);
  319.     }
  320.  
  321.     // precalculate cross-sections for each energy bin
  322.     for (int i = 0; i < N; i++){
  323.         elastic_vec[i] = interpolate(bin_width*(i+0.5), elastic_CS_temp); //elastiuc
  324.         inelastic1_vec[i] = interpolate(bin_width*(i+0.5), inelastic1_CS_temp); //triplet excitation
  325.         inelastic2_vec[i] = interpolate(bin_width*(i+0.5), inelastic2_CS_temp); //singlet excitation
  326.     }
  327.  
  328.     // precalculate superelastic cross-section (triplet -> ground) for each energy bin
  329.     // detailed balance gives: sigma_j_i(E) = (g_i/g_j)*((E+theshold)/E)*sigma_i_j(E+theshold)
  330.     for (int i = 0; i < N; i++){
  331.         double energy = Emin + (i + 0.5) * bin_width;
  332.         int thresh_bin = (int)( (thresh1 - Emin)/bin_width ); // calculating bin for threshold energy
  333.         superelastic1_vec[i] = (1.0/3.0)*((energy + thresh1)/energy)*interpolate(energy + thresh1, inelastic1_CS_temp); // using detailed balance, calculating backward deexcitation cross-section
  334.         superelastic2_vec[i] = (1.0/1.0)*((energy + thresh2)/energy)*interpolate(energy + thresh2, inelastic2_CS_temp);
  335.     }
  336.  
  337.     for (int i = 0; i < n_e; i++){
  338.         file1 << i << " " << electrons.at(i).energy << "\n";
  339.         file0 << i << " " << electrons[i].vx << " " << electrons[i].vy << " " << electrons[i].vz << "\n";
  340.     }
  341.  
  342.     // -----initial electrons energy distribution starts------------////
  343.     for (int i = 0; i < n_e; i++){
  344.         int bin = (int)( (electrons[i].energy - Emin)/bin_width );
  345.         if (bin >=0 && bin < histo_random.size())
  346.             histo_random[bin]++;
  347.     }
  348.  
  349.     for (int i = 0; i < histo_random.size(); i++){
  350.         double bin_center = Emin + (i + 0.5) * bin_width;
  351.         file3 << bin_center << " " <<  static_cast<double>(histo_random[i])/(electrons.size()*bin_width) << "\n"; // this is electron normalized distribution function
  352.     }
  353.  
  354.  
  355.  
  356.     //calculating excited specied population
  357.  
  358.     /*From Boltzman distribution y_k = g_k*exp(-E_k/kT)/norm, where g_k - stat weight of k-state,
  359.     E_k - threshold energy for k-state, norm is a total partition function or normaliztion factor     */
  360.  
  361.     double part_ground = 1.0*exp(-0.0/T_n); // partition function for ground state
  362.     double part_triplet = 3.0*exp(-thresh1/T_n); // partition function for triplet excited state
  363.     double part_singlet = 1.0*exp(-thresh2/T_n); // partition function for singlet excited state
  364.     double part_func_total = part_ground + part_triplet + part_singlet; // total partition function
  365.     double N_trpilet = (part_triplet/part_func_total)*N_He; // population of tripet state
  366.     double N_singlet = (part_singlet/part_func_total)*N_He; // population of singlet state
  367.  
  368.     std::vector<Excited_neutral> exc_1(static_cast<int>(N_trpilet));  // vector to track triplet excited atoms of Helium
  369.     std::vector<Excited_neutral> exc_2(static_cast<int>(N_singlet));  // vector to track singlet excited atoms of Helium    
  370.  
  371.     // adjusting neutrals number:
  372.  
  373.     N_He -= (N_trpilet + N_singlet);
  374.  
  375.     std::cout << N_He << "\n";
  376.  
  377.     // initializing excited species with Maxwellian distribution
  378.  
  379.     for (auto& exc : exc_1) {
  380.     NeutralParticle tmp_neutral;
  381.     tmp_neutral.initialize(gen, dis, maxwell_neutral);
  382.     exc.energy = tmp_neutral.energy;
  383.     exc.vx = tmp_neutral.vx;
  384.     exc.vy = tmp_neutral.vy;
  385.     exc.vz = tmp_neutral.vz;
  386.     }
  387.  
  388.     for (auto& exc : exc_2) {
  389.     NeutralParticle tmp_neutral;
  390.     tmp_neutral.initialize(gen, dis, maxwell_neutral);
  391.     exc.energy = tmp_neutral.energy;
  392.     exc.vx = tmp_neutral.vx;
  393.     exc.vy = tmp_neutral.vy;
  394.     exc.vz = tmp_neutral.vz;
  395.     }
  396.  
  397.     std::cout << "Triplet population initialized: " << exc_1.size() << "\n";
  398.     std::cout << "Singlet population initialized: " << exc_2.size() << "\n";    
  399.  
  400.     // calculating excited specied population finished //
  401.  
  402.  
  403.     //----- calculating number to calculate nu-average (both elastic/inelastic )from our electron distribution starts---------///
  404.     // --- calculating nu(E)*f(E) for later external integration, using initial f(E)
  405.     for (int i = 0; i < N; i++){
  406.         double bin_center = Emin + (i + 0.5) * bin_width;
  407.         file9 << bin_center << " " << (N_He/Volume)*elastic_vec[i] * sqrt(2.0*bin_center*q/m_e)*static_cast<double>(histo_random[i])/(electrons.size()*bin_width) << "\n";
  408.         file10 << bin_center << " " << (N_He/Volume)*inelastic1_vec[i] * sqrt(2.0*bin_center*q/m_e)*static_cast<double>(histo_random[i])/(electrons.size()*bin_width) << "\n";
  409.     }
  410.     //----- calculating nu-average from our electron distribution ends ---------///    
  411.  
  412.     // double dt = 0.1/nu_max;   // minimum should be 0.1/nu_max to get acceptable numerical error range see Vahedi Surrendra 1995
  413.     // double steps = static_cast<int>(time/dt);
  414.  
  415.     // std::cout << steps << "\n";
  416.     // std::cout << dt << "\n";
  417.  
  418.     // //using  null-collision technique, getting the number of particles colliding each step: P_collision = 1 - exp(-nu_max*dt)
  419.     // int Ne_collided = (1.0-exp(-1.0*dt*nu_max))*n_e;
  420.  
  421.     // std::cout << "Ne_collided:" << Ne_collided << "\n";
  422.  
  423.     int print_interval = 10;
  424.     int el_coll_counter = 0; // track all elastic collisions
  425.     int exc1_coll_counter = 0; // track all triplet excitation collisions
  426.     int exc2_coll_counter = 0; // track all singlet excitation collisions
  427.     int null_coll_counter = 0; // track null-collisions
  428.     int ee_coll_counter = 0; //track e-e Coulomb collisions
  429.     int super1_coll_counter = 0; // track superelastic triplet collisions
  430.     int super2_coll_counter = 0; // track superelastic triplet collisions    
  431.  
  432.  
  433.     double a_z = ((-1.0)*q * E_reduced) / m_e;
  434.     double mass_ratio = 2.0*(m_e/M_n);
  435.     double charge_mass_ratio = 0.5*m_e/q;
  436.     double sqrt_charge_mass = sqrt(2*q/m_e);
  437.     double C1 = -1.0*q*E_reduced;
  438.     double C2 = 0.5*C1*C1/m_e;
  439.  
  440.     double total_time = 5.0E-2; // total calculation time
  441.     double t_elapsed = 0.0;
  442.  
  443.     std::cout << C1 << "    " << C2 << "\n";
  444.  
  445.  
  446.     // -----calculating nu-max for null-collision method starts ------------////
  447.     double nu_max = 0.0;
  448.     double nu_max_temp = 0.0;
  449.     double sigma_total = 0.0;
  450.    
  451.     for (int i = 0; i < N; i++){
  452.         // Get initial densities
  453.         double n_ground = N_He / Volume;
  454.         double n_excited1 = exc_1.size() / Volume;
  455.         double n_excited2 = exc_2.size() / Volume;
  456.  
  457.         double energy = Emin + (i + 0.5) * bin_width;
  458.  
  459.         // Total collision frequency for this energy bin
  460.         double sigma_total =
  461.             elastic_vec[i] * n_ground +
  462.             inelastic1_vec[i] * n_ground +
  463.             inelastic2_vec[i] * n_ground +
  464.             superelastic1_vec[i] * n_excited1 +
  465.             superelastic2_vec[i] * n_excited2;
  466.  
  467.         double v = sqrt(2 * energy * q / m_e);
  468.         double nu_temp = sigma_total * v;
  469.        
  470.         if (nu_temp > nu_max) nu_max = nu_temp;
  471.     }
  472.  
  473.     std::cout << "initial nu_max: " <<nu_max << "\n";
  474.     // -----calculating nu-max for null-collision method ends ------------////    
  475.  
  476.     double dt = 0.1/nu_max;   // minimum should be 0.1/nu_max to get acceptable numerical error range see Vahedi Surrendra 1995
  477.  
  478.  
  479.     while (t_elapsed < total_time) {
  480.         // Handle edge case for final step
  481.         if (t_elapsed + dt > total_time) {
  482.             dt = total_time - t_elapsed;
  483.         }    
  484.  
  485.  
  486.         //using  null-collision technique, getting the number of particles colliding each step: P_collision = 1 - exp(-nu_max*dt)
  487.         int Ne_collided = (1.0-exp(-1.0*dt*nu_max))*n_e;  
  488.  
  489.         // Generate shuffled list of electron indices
  490.         int reshuffle_interval = 1;
  491.         std::vector<int> electron_indices(n_e);
  492.         std::iota(electron_indices.begin(), electron_indices.end(), 0); // fill with index
  493.  
  494.  
  495.         for (int i = 0; i < Ne_collided; ++i) {
  496.             int j = i + std::uniform_int_distribution<int>(0, n_e - i - 1)(gen);
  497.             std::swap(electron_indices[i], electron_indices[j]);
  498.         }
  499.  
  500.         int exc1_coll_counter_temp = 0;
  501.         int super1_coll_counter_temp = 0;
  502.         int exc2_coll_counter_temp = 0;
  503.         int super2_coll_counter_temp = 0;
  504.         int null_coll_counter_temp = 0;
  505.  
  506.         double energy_exc = 0.0; // calculating excitation losses each timestep
  507.         double energy_sup = 0.0; // calculating superelastic gains each timestep
  508.         double energy_Efield = 0.0; // calculating field gains/losses each timestep
  509.  
  510.  
  511.         // std::cout << "Progress: " << (t_elapsed/total_time)*100 << "\n";
  512.  
  513.         // setting flags to false each timestep
  514.         for (auto& e : electrons) e.collided_en = false;
  515.         for (auto& e : electrons) e.collided_ee = false;        
  516.  
  517.         int collision_counter_en = 0; // electron-neutral collision counter
  518.         int collision_counter_ee = 0; // e-e collisoin counter
  519.  
  520.         /// -- electrin field heating along E-Z axis begin--- /// -- first half!!!
  521.         for (int idx : electron_indices) {
  522.             double half_dt = dt/2.0;
  523.             energy_Efield += ( C1*electrons[idx].vz*half_dt + C2*half_dt*half_dt )/q; // dividing by q to get eV            
  524.             // Update velocity component due to electric field
  525.             // double a_z = ((-1.0)*q * E_reduced) / m_e; // acceleration in z-direction, m/s^2
  526.             electrons[idx].vz += a_z * (dt*0.5); // only half timestep
  527.  
  528.             // Recalculate energy from updated velocity
  529.             double vx = electrons[idx].vx;
  530.             double vy = electrons[idx].vy;
  531.             double vz = electrons[idx].vz;
  532.             electrons[idx].energy = (vx*vx + vy*vy + vz*vz)*charge_mass_ratio;
  533.         }
  534.         // -------------------------------------------- filed heating ends ------------------------//  
  535.  
  536.  
  537.         for (int idx : electron_indices) {
  538.  
  539.             if (collision_counter_en >= Ne_collided) break; // quit if reached all collisions
  540.  
  541.             Electron& e = electrons[idx];
  542.             if (e.collided_en) continue;  // Skip already collided electrons
  543.  
  544.             double dens_neutrals = (N_He/Volume);
  545.             double dens_exc_1 = (exc_1.size()/Volume);
  546.             double dens_exc_2 = (exc_2.size()/Volume);
  547.             double speed = sqrt_charge_mass*sqrt(e.energy);
  548.  
  549.             int bin_energy = static_cast<int>(e.energy / bin_width);
  550.             double nu_elastic = dens_neutrals * elastic_vec[bin_energy] * speed;
  551.             double nu_inelastic1 = dens_neutrals * inelastic1_vec[bin_energy] * speed;
  552.             double nu_superelastic1 = dens_exc_1 * superelastic1_vec[bin_energy] * speed;
  553.             double nu_inelastic2 = dens_neutrals * inelastic2_vec[bin_energy] * speed;
  554.             double nu_superelastic2 = dens_exc_2 * superelastic2_vec[bin_energy] * speed;
  555.  
  556.             double r = dis(gen);
  557.  
  558.             double P0 = nu_elastic/nu_max;
  559.             double P1 = (nu_elastic + nu_inelastic1)/nu_max;
  560.             double P2 = (nu_elastic + nu_inelastic1 + nu_superelastic1)/nu_max;
  561.             double P3 = (nu_elastic + nu_inelastic1 + nu_superelastic1 + nu_inelastic2)/nu_max;
  562.             double P4 = (nu_elastic + nu_inelastic1 + nu_superelastic1 + nu_inelastic2 + nu_superelastic2)/nu_max;            
  563.  
  564.             if (r < P0) {
  565.  
  566.                 // elastic collision happens
  567.  
  568.                 // ----   Collision energy redistribution module
  569.  
  570.  
  571.                 // electron particle X Y Z initial velocities and energy
  572.                 double V0_x = e.vx;
  573.                 double V0_y = e.vy;
  574.                 double V0_z = e.vz;
  575.                 double E_0 = e.energy;
  576.                
  577.                 // neutral that collides with electron
  578.  
  579.                 // randomize particles each collision
  580.  
  581.                 NeutralParticle tmp_neutral;
  582.                 tmp_neutral.initialize(gen, dis, maxwell_neutral);
  583.                 double V_x_n = tmp_neutral.vx;
  584.                 double V_y_n = tmp_neutral.vy;
  585.                 double V_z_n = tmp_neutral.vz;
  586.                 double E_n = tmp_neutral.energy;
  587.  
  588.  
  589.                 double V0 = sqrt(V0_x*V0_x + V0_y*V0_y + V0_z*V0_z);
  590.                
  591.                 // generating random variables to calculate random direction of center-of-mass after the collision
  592.  
  593.                 double R1 = dis(gen);
  594.                 double R2 = dis(gen);
  595.  
  596.                 //// calculating spherical angles for center-of-mass random direction
  597.                 // double theta = acos(1.0- 2.0*R1);
  598.                 // double phi = 2*M_PI*R2;
  599.                 double cos_khi = (2.0 + E_0 - 2.0*pow((1+E_0), R1))/E_0;
  600.                 if (cos_khi >= 1)
  601.                     cos_khi = 1.0 - dopant;
  602.                 if (cos_khi <= -1)
  603.                     cos_khi = -1.0 + dopant;
  604.                                      
  605.                 double sin_khi = sqrt(1.0 - cos_khi*cos_khi);
  606.  
  607.                 double phi = 2.0*M_PI*R2;
  608.                 double cos_theta = V0_x/V0;
  609.                 double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
  610.                 // //calculating final relative velocity with random direction
  611.  
  612.                 //calculating final velocity of electron
  613.  
  614.                 double i_scat = (V0_x/V0)*cos_khi + (1.0 - (V0_x/V0)*(V0_x/V0))*(sin_khi*cos(phi)/sin_theta);
  615.                 double j_scat = (V0_y/V0)*cos_khi +  (V0_z/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_y/V0)*sin_khi*cos(phi)/sin_theta;
  616.                 double k_scat = (V0_z/V0)*cos_khi - (V0_y/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_z/V0)*sin_khi*cos(phi)/sin_theta;
  617.  
  618.                 //updating electron energy and velocities  
  619.  
  620.                 double delta_E = mass_ratio*(1.0 - cos_khi)*E_0;
  621.                 if (e.energy < delta_E) {
  622.                     null_coll_counter++;
  623.                     collision_counter_en++;
  624.                     e.collided_en = true;
  625.                     continue;
  626.                 }    
  627.                 else {                          
  628.                     e.energy = E_0 - delta_E;
  629.                 }
  630.                
  631.                 double speed = sqrt_charge_mass*sqrt(e.energy);
  632.  
  633.                 e.vx = speed*i_scat;
  634.                 e.vy = speed*j_scat;
  635.                 e.vz = speed*k_scat;              
  636.  
  637.                 collision_counter_en++;
  638.                 el_coll_counter++;
  639.  
  640.                 e.collided_en = true;
  641.             }        
  642.  
  643.             else if (r < P1) {
  644.  
  645.                 //inelastic 1(triplet) collision happens
  646.  
  647.                 // ----   Collision energy redistribution module
  648.  
  649.                 // electron particle X Y Z initial velocities and energy
  650.                 double V0_x = e.vx;
  651.                 double V0_y = e.vy;
  652.                 double V0_z = e.vz;
  653.                 double E_0 = e.energy;
  654.                
  655.                 // neutral that collides with electron
  656.  
  657.                 // randomize particles each collision
  658.  
  659.                 NeutralParticle tmp_neutral;
  660.                 tmp_neutral.initialize(gen, dis, maxwell_neutral);
  661.                 double V_x_n = tmp_neutral.vx;
  662.                 double V_y_n = tmp_neutral.vy;
  663.                 double V_z_n = tmp_neutral.vz;
  664.                 double E_n = tmp_neutral.energy;
  665.  
  666.  
  667.                 double V0 = sqrt(V0_x*V0_x + V0_y*V0_y + V0_z*V0_z);
  668.                
  669.                 // generating random variables to calculate random direction of center-of-mass after the collision
  670.  
  671.                 double R1 = dis(gen);
  672.                 double R2 = dis(gen);
  673.  
  674.                 //// calculating spherical angles for center-of-mass random direction
  675.                 // double theta = acos(1.0- 2.0*R1);
  676.                 // double phi = 2*M_PI*R2;
  677.                 double cos_khi = (2.0 + E_0 - 2.0*pow((1+E_0), R1))/E_0;
  678.                 double sin_khi = sqrt(1.0 - cos_khi*cos_khi);
  679.  
  680.                 double phi = 2.0*M_PI*R2;
  681.                 double cos_theta = V0_x/V0;
  682.                 double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
  683.                 // //calculating final relative velocity with random direction
  684.  
  685.                 //calculating final velocity of electron
  686.  
  687.                 double i_scat = (V0_x/V0)*cos_khi + (1.0 - (V0_x/V0)*(V0_x/V0))*(sin_khi*cos(phi)/sin_theta);
  688.                 double j_scat = (V0_y/V0)*cos_khi +  (V0_z/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_y/V0)*sin_khi*cos(phi)/sin_theta;
  689.                 double k_scat = (V0_z/V0)*cos_khi - (V0_y/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_z/V0)*sin_khi*cos(phi)/sin_theta;
  690.  
  691.                 //updating electron energy and velocities        
  692.                
  693.                 if (e.energy < thresh1) {
  694.                     null_coll_counter++;
  695.                     collision_counter_en++;
  696.                     e.collided_en = true;
  697.                     continue;
  698.                 }
  699.                 else {
  700.                     e.energy = E_0 - thresh1;
  701.  
  702.                     double speed = sqrt_charge_mass*sqrt(e.energy);
  703.  
  704.                     e.vx = speed*i_scat;
  705.                     e.vy = speed*j_scat;
  706.                     e.vz = speed*k_scat;
  707.  
  708.                     collision_counter_en++;  
  709.                     exc1_coll_counter++;
  710.                     exc1_coll_counter_temp++;
  711.  
  712.                     e.collided_en = true;
  713.  
  714.                     // pushing this neutral to an array of excited species exc_1
  715.                     if (N_He > 0) {
  716.                         exc_1.push_back({E_n, V_x_n, V_y_n, V_z_n});
  717.                         N_He--;
  718.                     }
  719.                 }
  720.             }    
  721.  
  722.             else if (r < P2) {
  723.  
  724.                 //superelastic 1(triplet -> ground state) collision happens
  725.  
  726.                 if (exc_1.empty()) {
  727.                     null_coll_counter++;
  728.                     collision_counter_en++;
  729.                     e.collided_en = true;
  730.                     continue;            
  731.                 }
  732.  
  733.                 // ----   Collision energy redistribution module
  734.  
  735.                 // electron particle X Y Z initial velocities and energy
  736.                 double V0_x = e.vx;
  737.                 double V0_y = e.vy;
  738.                 double V0_z = e.vz;
  739.                 double E_0 = e.energy;
  740.  
  741.                 double V0 = sqrt(V0_x*V0_x + V0_y*V0_y + V0_z*V0_z);
  742.  
  743.                 // neutral that collides with electron
  744.                 // taking particles from dynamic array of excited neutrals
  745.  
  746.                 int index = std::uniform_int_distribution<int>(0, exc_1.size()-1)(gen);
  747.                 Excited_neutral& exc = exc_1[index];
  748.                 double V_x = exc.vx;
  749.                 double V_y = exc.vy;
  750.                 double V_z = exc.vz;
  751.                 double E = exc.energy;
  752.                
  753.                 // generating random variables to calculate random direction of center-of-mass after the collision
  754.  
  755.                 double R1 = dis(gen);
  756.                 double R2 = dis(gen);
  757.  
  758.                 //// calculating spherical angles for center-of-mass random direction
  759.                 // double theta = acos(1.0- 2.0*R1);
  760.                 // double phi = 2*M_PI*R2;
  761.                 double cos_khi = (2.0 + E_0 - 2.0*pow((1+E_0), R1))/E_0;
  762.                 double sin_khi = sqrt(1.0 - cos_khi*cos_khi);
  763.  
  764.                 double phi = 2.0*M_PI*R2;
  765.                 double cos_theta = V0_x/V0;
  766.                 double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
  767.                 // //calculating final relative velocity with random direction
  768.  
  769.                 //calculating final velocity of electron
  770.  
  771.                 double i_scat = (V0_x/V0)*cos_khi + (1.0 - (V0_x/V0)*(V0_x/V0))*(sin_khi*cos(phi)/sin_theta);
  772.                 double j_scat = (V0_y/V0)*cos_khi +  (V0_z/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_y/V0)*sin_khi*cos(phi)/sin_theta;
  773.                 double k_scat = (V0_z/V0)*cos_khi - (V0_y/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_z/V0)*sin_khi*cos(phi)/sin_theta;
  774.  
  775.                 //updating electron energy and velocities        
  776.                
  777.                 e.energy = E_0 + thresh1;
  778.  
  779.                 double speed = sqrt_charge_mass*sqrt(e.energy);
  780.  
  781.                 e.vx = speed*i_scat;
  782.                 e.vy = speed*j_scat;
  783.                 e.vz = speed*k_scat;
  784.  
  785.                 //counting collisions, working with flags, popping atom out of the vector
  786.                 if (!exc_1.empty()) {
  787.                     std::swap(exc_1[index], exc_1.back());
  788.                     exc_1.pop_back();
  789.                     N_He++;
  790.                 }
  791.                 collision_counter_en++;  
  792.                 super1_coll_counter++;
  793.                 super1_coll_counter_temp++;
  794.                 energy_sup += thresh1;
  795.  
  796.                 e.collided_en = true;
  797.             }  
  798.  
  799.             else if (r < P3) {
  800.  
  801.                 //inelastic 1(singlet) excitation collision happens
  802.  
  803.                 // ----   Collision energy redistribution module
  804.  
  805.                 // electron particle X Y Z initial velocities and energy
  806.                 double V0_x = e.vx;
  807.                 double V0_y = e.vy;
  808.                 double V0_z = e.vz;
  809.                 double E_0 = e.energy;
  810.                
  811.                 // neutral that collides with electron
  812.  
  813.                 // randomize particles each collision
  814.  
  815.                 NeutralParticle tmp_neutral;
  816.                 tmp_neutral.initialize(gen, dis, maxwell_neutral);
  817.                 double V_x_n = tmp_neutral.vx;
  818.                 double V_y_n = tmp_neutral.vy;
  819.                 double V_z_n = tmp_neutral.vz;
  820.                 double E_n = tmp_neutral.energy;
  821.  
  822.  
  823.                 double V0 = sqrt(V0_x*V0_x + V0_y*V0_y + V0_z*V0_z);
  824.                
  825.                 // generating random variables to calculate random direction of center-of-mass after the collision
  826.  
  827.                 double R1 = dis(gen);
  828.                 double R2 = dis(gen);
  829.  
  830.                 //// calculating spherical angles for center-of-mass random direction
  831.                 // double theta = acos(1.0- 2.0*R1);
  832.                 // double phi = 2*M_PI*R2;
  833.                 double cos_khi = (2.0 + E_0 - 2.0*pow((1+E_0), R1))/E_0;
  834.                 double sin_khi = sqrt(1.0 - cos_khi*cos_khi);
  835.  
  836.                 double phi = 2.0*M_PI*R2;
  837.                 double cos_theta = V0_x/V0;
  838.                 double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
  839.                 // //calculating final relative velocity with random direction
  840.  
  841.                 //calculating final velocity of electron
  842.  
  843.                 double i_scat = (V0_x/V0)*cos_khi + (1.0 - (V0_x/V0)*(V0_x/V0))*(sin_khi*cos(phi)/sin_theta);
  844.                 double j_scat = (V0_y/V0)*cos_khi +  (V0_z/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_y/V0)*sin_khi*cos(phi)/sin_theta;
  845.                 double k_scat = (V0_z/V0)*cos_khi - (V0_y/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_z/V0)*sin_khi*cos(phi)/sin_theta;
  846.  
  847.                 //updating electron energy and velocities        
  848.                
  849.                 if (e.energy < thresh2) {
  850.                     null_coll_counter++;
  851.                     collision_counter_en++;
  852.                     e.collided_en = true;
  853.                     continue;
  854.                 }
  855.                 else {
  856.                     e.energy = E_0 - thresh2;
  857.  
  858.                     double speed = sqrt_charge_mass*sqrt(e.energy);
  859.  
  860.                     e.vx = speed*i_scat;
  861.                     e.vy = speed*j_scat;
  862.                     e.vz = speed*k_scat;
  863.  
  864.                     collision_counter_en++;  
  865.                     exc2_coll_counter++;
  866.                     exc2_coll_counter_temp++;
  867.  
  868.                     e.collided_en = true;
  869.  
  870.                     // pushing this neutral to an array of excited species exc_2
  871.  
  872.                     if (N_He > 0) {
  873.                         exc_2.push_back({E_n, V_x_n, V_y_n, V_z_n});
  874.                         N_He--;
  875.                     }
  876.                 }
  877.             }
  878.  
  879.             else if (r < P4) {
  880.  
  881.                 //supernelastic 1(singlet -> ground state) collision happens
  882.  
  883.                 if (exc_2.empty()) {
  884.                     null_coll_counter++;
  885.                     collision_counter_en++;
  886.                     e.collided_en = true;
  887.                     continue;            
  888.                 }
  889.  
  890.                 // ----   Collision energy redistribution module
  891.  
  892.                 // electron particle X Y Z initial velocities and energy
  893.                 double V0_x = e.vx;
  894.                 double V0_y = e.vy;
  895.                 double V0_z = e.vz;
  896.                 double E_0 = e.energy;
  897.  
  898.                 double V0 = sqrt(V0_x*V0_x + V0_y*V0_y + V0_z*V0_z);
  899.  
  900.                 // neutral that collides with electron
  901.                 // taking particles from dynamic array of excited neutrals
  902.  
  903.                 int index = std::uniform_int_distribution<int>(0, exc_2.size()-1)(gen);
  904.                 Excited_neutral& exc = exc_2[index];
  905.                 double V_x = exc.vx;
  906.                 double V_y = exc.vy;
  907.                 double V_z = exc.vz;
  908.                 double E = exc.energy;
  909.                
  910.                 // generating random variables to calculate random direction of center-of-mass after the collision
  911.  
  912.                 double R1 = dis(gen);
  913.                 double R2 = dis(gen);
  914.  
  915.                 //// calculating spherical angles for center-of-mass random direction
  916.                 // double theta = acos(1.0- 2.0*R1);
  917.                 // double phi = 2*M_PI*R2;
  918.                 double cos_khi = (2.0 + E_0 - 2.0*pow((1+E_0), R1))/E_0;
  919.                 double sin_khi = sqrt(1.0 - cos_khi*cos_khi);
  920.  
  921.                 double phi = 2.0*M_PI*R2;
  922.                 double cos_theta = V0_x/V0;
  923.                 double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
  924.                 // //calculating final relative velocity with random direction
  925.  
  926.                 //calculating final velocity of electron
  927.  
  928.                 double i_scat = (V0_x/V0)*cos_khi + (1.0 - (V0_x/V0)*(V0_x/V0))*(sin_khi*cos(phi)/sin_theta);
  929.                 double j_scat = (V0_y/V0)*cos_khi +  (V0_z/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_y/V0)*sin_khi*cos(phi)/sin_theta;
  930.                 double k_scat = (V0_z/V0)*cos_khi - (V0_y/V0)*sin_khi*sin(phi)/sin_theta - (V0_x/V0)*(V0_z/V0)*sin_khi*cos(phi)/sin_theta;
  931.  
  932.                 //updating electron energy and velocities        
  933.                
  934.                 e.energy = E_0 + thresh2;
  935.  
  936.                 double speed = sqrt_charge_mass*sqrt(e.energy);
  937.  
  938.                 e.vx = speed*i_scat;
  939.                 e.vy = speed*j_scat;
  940.                 e.vz = speed*k_scat;
  941.  
  942.                 //counting collisions, working with flags, popping atom out of the vector
  943.  
  944.                 if (!exc_2.empty()) {
  945.                     std::swap(exc_2[index], exc_2.back());
  946.                     exc_2.pop_back();
  947.                     N_He++;
  948.                 }
  949.  
  950.                 collision_counter_en++;  
  951.                 super2_coll_counter++;
  952.                 super2_coll_counter_temp++;
  953.                 energy_sup += thresh2;
  954.  
  955.                 e.collided_en = true;
  956.             }              
  957.  
  958.             else {
  959.                 // null-collision
  960.                 collision_counter_en++;
  961.                 null_coll_counter++;
  962.                 e.collided_en = true;
  963.             }
  964.         }
  965.  
  966.  
  967.         /// -- electrin field heating along E-Z axis begin--- /// -- second half!!!
  968.         for (int idx : electron_indices) {
  969.             double half_dt = dt/2.0;
  970.             energy_Efield += ( C1*electrons[idx].vz*half_dt + C2*half_dt*half_dt )/q; //dividing by q to get eV
  971.             // Update velocity component due to electric field
  972.             // double a_z = ((-1.0)*q * E_reduced) / m_e; // acceleration in z-direction, m/s^2
  973.             electrons[idx].vz += a_z * (dt*0.5); // only half timestep
  974.  
  975.             // Recalculate energy from updated velocity
  976.             double vx = electrons[idx].vx;
  977.             double vy = electrons[idx].vy;
  978.             double vz = electrons[idx].vz;
  979.             electrons[idx].energy = (vx*vx + vy*vy + vz*vz) * charge_mass_ratio;
  980.         }
  981.         // -------------------------------------------- filed heating ends ------------------------////////////////
  982.  
  983.         int decay_counter = 0;
  984.  
  985.         // // Iterate backwards to safely remove elements
  986.         // for (int i = exc_2.size() - 1; i >= 0; --i) {
  987.         //     if (dis(gen) < dt / tau_singlet) {
  988.         //         // Swap with last element and pop (like your superelastic code)
  989.         //         std::swap(exc_2[i], exc_2.back());
  990.         //         exc_2.pop_back();
  991.         //         N_He++;
  992.         //         decay_counter++;
  993.         //     }
  994.         // }
  995.  
  996.  
  997.         t_elapsed += dt; // Advance time
  998.  
  999.         // Recalculate nu_max periodically (e.g., every 100 steps)
  1000.         static int recalc_counter = 0;
  1001.         if (++recalc_counter >= 10000) {
  1002.            
  1003.             recalc_counter = 0;
  1004.  
  1005.             // Recalculate nu_max with CURRENT densities
  1006.             nu_max = 0.0;
  1007.             for (int i = 0; i < N; i++) {
  1008.                 double energy = Emin + (i + 0.5) * bin_width;
  1009.                
  1010.                 // Get current densities
  1011.                 double n_ground = N_He / Volume;
  1012.                 double n_excited1 = exc_1.size() / Volume;
  1013.                 double n_excited2 = exc_2.size() / Volume;
  1014.                
  1015.                 // Total collision frequency for this energy bin
  1016.                 double sigma_total =
  1017.                     elastic_vec[i] * n_ground +
  1018.                     inelastic1_vec[i] * n_ground +
  1019.                     inelastic2_vec[i] * n_ground +
  1020.                     superelastic1_vec[i] * n_excited1 +
  1021.                     superelastic2_vec[i] * n_excited2;
  1022.  
  1023.                 double speed = sqrt_charge_mass*sqrt(energy);
  1024.                 double nu_temp = sigma_total * speed;
  1025.                
  1026.                 if (nu_temp > nu_max) nu_max = nu_temp;
  1027.             }
  1028.  
  1029.  
  1030.  
  1031.             // Update dt based on new nu_max
  1032.             dt = 0.1 / nu_max;        
  1033.         }  
  1034.  
  1035.         // calculating mean energy
  1036.         if (static_cast<int>(t_elapsed/dt)%print_interval == 0) {
  1037.             double total_energy = 0.0;
  1038.             for (const auto& e : electrons) total_energy += e.energy;
  1039.             double mean_energy = total_energy / n_e;
  1040.             file8 << t_elapsed << " " << mean_energy << "\n";            
  1041.             file_temp << t_elapsed << " " << exc_1.size() << " " << exc_2.size() << "\n";
  1042.             std::cout << "Progress: " << (t_elapsed/total_time)*100 << "%" << " ";
  1043.             std::cout << "   nu_max: " << nu_max << "    " << "dt: " << dt << " " << "decay counter: " << decay_counter <<   "\n";
  1044.             file16 << t_elapsed << " " << energy_Efield/n_e << " " << energy_sup/n_e << "\n";
  1045.         }        
  1046.  
  1047.     }
  1048.  
  1049.     // ----- final electron energies distribution begins
  1050.     for (int i = 0; i < n_e; i++){
  1051.  
  1052.         file2 << i << " " << electrons[i].energy << "\n";
  1053.  
  1054.         int bin = static_cast<int>( (electrons[i].energy - Emin)/bin_width_smooth);
  1055.         if (bin >=0 && bin < histo_maxwell.size())
  1056.             histo_maxwell[bin]++;
  1057.     }
  1058.  
  1059.     int check = 0;
  1060.     for (int i = 0; i < N_smooth; i++){
  1061.         check += histo_maxwell[i];
  1062.         double bin_center = Emin + (i + 0.5) * bin_width_smooth;
  1063.         file4 << bin_center << " " <<  static_cast<double>(histo_maxwell[i])/(electrons.size()*bin_width_smooth) << "\n"; // getting f(E)
  1064.     }
  1065.  
  1066.         std::cout << "Total # of electrons in a final histogram: " << check << "\n";
  1067.         std::cout << "Final nu max: " << nu_max << "\n";
  1068.  
  1069.     // ----- final electron energies distribution ends
  1070.  
  1071.  
  1072.     file0.close();
  1073.     file1.close();
  1074.     file2.close();
  1075.     file3.close();
  1076.     file4.close();
  1077.     file5.close();
  1078.     file6.close();
  1079.     file7.close();
  1080.     file8.close();
  1081.     file9.close();
  1082.     file10.close();
  1083.     file11.close();
  1084.     file12.close();
  1085.     file13.close();
  1086.     file14.close();
  1087.     file15.close();
  1088.     file_temp.close();
  1089.     file16.close();
  1090.  
  1091.     clock_t end = clock();
  1092.  
  1093.     double elapsed = (double)(end - start) / CLOCKS_PER_SEC;
  1094.  
  1095.     // std::cout << "# of steps: " << steps << "\n";
  1096.     // std::cout << "# of electrons collided each timesteps:" << Ne_collided << "\n";
  1097.    
  1098.     // std::cout << "Average elastic collisions per timestep: " << static_cast<int>(el_coll_counter/steps) << "\n";
  1099.     // std::cout << "Average null collisions per timestep: " << static_cast<int>(null_coll_counter/steps) << "\n";
  1100.     // std::cout << "\n";
  1101.  
  1102.     // std::cout << "triplet:________" << "\n";
  1103.     // std::cout << "Average triplet excitation collisions per timestep: " << static_cast<int>(exc1_coll_counter/steps) << "\n";
  1104.     // std::cout << "\n";
  1105.     // std::cout << "Average superelastic triplet collisions per timestep: " << static_cast<int>(super1_coll_counter/steps) << "\n";
  1106.     // std::cout << "\n";
  1107.  
  1108.     // std::cout << "singlet:________" << "\n";
  1109.     // std::cout << "Average singlet excitation collisions per timestep: " << static_cast<int>(exc2_coll_counter/steps) << "\n";
  1110.     // std::cout << "\n";
  1111.     // std::cout << "Average superelastic singlet collisions per timestep: " << static_cast<int>(super2_coll_counter/steps) << "\n";
  1112.     // std::cout << "\n";    
  1113.  
  1114.     // std::cout << "Average e-e collisions per timestep: " << static_cast<int>(ee_coll_counter/steps) << "\n";
  1115.  
  1116.     std::cout << "Elapsed time: %f seconds " << elapsed << "\n";
  1117.  
  1118.  
  1119.     return 0;
  1120.  
  1121. }
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement
Public Pastes
Advertisement
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.  OK, I Understand
Not a member of Pastebin yet?
Sign Up, it unlocks many cool features!