e-n collisions(v6) - elastic collisions as in Vahedi - just loosing energy

#include <iostream>
#include <random>
#include <fstream>

#include <math.h>
#include <time.h>
#include <iomanip>  // For std::fixed and std::setprecision

#include <algorithm>  // For std::shuffle
#include <numeric>    // For std::iota


#define n_e 50000
#define Emin 0.0
#define Emax 450.0
#define E_mean 100 // mean electron energy, initial distribution
#define bin_width 0.1
#define m_e 9.1E-31 // electron mass in kg
#define k_b 1.38E-23 // Boltzmann constant
#define q 1.602176634E-19 // elementary charge    - eV -> J transfer param
#define N ( (int)((Emax-Emin)/bin_width) ) // add 1 to include E_max if needed?
#define T_n 10.0 // Helium neutral temperature in eV
#define T_e 50.0    // electron Maxwell initial distribution
#define M_n 6.6464731E-29 // Helium atom mass
#define N_He 1000000 // Helium neutrals number
#define Volume 1.0E-12 // Volume to calculate netral density and collision frequency
#define time 5.0E-3 // 500 microsec time to equalibrate the system

struct Electron {

    //velocity components
    double vx = 0.0;
    double vy = 0.0;
    double vz = 0.0;
    //energy in eV
    double energy = 0.0;
    //Collision flag
    bool collided = false;

    //initialization function // void func(Type0& t) → means the function expects a reference to variable t of type0
    // void initialize(std::mt19937& gen, std::uniform_real_distribution<double>& dis) {
    //     // velocity angles in spherical coordinates
    //     double phi = 2*M_PI*dis(gen);
    //     double cosTheta = 2.0*dis(gen) - 1.0;
    //     double sinTheta = sqrt(1.0 - cosTheta*cosTheta);

    //     energy = E_mean*dis(gen);

    //     double speed = sqrt(2*energy*q/m_e);

    //     vx = speed * sinTheta * cos(phi);
    //     vy = speed * sinTheta * sin(phi);
    //     vz = speed * cosTheta;
    // }

    // initializing Maxwell-Boltzmann distribution with T_e
    void initialize(std::mt19937& gen, std::uniform_real_distribution<double>& dis, std::gamma_distribution<double>& maxwell) {

        double R = dis(gen);

        // velocity angles in spherical coordinates
        double phi = 2*M_PI*dis(gen);
        double cosTheta = 2.0*dis(gen) - 1.0;
        double sinTheta = sqrt(1.0 - cosTheta*cosTheta);


        energy = maxwell(gen); // neutrals energies sampled as Maxwell distribution in eV

        double speed = sqrt(2*energy*q/m_e);

        //velocity components of neutrals in m/s
        vx = speed * sinTheta * cos(phi);
        vy = speed * sinTheta * sin(phi);
        vz = speed * cosTheta;
    }


};


struct CrossSection {
    double energy;
    double sigma;
};

double interpolate (double energy, const std::vector<CrossSection>& elastic_CS) {


    if (energy < elastic_CS.front().energy) {
        std::cout << " required energy value lower than range of cross-section data" << "\n";
        return 0.0;
    }
    if (energy > elastic_CS.back().energy) {
        std::cout << " required energy value higher than range of cross-section data" << "\n";
        return 0.0;
    }

    int step = 0;
        while (step < elastic_CS.size() && energy > elastic_CS[step].energy) {
            step++;
        }

    double k = (elastic_CS[step].sigma - elastic_CS[step-1].sigma)/(elastic_CS[step].energy - elastic_CS[step-1].energy);
    double m = elastic_CS[step].sigma - k*elastic_CS[step].energy;

    return k*energy + m;
}


struct NeutralParticle {

    double energy = 0.0;
    double vx = 0.0;
    double vy = 0.0;
    double vz = 0.0;

    void initialize(std::mt19937& gen, std::uniform_real_distribution<double>& dis, std::gamma_distribution<double>& maxwell) {

        double R = dis(gen);

        // velocity angles in spherical coordinates
        double phi = 2*M_PI*dis(gen);
        double cosTheta = 2.0*dis(gen) - 1.0;
        double sinTheta = sqrt(1.0 - cosTheta*cosTheta);


        energy = maxwell(gen); // neutrals energies sampled as Maxwell distribution in eV

        double speed = sqrt(2*energy*q/M_n);

        //velocity components of neutrals in m/s
        vx = speed * sinTheta * cos(phi);
        vy = speed * sinTheta * sin(phi);
        vz = speed * cosTheta;
    }

};




int main() {

    clock_t start = clock();

    std::vector<Electron> electrons(n_e); // better to use vector instead of simple array as it's dynamically allocated (beneficial for ionization)
//    std::vector<double> neutrals(N_He); // vector for neutrals
    std::vector<NeutralParticle> neutrals(N_He);


    std::vector<int> histo_random(N, 0); // initialize N size zero-vector for random (initial) histogram
    std::vector<int> histo_maxwell(N, 0); // initialize N size zero-vector for maxwellian histogram
    std::vector<int> histo_neutral(N, 0); // initialize N size zero-vector for neutral distribution histogram

    std::vector<double> elastic(N, 0); // precompiled cross-section energy vector

    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_real_distribution<double> dis(0.0, 1.0);
    std::gamma_distribution<double> maxwell_neutral(1.5, T_n);
    std::gamma_distribution<double> maxwell_electron(1.5, T_e);

    std::uniform_int_distribution<int> pair(0, n_e-1);
    std::uniform_int_distribution<int> neutral_pair(0, N_He-1);


    std::ifstream elastic_cs("cross_sections/elastic.dat");
    if (!elastic_cs.is_open()) {
        std::cerr << "Error opening file!" << std::endl;
        return 1;
    }

    // --- starts reading elastic cross section datafile

    std::vector<CrossSection> elastic_CS;

    double energy, sigma;

    while (elastic_cs >> energy >> sigma) {
        elastic_CS.push_back({energy, sigma});
    }

    elastic_cs.close();

    // --- finish reading cross-section datafile

    std::ofstream file0("velocities.dat");
    std::ofstream file1("energies.dat");
    std::ofstream file2("energies_final.dat");

    std::ofstream file3("histo_random.dat");
    file3 << std::fixed << std::setprecision(10);

    std::ofstream file4("histo_maxwell.dat");
    file4 << std::fixed << std::setprecision(10);

    std::ofstream file5("neutral_distribution.dat");
    std::ofstream file6("E*f(E).dat");
    std::ofstream file7("nu_max.dat");
    std::ofstream file8("electron_mean_energy.dat");
    std::ofstream file9("nu.dat");

    // Initialize all electrons
    for (auto& e : electrons) {
//        e.initialize(gen, dis);
        e.initialize(gen, dis, maxwell_electron);
    }
    // initialize all nenutrals
    for (auto&n : neutrals) {
        n.initialize(gen, dis, maxwell_neutral);
    }
    // precalculate cross-sections for each energy bin
    for (int i = 0; i < N; i++){
        elastic[i] = interpolate(bin_width*(i+0.5), elastic_CS);
    }


    for (int i = 0; i < n_e; i++){
        file1 << i << " " << electrons.at(i).energy << "\n";
        file0 << i << " " << electrons[i].vx << " " << electrons[i].vy << " " << electrons[i].vz << "\n";
    }

    // -----initial electrons energy distribution starts------------////
    for (int i = 0; i < n_e; i++){
        int bin = (int)( (electrons[i].energy - Emin)/bin_width );
        if (bin >=0 && bin < histo_random.size())
            histo_random[bin]++;
    }

    for (int i = 0; i < histo_random.size(); i++){
        double bin_center = Emin + (i + 0.5) * bin_width;
        file3 << bin_center << " " <<  (i*bin_width)*static_cast<double>(histo_random[i])/(electrons.size()*bin_width) << "\n"; // this is electron normalized distribution function
    }
    // -----initial electrons energy distribution ends------------////

    // -----neutrals Maxwell-Boltzmann distribution starts------------////
    for (int i = 0; i < N_He; i++){
        int bin = (int)( (neutrals[i].energy - Emin)/bin_width );
        if (bin >=0 && bin < histo_neutral.size())
            histo_neutral[bin]++;
    }


    for (int i = 0; i < histo_neutral.size(); i++){
        double bin_center = Emin + (i + 0.5) * bin_width;
        file5 << bin_center << " " << static_cast<double>(histo_neutral[i])/(neutrals.size()*bin_width) << "\n"; // this is real f(E) - normalized distribution
        file6 << bin_center << " " << bin_center*static_cast<double>(histo_neutral[i])/(neutrals.size()*bin_width) << "\n"; // this should be E*f(E)
    }

    // -----neutrals Maxwell-Boltzmann distribution starts------------////

    // -----calculating nu-max for null-collision method starts ------------////
    double nu_max = 0.0;
    double nu_max_temp = 0.0;


    for (int i = 0; i < N; i++){
        nu_max_temp = (N_He/Volume)*elastic[i] * sqrt(2.0*(i*bin_width + bin_width/2.0)*q/m_e);
        file7 << (i+0.5)*bin_width << " " << nu_max_temp << "\n";
        if (nu_max_temp > nu_max)
            nu_max = nu_max_temp;
    }
    // -----calculating nu-max for null-collision method ends ------------////

    //----- calculating nu-average from our electron distribution starts---------///
    for (int i = 0; i < N; i++){
        double bin_center = Emin + (i + 0.5) * bin_width;
        file9 << bin_center << " " << (N_He/Volume)*elastic[i] * sqrt(2.0*bin_center*q/m_e)*static_cast<double>(histo_random[i])/(electrons.size()*bin_width) << "\n";
    }
    //----- calculating nu-average from our electron distribution ends ---------///

    double dt = 0.1/nu_max;   // minimum should be 0.1/nu_max to get acceptable numerical error range see Vahedi Surrendra 1995
    double steps = static_cast<int>(time/dt);

//    std::cout << steps << "\n";

    //using  null-collision technique, getting the number of particles colliding each step: P_collision = 1 - exp(-nu_max*dt)

    int Ne_collided = (1.0-exp(-1.0*dt*nu_max))*n_e;

//    int Ne_collided = n_e*0.98;  // in case I want to check smth


    // Generate shuffled list of electron indices
    std::vector<int> electron_indices(n_e);
    std::iota(electron_indices.begin(), electron_indices.end(), 0); // fill with index
    std::shuffle(electron_indices.begin(), electron_indices.end(), gen); // shuffle the indexes
    int reshuffle_interval = 1;
    int print_interval = 100;

    for (int t = 0; t < steps; t++){

        std::cout << "timestep remains: " << steps - t << "\n";

        //reshuffle the indices
        if (t % reshuffle_interval == 0) {
            std::shuffle(electron_indices.begin(), electron_indices.end(), gen);
        }

        // setting flags to false each timestep
        for (auto& e : electrons) e.collided = false;

        int collision_counter = 0;


        for (int idx : electron_indices) {

            if (collision_counter >= Ne_collided) break; // quit if reached all collisions

            Electron& e = electrons[idx];
            if (e.collided) continue;  // Skip already collided electrons

            double electron_energy = e.energy;
            int bin_energy = static_cast<int>(electron_energy / bin_width);
            double nu_elastic = (N_He/Volume) * elastic[bin_energy] * sqrt(2.0*electron_energy*q/m_e);

            if (dis(gen) < nu_elastic/nu_max) {

                // ----   Collision energy redistribution module

                // electron particle X Y Z initial velocities and energy
                double V0_x = e.vx;
                double V0_y = e.vy;
                double V0_z = e.vz;
                double E_0 = e.energy;

                double V0 = sqrt(V0_x*V0_x + V0_y*V0_y + V0_z*V0_z);

                // generating random variables to calculate random direction of center-of-mass after the collision

                double R1 = dis(gen);
                double R2 = dis(gen);

                //// calculating spherical angles for center-of-mass random direction
                // double theta = acos(1.0- 2.0*R1);
                // double phi = 2*M_PI*R2;
                double cos_khi = (2.0 + E_0 - 2.0*pow((1+E_0), R1))/E_0;
                double sin_khi = sqrt(1.0 - cos_khi*cos_khi);

                double phi = 2.0*M_PI*R2;
                double cos_theta = V0_x/V0;
                double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
                // //calculating final relative velocity with random direction

                //calculating final velocity of electron

                double i_scat = (V0_x/V0)*cos_khi + (1.0 - (V0_x/V0)*(V0_x/V0))*(sin_khi*cos(phi)/sin_theta);
                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;
                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;

                //updating electron energy and velocities

                double delta_E = (2*m_e/M_n)*(1-cos_khi)*e.energy;

                if (delta_E < e.energy)
                    e.energy = E_0 - delta_E;
                else
                    e.energy = E_0;

                double speed = sqrt(2*e.energy*q/m_e);

                e.vx = speed*i_scat;
                e.vy = speed*j_scat;
                e.vz = speed*k_scat;

                collision_counter++;

                e.collided = true;
            }
        }
                if (t%print_interval == 0){
                // open datafiles to write each time step to see evolution
                std::ostringstream filename;
                filename << "data/distribution_" << std::setw(4) << std::setfill('0') << t << ".dat";

                std::ofstream file(filename.str());
                if (!file.is_open()){
                std::cerr << "Error opening file: " << filename.str() << std::endl;
                return 1;
                }
                // end opening datafiles for each timestep

                // creating histogram each timestep
                for (int i = 0; i < n_e; i++){
                    int bin = (int)( (electrons[i].energy - Emin)/bin_width );
                    if (bin >=0 && bin < N)
                    histo_maxwell[bin]++;
                }

                // writing data each time step
                for (int i = 0; i < N; i++){
                    double bin_center = Emin + (i + 0.5) * bin_width;
                    file << bin_center << " " <<  static_cast<double>(histo_maxwell[i])/(electrons.size()*bin_width) << "\n"; // later need to divide by total partcles number to get normalized distribution
                    histo_maxwell[i] = 0;
                }

                file.close();
                // end writing data each timestep
            }

            // calculating mean energy
            double total_energy = 0.0;
            for (const auto& e : electrons) total_energy += e.energy;
            double mean_energy = total_energy / n_e;
            file8 << t*dt << " " << mean_energy << "\n";
    }


    for (int i = 0; i < n_e; i++){

        file2 << i << " " << electrons[i].energy << "\n";

        int bin = (int)( (electrons[i].energy - Emin)/bin_width );
        if (bin >=0 && bin < histo_maxwell.size())
            histo_maxwell[bin]++;
    }

    int check = 0;
    for (int i = 0; i < histo_maxwell.size(); i++){
        check += histo_maxwell[i];
        double bin_center = Emin + (i + 0.5) * bin_width;
        file4 << bin_center << " " <<  bin_center*static_cast<double>(histo_maxwell[i])/(electrons.size()*bin_width) << "\n"; // getting f(E)*E
    }
    std::cout << "Total # of electrons in histo: " << check << "\n";


    file0.close();
    file1.close();
    file2.close();
    file3.close();
    file4.close();
    file5.close();
    file6.close();
    file7.close();
    file8.close();
    file9.close();

    clock_t end = clock();

    double elapsed = (double)(end - start) / CLOCKS_PER_SEC;

    std::cout << "Ne collided each timesteps:" << Ne_collided << "\n";
    std::cout << "Energies written successfuly\n";
    std::cout << "Elapsed time: %f seconds " << elapsed << "\n";
    std::cout << "Nu_max: " << nu_max << "\n";


    return 0;

}