Thermalization

#include <iostream>
#include <random>
#include <fstream>
#include <math.h>

#define n_e 50000
#define V_0 30000.0     // max velocity using to generate random distribution ---- doesn't work -> produces skew distribution???
#define Emin 0.0
#define Emax 100.0
#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 1.6E-19 // elementary charge
#define N ( (int)((Emax-Emin)/bin_width) + 1 ) // add 1 to include E_max
#define P 0.5
#define steps 10000

int main() {

    double electron_vel[3*n_e];
    double electron_e[n_e];
    int histo_random[N] = {0};
    int histo_maxwell[N] = {0};
    bool collided[n_e] = {0};
    bool paired[n_e] = {0};
    double collisionProbability = 0.5;


    for (int i = 0; i < 3*n_e; i++){
        electron_vel[i] = 0.0;
    }

    for (int i = 0; i < n_e; i++){
        electron_e[i] = 0.0;
    }


    std::ofstream file("velocities.dat");
    if (!file.is_open()) {
        std::cerr << "Error opening file!" << std::endl;
        return 1;
    }

    std::ofstream file1("energies.dat");
    if (!file.is_open()) {
        std::cerr << "Error opening file!" << std::endl;
        return 1;
    }

    std::ofstream file2("energies_redistribute.dat");
    if (!file.is_open()) {
        std::cerr << "Error opening file!" << std::endl;
        return 1;
    }

    std::ofstream file3("histo_random.dat");
    if (!file.is_open()) {
        std::cerr << "Error opening file!" << std::endl;
        return 1;
    }

    std::ofstream file4("histo_maxwell.dat");
    if (!file.is_open()) {
        std::cerr << "Error opening file!" << std::endl;
        return 1;
    }

    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_real_distribution<double> dis(0.0, 1.0);

    std::random_device rd1;
    std::mt19937 gen1(rd1());
    std::uniform_int_distribution<int> pair(0, n_e-1);



    for (int i = 0; i < 3*n_e; i = i + 3){

        double phi = 2*M_PI*dis(gen);
        double sinTheta = dis(gen);
        double cosTheta = sqrt(1.0 - sinTheta*sinTheta);

        double energy = Emax*dis(gen);
        double speed = sqrt(2*energy*k_b/m_e);

        electron_vel[i] = speed * sinTheta * cos(phi); // x component
        electron_vel[i+1] = speed * sinTheta * sin(phi); // y component
        electron_vel[i+2] = speed * cosTheta; // z component

//        energy = (electron_vel[i]*electron_vel[i] + electron_vel[i+1]*electron_vel[i+1] + electron_vel[i+2]*electron_vel[i+2]) * m_e / (2.0*k_b);

        electron_e[i/3] = energy;

        file << electron_vel[i] << " " << electron_vel[i+1] << " " << electron_vel[i+2]  << "\n";

        file1 << i/3 << " " << electron_e[i/3] << "\n";
//        file2 << i/3 << " " << energy << "\n";

        energy = 0.0;
    }

    for (int i = 0; i < n_e; i++){
        int bin = (int)( (electron_e[i] - Emin)/bin_width );
        if (bin >=0 && bin < N)
            histo_random[bin]++;
    }

    for (int i = 0; i < N; i++){
        double bin_start = Emin + i*bin_width;
//        printf("%5.1f - %5.1f\t%d\n", bin_start, bin_start + bin_width, histo_random[i]);
        file3 << i*bin_width << " " <<  histo_random[i] << "\n";
    }


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

        // setting flags to false each timestep
        for (int j = 0; j < n_e; j++){
            collided[j] = false;
        }

        for (int i = 0 ; i < n_e; i++){
            if (dis(gen) < P) {
                int partner = -1;
                int attempts = 0;

                while (attempts < n_e){
                    int candidate = pair(gen1);
                    if (candidate != i && !collided[candidate]){
                        partner = candidate;
                        break;
                    }
                    attempts++;
                }

                if (partner != -1) {
                    collided[i] = true;
                    collided[partner] = true;
                }

                // //Collision energy redistribution

                // double totalEnergy = electron_e[i] + electron_e[partner];
                // double fraction = dis(gen);
                // electron_e[i] = totalEnergy*fraction;
                // electron_e[partner] = totalEnergy*(1.0 - fraction);

                // first particle X Y Z initial velocities
                double V0_x_1 = electron_vel[i*3 + 0];
                double V0_y_1 = electron_vel[i*3 + 1];
                double V0_z_1 = electron_vel[i*3 + 2];

                // second particle X Y Z initial velocities
                double V0_x_2 = electron_vel[partner*3 + 0];
                double V0_y_2 = electron_vel[partner*3 + 1];
                double V0_z_2 = electron_vel[partner*3 + 2];

                // initial relative velocity X Y Z (must be equal to final relative velocity in center-of-mass frame)

                double V0_rel_x = (V0_x_1 - V0_x_2)/2.0;
                double V0_rel_y = (V0_y_1 - V0_y_2)/2.0;
                double V0_rel_z = (V0_z_1 - V0_z_2)/2.0;

                double V0_rel = sqrt(V0_rel_x*V0_rel_x + V0_rel_y*V0_rel_y + V0_rel_z*V0_rel_z);

                // center-of-mass frame initial velocity (magnitude of it must be equal to the counterpart in this frame)

                double V_cm_x = (V0_x_1 + V0_x_2)/2.0;
                double V_cm_y = (V0_y_1 + V0_y_2)/2.0;
                double V_cm_z = (V0_z_1 + V0_z_2)/2.0;

                double V_cm = sqrt(V_cm_x*V_cm_x + V_cm_y*V_cm_y + V_cm_z*V_cm_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;

                //calculating final relative velocity with random direction

                double V_rel_x = V0_rel*sin(theta)*cos(phi);
                double V_rel_y = V0_rel*sin(theta)*sin(phi);
                double V_rel_z = V0_rel*cos(theta);

                double V_rel = sqrt(V_rel_x*V_rel_x + V_rel_y*V_rel_y + V_rel_z*V_rel_z);

                //calculating final velocity of first particle

                double V_x_1 = V_cm_x + V_rel_x/2.0;
                double V_y_1 = V_cm_y + V_rel_y/2.0;
                double V_z_1 = V_cm_z + V_rel_z/2.0;

                double V_1 = sqrt(V_x_1*V_x_1 + V_y_1*V_y_1 + V_z_1*V_z_1);

                //calculating final velocity of second particle

                double V_x_2 = V_cm_x - V_rel_x/2.0;
                double V_y_2 = V_cm_y - V_rel_y/2.0;
                double V_z_2 = V_cm_z - V_rel_z/2.0;

                double V_2 = sqrt(V_x_2*V_x_2 + V_y_2*V_y_2 + V_z_2*V_z_2);\

                // calculating final energies of first and second colliding particles

                electron_e[i] = V_1*V_1*m_e/(2.0*k_b);
                electron_e[partner] = V_2*V_2*m_e/(2.0*k_b);

            }
        }
    }

    for (int i = 0; i < n_e; i++){
        int bin = (int)( (electron_e[i] - Emin)/bin_width );
        if (bin >=0 && bin < N)
            histo_maxwell[bin]++;
    }

    for (int i = 0; i < N; i++){
        double bin_start = Emin + i*bin_width;
//        printf("%5.1f - %5.1f\t%d\n", bin_start, bin_start + bin_width, histo_maxwell[i]);
        file4 << i*bin_width << " " <<  histo_maxwell[i] << "\n";
    }


    file.close();
    file1.close();
    file2.close();
    file3.close();
    file4.close();

    std::cout << "Energies written successfuly\n";


    return 0;


}