main.cpp

Go to the documentation of this file.

 
#include <cmath>
#include <complex>
#include <fstream>
#include <omp.h>
#include <string>
#include <vector>
 
#include "PenningTrap.hpp"
#include "utils.hpp"
 
#define PARTICLES 100
#define N 40000
#define CHARGE 1. // unit: e
#define MASS 40.  // unit: amu
 
// Particles used for testing
Particle p1(CHARGE, MASS, vec_3d{20., 0., 20.}, vec_3d{0., 25., 0.}); 
Particle p2(CHARGE, MASS, vec_3d{25., 25., 0.}, vec_3d{0., 40., 5.}); 
 
vec_3d analytical_solution_particle_1(double t)
{
    double w_0 = T / MASS;
    double w_z2 = (50. * V / 1000.) / (MASS * 500. * 500.);
    double w_p = (w_0 + std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;
    double w_n = (w_0 - std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;
    double A_p = (25. + w_n * 20.) / (w_n - w_p);
    double A_n = -(25. + w_p * 20.) / (w_n - w_p);
    std::complex<double> f =
        A_p * std::exp(std::complex<double>(0., -w_p * t)) +
        A_n * std::exp(std::complex<double>(0., -w_n * t));
    vec_3d res{std::real(f), std::imag(f), 20. * std::cos(std::sqrt(w_z2) * t)};
    return res;
}
 
void simulate_single_particle()
{
    // Initialize trap with particle 1
    PenningTrap trap(std::vector<Particle>{p1});
 
    double time = 50.; // microseconds
 
    // Simulate and write results to file
    trap.write_simulation_to_dir("output/simulate_single_particle", time, N,
                                 "rk4", false);
}
 
void simulate_two_particles()
{
    // Initialize traps with particles
    PenningTrap trap_no_interaction(std::vector<Particle>{p1, p2});
    PenningTrap trap_with_interaction(std::vector<Particle>{p1, p2});
 
    double time = 50.; // microseconds
 
    // Simulate and write results to files
    trap_no_interaction.write_simulation_to_dir(
        "output/simulate_2_particles/no_interaction", time, N, "rk4", false);
    trap_with_interaction.write_simulation_to_dir(
        "output/simulate_2_particles/with_interaction", time, N);
}
 
void simulate_single_particle_with_different_steps()
{
    double time = 50.; // microseconds
 
    std::ofstream ofile;
 
    // Calculate relative error for RK4
    std::string path = "output/relative_error/RK4/";
    mkpath(path);
    for (int i = 0; i < 4; i++) {
        int steps = 4000 * std::pow(2, i);
        double dt = time / (double)steps;
        ofile.open(path + std::to_string(steps) + "_steps.txt");
        PenningTrap trap(std::vector<Particle>{p1});
        simulation_t res = trap.simulate(time, steps, "rk4", false);
        for (int i = 0; i < steps; i++) {
            ofile << arma::norm(res.r_vecs[0][i] -
                                analytical_solution_particle_1(dt*i))
                  << "\n";
        }
        ofile.close();
    }
 
    // Calculate relative error for forward Euler
    path = "output/relative_error/euler/";
    mkpath(path);
    for (int i = 0; i < 4; i++) {
        int steps = 4000 * std::pow(2, i);
        double dt = time / (double)steps;
        ofile.open(path + std::to_string(steps) + "_steps.txt");
        PenningTrap trap(std::vector<Particle>{p1});
        simulation_t res = trap.simulate(time, steps, "euler", false);
        for (int i = 0; i < steps; i++) {
            ofile << arma::norm(res.r_vecs[0][i] -
                                analytical_solution_particle_1(dt*i))
                  << "\n";
        }
        ofile.close();
    }
}
 
void simulate_100_particles()
{
    PenningTrap trap((unsigned)100);
 
    double time = 50.; // microseconds
 
    trap.write_simulation_to_dir("output/simulate_100_particles", time, N);
}
 
void simulate_100_particles_with_time_potential()
{
    double time = 500.;
 
    double amplitudes[]{.1, .4, .7};
 
    double freq_start = .2;
    double freq_end = 2.5;
    double freq_increment = .02;
    size_t freq_iterations = (size_t)((freq_end - freq_start) / freq_increment);
 
    double res[4][freq_iterations];
 
    std::string path = "output/time_dependent_potential/";
    mkpath(path);
 
    std::ofstream ofile;
 
    double freq = freq_start;
    for (size_t i = 0; i < freq_iterations; i++) {
        res[0][i] = freq;
        freq += freq_increment;
    }
 
#pragma omp parallel for collapse(2) num_threads(4)
    for (size_t i = 0; i < 3; i++) {
        for (size_t j = 0; j < freq_iterations; j++) {
            PenningTrap trap(
                (unsigned)100, T,
                std::bind(
                    [](double f, double r, double t) {
                        return (25. * V / 1000.) * (1. + f * std::cos(r * t));
                    },
                    amplitudes[i], res[0][j], std::placeholders::_1),
                500., 0.);
            res[i + 1][j] =
                trap.fraction_of_particles_left(time, N, "rk4", false);
        }
    }
 
    ofile.open(path + "res.txt");
    for (size_t i = 0; i < freq_iterations; i++) {
        ofile << res[0][i] << "," << res[1][i] << "," << res[2][i] << ","
              << res[3][i] << "\n";
    }
    ofile.close();
}
 
int main()
{
    double t0 = omp_get_wtime();
 
    // simulate_single_particle();
 
    // simulate_two_particles();
 
     simulate_single_particle_with_different_steps();
 
    double t1 = omp_get_wtime();
 
    simulate_100_particles();
 
    //simulate_100_particles_with_time_potential();
 
    double end = omp_get_wtime();
 
    std::cout << "Time: " << (end - t1) << " seconds" << std::endl;
 
    return 0;
}