# Penning Trap Simulation: src/main.cpp Source File

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main.cpp
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#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;
}
PenningTrap.hpp
A class for simulating a Penning trap.
Particle
A class that holds attributes of a particle.
Definition: Particle.hpp:21
PenningTrap
A class that simulates a Penning trap.
Definition: PenningTrap.hpp:31
PenningTrap::fraction_of_particles_left
double fraction_of_particles_left(double time, unsigned int steps, std::string method="rk4", bool particle_interaction=true)
Simulate and calculate what fraction of particles are still left inside the Penning trap after the si...
Definition: PenningTrap.cpp:281
PenningTrap::write_simulation_to_dir
void write_simulation_to_dir(std::string path, double time, unsigned int steps, std::string method="rk4", bool particle_interaction=true)
Simulate and write the displacement of all particles to files.
Definition: PenningTrap.cpp:246
T
#define T
1 Tesla. unit:
Definition: constants.hpp:17
V
#define V
1 Volt. unit:
Definition: constants.hpp:19
simulate_100_particles
void simulate_100_particles()
Simulate 100 particles over 50 .
Definition: main.cpp:131
simulate_100_particles_with_time_potential
void simulate_100_particles_with_time_potential()
Simulate 100 particles over 500 using a time dependent potential.
Definition: main.cpp:146
analytical_solution_particle_1
vec_3d analytical_solution_particle_1(double t)
The analytical solution for particle p1.
Definition: main.cpp:38
simulate_two_particles
void simulate_two_particles()
Simulate 2 particles over the period of 50 with and without particle interactions.
Definition: main.cpp:70
p1
Particle p1(CHARGE, MASS, vec_3d{20., 0., 20.}, vec_3d{0., 25., 0.})
Particle 1.
simulate_single_particle
void simulate_single_particle()
Simulate a single particle over the period of 50 .
Definition: main.cpp:55
p2
Particle p2(CHARGE, MASS, vec_3d{25., 25., 0.}, vec_3d{0., 40., 5.})
Particle 2.
simulate_single_particle_with_different_steps
void simulate_single_particle_with_different_steps()
Simulate a single particle over 50 using different amount of steps and different methods.
Definition: main.cpp:88
simulation
Typedef for PenningTrap::simulation return value.
Definition: typedefs.hpp:40
vec_3d
arma::vec::fixed< 3 > vec_3d
Typedef for a fixed 3d arma vector.
Definition: typedefs.hpp:36
utils.hpp
Function prototypes and macros that are useful.
mkpath
bool mkpath(std::string path, int mode=0777)
Make path given.
Definition: utils.cpp:74