A class that simulates a Penning trap. More...

#include <PenningTrap.hpp>

Public Member Functions
	PenningTrap (double B_0=T, double V_0=(25. *V)/1000., double d=500., double t=0.)
	Constructor for the PenningTrap class.

	PenningTrap (uint i, double B_0=T, double V_0=(25. *V)/1000., double d=500., double t=0.)
	Constructor for the PenningTrap class.

	PenningTrap (std::vector< Particle > particles, double B_0=T, double V_0=(25. *V)/1000., double d=500., double t=0.)
	Constructor for the PenningTrap class.

void	set_pertubation (double f, double omega_V)
	Time dependent perturbation to V_0.

void	reinitialize (double f, double omega_V, double t=0.)
	Give all particles new positions and velocities, and change t and V_0.

void	add_particle (Particle particle)
	Add a particle to the system.

void	evolve_RK4 (double dt, bool particle_interaction=true)
	Go forward one timestep using the RK4 method.

void	evolve_forward_euler (double dt, bool particle_interaction=true)
	Go forward one timestep using the forward Euler method.

simulation_t	simulate (double time, uint steps, std::string method="rk4", bool particle_interaction=true)
	Simulate the particle system inside the Penning trap over a certain amount of time.

void	write_simulation_to_dir (std::string path, double time, uint steps, std::string method="rk4", bool particle_interaction=true)
	Simulate and write the displacement of all particles to files.

double	fraction_of_particles_left (double time, uint 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 simulation.

Private Member Functions
vec3	v_func (uint i, uint j, double dt)
	Helper for evolve_RK4 when calculating \(k_{v,i,j}\) values.

vec3	r_func (uint i, uint j, double dt)
	Helper for evolve_RK4 when calculating \(k_{r,i,j}\) values.

vec3	external_E_field (vec3 r)
	Calculate E at point r.

vec3	external_B_field (vec3 r)
	Calculate B at point r.

vec3	force_on_particle (uint i, uint j)
	Calculate the force between 2 particles.

vec3	total_force_external (uint i)
	Calculate the total external force on a particle.

vec3	total_force_particles (uint i)
	Calculate the total force on a particle p_i from other particles.

vec3	total_force (uint i)
	calculate the total force on a particle p_i.

vec3	total_force_no_interaction (uint i)
	calculate the total force on a particle p_i without interaction

Private Attributes
double	B_0
	Magnetic field strength.

double	V_0
	Applied potential.

std::function< double(double)>	perturbation
	Time-dependent perturbation.

double	d
	Characteristic dimension.

double	t
	Current time.

std::vector< Particle >	particles
	The particles in the Penning trap.

sim_arr	k_v
	A 2D vector containing all \(k_{v,i,j}\) where \(j\) is the index of a particle.

sim_arr	k_r
	A 2D vector containing all \(k_{r,i,j}\) where \(j\) is the index of a particle.

Friends
class	PenningTrapTest
	Make PenningTrapTest a friend of PenningTrap.

Detailed Description

A class that simulates a Penning trap.

This class simulates a Penning trap. It can take in a number of particles and simulate how they would behave inside a Penning trap.

Definition at line 31 of file PenningTrap.hpp.

Constructor & Destructor Documentation

◆ PenningTrap() [1/3]

PenningTrap::PenningTrap	(	double	B_0 = `T`,
		double	V_0 = `(25. * V) / 1000.`,
		double	d = `500.`,
		double	t = `0.`
	)

Constructor for the PenningTrap class.

Parameters

B_0	The magnetic field strength
V_0	The time dependent applied potential
d	The characteristic dimension
t	The starting time

Definition at line 120 of file PenningTrap.cpp.

◆ PenningTrap() [2/3]

PenningTrap::PenningTrap	(	uint	i,
		double	B_0 = `T`,
		double	V_0 = `(25. * V) / 1000.`,
		double	d = `500.`,
		double	t = `0.`
	)

Constructor for the PenningTrap class.

Parameters

i	The number of particles to generate
B_0	The magnetic field strength
V_0	The time dependent applied potential
d	The characteristic dimension
t	The starting time

Definition at line 129 of file PenningTrap.cpp.

◆ PenningTrap() [3/3]

PenningTrap::PenningTrap	(	std::vector< Particle >	particles,
		double	B_0 = `T`,
		double	V_0 = `(25. * V) / 1000.`,
		double	d = `500.`,
		double	t = `0.`
	)

Constructor for the PenningTrap class.

Parameters

particles	The starting particles
B_0	The magnetic field strength
V_0	The time dependent applied potential
d	The characteristic dimension
t	The starting time

Definition at line 139 of file PenningTrap.cpp.

Member Function Documentation

◆ add_particle()

void PenningTrap::add_particle ( Particle particle )

Add a particle to the system.

Parameters

particle The particle to add to the Penning trap

Definition at line 166 of file PenningTrap.cpp.

◆ evolve_forward_euler()

void PenningTrap::evolve_forward_euler	(	double	dt,
		bool	particle_interaction = `true`
	)

Go forward one timestep using the forward Euler method.

Parameters

dt	The step length
particle_interaction	Turn particle interactions on/off

Definition at line 211 of file PenningTrap.cpp.

◆ evolve_RK4()

void PenningTrap::evolve_RK4	(	double	dt,
		bool	particle_interaction = `true`
	)

Go forward one timestep using the RK4 method.

Parameters

dt	The step length
particle_interaction	Turn particle interactions on/off

Definition at line 171 of file PenningTrap.cpp.

◆ external_B_field()

vec3 PenningTrap::external_B_field ( vec3 r )

private

Calculate B at point r.

Parameters

r	The position where we want to calculate the B field

Returns: vec3

Definition at line 67 of file PenningTrap.cpp.

◆ external_E_field()

vec3 PenningTrap::external_E_field ( vec3 r )

private

Calculate E at point r.

Parameters

r	The position where we want to calculate the E field

Returns: vec3

Definition at line 59 of file PenningTrap.cpp.

◆ force_on_particle()

vec3 PenningTrap::force_on_particle	(	uint	i,
		uint	j
	)

private

Calculate the force between 2 particles.

Calculate the force exhibited on particle p_i from particle p_j.

Parameters

i	The index of particle p_i
j	The index of particle p_j

Returns: vec3

Definition at line 72 of file PenningTrap.cpp.

◆ fraction_of_particles_left()

double PenningTrap::fraction_of_particles_left	(	double	time,
		uint	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 simulation.

Parameters

time	The time to simulate in microseconds
steps	The amount of steps for the whole simulation
method	The method to use when moving forward a timestep
particle_interaction	Turn particle interactions on/off

Returns: double

Definition at line 311 of file PenningTrap.cpp.

◆ r_func()

vec3 PenningTrap::r_func	(	uint	i,
		uint	j,
		double	dt
	)

private

Helper for evolve_RK4 when calculating \(k_{r,i,j}\) values.

Something

Parameters

i	Index i for \(k_{r,i,j}\)
j	Index j for \(k_{r,i,j}\)
dt	The step length (delta time)

Returns: vec3

Definition at line 40 of file PenningTrap.cpp.

◆ reinitialize()

void PenningTrap::reinitialize	(	double	f,
		double	omega_V,
		double	t = `0.`
	)

Give all particles new positions and velocities, and change t and V_0.

Parameters

V_0	The tiome dependent applied potential
t	The starting time

Definition at line 153 of file PenningTrap.cpp.

◆ set_pertubation()

void PenningTrap::set_pertubation	(	double	f,
		double	omega_V
	)

Time dependent perturbation to V_0.

Parameters

f	The amplitude of the perturbation @parma omega_V the angular frequency of the perturbation

Definition at line 146 of file PenningTrap.cpp.

◆ simulate()

simulation_t PenningTrap::simulate	(	double	time,
		uint	steps,
		std::string	method = `"rk4"`,
		bool	particle_interaction = `true`
	)

Simulate the particle system inside the Penning trap over a certain amount of time.

Parameters

time	The time to simulate in microseconds
steps	The amount of steps for the whole simulation
method	The method to use when moving forward a timestep
particle_interaction	Turn particle interactions on/off

Returns: simulation_t

Definition at line 240 of file PenningTrap.cpp.

◆ total_force()

vec3 PenningTrap::total_force ( uint i )

private

calculate the total force on a particle p_i.

Parameters

i	The index of particle p_i

Returns: vec3

Definition at line 104 of file PenningTrap.cpp.

◆ total_force_external()

vec3 PenningTrap::total_force_external ( uint i )

private

Calculate the total external force on a particle.

Calculate the total amount of force that E and B exhibits on particle p_i.

Parameters

i	The index of particle p_i

Returns: vec3

Definition at line 83 of file PenningTrap.cpp.

◆ total_force_no_interaction()

vec3 PenningTrap::total_force_no_interaction ( uint i )

private

calculate the total force on a particle p_i without interaction

Parameters

i	The index of particle p_i

Returns: vec3

Definition at line 112 of file PenningTrap.cpp.

◆ total_force_particles()

vec3 PenningTrap::total_force_particles ( uint i )

private

Calculate the total force on a particle p_i from other particles.

Parameters

i	The index of particle p_i

Returns: vec3

Definition at line 92 of file PenningTrap.cpp.

◆ v_func()

vec3 PenningTrap::v_func	(	uint	i,
		uint	j,
		double	dt
	)

private

Helper for evolve_RK4 when calculating \(k_{v,i,j}\) values.

Something

Parameters

i	Index i for \(k_{v,i,j}\)
j	Index j for \(k_{v,i,j}\)
dt	the step length (delta time)

Returns: vec3

Definition at line 21 of file PenningTrap.cpp.

◆ write_simulation_to_dir()

void PenningTrap::write_simulation_to_dir	(	std::string	path,
		double	time,
		uint	steps,
		std::string	method = `"rk4"`,
		bool	particle_interaction = `true`
	)

Simulate and write the displacement of all particles to files.

Parameters

path	The directory to save the data
time	The time to simulate in microseconds
steps	The amount of steps for the whole simulation
method	The method to use when moving forward a timestep
particle_interaction	Turn particle interactions on/off

Definition at line 273 of file PenningTrap.cpp.

Friends And Related Function Documentation

◆ PenningTrapTest

friend class PenningTrapTest

friend

Make PenningTrapTest a friend of PenningTrap.

Definition at line 35 of file PenningTrap.hpp.

Member Data Documentation

◆ B_0

double PenningTrap::B_0

private

Magnetic field strength.

Definition at line 37 of file PenningTrap.hpp.

◆ d

double PenningTrap::d

private

Characteristic dimension.

Definition at line 40 of file PenningTrap.hpp.

◆ k_r

sim_arr PenningTrap::k_r

private

A 2D vector containing all \(k_{r,i,j}\) where \(j\) is the index of a particle.

Definition at line 52 of file PenningTrap.hpp.

◆ k_v

sim_arr PenningTrap::k_v

private

A 2D vector containing all \(k_{v,i,j}\) where \(j\) is the index of a particle.

Definition at line 47 of file PenningTrap.hpp.

◆ particles

std::vector<Particle> PenningTrap::particles

private

The particles in the Penning trap.

Definition at line 42 of file PenningTrap.hpp.

◆ perturbation

std::function<double(double)> PenningTrap::perturbation

private

Time-dependent perturbation.

Definition at line 39 of file PenningTrap.hpp.

◆ t

double PenningTrap::t

private

Current time.

Definition at line 41 of file PenningTrap.hpp.

◆ V_0

double PenningTrap::V_0

private

Applied potential.

Definition at line 38 of file PenningTrap.hpp.

The documentation for this class was generated from the following files:

include/PenningTrap.hpp
src/PenningTrap.cpp

Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PenningTrap() [1/3]

◆ PenningTrap() [2/3]

◆ PenningTrap() [3/3]

Member Function Documentation

◆ add_particle()

◆ evolve_forward_euler()

◆ evolve_RK4()

◆ external_B_field()

◆ external_E_field()

◆ force_on_particle()

◆ fraction_of_particles_left()

◆ r_func()

◆ reinitialize()

◆ set_pertubation()

◆ simulate()

◆ total_force()

◆ total_force_external()

◆ total_force_no_interaction()

◆ total_force_particles()

◆ v_func()

◆ write_simulation_to_dir()

Friends And Related Function Documentation

◆ PenningTrapTest

Member Data Documentation

◆ B_0

◆ d

◆ k_r

◆ k_v

◆ particles

◆ perturbation

◆ t

◆ V_0