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

#include <PenningTrap.hpp>

Public Member Functions
	PenningTrap (double B_0=T, std::function< double(double)> V_0=[](double t) { return 25. *V/1000.;}, double d=500., double t=0.)
	Constructor for the PenningTrap class.

	PenningTrap (unsigned int i, double B_0=T, std::function< double(double)> V_0=[](double t) { return 25. *V/1000.;}, double d=500., double t=0.)
	Constructor for the PenningTrap class.

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

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

vec_3d	external_E_field (vec_3d r)
	Calculate E at point r.

vec_3d	external_B_field (vec_3d r)
	Calculate B at point r.

vec_3d	force_on_particle (unsigned int i, unsigned int j)
	Calculate the force between 2 particles.

vec_3d	total_force_external (unsigned int i)
	Calculate the total external force on a particle.

vec_3d	total_force_particles (unsigned int i)
	Calculate the total force on a particle p_i from other particles.

vec_3d	total_force (unsigned int i)
	calculate the total force on a particle p_i.

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, unsigned int 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, unsigned int 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, 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 simulation.

vec_3d	get_r (int i)

double	get_t ()

Private Member Functions
vec_3d	v_func (unsigned int i, unsigned int j, double dt)
	Helper for evolve_RK4 when calculating \(k_{v,i,j}\) values.

vec_3d	r_func (unsigned int i, unsigned int j, double dt)
	Helper for evolve_RK4 when calculating \(k_{r,i,j}\) values.

Private Attributes
double	B_0
	Magnetic field strength.

std::function< double(double)>	V_0
	Applied potential.

double	d
	Characteristic dimension.

double	t
	Current time.

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

sim_arr	k_v

sim_arr	k_r

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`,
		std::function< double(double)>	V_0 = `[](double t) { return 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 15 of file PenningTrap.cpp.

◆ PenningTrap() [2/3]

PenningTrap::PenningTrap	(	unsigned int	i,
		double	B_0 = `T`,
		std::function< double(double)>	V_0 = `[](double t) { return 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 24 of file PenningTrap.cpp.

◆ PenningTrap() [3/3]

PenningTrap::PenningTrap	(	std::vector< Particle >	particles,
		double	B_0 = `T`,
		std::function< double(double)>	V_0 = `[](double t) { return 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 36 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 79 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 183 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 148 of file PenningTrap.cpp.

◆ external_B_field()

vec_3d PenningTrap::external_B_field ( vec_3d r )

Calculate B at point r.

Parameters

r	The position where we want to calculate the B field

Returns: vec_3d

Definition at line 92 of file PenningTrap.cpp.

◆ external_E_field()

vec_3d PenningTrap::external_E_field ( vec_3d r )

Calculate E at point r.

Parameters

r	The position where we want to calculate the E field

Returns: vec_3d

Definition at line 84 of file PenningTrap.cpp.

◆ force_on_particle()

vec_3d PenningTrap::force_on_particle	(	unsigned int	i,
		unsigned int	j
	)

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: vec_3d

Definition at line 97 of file PenningTrap.cpp.

◆ fraction_of_particles_left()

double PenningTrap::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 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 281 of file PenningTrap.cpp.

◆ get_r()

vec_3d PenningTrap::get_r ( int i )

Definition at line 299 of file PenningTrap.cpp.

◆ get_t()

double PenningTrap::get_t ( )

Definition at line 304 of file PenningTrap.cpp.

◆ r_func()

vec_3d PenningTrap::r_func	(	unsigned int	i,
		unsigned int	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: vec_3d

Definition at line 61 of file PenningTrap.cpp.

◆ simulate()

simulation_t PenningTrap::simulate	(	double	time,
		unsigned int	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 212 of file PenningTrap.cpp.

◆ total_force()

vec_3d PenningTrap::total_force ( unsigned int i )

calculate the total force on a particle p_i.

Parameters

i	The index of particle p_i

Returns: vec_3d

Definition at line 140 of file PenningTrap.cpp.

◆ total_force_external()

vec_3d PenningTrap::total_force_external ( unsigned int i )

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: vec_3d

Definition at line 108 of file PenningTrap.cpp.

◆ total_force_particles()

vec_3d PenningTrap::total_force_particles ( unsigned int i )

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

Parameters

i	The index of particle p_i

Returns: vec_3d

Definition at line 123 of file PenningTrap.cpp.

◆ v_func()

vec_3d PenningTrap::v_func	(	unsigned int	i,
		unsigned int	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: vec_3d

Definition at line 43 of file PenningTrap.cpp.

◆ write_simulation_to_dir()

void PenningTrap::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.

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 246 of file PenningTrap.cpp.

Member Data Documentation

◆ B_0

double PenningTrap::B_0

private

Magnetic field strength.

Definition at line 33 of file PenningTrap.hpp.

◆ d

double PenningTrap::d

private

Characteristic dimension.

Definition at line 35 of file PenningTrap.hpp.

◆ k_r

sim_arr PenningTrap::k_r

private

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

Definition at line 40 of file PenningTrap.hpp.

◆ k_v

sim_arr PenningTrap::k_v

private

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

Definition at line 38 of file PenningTrap.hpp.

◆ particles

std::vector<Particle> PenningTrap::particles

private

The particles in the Penning trap.

Definition at line 37 of file PenningTrap.hpp.

◆ t

double PenningTrap::t

private

Current time.

Definition at line 36 of file PenningTrap.hpp.

◆ V_0

std::function<double(double)> PenningTrap::V_0

private

Applied potential.

Definition at line 34 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

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()

◆ get_r()

◆ get_t()

◆ r_func()

◆ simulate()

◆ total_force()

◆ total_force_external()

◆ total_force_particles()

◆ v_func()

◆ write_simulation_to_dir()

Member Data Documentation

◆ B_0

◆ d

◆ k_r

◆ k_v

◆ particles

◆ t

◆ V_0