.TH "PenningTrap" 3 "Sat Oct 14 2023" "Penning Trap Simulation" \" -*- nroff -*-
.ad l
.nh
.SH NAME
PenningTrap \- A class that simulates a Penning trap\&.  

.SH SYNOPSIS
.br
.PP
.PP
\fC#include <PenningTrap\&.hpp>\fP
.SS "Public Member Functions"

.in +1c
.ti -1c
.RI "\fBPenningTrap\fP (double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
.br
.RI "Constructor for the \fBPenningTrap\fP class\&. "
.ti -1c
.RI "\fBPenningTrap\fP (unsigned int i, double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
.br
.RI "Constructor for the \fBPenningTrap\fP class\&. "
.ti -1c
.RI "\fBPenningTrap\fP (std::vector< \fBParticle\fP > \fBparticles\fP, double \fBB_0\fP=\fBT\fP, std::function< double(double)> \fBV_0\fP=[](double \fBt\fP) { return 25\&. *\fBV\fP/1000\&.;}, double \fBd\fP=500\&., double \fBt\fP=0\&.)"
.br
.RI "Constructor for the \fBPenningTrap\fP class\&. "
.ti -1c
.RI "void \fBadd_particle\fP (\fBParticle\fP particle)"
.br
.RI "Add a particle to the system\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBexternal_E_field\fP (\fBvec_3d\fP r)"
.br
.RI "Calculate E at point r\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBexternal_B_field\fP (\fBvec_3d\fP r)"
.br
.RI "Calculate B at point r\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBforce_on_particle\fP (unsigned int i, unsigned int j)"
.br
.RI "Calculate the force between 2 particles\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBtotal_force_external\fP (unsigned int i)"
.br
.RI "Calculate the total external force on a particle\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBtotal_force_particles\fP (unsigned int i)"
.br
.RI "Calculate the total force on a particle p_i from other particles\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBtotal_force\fP (unsigned int i)"
.br
.RI "calculate the total force on a particle p_i\&. "
.ti -1c
.RI "void \fBevolve_RK4\fP (double dt, bool particle_interaction=true)"
.br
.RI "Go forward one timestep using the RK4 method\&. "
.ti -1c
.RI "void \fBevolve_forward_euler\fP (double dt, bool particle_interaction=true)"
.br
.RI "Go forward one timestep using the forward Euler method\&. "
.ti -1c
.RI "\fBsim_arr\fP \fBsimulate\fP (double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
.br
.RI "Simulate the particle system inside the Penning trap over a certain amount of time\&. "
.ti -1c
.RI "void \fBwrite_simulation_to_dir\fP (std::string path, double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
.br
.RI "Simulate and write the displacement of all particles to files\&. "
.ti -1c
.RI "double \fBfraction_of_particles_left\fP (double time, unsigned int steps, std::string method='rk4', bool particle_interaction=true)"
.br
.RI "Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation\&. "
.in -1c
.SS "Private Member Functions"

.in +1c
.ti -1c
.RI "\fBvec_3d\fP \fBv_func\fP (unsigned int i, unsigned int j, double dt)"
.br
.RI "Helper for evolve_RK4 when calculating $k_{v,i,j}$ values\&. "
.ti -1c
.RI "\fBvec_3d\fP \fBr_func\fP (unsigned int i, unsigned int j, double dt)"
.br
.RI "Helper for evolve_RK4 when calculating $k_{r,i,j}$ values\&. "
.in -1c
.SS "Private Attributes"

.in +1c
.ti -1c
.RI "double \fBB_0\fP"
.br
.RI "Magnetic field strength\&. "
.ti -1c
.RI "std::function< double(double)> \fBV_0\fP"
.br
.RI "Applied potential\&. "
.ti -1c
.RI "double \fBd\fP"
.br
.RI "Characteristic dimension\&. "
.ti -1c
.RI "double \fBt\fP"
.br
.RI "Current time\&. "
.ti -1c
.RI "std::vector< \fBParticle\fP > \fBparticles\fP"
.br
.RI "The particles in the Penning trap\&. "
.ti -1c
.RI "\fBsim_arr\fP \fBk_v\fP"
.br
.ti -1c
.RI "\fBsim_arr\fP \fBk_r\fP"
.br
.in -1c
.SH "Detailed Description"
.PP 
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\&. 
.PP
Definition at line \fB30\fP of file \fBPenningTrap\&.hpp\fP\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "PenningTrap::PenningTrap (double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"

.PP
Constructor for the \fBPenningTrap\fP class\&. 
.PP
\fBParameters\fP
.RS 4
\fIB_0\fP The magnetic field strength 
.br
\fIV_0\fP The time dependent applied potential 
.br
\fId\fP The characteristic dimension 
.br
\fIt\fP The starting time 
.RE
.PP

.PP
Definition at line \fB18\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "PenningTrap::PenningTrap (unsigned int i, double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"

.PP
Constructor for the \fBPenningTrap\fP class\&. 
.PP
\fBParameters\fP
.RS 4
\fIi\fP The number of particles to generate 
.br
\fIB_0\fP The magnetic field strength 
.br
\fIV_0\fP The time dependent applied potential 
.br
\fId\fP The characteristic dimension 
.br
\fIt\fP The starting time 
.RE
.PP

.PP
Definition at line \fB27\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "PenningTrap::PenningTrap (std::vector< \fBParticle\fP > particles, double B_0 = \fC\fBT\fP\fP, std::function< double(double)> V_0 = \fC[](double \fBt\fP) { return 25\&. * \fBV\fP / 1000\&.; }\fP, double d = \fC500\&.\fP, double t = \fC0\&.\fP)"

.PP
Constructor for the \fBPenningTrap\fP class\&. 
.PP
\fBParameters\fP
.RS 4
\fIparticles\fP The starting particles 
.br
\fIB_0\fP The magnetic field strength 
.br
\fIV_0\fP The time dependent applied potential 
.br
\fId\fP The characteristic dimension 
.br
\fIt\fP The starting time 
.RE
.PP

.PP
Definition at line \fB39\fP of file \fBPenningTrap\&.cpp\fP\&.
.SH "Member Function Documentation"
.PP 
.SS "void PenningTrap::add_particle (\fBParticle\fP particle)"

.PP
Add a particle to the system\&. 
.PP
\fBParameters\fP
.RS 4
\fIparticle\fP The particle to add to the Penning trap 
.RE
.PP

.PP
Definition at line \fB82\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "void PenningTrap::evolve_forward_euler (double dt, bool particle_interaction = \fCtrue\fP)"

.PP
Go forward one timestep using the forward Euler method\&. 
.PP
\fBParameters\fP
.RS 4
\fIdt\fP The step length 
.br
\fIparticle_interaction\fP Turn particle interactions on/off 
.RE
.PP

.PP
Definition at line \fB186\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "void PenningTrap::evolve_RK4 (double dt, bool particle_interaction = \fCtrue\fP)"

.PP
Go forward one timestep using the RK4 method\&. 
.PP
\fBParameters\fP
.RS 4
\fIdt\fP The step length 
.br
\fIparticle_interaction\fP Turn particle interactions on/off 
.RE
.PP

.PP
Definition at line \fB151\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::external_B_field (\fBvec_3d\fP r)"

.PP
Calculate B at point r\&. 
.PP
\fBParameters\fP
.RS 4
\fIr\fP The position where we want to calculate the B field
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB95\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::external_E_field (\fBvec_3d\fP r)"

.PP
Calculate E at point r\&. 
.PP
\fBParameters\fP
.RS 4
\fIr\fP The position where we want to calculate the E field
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB87\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::force_on_particle (unsigned int i, unsigned int j)"

.PP
Calculate the force between 2 particles\&. Calculate the force exhibited on particle p_i from particle p_j\&.
.PP
\fBParameters\fP
.RS 4
\fIi\fP The index of particle p_i 
.br
\fIj\fP The index of particle p_j
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB100\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "double PenningTrap::fraction_of_particles_left (double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"

.PP
Simulate and calculate what fraction of particles are still left inside the Penning trap after the simulation\&. 
.PP
\fBParameters\fP
.RS 4
\fItime\fP The time to simulate in microseconds 
.br
\fIsteps\fP The amount of steps for the whole simulation 
.br
\fImethod\fP The method to use when moving forward a timestep 
.br
\fIparticle_interaction\fP Turn particle interactions on/off
.RE
.PP
\fBReturns\fP
.RS 4
double 
.RE
.PP

.PP
Definition at line \fB266\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::r_func (unsigned int i, unsigned int j, double dt)\fC [private]\fP"

.PP
Helper for evolve_RK4 when calculating $k_{r,i,j}$ values\&. Something
.PP
\fBParameters\fP
.RS 4
\fIi\fP Index i for $k_{r,i,j}$ 
.br
\fIj\fP Index j for $k_{r,i,j}$ 
.br
\fIdt\fP the step length (delta time)
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB64\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBsim_arr\fP PenningTrap::simulate (double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"

.PP
Simulate the particle system inside the Penning trap over a certain amount of time\&. 
.PP
\fBParameters\fP
.RS 4
\fItime\fP The time to simulate in microseconds 
.br
\fIsteps\fP The amount of steps for the whole simulation 
.br
\fImethod\fP The method to use when moving forward a timestep 
.br
\fIparticle_interaction\fP Turn particle interactions on/off 
.RE
.PP

.PP
Definition at line \fB211\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::total_force (unsigned int i)"

.PP
calculate the total force on a particle p_i\&. 
.PP
\fBParameters\fP
.RS 4
\fIi\fP The index of particle p_i
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB146\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::total_force_external (unsigned int i)"

.PP
Calculate the total external force on a particle\&. Calculate the total amount of force that E and B exhibits on particle p_i\&.
.PP
\fBParameters\fP
.RS 4
\fIi\fP The index of particle p_i
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::total_force_particles (unsigned int i)"

.PP
Calculate the total force on a particle p_i from other particles\&. 
.PP
\fBParameters\fP
.RS 4
\fIi\fP The index of particle p_i
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB129\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "\fBvec_3d\fP PenningTrap::v_func (unsigned int i, unsigned int j, double dt)\fC [private]\fP"

.PP
Helper for evolve_RK4 when calculating $k_{v,i,j}$ values\&. Something
.PP
\fBParameters\fP
.RS 4
\fIi\fP Index i for $k_{v,i,j}$ 
.br
\fIj\fP Index j for $k_{v,i,j}$ 
.br
\fIdt\fP the step length (delta time)
.RE
.PP
\fBReturns\fP
.RS 4
vec_3d 
.RE
.PP

.PP
Definition at line \fB46\fP of file \fBPenningTrap\&.cpp\fP\&.
.SS "void PenningTrap::write_simulation_to_dir (std::string path, double time, unsigned int steps, std::string method = \fC'rk4'\fP, bool particle_interaction = \fCtrue\fP)"

.PP
Simulate and write the displacement of all particles to files\&. 
.PP
\fBParameters\fP
.RS 4
\fIpath\fP The directory to save the data 
.br
\fItime\fP The time to simulate in microseconds 
.br
\fIsteps\fP The amount of steps for the whole simulation 
.br
\fImethod\fP The method to use when moving forward a timestep 
.br
\fIparticle_interaction\fP Turn particle interactions on/off 
.RE
.PP

.PP
Definition at line \fB240\fP of file \fBPenningTrap\&.cpp\fP\&.
.SH "Member Data Documentation"
.PP 
.SS "double PenningTrap::B_0\fC [private]\fP"

.PP
Magnetic field strength\&. 
.PP
Definition at line \fB32\fP of file \fBPenningTrap\&.hpp\fP\&.
.SS "double PenningTrap::d\fC [private]\fP"

.PP
Characteristic dimension\&. 
.PP
Definition at line \fB34\fP of file \fBPenningTrap\&.hpp\fP\&.
.SS "\fBsim_arr\fP PenningTrap::k_r\fC [private]\fP"
A 2D vector containing all $k_{i,j}$ where $j$ is the index of a particle 
.PP
Definition at line \fB39\fP of file \fBPenningTrap\&.hpp\fP\&.
.SS "\fBsim_arr\fP PenningTrap::k_v\fC [private]\fP"
A 2D vector containing all $k_{i,j}$ where $j$ is the index of a particle 
.PP
Definition at line \fB37\fP of file \fBPenningTrap\&.hpp\fP\&.
.SS "std::vector<\fBParticle\fP> PenningTrap::particles\fC [private]\fP"

.PP
The particles in the Penning trap\&. 
.PP
Definition at line \fB36\fP of file \fBPenningTrap\&.hpp\fP\&.
.SS "double PenningTrap::t\fC [private]\fP"

.PP
Current time\&. 
.PP
Definition at line \fB35\fP of file \fBPenningTrap\&.hpp\fP\&.
.SS "std::function<double(double)> PenningTrap::V_0\fC [private]\fP"

.PP
Applied potential\&. 
.PP
Definition at line \fB33\fP of file \fBPenningTrap\&.hpp\fP\&.

.SH "Author"
.PP 
Generated automatically by Doxygen for Penning Trap Simulation from the source code\&.