Internal
Public APIs
TestParticle.BiMaxwellian — TypeType for BiMaxwellian velocity distributions with respect to the magnetic field.
TestParticle.BiMaxwellian — MethodBiMaxwellian(B::Vector{U}, u0::Vector{T}, ppar::T, pperp::T, n; m=mᵢ)Construct a BiMaxwellian distribution with magnetic field B, bulk velocity u0, parallel thermal pressure ppar, perpendicular thermal pressure pperp, and number density n in SI units. The default particle is proton.
TestParticle.Maxwellian — TypeType for Maxwellian velocity distributions.
TestParticle.Maxwellian — MethodMaxwellian(u0::Vector{T}, p::T, n; m=mᵢ)Construct a Maxwellian distribution with bulk velocity u0, thermal pressure p, and number density n in SI units. The default particle is proton.
TestParticle.prepare — Methodprepare(grid::CartesianGrid, E, B; kwargs...) -> (q2m, E, B)Return a tuple consists of particle charge-mass ratio for a prescribed species and interpolated EM field functions.
keywords
order::Int=1: order of interpolation in [1,2,3].bc::Int=1: type of boundary conditions, 1 -> NaN, 2 -> periodic.species::Species=Proton: particle species.q::AbstractFloat=1.0: particle charge. Only works whenSpecies=User.m::AbstractFloat=1.0: particle mass. Only works whenSpecies=User.prepare(grid::CartesianGrid, E, B, F; species=Proton, q=1.0, m=1.0) -> (q, m, E, B, F)
Return a tuple consists of particle charge, mass for a prescribed species of charge q and mass m, interpolated EM field functions, and external force F.
prepare(x::AbstractRange, y::AbstractRange, z::AbstractRange, E, B; kwargs...) -> (q2m, E, B)
+API · TestParticle.jl Internal
Public APIs
TestParticle.BiMaxwellian — TypeType for BiMaxwellian velocity distributions with respect to the magnetic field.
sourceTestParticle.BiMaxwellian — MethodBiMaxwellian(B::Vector{U}, u0::Vector{T}, ppar::T, pperp::T, n; m=mᵢ)
Construct a BiMaxwellian distribution with magnetic field B, bulk velocity u0, parallel thermal pressure ppar, perpendicular thermal pressure pperp, and number density n in SI units. The default particle is proton.
sourceTestParticle.Maxwellian — TypeType for Maxwellian velocity distributions.
sourceTestParticle.Maxwellian — MethodMaxwellian(u0::Vector{T}, p::T, n; m=mᵢ)
Construct a Maxwellian distribution with bulk velocity u0, thermal pressure p, and number density n in SI units. The default particle is proton.
sourceTestParticle.prepare — Methodprepare(grid::CartesianGrid, E, B; kwargs...) -> (q2m, E, B)
Return a tuple consists of particle charge-mass ratio for a prescribed species and interpolated EM field functions.
keywords
order::Int=1: order of interpolation in [1,2,3].
bc::Int=1: type of boundary conditions, 1 -> NaN, 2 -> periodic.
species::Species=Proton: particle species.
q::AbstractFloat=1.0: particle charge. Only works when Species=User.
m::AbstractFloat=1.0: particle mass. Only works when Species=User.
prepare(grid::CartesianGrid, E, B, F; species=Proton, q=1.0, m=1.0) -> (q, m, E, B, F)
Return a tuple consists of particle charge, mass for a prescribed species of charge q and mass m, interpolated EM field functions, and external force F.
prepare(x::AbstractRange, y::AbstractRange, z::AbstractRange, E, B; kwargs...) -> (q2m, E, B)
prepare(x, y, E, B; kwargs...) -> (q2m, E, B)
-prepare(x::AbstractRange, E, B; kwargs...) -> (q2m, E, B)
Direct range input for uniform grid in 2/3D is also accepted.
prepare(E, B; kwargs...) -> (q2m, E, B)
Return a tuple consists of particle charge-mass ratio for a prescribed species of charge q and mass m and analytic EM field functions. Prescribed species are Electron and Proton; other species can be manually specified with species=Ion/User, q and m.
prepare(E, B, F; kwargs...) -> (q, m, E, B, F)
Return a tuple consists of particle charge, mass for a prescribed species of charge q and mass m, analytic EM field functions, and external force F.
sourceTestParticle.sample — Methodsample(vdf::Maxwellian)
Sample a 3D velocity from a Maxwellian distribution vdf using the Box-Muller method.
sample(vdf::BiMaxwellian)
Sample a 3D velocity from a BiMaxwellian distribution vdf using the Box-Muller method.
sourceTestParticle.trace! — Methodtrace!(dy, y, p::TPTuple, t)
-trace!(dy, y, p::FullTPTuple, t)
ODE equations for charged particle moving in static EM field with in-place form.
ODE equations for charged particle moving in static EM field and external force field with in-place form.
sourceTestParticle.trace — Methodtrace(y, p::TPTuple, t) -> SVector{6, Float64}
-trace(y, p::FullTPTuple, t) -> SVector{6, Float64}
ODE equations for charged particle moving in static EM field with out-of-place form.
ODE equations for charged particle moving in static EM field and external force field with out-of-place form.
sourceTestParticle.trace_normalized! — Methodtrace_normalized!(dy, y, p::TPNormalizedTuple, t)
Normalized ODE equations for charged particle moving in static EM field with in-place form. If the field is in 2D X-Y plane, periodic boundary should be applied for the field in z via the extrapolation function provided by Interpolations.jl.
sourceTestParticle.trace_relativistic! — Methodtrace_relativistic!(dy, y, p::TPTuple, t)
ODE equations for relativistic charged particle moving in static EM field with in-place form.
sourceTestParticle.trace_relativistic — Methodtrace_relativistic(y, p::TPTuple, t) -> SVector{6, Float64}
ODE equations for relativistic charged particle moving in static EM field with out-of-place form.
sourceTestParticle.trace_relativistic_normalized! — Methodtrace_relativistic_normalized!(dy, y, p::TPNormalizedTuple, t)
Normalized ODE equations for relativistic charged particle moving in static EM field with in-place form.
sourcePrivate types and methods
TestParticle.AbstractTraceSolution — TypeAbstract type for tracing solutions.
sourceTestParticle.Field — TypeField{itd, F} <: AbstractField{itd}
A representation of a field function f, defined by:
time-independent field
\[\mathbf{F} = F(\mathbf{x}),\]
time-dependent field
\[\mathbf{F} = F(\mathbf{x}, t).\]
Arguments
field_function::Function: the function of field.itd::Bool: whether the field function is time dependent.F: the type of field_function.
sourceTestParticle.FullTPTuple — TypeThe type of parameter tuple for full test particle problem.
sourceTestParticle.Species — TypeType for the particles, Proton, Electron, Ion, or User.
sourceTestParticle.TPNormalizedTuple — TypeThe type of parameter tuple for normalized test particle problem.
sourceTestParticle.TPTuple — TypeThe type of parameter tuple for normal test particle problem.
sourceTestParticle.TraceSolution — MethodInterpolate solution at time x. Forward tracing only.
sourceTestParticle.VDF — TypeAbstract type for velocity distribution functions.
sourceTestParticle._boris! — MethodApply Boris method for particles with index in irange.
sourceTestParticle._prepare — MethodPrepare for advancing.
sourceTestParticle.cross! — MethodIn-place cross product.
sourceTestParticle.dipole — MethodCalculates the magnetic field from a dipole with magnetic moment M at r.
sourceTestParticle.dipole_fieldline — Functiondipole_fieldline(L, ϕ, nP)
Creates nP points on one field line of the magnetic field from a dipole. In a centered dipole magnetic field model, the path along a given L shell can be described as r = L*cos²λ, where r is the radial distance (in planetary radii) to a point on the line, λ is its co-latitude, and L is the L-shell of interest.
sourceTestParticle.getB_CS_harris — MethodgetB_CS_harris(B₀, L)
Return the magnetic field at location r near a current sheet with magnetic strength B₀ and sheet length L.
sourceTestParticle.getB_bottle — MethodgetB_bottle(x, y, z, distance, a, b, I1, I2) -> Vector{Float}
Get magnetic field from a magnetic bottle. Reference: https://en.wikipedia.org/wiki/Magneticmirror#Magneticbottles
Arguments
x,y,z::Float: particle coordinates in [m].distance::Float: distance between solenoids in [m].a::Float: radius of each side coil in [m].b::Float: radius of central coil in [m].I1::Float: current in the solenoid times number of windings in side coils.I2::Float: current in the central solenoid times number of windings in the
central loop.
sourceTestParticle.getB_dipole — MethodAnalytic magnetic field function for testing. Return in SI unit.
sourceTestParticle.getB_mirror — MethodgetB_mirror(x, y, z, distance, a, I1) -> Vector{Float}
Get magnetic field from a magnetic mirror generated from two coils.
Arguments
x,y,z::Float: particle coordinates in [m].distance::Float: distance between solenoids in [m].a::Float: radius of each side coil in [m].I1::Float: current in the solenoid times number of windings in side coils.
sourceTestParticle.getB_tokamak_coil — MethodgetB_tokamak_coil(x, y, z, a, b, ICoils, IPlasma)
Get the magnetic field from a Tokamak topology consists of 16 coils. Original: https://github.com/BoschSamuel/Simulation-of-a-Tokamak-Fusion-Reactor/blob/master/Simulation2.m
Arguments
x,y,z::Float: location in [m].a::Float: radius of each coil in [m].b::Float: radius of central region in [m].ICoil::Float: current in the coil times number of windings.IPlasma::Float: current of the plasma?
sourceTestParticle.getB_tokamak_profile — MethodgetB_tokamak_profile(x, y, z, q_profile, a, R₀, Bζ0)
Reconstruct the magnetic field distribution from a safe factor(q) profile. The formulations are from the book "Tokamak 4th Edition" by John Wesson.
Arguments
x,y,z::Float: location in [m].q_profile::Function: profile of q. The variable of this function must be the normalized radius.a::Float: minor radius [m].R₀::Float: major radius [m].Bζ0::Float: toroidal magnetic field on axis [T].
sourceTestParticle.getE_dipole — MethodAnalytic electric field function for testing.
sourceTestParticle.get_gc — Methodget_gc(param::Union{TPTuple, FullTPTuple})
Get three functions for plotting the orbit of guiding center.
For example:
param = prepare(E, B; species=Proton)
+prepare(x::AbstractRange, E, B; kwargs...) -> (q2m, E, B)
Direct range input for uniform grid in 2/3D is also accepted.
prepare(E, B; kwargs...) -> (q2m, E, B)
Return a tuple consists of particle charge-mass ratio for a prescribed species of charge q and mass m and analytic EM field functions. Prescribed species are Electron and Proton; other species can be manually specified with species=Ion/User, q and m.
prepare(E, B, F; kwargs...) -> (q, m, E, B, F)
Return a tuple consists of particle charge, mass for a prescribed species of charge q and mass m, analytic EM field functions, and external force F.
sourceTestParticle.sample — Methodsample(vdf::Maxwellian)
Sample a 3D velocity from a Maxwellian distribution vdf using the Box-Muller method.
sample(vdf::BiMaxwellian)
Sample a 3D velocity from a BiMaxwellian distribution vdf using the Box-Muller method.
sourceTestParticle.trace! — Methodtrace!(dy, y, p::TPTuple, t)
+trace!(dy, y, p::FullTPTuple, t)
ODE equations for charged particle moving in static EM field with in-place form.
ODE equations for charged particle moving in static EM field and external force field with in-place form.
sourceTestParticle.trace — Methodtrace(y, p::TPTuple, t) -> SVector{6, Float64}
+trace(y, p::FullTPTuple, t) -> SVector{6, Float64}
ODE equations for charged particle moving in static EM field with out-of-place form.
ODE equations for charged particle moving in static EM field and external force field with out-of-place form.
sourceTestParticle.trace_normalized! — Methodtrace_normalized!(dy, y, p::TPNormalizedTuple, t)
Normalized ODE equations for charged particle moving in static EM field with in-place form. If the field is in 2D X-Y plane, periodic boundary should be applied for the field in z via the extrapolation function provided by Interpolations.jl.
sourceTestParticle.trace_relativistic! — Methodtrace_relativistic!(dy, y, p::TPTuple, t)
ODE equations for relativistic charged particle moving in static EM field with in-place form.
sourceTestParticle.trace_relativistic — Methodtrace_relativistic(y, p::TPTuple, t) -> SVector{6, Float64}
ODE equations for relativistic charged particle moving in static EM field with out-of-place form.
sourceTestParticle.trace_relativistic_normalized! — Methodtrace_relativistic_normalized!(dy, y, p::TPNormalizedTuple, t)
Normalized ODE equations for relativistic charged particle moving in static EM field with in-place form.
sourcePrivate types and methods
TestParticle.AbstractTraceSolution — TypeAbstract type for tracing solutions.
sourceTestParticle.Field — TypeField{itd, F} <: AbstractField{itd}
A representation of a field function f, defined by:
time-independent field
\[\mathbf{F} = F(\mathbf{x}),\]
time-dependent field
\[\mathbf{F} = F(\mathbf{x}, t).\]
Arguments
field_function::Function: the function of field.itd::Bool: whether the field function is time dependent.F: the type of field_function.
sourceTestParticle.FullTPTuple — TypeThe type of parameter tuple for full test particle problem.
sourceTestParticle.Species — TypeType for the particles, Proton, Electron, Ion, or User.
sourceTestParticle.TPNormalizedTuple — TypeThe type of parameter tuple for normalized test particle problem.
sourceTestParticle.TPTuple — TypeThe type of parameter tuple for normal test particle problem.
sourceTestParticle.TraceSolution — MethodInterpolate solution at time x. Forward tracing only.
sourceTestParticle.VDF — TypeAbstract type for velocity distribution functions.
sourceTestParticle._boris! — MethodApply Boris method for particles with index in irange.
sourceTestParticle._prepare — MethodPrepare for advancing.
sourceTestParticle.cross! — MethodIn-place cross product.
sourceTestParticle.dipole — MethodCalculates the magnetic field from a dipole with magnetic moment M at r.
sourceTestParticle.dipole_fieldline — Functiondipole_fieldline(L, ϕ, nP)
Creates nP points on one field line of the magnetic field from a dipole. In a centered dipole magnetic field model, the path along a given L shell can be described as r = L*cos²λ, where r is the radial distance (in planetary radii) to a point on the line, λ is its co-latitude, and L is the L-shell of interest.
sourceTestParticle.getB_CS_harris — MethodgetB_CS_harris(B₀, L)
Return the magnetic field at location r near a current sheet with magnetic strength B₀ and sheet length L.
sourceTestParticle.getB_bottle — MethodgetB_bottle(x, y, z, distance, a, b, I1, I2) -> Vector{Float}
Get magnetic field from a magnetic bottle. Reference: https://en.wikipedia.org/wiki/Magneticmirror#Magneticbottles
Arguments
x,y,z::Float: particle coordinates in [m].distance::Float: distance between solenoids in [m].a::Float: radius of each side coil in [m].b::Float: radius of central coil in [m].I1::Float: current in the solenoid times number of windings in side coils.I2::Float: current in the central solenoid times number of windings in the
central loop.
sourceTestParticle.getB_dipole — MethodAnalytic magnetic field function for testing. Return in SI unit.
sourceTestParticle.getB_mirror — MethodgetB_mirror(x, y, z, distance, a, I1) -> Vector{Float}
Get magnetic field from a magnetic mirror generated from two coils.
Arguments
x,y,z::Float: particle coordinates in [m].distance::Float: distance between solenoids in [m].a::Float: radius of each side coil in [m].I1::Float: current in the solenoid times number of windings in side coils.
sourceTestParticle.getB_tokamak_coil — MethodgetB_tokamak_coil(x, y, z, a, b, ICoils, IPlasma)
Get the magnetic field from a Tokamak topology consists of 16 coils. Original: https://github.com/BoschSamuel/Simulation-of-a-Tokamak-Fusion-Reactor/blob/master/Simulation2.m
Arguments
x,y,z::Float: location in [m].a::Float: radius of each coil in [m].b::Float: radius of central region in [m].ICoil::Float: current in the coil times number of windings.IPlasma::Float: current of the plasma?
sourceTestParticle.getB_tokamak_profile — MethodgetB_tokamak_profile(x, y, z, q_profile, a, R₀, Bζ0)
Reconstruct the magnetic field distribution from a safe factor(q) profile. The formulations are from the book "Tokamak 4th Edition" by John Wesson.
Arguments
x,y,z::Float: location in [m].q_profile::Function: profile of q. The variable of this function must be the normalized radius.a::Float: minor radius [m].R₀::Float: major radius [m].Bζ0::Float: toroidal magnetic field on axis [T].
sourceTestParticle.getE_dipole — MethodAnalytic electric field function for testing.
sourceTestParticle.get_gc — Methodget_gc(param::Union{TPTuple, FullTPTuple})
Get three functions for plotting the orbit of guiding center.
For example:
param = prepare(E, B; species=Proton)
gc = get_gc(params)
# The definitions of stateinit, tspan, E and B are ignored.
prob = ODEProblem(trace!, stateinit, tspan, param)
@@ -12,10 +12,10 @@
f = Figure(fontsize=18)
ax = Axis3(f[1, 1], aspect = :data)
gc_plot(x,y,z,vx,vy,vz) = (gc([x,y,z,vx,vy,vz])...,)
-lines!(ax, sol, idxs=(gc_plot, 1, 2, 3, 4, 5, 6))
sourceTestParticle.get_rotation_matrix — Methodget_rotation_matrix(axis::AbstractVector, angle::Real) --> SMatrix{3,3}
Create a rotation matrix for rotating a 3D vector around a unit axis by an angle in radians. Reference: Rotation matrix from axis and angle
Example
using LinearAlgebra
+lines!(ax, sol, idxs=(gc_plot, 1, 2, 3, 4, 5, 6))
sourceTestParticle.get_rotation_matrix — Methodget_rotation_matrix(axis::AbstractVector, angle::Real) --> SMatrix{3,3}
Create a rotation matrix for rotating a 3D vector around a unit axis by an angle in radians. Reference: Rotation matrix from axis and angle
Example
using LinearAlgebra
v = [-0.5, 1.0, 1.0]
v̂ = normalize(v)
θ = deg2rad(-74)
-R = get_rotation_matrix(v̂, θ)
sourceTestParticle.getchargemass — Methodgetchargemass(species::Species, q::AbstractFloat, m::AbstractFloat)
Return charge and mass for species. if species = User, input q and m are returned.
sourceTestParticle.getinterp — Functiongetinterp(A, gridx, gridy, gridz, order::Int=1, bc::Int=1)
-getinterp(A, gridx, gridy, order::Int=1, bc::Int=1)
Return a function for interpolating array A on the grid given by gridx, gridy, and gridz.
Arguments
order::Int=1: order of interpolation in [1,2,3].bc::Int=1: type of boundary conditions, 1 -> NaN, 2 -> periodic, 3 -> Flat.
sourceTestParticle.guiding_center — Methodguiding_center(xu, param::Union{TPTuple, FullTPTuple})
Calculate the coordinates of the guiding center according to the phase space coordinates of a particle. Reference: https://en.wikipedia.org/wiki/Guiding_center
A simple definition:
\[\mathbf{X}=\mathbf{x}-m\frac{\mathbf{v}\times\mathbf{B}}{qB}\]
sourceTestParticle.is_time_dependent — MethodJudge whether the field function is time dependent.
sourceTestParticle.makegrid — MethodReturn uniform range from 2D/3D CartesianGrid.
sourceTestParticle.set_axes_equal — Methodset_axes_equal(ax)
Set 3D plot axes to equal scale for Matplotlib. Make axes of 3D plot have equal scale so that spheres appear as spheres and cubes as cubes. Required since ax.axis('equal') and ax.set_aspect('equal') don't work on 3D.
sourceTestParticle.solve — Functionsolve(prob::TraceProblem; trajectories::Int=1,
- savestepinterval::Int=1, isoutofdomain::Function=ODE_DEFAULT_ISOUTOFDOMAIN)
Trace particles using the Boris method with specified prob.
keywords
trajectories::Int: number of trajectories to trace.savestepinterval::Int: saving output interval.isoutofdomain::Function: a function with input of position and velocity vector xv that determines whether to stop tracing.
sourceTestParticle.sph2cart — MethodConvert from spherical to Cartesian coordinates vector.
sourceTestParticle.update_location! — MethodUpdate location in one timestep dt.
sourceTestParticle.update_velocity! — Methodupdate_velocity!(xv, paramBoris, param, dt)
Update velocity using the Boris method, Birdsall, Plasma Physics via Computer Simulation. Reference: https://apps.dtic.mil/sti/citations/ADA023511
sourceSettings
This document was generated with Documenter.jl version 1.3.0 on Tuesday 19 March 2024. Using Julia version 1.10.2.
TestParticle.getchargemass — Methodgetchargemass(species::Species, q::AbstractFloat, m::AbstractFloat)Return charge and mass for species. if species = User, input q and m are returned.
TestParticle.getinterp — Functiongetinterp(A, gridx, gridy, gridz, order::Int=1, bc::Int=1)
+getinterp(A, gridx, gridy, order::Int=1, bc::Int=1)Return a function for interpolating array A on the grid given by gridx, gridy, and gridz.
Arguments
order::Int=1: order of interpolation in [1,2,3].bc::Int=1: type of boundary conditions, 1 -> NaN, 2 -> periodic, 3 -> Flat.
TestParticle.guiding_center — Methodguiding_center(xu, param::Union{TPTuple, FullTPTuple})Calculate the coordinates of the guiding center according to the phase space coordinates of a particle. Reference: https://en.wikipedia.org/wiki/Guiding_center
A simple definition:
\[\mathbf{X}=\mathbf{x}-m\frac{\mathbf{v}\times\mathbf{B}}{qB}\]
TestParticle.is_time_dependent — MethodJudge whether the field function is time dependent.
TestParticle.makegrid — MethodReturn uniform range from 2D/3D CartesianGrid.
TestParticle.set_axes_equal — Methodset_axes_equal(ax)Set 3D plot axes to equal scale for Matplotlib. Make axes of 3D plot have equal scale so that spheres appear as spheres and cubes as cubes. Required since ax.axis('equal') and ax.set_aspect('equal') don't work on 3D.
TestParticle.solve — Functionsolve(prob::TraceProblem; trajectories::Int=1,
+ savestepinterval::Int=1, isoutofdomain::Function=ODE_DEFAULT_ISOUTOFDOMAIN)Trace particles using the Boris method with specified prob.
keywords
trajectories::Int: number of trajectories to trace.savestepinterval::Int: saving output interval.isoutofdomain::Function: a function with input of position and velocity vectorxvthat determines whether to stop tracing.
TestParticle.sph2cart — MethodConvert from spherical to Cartesian coordinates vector.
TestParticle.update_location! — MethodUpdate location in one timestep dt.
TestParticle.update_velocity! — Methodupdate_velocity!(xv, paramBoris, param, dt)Update velocity using the Boris method, Birdsall, Plasma Physics via Computer Simulation. Reference: https://apps.dtic.mil/sti/citations/ADA023511
