API Reference

plasma_beta(T, n, B)

Compute the plamsa beta (β), the ratio of thermal pressure to magnetic pressure.

Arguments

• T: The temperature of the plasma.
• n: The particle density of the plasma.
• B: The magnetic field in the plasma.

Example

julia> plasma_beta(1e6u"K", 1e19u"m^-3", 0.2u"T")
0.008674873511172188

References

• PlasmaPy Documentation
• Wikipedia

plasma_frequency(n::NumberDensity, [q::Charge, mass::Mass]; to_hz = false)
plasma_frequency(n::NumberDensity, p::ParticleLike; kw...)

Calculate the plasma frequency of a species.

\[ω_p = \sqrt{\frac{n q^2}{m ε₀}}\]

The plasma frequency is a characteristic frequency of the plasma. More often, it refers to the frequency at which electrons oscillate in the plasma.

Set to_hz = true to convert output from angular frequency to Hz.

Examples

julia> plasma_frequency(1e19u"m^-3")  # plasma frequency
1.7839863654934653e11 rad s⁻¹

julia> plasma_frequency(1e19u"m^-3", :p)  # proton plasma frequency
4.1632945624883513e9 rad s⁻¹

References

• Wikipedia
• PlasmaPy Documentation

gyrofrequency(B::BField, p::ParticleLike; kw...)
gyrofrequency(B::BField, mass::Mass, q::Charge; to_hz = false)

Calculate the gyrofrequency (or cyclotron frequency) of a charged particle's circular motion in a magnetic field. The gyrofrequency is the angular frequency of a charged particle's gyromotion around magnetic field lines.

Set to_hz = true to convert output from angular frequency to Hz.

References:

• PlasmaPy Documentation

Examples

julia> gyrofrequency(0.01u"T", :p)  # proton gyrofrequency
957883.3292211705 rad s⁻¹

julia> gyrofrequency(0.1u"T", :e; to_hz = true)  # electron gyrofrequency as frequency
2.799248987233304e9 Hz

julia> gyrofrequency(250u"Gauss", "Fe"; z=13)  # Fe2+ ion gyrofrequency
560682.3520611608 rad s⁻¹

lower_hybrid_frequency(B::BField, n_i::NumberDensity, ion::ParticleLike; kw...)

Calculate the lower hybrid frequency.

\[\frac{1}{ω_{lh}^2} = \frac{1}{ω_{ci}^2 + ω_{pi}^2} + \frac{1}{ω_{ci} ω_{ce}}\]

where ωci is the ion gyrofrequency, ωce is the electron gyrofrequency, and ω_pi is the ion plasma frequency.

Set to_hz = true to convert output from angular frequency to Hz.

Examples

julia> lower_hybrid_frequency(0.2u"T", 5e19u"m^-3", "D+")
5.783727350182709e8 rad s⁻¹

References

• Wikipedia
• PlasmaPy Documentation

upper_hybrid_frequency(B::BField, n_e::NumberDensity; to_hz = false)

Calculate the upper hybrid frequency.

\[ω_{uh}^2 = ω_{ce}^2 + ω_{pe}^2\]

where ωce is the electron gyrofrequency and ωpe is the electron plasma frequency.

Set to_hz = true to convert output from angular frequency to Hz.

Examples

julia> upper_hybrid_frequency(0.2u"T", 5e19u"m^-3")
4.004594195988481e11 rad s⁻¹

julia> upper_hybrid_frequency(0.2u"T", 5e19u"m^-3"; to_hz = true)
6.37350961368681e10 Hz

References

• Wikipedia
• PlasmaPy Documentation

Calculate the radius of circular motion for a charged particle in a uniform magnetic field

References: PlasmaPy API Documentation

Examples

julia> gyroradius(0.2u"T", Unitful.me, Unitful.q, 1e6u"K")
0.00015651672339994665 m

inertial_length(n::NumberDensity, q::Charge, mass::Mass)
inertial_length(n::NumberDensity, p::ParticleLike; kw...)

Calculate the inertial length, the characteristic length scale for a particle to be accelerated in a plasma:

\[dᵢ = \frac{c}{ω_p}\]

where $ω_p$ is the plasma frequency.

The Hall effect becomes important on length scales shorter than the ion inertial length.

See also: plasma_frequency.

References: PlasmaPy API Documentation

Debye_length(n::NumberDensity, T::EnergyOrTemp)

Calculate the Debye length, exponential scale length for charge screening in an electron plasma with stationary ions:

\[λ_D = \sqrt{\frac{ε₀ k_B T}{n q^2}}\]

where $T$ is the electron temperature, $n$ is the electron density, and $q$ is the elementary charge.

Alfven_velocity(B::BField, ρ)
Alfven_velocity(𝐁::Vector{BField}, ρ)

Calculate the Alfven velocity for magnetic field vector. See also Alfven_speed.

diamagnetic_drift(∇p, B::BFields, n, q)

Calculate the diamagnetic drift velocity given by:

\[𝐯 = - (∇p × 𝐁) / (q n |𝐁|^2)\]

where $∇p$ is the pressure gradient.

ExB_drift(𝐄::EFields, 𝐁::BFields)

Calculate the $E × 𝐁$ drift velocity given by:

\[𝐯 = (𝐄 × 𝐁) / |𝐁|^2\]

force_drift(𝐅, 𝐁::BFields, q)

Calculate the general force drift for a particle in a magnetic field given by:

\[𝐯 = (𝐅 × 𝐁) / (q |𝐁|^2)\]

Alfven_speed(B::BFieldOrBFields, ρ)
Alfven_speed(B::BFieldOrBFields, n::NumberDensity, mass_number = 1)

Alfvén speed $V_A$, the typical propagation speed of magnetic disturbances in a quasineutral plasma.

Note that this is different from the Alfven velocity, see also Alfven_velocity. References: PlasmaPy API Documentation

ion_sound_speed(T_e, T_i, m_i, Z; γ_e=1, γ_i=3, n_e=nothing, k=nothing)

Calculate the ion sound speed for an electron-ion plasma given by:

\[V_S = \sqrt{\frac{γ_e Z k_B T_e + γ_i k_B T_i}{m_i (1 + k^2 λ_{D}^2)}}\]

If both n_e and k are given, includes dispersive correction.

Arguments

• T_e: Electron temperature (K or energy per particle)
• T_i: Ion temperature (K or energy per particle)
• m_i: Ion mass
• Z: Ion charge state (default: 1)
• γ_e: Electron adiabatic index (default: 1)
• γ_i: Ion adiabatic index (default: 3)
• n_e: Electron number density (optional)
• k: Wavenumber (optional)

thermal_speed(T::EnergyOrTemp, mass::Mass, method::ThermalVelocityMethod = MostProbable(), ndim = 3)

Calculate the speed of thermal motion for particles with a Maxwellian distribution.

\[v_{th} = C_o \sqrt{\frac{k_B T}{m}}\]

where $T$ is the temperature associated with the distribution, $m$ is the particle's mass, and $C_o$ is a constant of proportionality. ```

thermal_temperature(V::Velocity, mass::Mass, method::ThermalVelocityMethod = MostProbable(), ndim = 3)

Alfven_current_density(Va::Velocity, n::NumberDensity)
Alfven_current_density(B::BFieldOrBFields, n::NumberDensity)
Alfven_current_density(B::BFieldOrBFields, dᵢ::Length)

Calculate the Alfvén current density $J_A$, a natural scaling for current density:

\[J_A = e n V_A = \frac{B}{μ₀ dᵢ}\]

where $V_A$ is the Alfven speed, $dᵢ$ is ion inertial length.

See also: Alfven_speed, inertial_length.

This module provides aliases of the most common plasma functionality for user convenience.

Aliases are denoted with a trailing underscore (e.g., alias_).

thermal_velocity_coefficients(method::ThermalVelocityMethod, ndim::Int)

Get the thermal speed coefficient corresponding to the desired thermal speed definition.

Arguments

• method::ThermalVelocityMethod: Method to be used for calculating the thermal speed. Valid values are MostProbable(), RMS(), MeanMagnitude(), and NRL().
• ndim::Val{Int}: Dimensionality (1D, 2D, 3D) of space in which to calculate thermal speed. Valid values are Val(1), Val(2), or Val{3}.

magnetic_pressure(B)

Calculate the magnetic pressure.

thermal_pressure(T, n)

Calculate the thermal pressure for a Maxwellian distribution.

Arguments

• T: The particle temperature or energy.
• n: The particle number density.