The formulary subpackage contains commonly used formulae from plasma science.

Sub-Packages & Modules

braginskii Functions to calculate classical transport coefficients.
collisions Functions to calculate transport coefficients.
dielectric Functions to calculate plasma dielectric parameters
dimensionless Module of dimensionless plasma parameters.
distribution Common distribution functions for plasmas, such as the Maxwelian or Kappa distributions.
drifts Formulas for calculating particle drifts.
ionization This module gathers functions relating to ionization states and the properties thereof.
magnetostatics Define MagneticStatics class to calculate common static magnetic fields as first raised in issue #100.
mathematics This module gathers highly theoretical mathematical formulas relevant to plasma physics.
parameters This module gathers basic and general plasma parameters such as the plasma frequency or Debye length.
quantum Functions for quantum parameters, including electron degenerate gases and warm dense matter.
relativity Functionality for calculating relativistic quantities (\(v \to c\)).


Alfven_speed(B, density, Unit(“kg / m3”)], …) Calculate the Alfvén speed.
Bohm_diffusion(T_e, B) The Bohm diffusion coefficient was conjectured to follow Bohm model of the diffusion of plasma across a magnetic field and describe the diffusion of early fusion energy machines.
Coulomb_cross_section(impact_param) Cross section for a large angle Coulomb collision.
Coulomb_logarithm(T, n_e, species, …[, method]) Estimates the Coulomb logarithm.
DB_(T_e, B) Alias to Bohm_diffusion().
Debye_length(T_e, n_e) Calculate the characteristic decay length for electric fields,
Debye_number(T_e, n_e) Return the number of electrons within a sphere with a radius of the Debye length.
Ef_(n_e) Alias to Fermi_energy().
ExB_drift(E, B) Calculate the “electric cross magnetic” particle drift.
Fermi_energy(n_e) Calculate the kinetic energy in a degenerate electron gas.
Fermi_integral(x, int, complex, …) Calculate the complete Fermi-Dirac integral.
Hall_parameter(n, T, B, ion, particle[, …]) Calculate the ratio between the particle gyrofrequency and the particle-ion particle collision rate.
Knudsen_number(characteristic_length, T, …) Knudsen number (dimensionless)
Lorentz_factor(V) Return the Lorentz factor.
Mag_Reynolds(U, L, sigma) The Magnetic Reynolds number is a dimensionless quantity that estimates the relative contributions of advection and induction to magnetic diffusion in a conducting medium.
Maxwellian_1D(v, T[, particle, v_drift, …]) Probability distribution function of velocity for a Maxwellian distribution in 1D.
Maxwellian_speed_1D(v, T[, particle, …]) Probability distribution function of speed for a Maxwellian distribution in 1D.
Maxwellian_speed_2D(v, T[, particle, …]) Probability distribution function of speed for a Maxwellian distribution in 2D.
Maxwellian_speed_3D(v, T[, particle, …]) Probability distribution function of speed for a Maxwellian distribution in 3D.
Maxwellian_velocity_2D(vx, vy, T[, …]) Probability distribution function of velocity for a Maxwellian distribution in 2D.
Maxwellian_velocity_3D(vx, vy, vz, T[, …]) Probability distribution function of velocity for a Maxwellian distribution in 3D.
Re_(rho, U, L, mu) Alias to Reynolds_number().
Reynolds_number(rho, U, L, mu) The Reynolds Number is a dimensionless quantity that is used to predict flow patterns in fluids.
Rm_(U, L, sigma) Alias to Mag_Reynolds().
Saha(g_j, g_k, n_e, E_jk, T_e) The Saha equation, derived in statistical mechanics, gives an approximation of the ratio of population of ions in two different ionization states in a plasma.
Spitzer_resistivity(T, n, species, z_mean, V) Spitzer resistivity of a plasma
Thomas_Fermi_length(n_e) Calculate the exponential scale length for charge screening for cold and dense plasmas.
Wigner_Seitz_radius(n) Calculate the Wigner-Seitz radius, which approximates the inter- particle spacing.
Z_bal_(n, T_e) Alias for ionization_balance().
beta(T, n, B) The ratio of thermal pressure to magnetic pressure.
betaH_(n, T, B, ion, particle[, …]) Alias to Hall_parameter().
chemical_potential(n_e, T) Calculate the ideal chemical potential.
cold_plasma_permittivity_LRP(B, species, n, …) Magnetized Cold Plasma Dielectric Permittivity Tensor Elements.
cold_plasma_permittivity_SDP(B, species, n, …) Magnetized Cold Plasma Dielectric Permittivity Tensor Elements.
collision_frequency(T, n, species, z_mean, V) Collision frequency of particles in a plasma.
coupling_parameter(T, n_e, species, z_mean, V) Coupling parameter.
cs_(T_e, T_i, ion, n_e, k[, gamma_e, …]) Alias to ion_sound_speed().
cwp_(n, particle) Alias to inertial_length().
deBroglie_wavelength(V, particle) Calculates the de Broglie wavelength.
electron_thermal_conductivity(T_e, n_e, T_i, …) Calculate the thermal conductivity for electrons.
electron_viscosity(T_e, n_e, T_i, n_i, ion) Calculate the electron viscosity.
force_drift(F, B, q) Calculate the general force drift for a particle in a magnetic field.
fundamental_electron_collision_freq(T_e, …) Average momentum relaxation rate for a slowly flowing Maxwellian distribution of electrons.
fundamental_ion_collision_freq(T_i, n_i, ion) Average momentum relaxation rate for a slowly flowing Maxwellian distribution of ions.
gyrofrequency(B, particle[, signed, Z, to_hz]) Calculate the particle gyrofrequency in units of radians per second.
gyroradius(B, particle, *, Vperp, T_i) Return the particle gyroradius.
impact_parameter(T, n_e, species, z_mean, V) Impact parameters for classical and quantum Coulomb collision
impact_parameter_perp(T, species, <class >), V) Distance of closest approach for a 90 degree Coulomb collision.
inertial_length(n, particle) Calculate a charged particle’s inertial length.
ion_sound_speed(T_e, T_i, ion, n_e, k[, …]) Return the ion sound speed for an electron-ion plasma.
ion_thermal_conductivity(T_e, n_e, T_i, n_i, ion) Calculate the thermal conductivity for ions.
ion_viscosity(T_e, n_e, T_i, n_i, ion[, …]) Calculate the ion viscosity.
ionization_balance(n, T_e) Z_bal is the estimate average ionization level of a plasma in thermal equilibrium that balances the number density of ions in two different ionization states.
kappa_thermal_speed(T, kappa, particle[, method]) Return the most probable speed for a particle within a Kappa distribution.
kappa_velocity_1D(v, T, kappa[, particle, …]) Return the probability density at the velocity v in m/s to find a particle particle in a plasma of temperature T following the Kappa distribution function in 1D.
kappa_velocity_3D(vx, vy, vz, T, kappa[, …]) Return the probability density function for finding a particle with velocity components v_x, v_y, and v_z`in m/s in a suprathermal plasma of temperature `T and parameter ‘kappa’ which follows the 3D Kappa distribution function.
lambdaDB_(V, particle) Alias to deBroglie_wavelength().
lambdaDB_th_(T_e) Alias to thermal_deBroglie_wavelength().
lambdaD_(T_e, n_e) Alias to Debye_length().
lower_hybrid_frequency(B, n_i, ion[, to_hz]) Return the lower hybrid frequency.
magnetic_energy_density(B) Calculate the magnetic energy density.
magnetic_pressure(B) Calculate the magnetic pressure.
mass_density(density, Unit(“kg / m3”)], …) Calculates the mass density from a number density.
mean_free_path(T, n_e, species, z_mean, V[, …]) Collisional mean free path (m)
mobility(T, n_e, species, z_mean, V[, method]) Electrical mobility (m^2/(V s))
nD_(T_e, n_e) Alias to Debye_number().
oc_(B, particle[, signed, Z, to_hz]) Alias to gyrofrequency().
permittivity_1D_Maxwellian(omega, kWave, T, …) The classical dielectric permittivity for a 1D Maxwellian plasma.
plasma_frequency(n, particle[, z_mean, to_hz]) Calculate the particle plasma frequency.
pmag_(B) Alias to magnetic_pressure().
pth_(T, n) Alias to thermal_pressure().
quantum_theta(T, n_e) Compares Fermi energy to thermal kinetic energy to check if quantum effects are important.
rc_(B, particle, *, Vperp, T_i) Alias to gyroradius().
relativistic_energy(m, v) Calculate the relativistic energy (in Joules) of an object of mass m and velocity v.
resistivity(T_e, n_e, T_i, n_i, ion[, m_i, …]) Calculate the resistivity.
rho_(density, Unit(“kg / m3”)], particle, …) Alias to mass_density().
rhoc_(B, particle, *, Vperp, T_i) Alias to gyroradius().
thermal_deBroglie_wavelength(T_e) Calculate the thermal deBroglie wavelength for electrons.
thermal_pressure(T, n) Return the thermal pressure for a Maxwellian distribution.
thermal_speed(T, particle[, method, ndim]) Return the most probable speed for a particle within a Maxwellian distribution.
thermoelectric_conductivity(T_e, n_e, T_i, …) Calculate the thermoelectric conductivity.
ub_(B) Alias to magnetic_energy_density().
upper_hybrid_frequency(B, n_e[, to_hz]) Return the upper hybrid frequency.
va_(B, density, Unit(“kg / m3”)], ion, z_mean) Alias to Alfven_speed().
veb_(E, B) Alias to ExB_drift().
vfd_(F, B, q) Alias to force_drift().
vth_(T, particle[, method, ndim]) Alias to thermal_speed().
vth_kappa_(T, kappa, particle[, method]) Alias to kappa_thermal_speed().
wc_(B, particle[, signed, Z, to_hz]) Alias to gyrofrequency().
wlh_(B, n_i, ion[, to_hz]) Alias to lower_hybrid_frequency().
wp_(n, particle[, z_mean, to_hz]) Alias to plasma_frequency().
wuh_(B, n_e[, to_hz]) Alias to upper_hybrid_frequency().


CircularWire(normal, center, radius, current) Circular wire(coil) class
ClassicalTransport(T_e, n_e, T_i, n_i, ion, m_i) Classical transport coefficients (e.g.
FiniteStraightWire(p1, p2, current) Finite length straight wire class.
GeneralWire(parametric_eq, t1, t2, current) General wire class described by its parametric vector equation
InfiniteStraightWire(direction, p0, current) Infinite straight wire class.
MagneticDipole(moment, p0) Simple magnetic dipole - two nearby opposite point charges.
MagnetoStatics Abstract class for all kinds of magnetic static fields
Wire Abstract wire class for concrete wires to be inherited from.

Class Inheritance Diagram

Inheritance diagram of plasmapy.formulary.magnetostatics.CircularWire, plasmapy.formulary.braginskii.ClassicalTransport, plasmapy.formulary.magnetostatics.FiniteStraightWire, plasmapy.formulary.magnetostatics.GeneralWire, plasmapy.formulary.magnetostatics.InfiniteStraightWire, plasmapy.formulary.magnetostatics.MagneticDipole, plasmapy.formulary.magnetostatics.MagnetoStatics, plasmapy.formulary.magnetostatics.Wire