kappa_thermal_speed

plasmapy.formulary.speeds.kappa_thermal_speed(
T: Annotated[Quantity, Unit('K')],
kappa,
particle: str | int | integer | Particle | CustomParticle | Quantity,
method: Literal['most_probable', 'rms', 'mean_magnitude'] = 'most_probable',
*,
mass_numb: int | None = None,
Z: float | None = None,
) → Annotated[Quantity, Unit('m / s')][source]

Return the most probable speed for a particle within a kappa distribution.

Aliases: vth_kappa_

Parameters:

  • T (Quantity) – The particle temperature in either kelvin or energy per particle

  • kappa (float) – The kappa parameter is a dimensionless number which sets the slope of the energy spectrum of suprathermal particles forming the tail of the kappa velocity distribution function. kappa must be greater than 3/2.

  • particle (particle-like) – Representation of the particle species (e.g., 'p+' for protons, 'D+' for deuterium, or ‘He-4 +1’ for singly ionized helium-4).

  • method (str, default: "most_probable") – Method to be used for calculating the thermal speed. Options are 'most_probable', 'rms', and 'mean_magnitude'.

  • mass_numb (integer, optional) – The mass number corresponding to particle.

  • Z (real number, optional) – The charge number corresponding to particle.

Returns:

V – Particle thermal speed.

Return type:

Quantity

Raises:

  • TypeError – The particle temperature is not a Quantity.

  • UnitConversionError – If the particle temperature is not in units of temperature or energy per particle.

  • ValueError – The particle temperature is invalid or particle cannot be used to identify an isotope or particle.

Warns:

  • RelativityWarning – If the particle thermal speed exceeds 5% of the speed of light.

  • UnitsWarning – If units are not provided, SI units are assumed.

See also

kappa_thermal_speed, kappa_velocity_1D

Notes

The particle thermal speed is given by:

\[V_{th,i} = \sqrt{(2 κ - 3)\frac{2 k_B T_i}{κ m_i}}\]

For more discussion on the 'mean_magnitude' calculation method, see PlasmaPy issue #186.

Examples

>>> import astropy.units as u
>>> kappa_thermal_speed(5 * u.eV, 4, "p")  # defaults to most probable
<Quantity 24467.87... m / s>
>>> kappa_thermal_speed(5 * u.eV, 4, "p", "rms")
<Quantity 37905.47... m / s>
>>> kappa_thermal_speed(5 * u.eV, 4, "p", "mean_magnitude")
<Quantity 34922.98... m / s>