plasmapy.formulary.parameters.kappa_thermal_speed(T: Unit('K'), kappa, particle: plasmapy.particles.particle_class.Particle, method='most_probable')

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

Aliases: vth_kappa_

  • 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) – Representation of the particle species (e.g., ‘p’ for protons, ‘D+’ for deuterium, or ‘He-4 +1’ for singly ionized helium-4). If no charge state information is provided, then the particles are assumed to be singly charged.

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


V – Particle thermal speed.

Return type


  • 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.

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

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


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 1.


>>> from astropy import 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>



PlasmaPy Issue #186, https://github.com/PlasmaPy/PlasmaPy/issues/186

See also

kappa_thermal_speed, kappa_velocity_1D