kappa_thermal_speed
- plasmapy.formulary.speeds.kappa_thermal_speed(T: Unit('K'), kappa, particle: Union[str, Integral, Particle, CustomParticle], method='most_probable')
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 particlekappa (
float
) – Thekappa
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'
.
- Returns
V – Particle thermal speed.
- Return type
- Raises
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.
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
>>> 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>
See also