thermal_speed¶
-
plasmapy.physics.parameters.
thermal_speed
(T, particle: plasmapy.atomic.particle_class.Particle = 'e-', method='most_probable', mass=<Quantity nan kg>)¶ Return the most probable speed for a particle within a Maxwellian distribution.
Parameters: - T (Quantity) – The particle temperature in either kelvin or energy per particle
- particle (str, optional) – Representation of the particle species (e.g.,
'p'
for protons,'D+'
for deuterium, or'He-4 +1'
for singly ionized helium-4), which defaults to electrons. 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'
. - mass (Quantity) – The particle’s mass override. Defaults to NaN and if so, doesn’t do
anything, but if set, overrides mass acquired from
particle
. Useful with relative velocities of particles.
Returns: V – particle thermal speed
Return type: Raises: TypeError
– The particle temperature is not a ~astropy.units.QuantityUnitConversionError
– If the particle temperature is not in units of temperature or energy per particleValueError
– The particle temperature is invalid or particle cannot be used to identify an isotope or particle
Warns: - RelativityWarning – If the ion sound speed exceeds 5% of the speed of light, or
- ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed.
Notes
The particle thermal speed is given by:
\[V_{th,i} = \sqrt{\frac{2 k_B T_i}{m_i}}\]This function yields the most probable speed within a distribution function. However, the definition of thermal velocity varies by the square root of two depending on whether or not this velocity absorbs that factor in the expression for a Maxwellian distribution. In particular, the expression given in the NRL Plasma Formulary [1] is a square root of two smaller than the result from this function.
Examples
>>> from astropy import units as u >>> thermal_speed(5*u.eV, 'p') <Quantity 30949.69018286 m / s> >>> thermal_speed(1e6*u.K, particle='p') <Quantity 128486.55193256 m / s> >>> thermal_speed(5*u.eV) <Quantity 1326205.12123959 m / s> >>> thermal_speed(1e6*u.K) <Quantity 5505693.98842538 m / s> >>> thermal_speed(1e6*u.K, method="rms") <Quantity 6743070.47577549 m / s> >>> thermal_speed(1e6*u.K, method="mean_magnitude") <Quantity 6212510.3969422 m / s>