thermal_speed¶

plasmapy.formulary.
thermal_speed
(T: Unit("K"), particle: plasmapy.particles.particle_class.Particle, method='most_probable', mass: Unit("kg") = <Quantity nan kg>, ndim=3) > Unit("m / s")¶ Return the most probable speed for a particle within a Maxwellian distribution.
Aliases:
vth_
 Parameters
T (
Quantity
) – The particle temperature in either kelvin or energy per particleparticle (
Particle
) – Representation of the particle species (e.g.,'p'
for protons,'D+'
for deuterium, or'He4 +1'
for singly ionized helium4). 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 tonan
and if so, doesn’t do anything, but if set, overrides mass acquired fromparticle
. Useful with relative velocities of particles.ndim (
int
) – Dimensionality of space in which to calculate thermal velocity. Valid values are 1, 2, or 3.
 Returns
V – The particle’s 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 ion sound 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:
\[V_{th,i} = \sqrt{\frac{N k_B T_i}{m_i}}\]where the value of \(N\) depends on the dimensionality and the definition of \(v_{th}\): most probable, rootmeansquare (RMS), or mean magnitude. The value of \(N\) in each case is
¶ Dim.
MostProbable
RMS
MeanMagnitude
1D
0
1
\(2/π\)
2D
1
2
\(π/2\)
3D
2
3
\(8/π\)
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 30949.6... m / s> >>> thermal_speed(1e6*u.K, particle='p') <Quantity 128486... m / s> >>> thermal_speed(5*u.eV, particle='e') <Quantity 132620... m / s> >>> thermal_speed(1e6*u.K, particle='e') <Quantity 550569... m / s> >>> thermal_speed(1e6*u.K, "e", method="rms") <Quantity 674307... m / s> >>> thermal_speed(1e6*u.K, "e", method="mean_magnitude") <Quantity 621251... m / s>