Maxwellian_speed_3D¶

plasmapy.formulary.distribution.
Maxwellian_speed_3D
(v, T, particle='e', v_drift=0, vTh=nan, units='units')¶ Probability distribution function of speed for a Maxwellian distribution in 3D.
Return the probability density function for finding a particle with speed components
vx
,vy
, andvz
in m/s in an equilibrium plasma of temperatureT
which follows the 3D Maxwellian distribution function. This function assumes Cartesian coordinates.Parameters:  v (Quantity) – The speed in units convertible to m/s.
 T (Quantity) – The temperature, preferably in Kelvin.
 particle (str, optional) – Representation of the particle species(e.g.,
'p'
for protons,'D+'
for deuterium, or'He4 +1'
for \(He_4^{+1}\) (singly ionized helium4)), which defaults to electrons.  v_drift (Quantity) – The drift speed in units convertible to m/s.
 vTh (Quantity, optional) – Thermal velocity (most probable) in m/s. This is used for optimization purposes to avoid recalculating vTh, for example when integrating over velocityspace.
 units (str, optional) – Selects whether to run function with units and unit checks (when equal to “units”) or to run as unitless (when equal to “unitless”). The unitless version is substantially faster for intensive computations.
Returns: f – Probability density in speed^1, normalized so that: \(\iiint_{0}^{\infty} f(\vec{v}) d\vec{v} = 1\).
Return type: Raises: TypeError
– A parameter argument is not aQuantity
and cannot be converted into aQuantity
.UnitConversionError
– If the parameters is not in appropriate units.ValueError
– If the temperature is negative, or the particle mass or charge state cannot be found.
Notes
In 3D, the Maxwellian speed distribution function describing the distribution of particles with speed \(v\) in a plasma with temperature \(T\) is given by:
\[f = 4 \pi \left v^{2} (\pi v_{Th}^2)^{3/2} \exp(v^{2} / v_{Th}^2)\]where \(v_{Th} = \sqrt{2 k_B T / m}\) is the thermal speed.
See also
Example
>>> from astropy import units as u >>> v=1 * u.m / u.s >>> Maxwellian_speed_3D(v=v, T=30000*u.K, particle='e', v_drift=0 * u.m / u.s) <Quantity 2.60235...e18 s / m>