plasmapy.formulary.collisions.lengths.impact_parameter_perp(T: ~astropy.units.quantity.Quantity, species: (<class 'plasmapy.particles.particle_class.Particle'>, <class 'plasmapy.particles.particle_class.Particle'>), V: ~astropy.units.quantity.Quantity = <Quantity nan m / s>) Quantity[source]

Distance of the closest approach for a 90° Coulomb collision.

  • T (Quantity) – Temperature in units of temperature or energy per particle, which is assumed to be equal for both the test particle and the target particle

  • species (tuple) – A tuple containing string representations of the test particle (listed first) and the target particle (listed second)

  • V (Quantity, optional) – The relative velocity between particles. If not provided, thermal velocity is assumed: \(μ V^2 \sim 2 k_B T\) where \(μ\) is the reduced mass.


impact_parameter_perp – The distance of the closest approach for a 90° Coulomb collision.

Return type:

float or numpy.ndarray

  • ValueError – If the mass or charge of either particle cannot be found, or any of the inputs contain incorrect values.

  • UnitConversionError – If the units on any of the inputs are incorrect.

  • TypeError – If either of T or V is not a Quantity.

  • RelativityError – If the input velocity is same or greater than the speed of light.

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

  • RelativityWarning – If the input velocity is greater than 5% of the speed of light.


The distance of closest approach, impact_parameter_perp, is given by (see Ch. 5 of Chen [2016]):

\[b_⟂ = \frac{Z_1 Z_2}{4 π \epsilon_0 m v^2}\]


>>> import astropy.units as u
>>> T = 1e6 * u.K
>>> species = ("e", "p")
>>> impact_parameter_perp(T, species)
<Quantity 8.3550...e-12 m>