Collisionality

In a plasma, the collision time τ_coll is defined as the time in which the trajectory of a (charged) particle undergoes a change of direction of 90 degrees. Due to the long range of the Coulomb force, Coulomb interactions are typically small angle scattering events, so that this direction change typically requires a large number of interactions.

Consider a test particle with charge q, mass m, and velocity v colliding with bulk particles with charge q*, mass m*, and thermal velocity v*. Then the collision frequency ν = 1/τ_coll is given by

$\nu =\left({\frac {qq^{*}n^{*}}{\varepsilon _{0}m}}\right)^{2}{\frac {\ln \Lambda }{4\pi (m_{r}/m)v^{3}n^{*}}}$

assuming v > v*, where m_r = mm*/(m+m*) is the reduced mass and n* the bulk particle density. The factor ln Λ appears due to the accumulation of many small-angle collisions within a Debye sphere.

Dimensionless collisionality

The dimensionless collisionality ν^* is defined as

$\nu ^{*}={\frac {\rm {connection~length}}{\rm {trapped~particle~mean~free~path}}}$

See Connection length. The mean free path is estimated by the thermal velocity divided by the collision frequency, v_th / ν.