# 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

^{[1]}

- $ \nu = \left ( \frac{qq^*n^*}{\varepsilon_0 m}\right )^2 \frac{\ln \Lambda}{4\pi (m_r/m)v^3n^*} $

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

^{[2]}

- $ \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*.

## References

- ↑ K. Miyamoto,
*Plasma Physics and Controlled Nuclear Fusion*, Springer-Verlag (2005) ISBN 3540242171 - ↑ ITER Physics Basis, Nucl. Fusion
**39**(1999) 2137