# Collisionality

In plasma physics of tokamaks, collisionality is a dimensionless parameter which expresses the ratio of the electron-ion collision frequency to the banana orbit frequency.

## Definition

The plasma collisionality $\nu^*$ is defined as[1][2]

$\nu^* = \nu_\mathrm{ei}\,\sqrt{\frac{m_\mathrm{i}}{k_\mathrm{B} T_\mathrm{i}}}\,\epsilon^{-3/2}\,qR,$

where $\nu_\mathrm{ei}$ denotes the electron-ion collision frequency, $R$ is the plasma major radius, $\epsilon$ is the inverse aspect-ratio, and $q$ is the safety factor. The plasma parameters $m_\mathrm{i}$ and $T_\mathrm{i}$ denote, respectively, the mass and temperature of the ions, and $k_\mathrm{B}$ is the Boltzmann constant.