Coulomb Collision Frequency
The rate at which cumulative small-angle Coulomb encounters deflect a charged particle by a large angle.
Collisions in a plasma
Charged particles interact through the long-range Coulomb force, so a single large-angle scattering is rare; instead many small deflections accumulate. The effective collision frequency is the rate at which these add up to a ninety-degree deflection. For electron-ion collisions it scales as:
nu_ei ~ n_e Z^2 ln(Lambda) / T_e^(3/2)The steep T^(-3/2) dependence means hot plasmas are nearly collisionless: fast particles are barely deflected. The Coulomb logarithm ln(Lambda) accounts for the range of impact parameters, from the Debye length down to the closest approach.
Different collision rates
Electron-electron, ion-ion, and electron-ion collisions have different rates because of the mass and charge factors. Electrons thermalize among themselves fastest, ions among themselves next, and electron-ion energy exchange is slowest, scaled by the mass ratio. This ordering explains why electron and ion temperatures can differ.
Collisionality regimes
- Collisional (Pfirsch-Schluter) regime at high density and low temperature
- Plateau regime at intermediate collisionality
- Banana regime at low collisionality, where trapped-particle orbits complete without a collision
The dimensionless collisionality nu-star compares the collision frequency to the bounce frequency and selects the neoclassical transport regime.
How it is used
Collision frequencies set the coefficients in the Fokker-Planck operator, the Spitzer resistivity, and the equilibration of temperatures. Transport and heating codes evaluate them from local n, T, and Z. For the hot core of the Hyperion breeder, low collisionality places it in the banana regime, which is where neoclassical transport and bootstrap current are computed.