Collisional effects in low collisionality plasmas

The effects of collisions are often neglected in theoretical analyses of low collisionality plasmas where the collision rate nu is smaller than the frequency of waves or other physical processes being considered. However, small angle Coulomb collisions scatter the velocity vector v of charged particles and produce slightly probabilistic rather than fully deterministic charged particle trajectories in a plasma. These diffusive effects produce an effective collision rate nu(eff) similar to nu / (vertical bar delta v vertical bar/nu)(2) >> nu for relaxation of plasma responses localized to a small region delta v in velocity space. In particular, they create narrow dissipative boundary layers in the vicinity of resonant collisionless responses of the plasma to waves which resolve these singular responses and create temporal irreversibility. A new Green-function-based procedure is being developed for exploring these low collisionality effects. This new procedure is first used to explore Coulomb collisional scattering effects on the temporal evolution of the linear Landau damping of Langmuir waves. On collision and longer time scales the relevant plasma kinetic equation becomes an extended Chapman-Enskog type equation. Green function solutions of this kinetic equation can be used to determine self-consistent closures for fluid moment equations. A multiple time scale and systematic small gyroradius and perturbation level analysis has been used to develop descriptions of toroidal magnetically confined plasmas in tokamaks on collision and transport time scales. Some examples of low collisionality closures and their effects on the behavior of tokamak plasmas are noted.