Kinetic theory of a two-dimensional magnetized plasma. Part 2. Balescu-Lenard limit

The kinetic theory of a two-dimensional one-species plasma in a uniform d.c. magnetic field is investigated in the small plasma parameter limit. The plasma consists of charged rods interacting through the logarithmic Coulomb potential. Vahala & Montgomery earlier derived a Fokker -Planck equation for this system, but it contained a divergent integral, which had to be cut-off on physical grounds. This cut-off is compared to the standard cut-off introduced in the two-dimensional unmagnetized Fokker -Planck equation. In the small plasma parameter limit, it is shown (under the assumption that for large integer n, γ_n/γ_n+1 = O(n^p), with p < 2, where γ_n = ω_n -nΩ. with ω_n the nth. Bernstein mode and Q the electron gyro frequency) that the Balescu-Lenard collision term is zero in the long time average limit if one considers only two-body interactions. The energy transfer from a test particle to an equilibrium plasma is discussed and also shown to be zero in the long time average limit. This supports the unexpected result of zero Balescu-Lenard collision term.