Collisionless dissipation of a cross-field electric current

A detailed analysis is given of the development of the electrostatic turbulence excited by a cross-field current in a high density (ωp e ≫ Ωe ) collisionless plasma, as obtained from one- and two-dimensional computer simulations. The drift velocity required for instability is found to be only slightly smaller than the critical drift for the unmagnetic two-stream instability in contrast to the electron cyclotron drift instability. In one dimension the system remains self-similar in the turbulent phase, < Ẽ2 > /8πnTe ≃ const, while the electron thermal velocity and the effective collision frequency increase linearly with time, ν* ∝ Ωet, in agreement with the theory of coherent trapped-electron heating by Forslund, Morse, and Nielson. The switch-off drift velocity, however, is νd ≈ 2cs, and hence the thickness of a magnetic sheath would be Δ ∼ c/ωpi instead of Δ ∼ c/Ωe. In two dimensions two projections are investigated, the j-B plane and the plane perpendicular to B, the latter being the more relevant. The heating is much less efficient than in one dimension, ν * ≲ 5 × 10−3 ωpe. It is found that ν* ∝ 〈Ẽ2〉/8πnT, indicating stochastic dissipation. The gross features of the two-dimensional behavior correspond to the picture of ion-sound instability with electron runaway prevented by gyration.