Anomalous resistivity of current-driven isothermal plasmas due to phase space structuring

Abstract

The anomalous electric resistivity of collisionless plasmas is an important issue in the physics of hot plasmas, e.g., in the context of auroral particle acceleration and of reconnection in the solar corona. The linear stability theory of isothermal current driven space plasmas predicts an ion-acoustic instability if the relative drift velocity of the current carrying particles exceeds a certain threshold, which, generally, depends on the plasma parameters. The spectrum of waves, excited by a marginal instability, is very narrow. Hence, the wave power at saturation and the corresponding electric resistivity due to wave-particle interaction cannot be obtained by means of a quasilinear, weak turbulence approach and the nonlinear single mode theory provides too small saturation amplitudes. To solve the nonlinear problem a newly developed unsplit conservative Eulerian Vlasov code is applied to simulate a strongly magnetized current driven plasma, which can be considered in 1D1V (one spatial, one velocity space direction). Instead of periodic boundary conditions, usually used as they are simpler to treat, open boundaries are implemented which allow to maintain a constant current flow. Simulated is a typical almost isothermal (Te=2Ti) hot (κTi=1keV) space plasma for the real mass ratio mi∕me=1836. The initial spontaneous instability is followed by a three-stage nonlinear evolution: First electron trapping leads to the formation of electron phase space holes. Due to a steepening of the leading edges of the potential wells the electron phase space holes gradually become asymmetric, they grow in size and deepen. The phase space holes accelerate until they move much faster than the initial ion-acoustic waves. The interaction of the current carriers with the asymmetric potential wells and causes a nonvanishing net momentum transfer between the particles and the self-generated electric field. After a few ion plasma periods ion trapping starts until, finally, an electrostatic double layer arises. It is found that the nonlinear saturated state of the system is dominated by the particle interaction with coherent phase space structures. The corresponding anomalous resistivity is slightly modulated with an oscillation period τ≈ωpi−1). For a macroscopic description its major part can be parameterized by means of an effective collision rate νeff of the order of 10−2ωpe≈0.5ωpi, where ωpe is the electron and ωpi the ion plasma frequency.