The Nonlinear Ohm's Law: Plasma Heating by Strong Electric Fields and its Effects on the Ionization Balance in Protoplanetary Disks

摘要

The ionization state of the gas plays a key role in the MHD of protoplanetarydisks. However, the ionization state can depend on the gas dynamics, becauseelectric fields induced by MHD turbulence can heat up plasmas and therebyaffect the ionization balance. To study this nonlinear feedback, we constructan ionization model that includes plasma heating by electric fields and impactionization by heated electrons, as well as charging of dust grains. We showthat when plasma sticking onto grains is the dominant recombination process,the electron abundance in the gas decreases with increasing electric fieldstrength. This is a natural consequence of electron-grain collisions whosefrequency increases with electron's random velocity. The decreasing electronabundance may lead to a self-regulation of MHD turbulence. In some cases, notonly the electron abundance but also the electric current decreases withincreasing field strength in a certain field range. The resulting N-shapedcurrent--field relation violates the fundamental assumption of thenon-relativistic MHD that the electric field is uniquely determined by thecurrent density. At even higher field strengths, impact ionization causes anabrupt increase of the electric current as expected by previous studies. Wefind that this discharge current is multi-valued (i.e., the current--fieldrelation is S-shaped) under some circumstances, and that the intermediatebranch is unstable. The N/S-shaped current--field relations may yieldhysteresis in the evolution of MHD turbulence in some parts of protoplanetarydisks.