Quasi‐linear analysis of ion Weibel instability in the Earth's neutral sheet

Abstract

The development of the ion Weibel instability in the Earth's neutral sheet is examined by quasi‐linear analysis for waves propagating along the ambient magnetic field. For ion drift speed reaching a sizable fraction (∼0.5 to 1) of the ion thermal speed, numerical solution of the quasi‐linear kinetic equations shows the wave growth reaching the nonlinear stage in less than one ion gyroperiod. The saturation level is attained with the ion drift speed reducing by ∼15 to 28% of its initial value, wave amplitudes ranging from ∼0.2 to 0.8 of the ambient magnetic field, and the ion temperature along the magnetic field increasing by ∼25 to 90%. This instability thus provides a means for non‐adiabatic heating of ions during substorms. The resulting anomalous resistivity is estimated to be ∼1×10−7 to 1×10−6 s, about 11 to 12 orders of magnitude above the classical Coulomb resistivity. These predictions may be regarded as lower limits on the effects of the nonlinear stage of this instability since only parallel propagating waves are considered. Nevertheless, the calculated reduction in the ion drift speed compares reasonably well with the inferred amount of current reduction from observations of current disruption events, and the anomalous resistivity is within the range of values estimated for active magnetotail regions during substorm expansion. The difference in the nonlinear evolution with different initial ion drift speeds suggests that a current system in the same sense as the substorm current wedge is expected to be established in the midnight region as a result of this instability occurring in the nightside neutral sheet. For a typical amount of current reduction, it is estimated that the plasma in this region is subjected to a substantial net force injecting it earthward.