Quasi-linear analysis of ion Weibel instability in the earth's neutral sheet

A quasi-linear analysis of the ion Weibel instability (IWI) for waves with parallel propagation is carried out for parameters appropriate to the earth's neutral sheet during the substorm interval. For ion drift speed reaching sizable fraction of the ion thermal speed, unstable waves grow to a nonlinear regime in a time interval greater than an ion gyroperiod. The saturation level is attained with current density reduced to about 15-28 percent of its preactivity level. The unstable wave amplitude normalized to the initial ambient field is found to be in the range of 0.2-0.8. This is accompanied by ion heating along the magnetic field with the parallel temperature being enhanced by 25-90 percent. Thus, the IWI can provide nonadiabatic heating of ions in current disruptions during substorms. The associated anomalous resistivity is estimated to be about 1 x 10 exp -7 to 1 x 10 exp -6 s, which is about 11 to 12 orders of magnitude above the classical resistivity.