PRELIMINARY NONLOCAL ANALYSIS OF CROSS-FIELD CURRENT INSTABILITY FOR SUBSTORM EXPANSION ONSET

The modified-two-stream instability (MTSI) is one of the modes of the cross-field current instability which has recently been considered as one plausible mechanism for substorm expansion onset and intensification. This paper extends the previous analysis of this instability to nonlocal treatment under the simplifying assumptions of electrostatic perturbations and neglect of thermal and kinetic effects. The result enables us to gain new insights on the onset threshold of the instability. We find that a current sheet with a constant velocity associated with the current (exemplified by the Harris equilibrium current sheet) is stable with respect to MTSI, whereas one with a prominent velocity peak at its center is unstable when it is sufficiently thin. This result therefore indicates that the onset threshold of the instability is very sensitive to the global characteristics of the current sheet, and its value can be determined only through nonlocal analysis. The higher onset threshold than that predicted by the local theory allows one to better understand why a substantial cross-tail current enhancement can develop and a thin current sheet can remain stable for an extended period before the onset of substorm expansion and current disruption.