On ballooning instability in current sheets

Abstract

The problem of instability of azimuthally small-scale Alfven and slow magnetosonic (SMS) waves in the geotail is solved. The solutions describe unstable oscillations in the presence of a current sheet and correspond to the region of stretched closed field lines of the magnetotail. The spectra of eigen-frequencies of several basic harmonics of standing Alfven and SMS waves are found in the local and WKB approximation, which are compared. It is shown that the oscillation properties obtained in these approximations differ radically. In the local approximation, the Alfven waves are stable in the entire range of magnetic shells. SMS waves go into the aperiodic instability regime (the regime of the ‘ballooning’ instability), on magnetic shells crossing the current sheet. In the WKB approximation, both the Alfven and SMS oscillations go into an unstable regime with a non-zero real part of their eigen-frequency, on magnetic shells crossing the current sheet. The structure of azimuthally small-scale Alfven waves across magnetic shells is determined.