Precession and kink motion of long astron layers

A study is made of the stability of the low-frequency precession and kink modes of a long astron particle layer embedded in a dense low-temperature plasma. Two types of precession of ion layers are discussed in detail. At relatively high frequencies there is a precession mode with frequency ω approximately -(eta/sub e//2)Ω which shows the well-known negative energy type of instability for negative values of the effective external field index eta/sub e/. For low frequencies there is a magnetohydrodynamic precession mode with frequency ω approximately +- (eta/sub e//zeta)/sup 1/2/(v/sub A//anti v/sub theta/)Ω which is purely growing for eta/sub e/ less than 0. Here, Ω is the average circulation frequency for the layer particles; zeta is the loading factor, which is a measure of the layer strength; anti v/sub theta/ is the average azimuthal velocity of the layer ions; and v/sub A/ is the Alfven speed of the plasma. For the kink modes, a sufficient condition for stability is shown to be eta/sub S/ less than 3, where eta/sub S/ is the self-magnetic field index. For eta/sub S/ greater than 3 the kink motion is found to be purely growing