This article discusses in quasi-linear approximation the convective instability of a dilute plasma that occurs when the plasma density exceeds a certain critical value. It is shown that the equations determining the frequency and amplitude of non-linear oscillations enable introduction of an effective potential energy. The oscillations themselves in a certain sense equivalent to the oscillations of a non-linear, two-dimensional, axially symmetric oscillator (rotator) that moves without friction. Consideration of non-linear effects has made possible considerable specification of the instability criterion found in the linear approximation. It is shown that plasma stability with respect to finite-amplitude oscillations depends on the quantity d3n/d(r2)3; here n is plasma density, r the distance from the axis of the system.
Kinetic instability of flute oscillations