Cyclotron instability of the slow extraordinary wave in a magnetoactive plasma

The dipole approximation is applied to the kinetic instability in longitudinally propagating whistlers and the Z mode at frequencies below the nonrealtivistic electron gyrofrequency, which is due to a group of fast electrons in a magnetic trap. Numerical calculations are used to analyze the effects from the parameters of the hot and cold components on the increment for the waves propagating parallel to the magnetic field and at a small angle to it; it is shown that relativistic effects allow marked instability for the oblique Z mode only in a restricted energy range for the hot component. The relation between the extraordinary-wave increments is considered for longitudinal and transverse propagation. Analytic estimates are obtained for the increment and amplification coefficient for the Z mode in the case of perpendicular propagation.