Parametric instabilities of electrostatic electron waves in relatively weak magnetic fields were investigated in a unified manner. As the propagation angle is shifted from the angle parallel to the ambient magnetic field to the perpendicular one, the electrostatic electron normal modes in such a system change from Langmuir to upper-hybrid waves through oblique Langmuir waves. These waves are unstable to various parametric instabilities, such as the modulational and decay instabilities. The present analysis extends the previous work (Akimoto K 1989 Phys. Fluids B1 1998) on parametric instabilities of Langmuir waves to those of electrostatic electron waves that are not field-aligned, and carries out a comparative study of parametric instabilities of the electron waves by numerically solving a dispersion equation. The author finds that as the propagation angle shifts from the field-aligned direction, the maximum growth rate of the dominant instability frequently increases, yet remains of the same order of magnitude; on the other hand, the topological structure of the growth rate contours may change dramatically, even if the propagation angle is only slightly shifted. In addition, the growth rate contours for an upper-hybrid wave show a variety of interesting patterns as the parameters, such as the wavenumber of the pump waves are varied. The overall results indicate that upper-hybrid and oblique Langmuir turbulence isotropizes faster than Langmuir turbulence, and may often be dissipated without the formation of the condensate at any point in the process.
Parametric instabilities excited by ion sound and ion cyclotron quasi-modes during lower hybrid heating of tokamak plasmas