Absolute parametric instability of low frequency waves in a 2-D nonuniform anisotropic warm plasma

Using the separation method, the problem of absolute parametric instability (API) of electrostatic waves in magnetized pumped warm plasma is investigated. In this case the effect of static strong magnetic field is considered. The problem of strong magnetic field is solved in 2-D nonuniform in plane plasma. The equations, which describe the spatial part of the electric potential, are obtained. Also, the growth rates and conditions of the parametric instability for periodic and aperiodic cases are obtained. It is found that the spatial nonuniformity of the plasma exerts a stabilizing effect on the API. It is shown that the growth rates of periodic and aperiodic API in warm plasma are reduced in comparison with a cold plasma case. Also, it is found that the warmness of the plasma electrons has no effect on the solution of the space part of the problem.