Beat excitation of whistler waves

This report provides a clear example of how the nonlinear efficiency for the radiation of a low frequency electromagnetic signal due to the beat of two high frequency pumps can be determined from first principles. The calculation includes plasma nonuniformity as well as finite spatial extent of the pumps. The figure of merit for the beat process is given by the compact expression. A rough order of magnitude evaluation of this expression shows a radiated power whose dependence on pump power scales as P sub R is equivalent to V sub os squared P sub p, where V sub S refers to the oscillating velocity of an electron due to the high frequency pump, and c is the speed of light. This dependence illustrates readily the extreme inefficiency of the process at low pump power (i.e., v sub os). Another fundamental factor which lowers the efficiency is that the coupling to the whistler wave occurs through electric dipole excitation. A more efficient excitation mechanism would be to use magnetic coupling, i.e., to generate a nonlinear transverse current oscillating at the beat frequency. However, within the constraints of the present geometry this more desireable situation cannot be realized directly. The most advantageous feature of the beat excitation described here is the controllability of the spatial location from which the whistler emanates.