Echo Processes in a Plasma

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Abstract
The generation of echoes in classical systems is discussed with particular reference to cyclotron echoes in a plasma. A system of oscillators subjected to a sequence of pulses will produce an echo if the interaction contains appropriate nonlinear terms. A formal description of the echo mechanism is given for the case where nonlinear effects are confined to the times at which pulses are present, with emphasis on wave-propagation aspects. Diagrams are introduced for the classification of various nonlinear processes. The generation of echoes in a plasma interacting with microwave pulses propagating normal to an applied magnetic field is analyzed in a small-signal approximation. Echoes are found to arise from nonlinear terms associated with the convective motion of the electrons, and from the interaction with the magnetic component of the microwave pulses. Equations for the echo amplitude, in terms of the pulse widths and intensities, are given for transverse and longitudinal propagation.