Longitudinal Plasma Wave Echo Excited by Two Cyclotron Waves

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It is shown that successive excitation of two cyclotron waves with a time interval longer than their cyclotron damping periods leads to a spontaneous appearance of a longitudinal plasma wave in a collisionless plasma. The longitudinal plasma wave (i. e., the echo), has the frequency shifted by the cyclotron frequency and appears at the same time as in the case of the excitation by two plasma waves. The line shapes of temporal echoes, together with the phase mixing processes of the second order distribution functions, are studied numerically.

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