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Decay instability of cyclotron harmonic plasma waves. (English) Zbl 1230.76053
Summary: The decay instability of cyclotron harmonic plasma waves is investigated by solving the nonlinear Vlasov equation to the second order in powers of the wave amplitude. For a Maxwellian plasma, it is shown that a single cyclotron harmonic wave with frequency \(\omega_0(k_0)\) can decay into two other modes with \(\omega_1(k_1)\) and \(\omega_2(k_2)\) when the three waves satisfy the decay condition: \(\omega_0=\omega_1+\omega_2\), \(k_0=k_1+k_2\). For a ring velocity distribution, it is shown that a mode with \(\omega_0\) decays into a negative energy wave \(\omega_1\) and a positive one \(\omega_2\) under the matching condition: \(\omega_0=\omega_1\sim\omega_2\), \(k_0=k_1\sim+k_2\), where \(\sim\) denotes the difference. The growth rates of the decay instability are solved numerically and the results are illustrated.

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanical studies of plasmas
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