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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.

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