In the paper, the decay instabilities of the hydromagnetic oscillations in a plasma cylinder placed in the field of a direct magneto-sonic wave Hz = 0I0(k0r)cosΩ0t (I0 is the Bessel function, k0 is the radial wave number, ) and 0 is the amplitude of the high-frequency field) are studied. Instability growth rates were derived for decay in cases where the result is the excitation of short-wave Alfvén and slow magneto-sonic oscillations. Calculations were carried out for various distributions of the field of the background wave over the cylinder cross-section: k0a ≪ 1; k0a = 2.405; a is the radius of the cylinder. The growth-rates are determined by formulae of the type γ = Ω0A0/H0, where H0 is the strength of the static field, A is a coefficient less than or of the order of unity, depending on the type of decay, the plasma parameters and the wave numbers for the excited waves. Formulae are presented for the determination of the threshold amplitudes for excitation of the instabilities. The possibility of using these instabilities for plasma heating is briefly discussed.
Parametric excitation of ion-sound instability in a magnetized plasma located in a high-frequency electric field