Modulational instability of electromagnetic ion-cyclotron waves by ion acoustic waves in a collisionless plasma

Using the hydrodynamic model for a homogeneous plasma, we have investigated the modulational instability of an electromagnetic ion-cyclotron wave by a low-frequency electrostatic ion acoustic mode in a collisionless plasma. The low-frequency nonlinearity of the instability arises through the parallel ponderomotive force on the ions, and the high-frequency nonlinearity arises through the nonlinear current densities of the ions. For typical plasma parameters $n_0^0={10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$, $\frac{{\omega }_{\mathrm{ci}}}{{\omega }_0}=1.2\mathrm{}$, $B_s=10\mathrm{}$ kG, $T_i=1\mathrm{}$ keV, $T_i=0.05\mathrm{}$ keV, and $\theta =30\mathrm{}°$, the growth rate of the instability turns out to be ∼${10}^4$ rad ${\sec }^{-1\mathrm{}}$ for $\left|v_{0ix}\right|C_s|={10}^{-2\mathrm{}}$, where $v_{0ix}$ is the pump-induced drift velocity of the ions and $C_s$ is the ion acoustic velocity in the plasma.