Instability of short wavelength electrostatic electron-cyclotron modes in the presence of an ion density ripple in plasmas

It is shown that short wavelength (in comparison with the ion thermal gyroradius), high-frequency (HF) electrostatic electron-cyclotron (EEC) modes can be excited by the pre-existing ion density ripple across the external magnetic field in a dusty magnetoplasma. For this purpose, we use the Boltzmann distributed ion density perturbation, together with the electron continuity and momentum equations, and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that the short wavelength HF-EEC-like modes in dusty magnetoplasmas can be driven due to the free energy in the ion density ripple.