Acceleration and Cyclotron Radiation, Induced by Gravitational Waves

The equations which determine the response of a charged particle moving in a magnetic field to an incident gravitational wave(GW) are derived in the linearized approximation to general relativity. We briefly discuss several astrophysical applications of the derived formulae taking into account the resonance between the wave and the particle's motion which occurs at $\omega_g=2\Omega$, whenever the GW is parallel to the constant magnetic field. In the case where the GW is perpendicular to the constant magnetic field, magnetic resonances appear at $\omega_g=\Omega$ and $\omega_g=2\Omega$. Such resonant mechanism may be useful to build models of GW driven cyclotron emitters.