Interaction of longitudinal and transverse wave modes with quantum plasma

Abstract We examine the degenerate gravity waves in the presence of damped longitudinal waves. Specifically, under the assumption of linear longitudinal wave propagation in degenerate self-gravitating electron-ion plasmas, damp-wave is shown to reduce the Jeans instability (JI) as a function of degeneracy corrections, provided Jeans frequency is either equal to or less than the quantum ion-acoustic frequency. The Jeans threshold wavelength is an inverse function of quantum parameters. Whereas, if the Jeans frequency exceeds the ion-acoustic frequency at some specific gravitational scale length, the growth rate of gravitational waves is a function of both ion density concentration and quantum corrections via damp-longitudinal wave. The associated Jeans wavelengths and Jeans critical mass are defined. Next, the nonlinear interaction of short-scale transverse electromagnetic (EM) waves of two different harmonics with isotropic plasma under study are investigated to account for quantum nonlinear Landau damping (QNLD) of EM waves. We calculate the response of Fermi electrons to the nonlinear interaction of beat waves while considering a specific quantum regime where the group velocity of beat waves is comparable to the electron Fermi velocity. The Fermi electron population is then modelled by deriving a new type of nonlinear Schrödinger (NLS) equation involving the nonlocal nonlinear term, which accounts for the QNLD, and the damping rate is calculated. Signatures of degeneracy effects on nonlinear decrement of EM beat waves are found more prominent at smaller values of Fermi electron density concentrations. Thereby, more energy can be available from the pump EM waves to the Fermi electrons, which may be used to accelerate them. Finally, we investigate the analytical results within astrophysical settings using numerical techniques.