Quantum Faraday excitations in degenerate electron-ion plasma

A hydrodynamic two-fluid model encompassing inertialess electrons of arbitrary degree of degeneracy and cold ions using the quasineutrality assumption are reduced to an effective nonlinear Schrödinger equation (NLSE) which is used to investigate driven electrostatic plasma-phonon excitations. The quantized frequency spectrum of these plasma-phonon excitations in a one-dimensional quasineutral electron-ion plasma confined in rectangular potential well is calculated. The spectrum shows a quadratic energy level increase quite similar to that of a single electron confined in a hard box, with much reduced level spacings proportional to the electron-to-ion mass ratio. The parametrically driven NLSE is also used to study the quantum Faraday excitations in both weakly and fully nonlinear regimes by employing the pseudo-potential technique. The quantization criterion for fully nonlinear driven quantum Faraday excitations in an arbitrary degenerate plasma confined in a hard box of length l is derived, and it is shown that these excitations constitute a full frequency spectrum level starting with those of small amplitude, high frequency sinusoidal plasma-phonon up to the topmost zero-frequency level solitary plasma-phonon excitations (plasma-soliton level). (paper)