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Abstract
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In this research, we study the traveling wave solution of an effective Schr€ odinger–Poisson system in the framework of quantum
hydrodynamic model of a drifting electron gas with arbitrary degeneracy. It is shown that collective excitations in a quantum electron beam
are characterized by two distinct particle-like and wave-like (de Broglie) wavenumbers depending on many beam parameters such as the drift
speed, chemical potential, and background electromagnetic potential energies. Moreover, a new kind of beam-plasmon instability, referred to
as the quantum drift instability, is found to exist in this system, which is caused by imbalance between the kinetic energy of the beam and the
ambient electromagnetic and chemical potential energies. The quantum drift instability is an effect in which the energy flow from small
wavelength particle-like excitations to long wavelength collective excitations occurs below a critical beam drift speed and may be characterized as the inverse of the usual Landau damping effect. We also investigate different kinds of quantum electron fluid interference effects
based on generalized de Broglie wavenumbers. It is shown that in the limit of very low electron concentration and high drift the electron
beam is described by the characteristic quantum de Broglie wavenumber. The fully nonlinear isothermal and adiabatic beam excitations are
also numerically investigated. It is shown that quantized values of the mono-energetic electron beam speed give rise to resonant selfinterference condition.
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