Quantum drift instability and self-interference of electron beam

Abstract

In this research, we study the traveling wave solution of an effective Schrödinger–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 self-interference condition.