Nonlinear Quantum Plasma Physics

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We present simulation studies of the formation and dynamics of dark solitons and vortices, and of nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) dense in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schrodinger and Poisson system of equations, which conserves electrons and their momentum and energy. Nonlinear fluid simulations are carried out to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a dense Fermi (quantum) plasma. We report several distinguished features that have resulted from our 2D computer simulations of the nonlinear equations which govern the dynamics of nonlinearly interacting electron plasma oscillations (EPOs) in the Fermi plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations determined critically by quantum tunneling effect. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory. The dynamics of the CPEM waves is also governed by a nonlinear schrodinger equation, which is nonlinearly coupled with the nonlinear Schrodinger equation of the EPOs via the relativistic ponderomotive force, the relativistic electron mass increase in the CPEM field, and the electron density fluctuations. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma.