Analytische und numerische Untersuchung von Plasmawellen in idealen Quantenplasmen im Rahmen eines Mehrstrommodells der Elektronen

  • Analytical and numerical study of plasma waves in ideal quantum plasmas within the framework of a multistream model of the electrons

Steffen, Wibke; Kull, Hans-Jörg (Thesis advisor); Schmitz, Rudolf (Thesis advisor)

Aachen (2015, 2016)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2015


The electron dynamics in ideal quantum plasmas are fundamentally described by the quantum Vlasov theory, the quantummechanical analogue to the classical Vlasov theory. Oscillations and relaxation of oscillations in a quantum plasma differ considerably from oscillations and their relaxation in a classical plasma. In the present work electron dynamics in an ideal quantum plasma are studied within the framework of an ensemble model for the electrons. The ensemble model is derived from the quantum Vlasov equation by a discretization of the statistcal operator of the electrons for representative electron states. The ensemble model forms the theoretical basis for the numerical carrier-envelope wave (CEW) method. With the CEW method efficient numerical calculations of the electron dynamics in an ideal quantum plasma are carried out. Numerical calculations of linear plasma waves with the CEW method reproduce the well-known results from Landau-Lindhard-theory (LLT) for the dispersion of plasma waves in quantum plasmas. However, additional effects are observed in the evolution of the electrostatic potential. Those effects are a non-exponential damping of the plasma wave, beat waves and echoes. The objective of this work is the analytical description of those additional effects for linear plasma waves in quantum plasmas as well as the analysis of the convergence of the ensemble model and the CEW method with an increasing number of representative electron states. Linear plasma waves are analytically described by an analysis of stationary and generalized stationary modes within the ensemble model of the electrons. Within this framework, a complete analytical solution of the initial value problem is derived in this work. The complete evolution of the oscillation and relaxation behaviour of linear plasma waves for arbitrary initial conditions is derived. The analysis of linear plasma waves yields the following essential results: The electrostatic potential for linear plasma waves in the multistream model converges quickly with the number of representative states. The echoes in the potential are caused by the discretization of the electron ensemble by a finite number of representative states and do not occur in the continuum limit. The beat waves and the non-exponential damping of linear plasma waves in quantum plasmas are no discretization effect but an essential feature of the oscillation and relaxation of plasma waves in quantum plasmas. For classical plasmas with a maxwellian distribution of electron momenta the phase relaxation of the superposition of stationary modes is asymptotically described by exponential Landau damping of the collective plasma mode. For degenerate quantum plasmas with a Fermi-Dirac distribution of electron momenta, however, the phase relaxation is asymptotically given by a weaker, non-exponential damping. The numerical study of nonlinear plasma waves in the wavebreaking regime with the CEW method shows the quick convergence of the CEW method with an increasing number of representative states for nonlinear plasma waves.