Landau damping and the onset of particle trapping in quantum plasmas

Abstract

Using analytical theory and simulations, we assess the impact of quantum effects on non-linear wave-particle interactions in quantum plasmas. We more specifically focus on the resonant interaction between Langmuir waves and electrons, which, in classical plasmas, lead to particle trapping. Two regimes are identified depending on the difference between the time scale of oscillation tB(k)=m/eEk of a trapped electron and the quantum time scale tq(k)=2m/ℏk2 related to recoil effect, where E and k are the wave amplitude and wave vector. In the classical-like regime, tB(k) < tq(k), resonant electrons are trapped in the wave troughs and greatly affect the evolution of the system long before the wave has had time to Landau damp by a large amount according to linear theory. In the quantum regime, tB(k) > tq(k), particle trapping is hampered by the finite recoil imparted to resonant electrons in their interactions with plasmons.