Landau Damping and the Onset of Particle Trapping in Quantum Plasmas

The notion of wave-particle interactions, the couplings between collective and individual particle behaviors, is fundamental to our comprehension of plasma phenomenology. Such is the case when the electrons' thermal energy $k_BT$ is of the order of or smaller than their Fermi energy $E_F\!\!=\!\!\frac{\hbar^2}{2m}(3\pi^2n)^{1/3}$ ($n$ and $m$ are the electron density and mass). The physics of quantum plasmas (e.g., of the warm dense matter regime) is a frontier of high-energy density physics with relevance to many laboratory experiments and to astrophysics. The question arises as to how wave-particle interactions are modified when the quantum nature of the electrons can no longer be ignored. Using analytical theory and simulations, we assess the impact of quantum effects on non-linear wave-particle interactions in quantum plasmas. Two regimes are identified depending on the difference between the time scale of oscillation $t_B(k)\!=\!\sqrt{m/eEk}$ of a trapped electron and the quantum time scale $t_q(k)\!=\!2m/\hbar k^2$ related to recoil effect, where $E$ and $k$ are the wave amplitude and wave vector. In the classical-like regime, $t_B(k)\!<\!t_q(k)$, 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, $t_B(k)\!>\!t_q(k)$, particle trapping is hampered by the finite recoil imparted to resonant electrons in their interactions with plasmons. \\[4pt] Reference: J. Daligault, Phys. Plasmas 21, 040701 (2014).