Effects of group velocity and multiplasmon resonances on the modulation of Langmuir waves in a degenerate plasma

Abstract

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schrödinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multi-plasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multiplasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where k ∼ mvF with denoting the reduced Planck's constant, m the electron mass and vF the Fermi velocity, however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multi-plasmon effects are forbidden.

Landau damping of electron-acoustic waves due to multi-plasmon resonances

“…Substituting the stretched coordinates (17) and the expansions ( 16) and ( 18) into Eqs. ( 1) and ( 2) we obtain in one-dimensional geometry…”

“…In plasmas with two-temperature electrons, the nonlinear theory of EAWs has been investigated by many authors, however, using the fluid theory approach, i.e., without the Landau damping effects [10,11]. On the other hand, after the work of Ott and Sudan [12] on nonlinear theory of ion-acoustic waves with linear Landau damping, many authors have studied the Landau damping of low-frequency electrostatic waves [13][14][15] as well as high-frequency wave envelopes [16,17], however, no nonlinear theory of EAWs with Landau damping has been developed in the context of quantum plasmas. While the linear plasmon resonance is known in the literature, the multi-plasmon resonance [18] in the nonlinear regime has not yet been fully explored, especially in the context of KdV equation.…”

“…Refs. [17,18]) where we can have simultaneous absorption (or emission) of multiple plasmon quanta. Including this mechanism into the calculation scheme, an additional wave damping due to the two-plasmon resonance is seen to occur in the evolution of EAWs along with the resonance of linear theory.…”

Kinetic theory for spin-1/2 particles in ultrastrong magnetic fields

“…Our approach now is to calculate the commutators occurring in (6) to all orders in the magnetic field. In doing this we will expand some of them in a series using Ref.…”

“…Quantum kinetic descriptions of plasmas are typically of most interest for high densities and modest temperature [1]. For this purpose, typically the starting point is the Wigner-Moyal equation [1][2][3][4][5][6], or various generalizations thereof also accounting for physics associated with the electron spin, such as the magnetic dipole force [7,8], spin magnetization [7,9], and spin-orbit interaction [9]. Both weakly [10,11] and strongly [12,13] relativistic treatments have been presented in the recent literature.…”