Different kλD regimes for nonlinear effects on Langmuir waves

Abstract

As Langmuir waves (LWs) are driven to large amplitude in plasma, they are affected by nonlinear mechanisms. A global understanding, based on simulations and experiments, has emerged that identifies various nonlinear regimes depending on the dimensionless parameter kλD, where k is the Langmuir wave number and λD is the electron Debye length. The nonlinear phenomena arise due to wave-wave and wave-particle coupling mechanisms, and this basic separation between fluid-like nonlinearities and kinetic nonlinearities depends on the degree to which electron and ion Landau damping, as well as electron trapping, play a role. Previous ionospheric heating experiments [Cheung et al. Phys. Plasmas 8, 802 (2001)] identified cavitation/collapse and Langmuir decay instability (LDI), predominantly wave-wave mechanisms, to be the principal nonlinear effects for driven LWs with kλD<0.1, in agreement with fluid simulations [DuBois et al. Phys. Plasmas 8, 791 (2001)]. In the present research, collective Thomson scattering measurements of LWs driven by stimulated Raman scattering in laser-plasma experiments are used to study both wave-wave and wave-particle nonlinearities [Kline et al. Phys. Rev. Lett. 94, 175003 (2005)]. For kλD<0.29, multiple LWs are detected and are attributed to LDI, a wave-wave nonlinear regime. For kλD>0.29, a single-wave, frequency-broadened spectrum is observed associated with electron trapping, a wave-particle nonlinear regime. The transition from wave-wave to wave-particle nonlinear behavior is qualitatively consistent with particle-in-cell simulations and with the crossing of the LDI threshold above that for LW self-focusing. The fact that LDI is observed in both ionospheric and laser-plasma experiments for similar values of kλD, though vastly differing in plasma conditions and scales, and that simulations predict the various observed nonlinear regimes over a large range of kλD, supports our global view of LW nonlinear behavior.

Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations

“…[14] and [11] suggest that kinetic effects might dominate fluid effects even for large amplitudes of LW if kλ D > 0.3. Though the trapped electron frequency shift, perturbatively, varies as |E| 1/2 [6,9,10], and therefore cannot lead to LW collapse [13,45,46], 3D PIC simulation results [18] have been interpreted as showing that the trapped electron LW filamentation instability can saturate [19] stimulated Raman back-scatter (SRS) [21] by reducing the LWs coherence.…”

“…It was shown in Refs. [35] and [1] that taking the double limit (13) in the equation Eq. (12) we get…”

“…There are two methods to construct BGK modes in question. First method is numerical one and implies that we numerically solve equations (8)- (12) for each values of φ pump and ν SideLoss followed by taking numerically the double limit (13). Second method is analytical one and is based on the integration along the particle orbits of the time independent solution of Eq.…”

“…[11]. Thus ∆ω trapped at kλ D 0.2 may dominate [8,[11][12][13][14] over ∆ω f luid . Negative ∆ω trapped , with positive diffraction, imply LW filamentation [8,[15][16][17].…”

Kinetic enhancement of Raman backscatter, and electron acoustic Thomson scatter

“…However, recent experiments [4][5][6] and kinetic simulations [7][8][9][10][11][12] have shown SRBS reflectivities well above coupled-mode convective gain levels. * Electronic address: dstrozzi@llnl.gov This kinetic inflation or enhancement of SRBS is widely attributed to electron trapping in the EPW potential well, which flattens the electron distribution function near the EPW phase velocity v p2 [7,13]. As has long been known, trapping reduces the EPW damping rate [14] and induces an amplitude-dependent frequency downshift [15].…”