Kinetic simulations and reduced modeling of longitudinal sideband instabilities in non-linear electron plasma waves

Abstract

Kinetic Vlasov simulations of one-dimensional finite amplitude Electron Plasma Waves are performed in a multi-wavelength long system. A systematic study of the most unstable linear sideband mode, in particular its growth rate γ and quasi- wavenumber δk, is carried out by scanning the amplitude and wavenumber of the initial wave. Simulation results are successfully compared against numerical and analytical solutions to the reduced model by Kruer et al. [Phys. Rev. Lett. 23, 838 (1969)] for the Trapped Particle Instability (TPI). A model recently suggested by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)], which in addition to the TPI accounts for the so-called Negative Mass Instability because of a more detailed representation of the trapped particle dynamics, is also studied and compared with simulations.

Longitudinal and Transverse Instability of Ion Acoustic Waves

“…2(d), but does not permit OAI (this was confirmed by comparing 1D and 2D simulations). As in related 1D studies [17,29], Bloch-Floquet type eigenmodes are present [i.e., γ(k x , 0) is symmetric about k n over the interval ([n − 1/2]k 1 , [n + 1/2]k 1 ), where n = 1, 2, . .…”

Quantitative study of the trapped particle bunching instability in Langmuir waves

“…20,21 In longer systems (L ) k L ), sideband growth alters the amplitude of the carrier wave resulting in turbulence. 9,10 The role of the NMI in the excitation and evolution of nonlinear plasma waves, when sidebands and significant harmonic content of the carrier waves are present, will be addressed in future work. …”

“…In order to compare the simulation results with theory, 4,9 we have revisited the theory and obtained a more accurate dispersion relation from which the growth rate can be obtained.…”

“…1,9,19 Here, a periodic system is considered. Decomposition of Vlasov and Poisson equations in Fourier series leads to Bloch-type modes, the superposition of Fourier components dE n with frequency x n ¼ dx þ nx L and wavenumber k n ¼ dk þ nk L for integers n ¼ 0, 61, 62,….…”

“…In the SI, unstable sidebands are resonant in the wave frame with the trapped particle bounce motion as well as satisfying the Langmuir dispersion relation. Recent advances in the theory of trapped particles 4,9 have accounted for the energy dependence of the bounce frequency and allowed multiple unstable branches of the dispersion relation, providing a more complex picture where SI and NMI are coexistent. By considering, as here, a periodic system restricted to length L ¼ k L 2p=k L , where k L and k L are the wavelength and wavenumber of the carrier wave, only wavenumbers k ¼ nk L (n ¼ 1, 2,…) are permitted in the system.…”