Cold-hot coupled waves in a flowing magnetized plasma

Abstract

Nonlinear coupling of cold and hot waves in a flowing magnetized plasma is analyzed with the Vlasov equation. An analytical solution is obtained for cold waves of a small amplitude (weak flow) and a long wavelength. The distribution function is obtained by integrating the kinetic equation along a perturbed phase-space trajectory for a time-varying plasma flow. The kinetic description presents a generalized dispersion relation that involves resonances depending on cold and hot wave dispersions. Coherent fluid motion leads to radiation peaks in addition to the cyclotron harmonics, where the wavenumber of the cold wave determines the peak frequencies. The peaks appear narrow when the wave propagates perpendicular to the time-averaged flow while they become broad due to the Doppler effect when the wave propagates parallel to the flow. Fully kinetic particle-in-cell simulations corroborate the theoretical predictions. The dispersion relation and resulting wave spectra provide information about plasma parameters and flow properties.

Nonlinear harmonics coupled by parallel wave propagations in a time-dependent plasma flow

“…The lowest order solution of the zerothorder Vlasov equation (ω l / kl ≫ v Ts ) gives the cold wave dispersion relation and the associated mobility for ũs0 . By solving the linearized Vlasov equation for f s1 , E 1 , and B 1 , the dielectric tensor of the time-varying plasma is obtained [23].…”

“…From the generalized dielectric tensor of a time-varying plasma (equation (24) in reference [23]), we obtain a dielectric tensor for the parallel propagation (k → k ∥ ),…”

“…waves. Fully kinetic PIC simulations showed that a nonlinear coupling between the conventional mode ω and the fluid wave harmonics ∑ N l=1 m l ωl satisfies the wavenumber selection rule [23]: For example, the conventional cyclotron harmonics ω ≃ nω cs due to thermal motions and the fluid wave harmonics ∑ N l=1 m l ωl due to plasma flows excite the harmonics ω ≃ nω cs + ∑ N l=1 m l ωl . On the other hand, from various studies of the coupling between oscillation modes [31][32][33][34][35], it has been shown that the coupling may satisfy the wavenumber selection rule as well as the frequency selection rule.…”

“…However, plasmas involve nonlinearly coupled fields and associated particle motions [17][18][19][20]. Even when the intensity of a nonlinearly excited wave is small compared to a linear wave, the nonlinear wave can carry information of a plasma or trigger instabilities [17,[21][22][23]. By investigating the nonlinearity, one can understand plasma kinetics which cannot be explained by linear theory.…”

“…In our previous work [23], we reported a dispersion relation that involved the nonlinear coupling of a cold (or warm) wave and a hot wave via time-dependent plasma flows. As an example, the couplings between extraordinary waves (Xwaves) are demonstrated by the Vlasov analysis and particlein-cell (PIC) simulations, where the waves are electromagnetic and perpendicular to the equilibrium magnetic field.…”