Evidence for four- and three-wave interactions in solar type III radio emissions

Abstract

The high time resolution observations obtained by the STEREO/WAVES experiment show that in the source regions of solar type III radio bursts, Langmuir waves often occur as intense localized wave packets with short durations of only few ms. One of these wave packets shows that it is a three-dimensional field structure with <span style="border-bottom: 1px solid #000; vertical-align: 50%; font-size: .7em; color: #000;"><I>W</I>_L</span><span style="margin-left: -1.3em; margin-right: .5em; vertical-align: -15%; font-size: .7em; color: #000;"><I>n</I>_e<I>T</I>_e</span> ~ 10^&minus;3, where <I>W</I>_L is the peak energy density, and <I>n</I>_e and <I>T</I>_e are the electron density and temperature, respectively. For this wave packet, the conditions of the oscillating two-stream instability (OTSI) and supersonic collapse are satisfied within the error range of determination of main parameters. The density cavity, observed during this wave packet indicates that its depth, width and temporal coincidence are consistent with those of a caviton, generated by the ponderomotive force of the collapsing wave packet. The spectrum of each of the parallel and perpendicular components of the wave packet contains a primary peak at <I>f</I>_pe, two secondary peaks at <I>f</I>_pe ± <I>f</I>_S and a low-frequency enhancement below <I>f</I>_S, which, as indicated by the frequency and wave number resonance conditions, and the fast Fourier transform (FFT)-based tricoherence spectral peak at (<I>f</I>_pe, <I>f</I>_pe, <I>f</I>_pe + <I>f</I>_S, <I>f</I>_pe &minus; <I>f</I>_S), are coupled to each other by the OTSI type of four-wave interaction (<I>f</I>_pe is the local electron plasma frequency and <I>f</I>_S is the frequency of ion sound waves). In addition to the primary peak at <I>f</I>_pe, each of these spectra also contains a peak at 2<I>f</I>_pe, which as indicated by the frequency and wave number resonance conditions, and the wavelet-based bicoherence spectral peak at (<I>f</I>_pe, <I>f</I>_pe), appears to correspond to the second harmonic electromagnetic waves generated as a result of coalescence of oppositely propagating sidebands excited by the OTSI. Thus, these observations for the first time provide combined evidence that (1) the OTSI and related strong turbulence processes play a significant role in the stabilization of the electron beam, (2) the coalescence of the oppositely propagating up- and down-shifted daughter Langmuir waves excited by the OTSI probably is the emission mechanism of the second harmonic radiation, and (3) the Langmuir collapse follows the route of OTSI in some of the type III radio bursts

Current‐driven Langmuir oscillations and formation of wave packets via modulational instability: Relevance to STEREO observations

“…In a certain sense, this mechanism is very similar to that presented in papers by Thejappa et al . [, , , , , ]. The essential difference, however, is that in our approach Langmuir oscillations with ω = ω e and k = 0 take over the role of beam‐generated Langmuir waves having wave numbers kλ D ~ 1/( V b / V e ) where V b is the beam speed.…”

“…Finally, we point out that the Langmuir wave packets described by Thejappa et al . [, , , , , ] evidently have similarities to the one‐spectral‐peak events which have been analyzed by Graham et al . [].…”

“…For the measured amplitude E / E 0 = 0.06 this would lead to δn i / n 0 ~ 10 −3 which again is in good agreement with the measurements presented in Figure 5 of Thejappa et al . []. Altogether, the evidence of the modulational instability which is pumped by Langmuir oscillations instead of beam‐excited waves of finite wave number possibly resolves the controversy between the conclusions of Thejappa et al and the objections by Graham et al .…”

Ion dynamics in electron beam–plasma interaction: particle-in-cell simulations

“…Among them are spectra with power at ω pe only (e.g., Sigsbee et al, 2010), a double peak in absence of ion acoustic activity (e.g., Sigsbee et al, 2010), multiple spectral peaks (e.g., Graham and Cairns, 2013a), a single peak with side-band structure (e.g., Gurnett at al., 1981;Thejappa et al, 2013), Langmuir eigenmodes localized in density wells (Ergun et al, 2008;Graham and Cairns, 2013b) and waveforms resulting from the interaction of Langmuir waves with electrostatic whistler/lower hybrid waves instead of ion sound (Stasiewicz et al, 1996).…”

Nonlocal nonlinear coupling of kinetic sound waves

“…In the MHD low-frequency range, the slow-mode waves are O. Lyubchyk and Y. Voitenko: Nonlinear coupling of kinetic sound waves almost electrostatic in low-β plasmas, like solar corona. High-frequency electrostatic SWs have been also involved in the modelling of type III radio bursts that trace the flareaccelerated electron beams in the solar corona and solar wind (see Thejappa et al, 2013, and references therein).…”