Nonlocal nonlinear coupling of kinetic sound waves

Abstract

Abstract. We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a twofluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay), and another into counter-propagating product waves (reverse decay). All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.

Nonlinear wave interactions of kinetic sound waves

“…(14). If such fluid-type of approximations are made, C 2 coincides with the expression for the coupling coefficient presented in Lyubchyk and Voitenko (2014), used to describe the parametric excitation of KSW : s. However, our general expression also contains a term C 1 that cannot be neglected in general. We note that in C 1 , both the electron and ion contributions must typically be kept, at least if the electron and ion temperatures are of the same order.…”

“…Thus for pump waves with k 3z k 3⊥ , the result of Lyubchyk and Voitenko (2014) is essentially confirmed. Nevertheless, we note the usefulness of kinetic theory presented here, as this theory is needed to describe the finite Larmor radius effects that saturates the growth of C 2 with k 2 1,2⊥ , as contained in the Bessel function dependence of G (v z ).…”

“…Waves in this regime are so-called kinetic sound waves (KSWs, see e.g. Lyubchyk andVoitenko, 2014 or Zhao et al, 2014b). Evaluating the electrostatic dispersion relation ε(ω, k) = 0 for a two-component plasma (electrons and ions) in the low-frequency limit we obtain…”

“…below the ion-cyclotron frequency ω ci ) was studied in a recent paper (Lyubchyk and Voitenko, 2014) by means of a two-fluid plasma model. Such wave interactions are of basic interest in investigations of the solar corona and the solar wind, as well as in the Earth's magnetosphere and ionosphere, and the corresponding nonlinear phenomena (Shukla, 1999;Eliasson and Shukla, 2009) have also been observed by spacecrafts (Briand, 2009).…”

“…It should be noted here that the space-frame frequencies measured in the solar wind plasma are strongly Doppler-shifted, and that the plasma rest-frame frequencies can be significantly lower than ω ci . Lyubchyk and Voitenko (2014) have studied the nonlinear interaction of these waves in the electrostatic limit and outlined, with much physical insight, the decay processes as well as possible applications.…”