Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares

Abstract

Context. High-energy electrons accelerated during solar flares are abundant in the solar corona and in interplanetary space. Commonly, the number and energy of non-thermal electrons at the Sun is estimated through hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims. We aim to investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods. We numerically simulated the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma, including wave-particle and wave-wave interactions.Results. The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of the Langmuir wave spectrum towards smaller wavenumbers, caused by large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased because of acceleration of non-thermal electrons through Langmuir waves. Conclusions. The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona.

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“…Kontar et al (2012) also demonstrate numerically that nonlinear wave-wave interactions are important. However, since these authors did not consider nonlinear mode coupling physics in 2D, the Langmuir spectrum in such a scheme does not give the wave vector pitch angle evolution.…”

“…The above references, however, also heuristically included collisional damping term for the Langmuir waves, whereas in the present approach, the collisional effects influence the Langmuir dynamics indirectly and only through the electron distribution function evolution. In spite of this caveat, however, our work is more general in the sense that we consider twodimensional dynamics and also allow nonlinear wave processes, such as the decay interaction and nonlinear wave-particle scattering similar to Kontar et al (2012) and Karlický & Kontar (2012). Also, the above references employed simplified Coulomb collisional integral for the particles, whereas our numerical solution is based upon the Landau operator.…”

“…These electrons traveling down towards the chromosphere are responsible for X-rays emitted via bremsstrahlung (see, e.g., Holman et al 2011). There have been recent discussions (Hannah et al 2009;Hannah & Kontar 2011;Zharkova & Siversky 2011;Kontar et al 2012) that show that the collective Langmuir-wave dynamics of the X-ray generating electrons may be important for interpretations of X-ray spectra from RHESSI spacecraft (Lin et al 2002).…”

“…Zharkova & Siversky (2011) also studied a similar problem. Moreover, Kontar et al (2012) have shown that the presence of plasma inhomogeneity and/or nonlinear wave-wave interactions can lead to an overestimated number and energy of energetic electrons accelerated in the corona even in the case of stationary electron injection.…”

“…The purpose of the present paper is not to revisit the plasma emission, which has recently been discussed by Ziebell et al (2014aZiebell et al ( , 2015 and by in application to flaring loops, or to address the issue of the influence of collective processes on the X-ray generation by bremsstrahlung per se, which was addressed by Hannah et al (2009) and Kontar et al (2012). Instead, we address a fundamental 2D plasma physics problem that may be related to both the type-III-generating electrons and the X-ray-generating non-thermal electrons.…”