The spectral difference between solar flare HXR coronal and footpoint sources due to wave-particle interactions

Abstract

Aims. We investigate the spatial and spectral evolution of hard X-ray (HXR) emission from flare accelerated electron beams subject to collisional transport and wave-particle interactions in the solar atmosphere. Methods. We numerically follow the propagation of a power-law of accelerated electrons in 1D space and time with the response of the background plasma in the form of Langmuir waves using the quasilinear approximation. Results. We find that the addition of wave-particle interactions to collisional transport for a transient initially injected electron beam flattens the spectrum of the footpoint source. The coronal source is unchanged and so the difference in the spectral indices between the coronal and footpoint sources is Δγ > 2, which is larger than expected from purely collisional transport. A steady-state beam shows little difference between the two cases, as has been previously found, as a transiently injected electron beam is required to produce significant wave growth, especially at higher velocities. With this transiently injected beam the wave-particle interactions dominate in the corona whereas the collisional losses dominate in the chromosphere. The shape of the spectrum is different with increasing electron beam density in the wave-particle interaction case whereas with purely collisional transport only the normalisation is changed. We also find that the starting height of the source electron beam above the photosphere affects the spectral index of the footpoint when Langmuir wave growth is included. This may account for the differing spectral indices found between double footpoints if asymmetrical injection has occurred in the flaring loop.

Effect of turbulent density-fluctuations on wave-particle interactions and solar flare X-ray spectra

“…Another observational challenge is the difference in the HXR spectral indices found between the footpoint and coronal sources, which the CTTM predicts to be Δγ = 2, yet RHESSI's imaging spectroscopy of some flares has found values with Δγ > 2 (Emslie et al 2003;Battaglia & Benz 2007;Saint-Hilaire et al 2008;Battaglia & Benz 2008;Su et al 2009). We found that the flattening of the electron distribution as it propagates from the corona to the chromosphere due to the generation of Langmuir waves can produce the observed larger differences (Hannah & Kontar 2011).…”

“…The simulations here feature two changes over the previous work (Hannah et al 2009;Hannah & Kontar 2011). The first minor change is the inclusion of the diffusion in velocity space due to collisions (final term in the brackets at the end of Eq.…”

“…It is shown in Fig. 1 and was used previously in Hannah & Kontar (2011). The additional components presented in this paper are the density fluctuations, which are drawn from a turbulent Kolmogorov-type β = 5/3 power density spectrum, i.e.…”

Two-dimensional time evolution of beam-plasma instability in the presence of binary collisions

“…In the context of the solar applications, the third panels are similar to those considered (e.g., Hamilton & Petrosian 1987;McClements 1989;Hannah et al 2009;Hannah & Kontar 2011;Zharkova & Siversky 2011), in that both the Coulomb collisional dynamics and self-consistent Langmuir wave dynamics are considered. 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 the context of solar applications, Hamilton & Petrosian (1987), McClements (1989), Hannah et al (2009), Kontar (2011), andZharkova &Siversky (2011), solved selfconsistent Langmuir wave kinetic equations. Kontar et al (2012) also demonstrate numerically that nonlinear wave-wave interactions are important.…”