The aim of this paper is to demonstrate the effect of turbulent background density fluctuations on flare-accelerated electron transport in the solar corona. Using the quasi-linear approximation, we numerically simulated the propagation of a beam of a
ccelerated electrons from the solar corona to the chromosphere, including the self-consistent response of the inhomogeneous background plasma in the form of Langmuir waves. We calculated the X-ray spectrum from these simulations using the bremsstrahlung cross-section and fitted the footpoint spectrum using the collisional thick-target model, a standard approach adopted in observational studies. We find that the interaction of the Langmuir waves with the background electron density gradient shifts the waves to a higher phase velocity where they then resonate with higher velocity electrons. The consequence is that some of the electrons are shifted to higher energies, producing more high-energy X-rays than expected if the density inhomogeneity is not considered. We find that the level of energy gain is strongly dependent on the initial electron beam density at higher energy and the magnitude of the density gradient in the background plasma. The most significant gains are for steep (soft) spectra that initially had few electrons at higher energies. If the X-ray spectrum of the simulated footpoint emission are fitted with the standard thick-target model (as is routinely done with RHESSI observations) some simulation scenarios produce more than an order-of-magnitude overestimate of the number of electrons $>50$keV in the source coronal distribution.
We investigate the type III radio bursts and X-ray signatures of accelerated electrons in a well observed solar flare in order to find the spatial properties of the acceleration region. Combining simultaneous RHESSI hard X-ray flare data and radio da
ta from Phoenix-2 and the Nanc{c}ay radioheliograph, the outward transport of flare accelerated electrons is analyzed. The observations show that the starting frequencies of type III bursts are anti-correlated with the HXR spectral index of solar flare accelerated electrons. We demonstrate both analytically and numerically that the type III burst starting location is dependent upon the accelerated electron spectral index and the spatial acceleration region size, but weakly dependent on the density of energetic electrons for relatively intense electron beams. Using this relationship and the observed anti-correlation, we estimate the height and vertical extent of the acceleration region, giving values of around 50 Mm and 10 Mm respectively. The inferred acceleration height and size suggests that electrons are accelerated well above the soft X-ray loop-top, which could be consistent with the electron acceleration between 40 Mm and 60 Mm above the flaring loop.
Solar flare accelerated electron beams propagating away from the Sun can interact with the turbulent interplanetary media, producing plasma waves and type III radio emission. These electron beams are detected near the Earth with a double power-law en
ergy spectrum. We simulate electron beam propagation from the Sun to the Earth in the weak turbulent regime taking into account the self-consistent generation of plasma waves and subsequent wave interaction with density fluctuations from low frequency MHD turbulence. The rate at which plasma waves are induced by an unstable electron beam is reduced by background density fluctuations, most acutely when fluctuations have large amplitudes or small wavelengths. This suppression of plasma waves alters the wave distribution which changes the electron beam transport. Assuming a 5/3 Kolmogorov-type power density spectrum of fluctuations often observed near the Earth, we investigate the corresponding energy spectrum of the electron beam after it has propagated 1 AU. We find a direct correlation between the spectrum of the double power-law below the break energy and the turbulent intensity of the background plasma. For an initial spectral index of 3.5, we find a range of spectra below the break energy between 1.6-2.1, with higher levels of turbulence corresponding to higher spectral indices.
Impulsive solar energetic electrons are often observed in the interplanetary space near the Earth and have an attractive diagnostic potential for poorly understood solar flare acceleration processes. We investigate the transport of solar flare energe
tic electrons in the heliospheric plasma to understand the role of transport to the observed onset and spectral properties of the impulsive solar electron events. The propagation of energetic electrons in solar wind plasma is simulated from the acceleration region at the Sun to the Earth, taking into account self-consistent generation and absorption of electrostatic electron plasma (Langmuir) waves, effects of non-uniform plasma, collisions and Landau damping. The simulations suggest that the beam-driven plasma turbulence and the effects of solar wind density inhomogeneity play a crucial role and lead to the appearance of a) spectral break for a single power-law injected electron spectrum, with the spectrum flatter below the break, b) apparent early onset of low-energy electron injection, c) the apparent late maximum of low-energy electron injection. We show that the observed onsets, spectral flattening at low energies, and formation of a break energy at tens of keV is the direct manifestation of wave-particle interactions in non-uniform plasma of a single accelerated electron population with an initial power-law spectrum.
