Thermalisation and hard X-ray bremsstrahlung efficiency of self-interacting solar flare fast electrons

Most theoretical descriptions of the production of solar flare bremsstrahlung radiation assume the collision of dilute accelerated particles with a cold, dense target plasma, neglecting interactions of the fast particles with each other. This is inadequate for situations where collisions with this background plasma are not completely dominant, as may be the case in, for example, low-density coronal sources. We aim to formulate a model of a self-interacting, entirely fast electron population in the absence of a dense background plasma, to investigate its implications for observed bremsstrahlung spectra and the flare energy budget. We derive approximate expressions for the time-dependent distribution function of the fast electrons using a Fokker-Planck approach. We use these expressions to generate synthetic bremsstrahlung X-ray spectra as would be seen from a corresponding coronal source. We find that our model qualitatively reproduces the observed behaviour of some flares. As the flare progresses, the model's initial power-law spectrum is joined by a lower energy, thermal component. The power-law component diminishes, and the growing thermal component proceeds to dominate the total emission over timescales consistent with flare observations. The power-law exhibits progressive spectral hardening, as is seen in some flare coronal sources. We also find that our model requires a factor of 7 - 10 fewer accelerated electrons than the cold, thick target model to generate an equivalent hard X-ray flux. This model forms the basis of a treatment of self-interactions among flare fast electrons, a process which affords a more efficient means to produce bremsstrahlung photons and so may reduce the efficiency requirements placed on the particle acceleration mechanism. It also provides a useful description of the thermalisation of fast electrons in coronal sources.
Comment: 9 pages, 7 figures, accepted for Astronomy & Astrophysics; this version clarifies arguments around Eqs. (11) and (20)