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Numerical simulations of chromospheric hard X-ray source sizes in solar flares

X-ray observations are a powerful diagnostic tool for transport, acceleration, and heating of electrons in solar flares. Height and size measurements of X-ray footpoints sources can be used to determine the chromospheric density and constrain the parameters of magnetic field convergence and electron pitch-angle evolution. We investigate the influence of the chromospheric density, magnetic mirroring and collisional pitch-angle scattering on the size of X-ray sources. The time-independent Fokker-Planck equation for electron transport is solved numerically and analytically to find the electron distribution as a function of height above the photosphere. From this distribution, the expected X-ray flux as a function of height, its peak height and full width at half maximum are calculated and compared with RHESSI observations. A purely instrumental explanation for the observed source size was ruled out by using simulated RHESSI images. We find that magnetic mirroring and collisional pitch-angle scattering tend to change the electron flux such that electrons are stopped higher in the atmosphere compared with the simple case with collisional energy loss only. However, the resulting X-ray flux is dominated by the density structure in the chromosphere and only marginal increases in source width are found. Very high loop densities (>10^{11} cm^{-3}) could explain the observed sizes at higher energies, but are unrealistic and would result in no footpoint emission below about 40 keV, contrary to observations. We conclude that within a monolithic density model the vertical sizes are given mostly by the density scale-height and are predicted smaller than the RHESSI results show.