The propagation of solar flare particles in a coronal loop
A time-dependent diffusion equation with velocity-dependent diffusion and energy-loss coefficients was solved for the case where energetic solar particles are injected into a coronal loop and then diffuse out the ends of the loop into the lower corona/chromosphere. The solution yields for the case of relativistic electrons, precipitation rates and populations which are necessary for calculating thick and thin target X-ray emission. It follows that the thick target emission is necessarily delayed with respect to the particle acceleration on injection by more than the mere travel time of the particle over the loop length. In addition the time-dependent electron population at the top of the loop is calculated. This is useful in estimating the resulting micron-wave emission. The results show relative timing differences in the different emission processes which are functions of particle species, energy and the point of injection of the particles into the loop. Equivalent quantities are calculated for non-relativistic protons.