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Investigate the spatial and spectral evolution of hard X-ray (HXR) emissionfrom flare accelerated electron beams subject to collisional transport andwave-particle interactions in the solar atmosphere. We numerically follow thepropagation of a power-law of accelerated electrons in 1D space and time withthe response of the background plasma in the form of Langmuir waves using thequasilinear approximation.}{We find that the addition of wave-particleinteractions to collisional transport for a transient initially injectedelectron beam flattens the spectrum of the footpoint source. The coronal sourceis unchanged and so the difference in the spectral indices between the coronaland footpoint sources is \Delta \gamma > 2, which is larger than expected frompurely collisional transport. A steady-state beam shows little differencebetween the two cases, as has been previously found, as a transiently injectedelectron beam is required to produce significant wave growth, especially athigher velocities. With this transiently injected beam the wave-particleinteractions dominate in the corona whereas the collisional losses dominate inthe chromosphere. The shape of the spectrum is different with increasingelectron beam density in the wave-particle interaction case whereas with purelycollisional transport only the normalisation is changed. We also find that thestarting height of the source electron beam above the photosphere affects thespectral index of the footpoint when Langmuir wave growth is included. This mayaccount for the differing spectral indices found between double footpoints ifasymmetrical injection has occurred in the flaring loop.

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