Difference in the spectral index of the coronal source and footpoint for the mean electron spectrum Δδ (left) and X-ray spectrum Δγ (right) as a function of the spectral index of the injected electron beam δ_b and beam density n_b (blue 10⁷ cm^-3, red 10⁸ cm^-3). Shown are the results for the beam only propagation (subject only to Coulomb collisions) and the beams and waves simulation. The grey points indicate the results when a higher maximum velocity is used, discussed in Sect. 3.3.1.