tokens: index increases and the energy distribution becomes steeper, limiting the number of higher energy electrons. This leads to spectra becoming more ‘thermal’ in shape, with the peak generated from the non-thermal particles flattening out. This is seen in the spectra of Fig. 10 compared to the Z LOS spectra from Fig. 7 . At earlier times, the peaks are similar, with the power-law index not increasing noticeably until later times where the system relaxes to a thermal state much faster than when the index was a constant value. The addition of an increasing power-law index therefore results in the spectral peak being reduced faster and pushed to lower frequencies as the contribution of higher energy particles is reduced. 3.2.2 Distribution along the loop The distribution of non-thermal particles within the loop is defined by equation ( 2 ). As described in Section 2.2 , l is the distance from the loop top to one footpoint, or the loop half length. The factor that controls the distribution within the loop, s , is initially set as this half loop length. As is seen in Fig. 4 the density is always highest at the apex of the loop, dropping off to a minimum at the footpoints. The parameter s was varied to investigate the effect on spectra of different spreads in non-thermal electrons within the loop. The results from using two values of s are shown in Fig. 11 . The top two panels show the spectra along the Z LOS for s parameter values of 0.3 times the half loop length (same as the Z LOS spectra in Fig. 7 ) and 1.5 times the half loop length. Figure 11. Spectra along the Z LOS resulting from changing the non-thermal electron density spatial distribution (top two plots). Two different configurations ( s = 0.3 and 1.5) are considered over the seven time-steps. The results for s = 1.0 are seen in the Z LOS spectra of Fig. 7 . Bottom images are 3D visualization of sample flux tube field lines at 4112 s and their electron distributions. Colour bar units are cm −3 . Also shown in Fig. 11 is a 3D visualization of these two different distributions along the field lines (and throughout the total flux tube) at 4112 s (bottom two panels of Fig. 11 ). For a smaller value of s , the particles are more constrained to the loop top, while a larger s value leads to a more even distribution from the apex down towards the foot points. The point of highest non-thermal density is found in the s = 0.3 plot as the total mass is conserved before the time decay component is added (equation 4 ). For the more compact distribution ( s = 0.3), in Fig. 11 it is clear the system relaxes to a thermal state quicker than for the more extended distribution of electrons and has a lower peak flux overall. However, the peak in emission occurs at 1790 s, later than the 169 s seen for the other distributions and LOSs. Overall, however, the pattern of the spectral evolution is similar. After the peak flux is reached, the decay of the non-thermal particles leads to the decrease in peak flux
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