Parametric evolution of power-law energy spectra of energetic electrons in the coronal loops


 Fast electron beams (FEBs) are one of the main products of various active events and ubiquitous in solar, space and cosmic plasmas. They reveal themselves in hard X-ray and radio emissions. The observed characteristics of X-ray and radio emissions sensitively depend on the energy distribution of FEBs, which usually have a power-law energy spectrum. As FEBs traveling in the solar atmosphere, their energy distribution can considerably vary due to the interaction with ambient plasmas. Tang et al. (2020) investigated the evolution of the energy spectrum of the FEBs traveling along the flare loop and discussed the possible effects on the HXRs and radio emissions. Considering the ubiquitous coronal loops in the active regions, in the present paper, we investigate the parametric evolution of the energy spectra of FEBs when propagating along coronal loops. Here, we take the sunpot atmospheric model as approximate the coronal loop atmosphere model. The results show that the energy loss has an important impact on the cutoff behavior and energy spectra of FEBs when precipitating in a coronal loop with density ratio nb/ne = 0.01. The initially single power-law spectrum with a steepness cutoff can evolve into a more complex double power-law spectrum or two ’knees’ power-law spectrum with a flatted steepness cutoff behavior or saturation cutoff behavior. Our calculations also show that the energy spectrum evolution is not obvious if nb/n0 = 0.001 as Tang et al. (2020) taken. The present results are helpful for a more comprehensive understanding of the dynamics spectra of hard X-ray and radio emissions from FEBs.