Spatiotemporal analysis of the runaway distribution function based on green function and regularization method

Runaway electrons (REs) in experimental advanced superconducting tokamak (EAST) typically have an energy level of tens of MeV. Synchrotron radiation images of REs contain a wealth of information, making it crucial to handle this data properly to uncover hidden features. We observed distinct synchrotron radiation images emitted by the REs at different time points throughout the discharges and the focus of our study was an Ohmic discharge characterized by an evident synchrotron pattern and weaker background radiation. This paper aims to verify the feasibility of utilizing the green function and regularization method to obtain the distribution function information of synchrotron radiation images on EAST. We reconstruct the radial density profile of the REs beam by assuming the monoenergetic nature of REs at different time points. We employ the Tikhonov regularization method for this purpose. The results indicate that the radial density profile of the REs beam follows a roughly Gaussian distribution. Moreover, the peak density of the REs beam shifts inward to the magnetic axis as time progresses, a behavior also observed in the experimental image. However, a good fit between the simulated and experimental images is not achieved for all time points. This discrepancy is likely due to the intervention of q=2/1 magnetic islands and the increased complexity of the distribution function in both radial and momentum spaces.