In this paper, we investigate the fundamental mathematical parameters governing the mechanism of fast radio bursts (FRBs) within the framework of magnetohydrodynamics (MHD) FRBs are intense, millisecond-duration bursts of radio waves originating from extragalactic sources, and understanding their underlying processes is crucial for advancing astrophysical theories. Our study focuses on a collective radiation mechanism, where plasma instability triggers interactions between a relativistic electron beam and a plasma target, resulting in strong turbulence. This turbulence is characterized by soliton-like wave packets, known as cavitons. By calculating the time-averaged radiated power per electron in the beam, we derive an exact solution for the total energy of an FRB which comes out to be of the order of 1037 erg. This energy is due to the interaction between the turbulent plasma and the relativistic electron beam. Our analysis reveals a direct proportionality between caviton size and the radius of plasma cloud, and an inverse relationship with the plasma frequency. Our results provide new insights into the dynamics of turbulent plasma interactions, offering a deeper understanding of the physical processes underlying FRBs.
Pant et al. (Wed,) studied this question.