Improved calculation of the radiation power of a charged particle undergoing hyperbolic motion

Within classical electrodynamics, exact formulas for calculating the radiation loss of the energy of a point charge undergoing hyperbolic motion, including the relativistic region, are proposed. For an ultrarelativistic particle, the improved radiation loss factor \(\frac{4}{5}\) γ ² · e ² · a ² was obtained instead of the commonly used Larmor quantity \(\frac{2}{3}\) γ ² · e ² · a ².