Characteristics of betatron radiation from direct-laser-accelerated electrons

Betatron radiation from direct-laser-accelerated electrons is characterized analytically and numerically. It is shown here that the electron dynamics is strongly dependent on a self-similar parameter S(≡n_{e}/n_{c}a_{0}). Both the electron transverse momentum and energy are proportional to the normalized amplitude of laser field (a_{0}) for a fixed value of S. As a result, the total number of radiated photons scales as a_{0}^{2}/sqrt[S] and the energy conversion efficiency of photons from the accelerated electrons scales as a_{0}^{3}/S. The particle-in-cell simulations agree well with the analytical scalings. It is suggested that a tunable high-energy and high-flux radiation source can be achieved by exploiting this regime.