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A Novel Emission Spectrum From A Relativistic Electron Moving In A Random Magnetic Field

We calculate numerically the radiation spectrum from relativistic electrons moving in small scale turbulent magnetic fields expected in high energy astrophysical sources. Such radiation spectrum is characterized by the strength parameter $a = λ_{B}} e|B|/mc^2$, where $λ_{B}}$ is the length scale of the turbulent field. When $a$ is much larger than the Lorentz factor of a radiating electron $γ$, synchrotron radiation is realized, while $a\ll 1$ corresponds to the so-called jitter radiation regime. Because for $1<a<γ$ we cannot use either approximations, we should have recourse to the Lienard-Wiechert potential to evaluate the radiation spectrum, which is performed in this paper. We generate random magnetic fields assuming Kolmogorov turbulence, inject monoenergetic electrons, solve the equation of motion, and calculate the radiation spectrum. We perform numerical calculations for several values of $a$ with $γ= 10$. We obtain various types of spectra ranging between jitter radiation and synchrotron radiation. For $a\sim 7$, the spectrum turns out to take a novel shape which has not been noticed up to now. It is like a synchrotron spectrum in the middle energy region, but in the low frequency region it is a broken power law and in the high frequency region an extra power law component appears beyond the synchrotron cutoff. We give a physical explanation of these features.