Abstract
Abstract We demonstrate that the exact solution for the spectrum of synchrotron radiation from an isotropic population of monoenergetic electrons in a turbulent magnetic field with a Gaussian distribution of local field strengths can be expressed in the simple analytic form: , where We use this expression to find the approximate synchrotron spectra for power-law electron distributions with -type high-energy cutoff; the resulting synchrotron spectrum has the exponential cutoff factor with a frequency raised to the 2β/(3β + 4) power in the exponent. For the power-law electron distribution without a high-energy cutoff, we find the coefficient a m as a function of the power-law index, which results in the exact expression for the synchrotron spectrum when using the monochromatic (i.e., each electron radiates at the frequency ) approximation.
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