Derivation of the function describing the energy distribution of particles in a turbulent synchrotron pile

Astronomy and Astrophysics – Astronomy

Scientific paper

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Extragalactic Radio Sources, Radio Astronomy, Relativistic Particles, Spectral Energy Distribution, Synchrotron Radiation, Turbulent Diffusion, Astronomical Models, Bessel Functions, Diffusion Coefficient, Distribution Functions, Kinetic Equations, Laplace Transformation, Maclaurin Series

Scientific paper

The paper derives an explicit form of the unsteady distribution function of relativistic particle energy in a turbulent synchrotron pile. It is shown that in the case of a monoenergetic initial distribution, the distribution function is of a power-law form with an index that depends on time and tends to a specific steady state value. The analysis is used to explain the difference in the power-spectral indices of extragalactic radio sources in terms of their age.

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