On the Momentum Diffusion of Radiating Ultrarelativistic Electrons in a Turbulent Magnetic Field

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Here we investigate some aspects of stochastic acceleration of ultrarelativistic electrons by magnetic turbulence.

• In particular, we discuss the steady-state energy spectra of particles undergoing momentum diffusion due to resonant interactions with turbulent MHD modes, taking rigorously into account direct energy losses connected with different radiative cooling processes.
• For the magnetic turbulence we assume a given power spectrum of the type $W(k) \propto k^{-q}$.
• In contrast to the previous approaches, however, we assume a finite range of turbulent wavevectors $k$, consider a variety of turbulence spectral indexes $1 =< q =< 2$, and concentrate on the case of a very inefficient particle escape from the acceleration site.