A Microscopic Analysis of Shear Acceleration

A microscopic analysis of the viscous energy gain of energetic particles in(gradual) non-relativistic shear flows is presented. We extend previous workand derive the Fokker-Planck coefficients for the average rate of momentumchange and dispersion in the general case of a momentum-dependent scatteringtime $\tau(p) \propto p^{\alpha}$ with $\alpha \geq 0$. We show that incontrast to diffusive shock acceleration the characteristic shear accelerationtimescale depends inversely on the particle mean free path which makes themechanism particularly attractive for high energy seed particles. Based on ananalysis of the associated Fokker-Planck equation we show that above theinjection momentum $p_0$ power-law differential particle number density spectra$n(p) \propto p^{-(1+ \alpha)}$ are generated for $\alpha >0$ if radiativeenergy losses are negligible. We discuss the modifications introduced bysynchrotron losses and determine the contribution of the accelerated particlesto the viscosity of the background flow. Possible implications for the plasmacomposition in mildly relativistic extragalactic jet sources (WATs) areaddressed.Comment: 16 pages, two figures; accepted for publication in Astrophysical Journa