Particle Acceleration Due to Cosmic-ray Viscosity and Fluid Shear in Astrophysical Jets

An analytical model describing the acceleration of energetic charged particles due to cosmic-ray viscosity and fluid shear in radio jets based on the diffusive transport equation for cosmic rays is developed. The model indicates that laminar shear is not a significant mechanism for particle acceleration in nonrelativistic jets but may be important in relativistic jets. The model produces a power-law momentum spectrum of particles accelerated by the shear (i.e., f(0) proportional to p(-mu infinity)as p -> infinity, where f(0) is the isotropic phase space distribution in the scattering frame). For ultrarelativistic jets with no back-flowing cocoon, mu(infinity) -> 3 + alpha for the energetic particle diffusion coefficient case kappa proportional to p(alpha). Increasing the shear in the background flow gives harder accelerated particle momentum spectra. Monoenergetic source solutions (Green's functions) and Green's formula are derived and used to obtain solutions for monoenergetic particle momentum spectra specified on the edge of the jet at radius r = r(2).