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  1. Abstract

    A steady-state, semi-analytical model of energetic particle acceleration in radio-jet shear flows due to cosmic-ray viscosity obtained by Webb et al. is generalized to take into account more general cosmic-ray boundary spectra. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The energetic particle distribution functionf0(r,p) at cylindrical radiusrfrom the jet axis (assumed to lie along thez-axis) is given by convolving the particle momentum spectrumf0(,p)with the Green’s functionG(r,p;p), which describes the monoenergetic spectrum solution in whichf0δ(pp)asr→ ∞ . Previous work by Webb et al. studied only the Green’s function solution forG(r,p;p). In this paper, we explore for the first time, solutions for more general and realistic forms forf0(,p). The flow velocityu=u(r)ezis along the axis of the jet (thez-axis).uis independent ofz, andu(r) is a monotonic decreasing function ofr. The scattering timeτ(r,p)=τ0(p/p0)αin the shear flow region 0 <r<r2, andτ(r,p)=τ0(p/p0)α(r/r2)s, wheres> 0 in the regionr>r2is outside the jet. Other original aspects of the analysis are (i) the use of cosmic ray flow lines in (r,p) space to clarify the particle spatial transport and momentum changes and (ii) the determination of the probability distributionψp(r,p;p)that particles observed at (r,p) originated fromr→ ∞ with momentump. The acceleration of ultrahigh-energy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described.

     
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    Free, publicly-accessible full text available November 22, 2024