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 function
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Abstract f 0(r ,p ) at cylindrical radiusr from the jet axis (assumed to lie along thez -axis) is given by convolving the particle momentum spectrum with the Green’s function , which describes the monoenergetic spectrum solution in which asr → ∞ . Previous work by Webb et al. studied only the Green’s function solution for . In this paper, we explore for the first time, solutions for more general and realistic forms for . The flow velocity =u u (r )e z is along the axis of the jet (thez -axis). is independent ofu z , andu (r ) is a monotonic decreasing function ofr . The scattering time in the shear flow region 0 <r <r 2, and , wheres > 0 in the regionr >r 2is 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 distribution that particles observed at (r ,p ) originated fromr → ∞ with momentum . The acceleration of ultrahigh-energy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described.Free, publicly-accessible full text available November 22, 2024 -
Webb, G. M. ; Mostafavi, P. ; Al-Nussirat, S. ; Barghouty, A. F. ; Li, G. ; le Roux, J. A. ; Zank, G. P. ( , The Astrophysical Journal)