Anomalous He Acceleration, the Particle Source and the Transport Coefficient

Abstract

Anomalous He⁺component acceleration at the heliospheric termination shock is modelled numerically via a steady-state solution to the combined cosmic-ray transport equation and shock boundary condition via a matrix inversion technique. This numerical solution automatically provides a no-drift modulation solution for the He⁺. Consistency with experimental data on the anomalous component is obtained for injection at 10 keV nucl^-1, at 120 AU, with a distribution function f(v)=2.75 × 10^-24 m^-6 s³ and a radial diffusion coefficient k=2.24× 10²² cm² s^-1 at 20 AU and for 100 MeV nucl^-1 particles but which varied proportional to v ^γr^δ where v and r are, respectively, particle velocity and solar distance,γ=1.3 and δ=0.5. However, a range of values of (γ,δ) between (1,0) and (2.4,1.4) were found to yield acceptable fits to the data. Pre-acceleration of ionised He at CIRs is possible as a source, although there is sufficient quiet-solar-wind-associated He⁺ for the required injection flux and the constraints on the injection efficiency are less at the terminal shock. These conclusions are insensitive to the terminal shock position and to the value of the injection energy.