Interplanetary diffusive shock acceleration: Exponential or power-law spectra?

A new method for solving the transport equation and boundary condition describing diffusive shock acceleration for interplanetary corotating interaction regions is provided. It involves inverting a quindiagonal matrix. Application of this method to realistic parameters indicates that the parallel diffusion coefficient magnitude is critical in determining whether observed particle distribution functions are exponential or power law.     

Ambiguity in Determining the Diffusion Coefficient from Shock-Associated Energetic Particle Increases

A numerical solution to the Fisk and Lee (1980) equations for the particle intensity upstream of a corotating interplanetary shock is considered for the November 1991 event observed at Ulysses. A numerically derived parallel diffusion coefficient is available for this region (Quenby et al., 1993), based upon in-situ magnetometer data. Fitting the transport equations solution to the upstream energetic particle distribution function, employing a radial diffusion coefficient = ₀ r, where r and are, respectively, radial distance from the Sun and particle velocity, and with ₀ fixed from the magnetometer derived coefficient yielded a range of statistically acceptable values of (, ). These ran from (0.5, 0.0) to (1.8, 1.6) along a thin strip of — space, hence demonstrating the improbability that the velocity and radial dependence of the particle diffusion can be fixed from such particle and magnetic field data alone.     

Anomalous He Acceleration,the Particle Source and the Transport Coefficient

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 r where v and r are, respectively, particle velocity and solar distance,=1.3 and =0.5. However, a range of values of (,) 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.