Diffusion Coefficients of WIND/STICS Protons from Diffusive Shock Acceleration with Finite Escape Boundaries

Abstract Heliospheric suprathermal ions include inner-source pickup ions, cometary ions, solar energetic particles, and suprathermal tail particles. Despite exhaustive observation and formalisms, their role in interplanetary shock acceleration has yet to be ascertained. Their role becomes ambiguous with observed departures from idealized, one-dimensional diffusive shock acceleration (DSA) theory, comprising an infinitesimally thin shock with escape at infinity. Applying a spatial free-escape boundary (FEB), a one-dimensional configuration is retained, yet the ion velocity distribution becomes expressible as a function of the spatial diffusion coefficient. The coefficient and its energy dependence serve to characterize magnetic irregularities, signatures from shock obliquity, and acceleration scales. Thus, study of proton diffusion coefficients in interplanetary shocks may elucidate the relative prevalence of DSA and more microscopic processes, and the applicability of frameworks such as quasilinear theory (QLT). Here, proton velocity distribution functions (VDFs) from the WIND Suprathermal Ion Composition Spectrometer (WIND/STICS) are studied, with energies per charge of 6.2–223.1 keV/ e , for two shocks having quasi-parallel and quasi-perpendicular orientations. The VDFs are then averaged over the STICS field of view and expressed as a function of distance from the shock, and fit to the exponential in position from convection/diffusion with the FEB. The energy dependence of diffusion coefficients, and the relative importance of acceleration mechanisms, are then examined. The coefficients are power laws in proton energy, more proper to QLT than to DSA under classical scattering, although behavior is variously described by both regimes. The quasi-perpendicular shock yields a negative power-law slope downstream, an effect suggesting both convergence of mechanisms and the model’s shortcomings.