The modulation of low‐energy proton distributions by propagating interplanetary shock waves: A numerical simulation

Abstract

A numerical simulation has been developed to study the formation in the intensities of ≲0.1‐ to ∼10.0‐MeV protons of the long‐lived energetic storm particle (ESP) events observed in association with the passage of flare‐produced fast mode MHD shocks. Protons are traced numerically backward in time from a given observation point (i.e., particle detector), through their adiabatic scatter‐free motion along the assumed laminar spiral interplanetary magnetic field (IMF), and finally through the shock discontinuity to their pre‐shock interaction state. An ambient proton can undergo at most one shock encounter, during which, as seen in the shock frame, the proton is accelerated by its effective ‘grad‐B drift’ along the induced electric field each time it crosses the shock. The time‐reversed calculation reveals which of the observed protons interacted with the shock, where the shock interaction occurred, and by how much each interacting proton's kinetic energy was increased at the shock. Time profiles of the omnidirectional and unidirectional protons fluxes are formed from the trajectories by invoking Liouville's theorem and an ambient proton unidirectional flux j ∼T−γ, where T is the kinetic energy and γ the spectral exponent. Simulation predictions are shown for different observed proton energies under various assumptions concerning the shock speed and strength, the slope of the ambient proton energy spectrum, the variation of the angle β1 between the shock surface and the upstream IMF vector, and the heliocentric radial position r of the observation point. The simulation model correctly recovers the gross features of the intensity variations, flux anisotropies, and energy spectra time evolutions of many observed ESP events. Representative simulation results predict shock‐induced enhancements in low‐energy proton fluxes that are characterized by (1) long, steady preshock or upstream rises to peaks before the shock arrival and abrupt declines following the shock passage; (2) peak enhancement amplitudes that increase for lower‐energy protons, stronger and faster shocks, softer ambient proton spectra, decreased β1 and increased r, (3) large, highly field‐aligned preshock flux anisotropies directed away from the sun along the IMF, (4) small postshock flux anisotropies nearly perpendicular to the magnetic field and directed towards the sun along the IMF, and (5) steadily softening preshock energy spectra that are steepest at the peak flux enhancement and slightly softer than the ambient spectra after the shock passage.

Shock Acceleration of Ions in the Heliosphere

“…The events in Category C are so-called "shock spike" events (Sarris and Van Allen 1974) which peak at nearly perpendicular shocks and are thought to arise from scatter-free particle reflection at the increased strength of the magnetic field at a fast shock (Hudson 1965;Decker 1981). This process cannot be described by DSA; the spectrum is presumably determined by the advected upstream spectrum and should not satisfy β = (X + 2)/(2X − 2).…”

Coupled Hydromagnetic Wave Excitation and Ion Acceleration at an Evolving Coronal/Interplanetary Shock

“…Following the suggestion that particles gain energy when they bounce off shocks (Parker 1958;Shabanskii 1962;Schatzman 1963), Hudson (1965) evaluated quantitatively the energy gains of particles that are reflected or transmitted at a planar oblique shock characterized by constant magnetic fields on both sides of the shock discontinuity. This mechanism was coined ''shock drift'' acceleration and invoked by Sarris & Van Allen (1974), Armstrong et al (1977), Pesses et al (1979), and Decker (1981) to account for the anisotropic ''shock spike'' and ESP events observed at quasi-perpendicular traveling shocks.…”

Diffusive acceleration

“…In this socalled V x B mechanism, particles gain energy in a single shock encounter by drifting in the inhomogeneous magnetic field at the shock front parallel to the V x B electric field. The most detailed theoretical analysis of this process has been given by Decker [1981Decker [ , 1983 and most recently in a review by Armstrong [this volume]. We will concentrate on those energetic storm particle events and postshock enhancements which are associated with quasi-parallel shocks since considerable evidence has been accumulated in recent years that these events can be understood by a diffusive acceleration process.…”