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

Abstract

An analytical quasilinear theory is presented for the evolution of a ''gradual'' event consisting of solar energetic particles (SEPs) accelerated at an evolving coronal/interplanetary shock. The upstream ion transport is described by the two-stream moments of the focused transport equation, which accommodate the large streaming anisotropies observed near event onset. The proton transport equations and a wave kinetic equation are solved together for the coupled behavior of the hydromagnetic waves and the energetic protons. The theory includes diffusive shock acceleration, ion advection with the solar wind, spatial diffusion upstream of the shock, magnetic focusing, wave excitation by the energetic protons, and minor ions as test particles. A number of approximations are made for analytical tractability. The predictions reproduce the observed phases of most gradual SEP events: onset, a ''plateau'' with large streaming anisotropy, an ''energetic storm particle'' (ESP) enhancement prior to shock passage, and the decaying ''invariant spectra'' after shock passage. The theory treats naturally the transition from a scatter-dominated sheath adjacent to the shock where the wave intensity is enhanced to the nearly scatter-free ion transport in interplanetary space. The plateau is formed by ions that are extracted from the outer edge of the scatter-dominated sheath by magnetic focusing and escape into interplanetary space; it corresponds quantitatively to the ''streaming limit'' identified and interpreted in gradual events by D. V. Reames and C. K. Ng. The ion energy spectra at the shock have the standard power-law form dependent on shock strength, which is expected for diffusive shock acceleration, with a high-energy cutoff whose form is determined self-consistently by the ion escape rate. The increased shock strength, magnetic field magnitude, and injection energies close to the Sun account for the observed predominance of high-energy ions early in the event. The downstream ion transport is determined under two extreme assumptions: (i) vanishing diffusive transport and (ii) effective diffusive transport leading to small ion spatial gradients. The latter assumption reproduces the invariant spectra, spatial gradients, and exponential temporal decay observed in the late phase of many events. The minor ion distributions exhibit fractionation due to rigidity-dependent transport and acceleration. However, their energy spectra, spatial gradients, and high-energy cutoffs do not reproduce observed forms and lead to excessive fractionation. The origin of these discrepancies is probably the neglect of nonlinear processes. Although not easily incorporated in the theory, these processes could substantially modify the predicted wave intensity. An illustrative calculation assuming an arbitrary power-law form for the wave intensity demonstrates the sensitive dependence of ion fractionation on the power-law index. Subject headingg s: acceleration of particles -interplanetary medium -MHD -shock wavesSun: particle emission

Seed Populations for Large Solar Particle Events Of Cycle 23

“…Such systematic energy dependence of the SEP Fe/0 ratios were also reported by a number of previous studies [9,[25][26][27]. Likewise, the Fe/0 ratios in IP shock events at ACE also exhibited similar properties [20,24], and are consistent with expectations from shock acceleration models [28][29] where ions with higher M/Q ratios are accelerated less efficiently than those with lower M/g ratios.…”

STEREO IMPACT Investigation Goals, Measurements, and Data Products Overview

“…Adequate abundance measurements were not available on Helios to allow multipoint ion composition studies. Nevertheless, theoretical analyses suggest that as protons stream away from the shock they generate Alfven waves that trap the particles that follow, causing efficient acceleration to higher energies (Lee 1983(Lee , 2005. The spectrum of these self-generated waves is related to the proton energy spectrum and varies with space and time, throttling the flow of SEP ions away from the shock.…”

Space Weather: Physics, Effects and Predictability

“…Models based on evolving shock properties, wave-particle interactions and particle transport processes have been developed (Lee 2005;Laitinen 2007, 2008;Ng and Reames 2008;Vainio et al 2009) which could reproduce some features of shock associated SEP events. Characteristic features such as the start time of the event, peak flux, fluence and the corresponding energy spectrum, etc., are not predicted.…”

“…Major features of shock-associated SEP events are reproduced by detailed models of the evolving shock properties, wave-particle interactions and particle transport processes (Lee 2005;Laitinen 2007, 2008;Ng and Reames 2008;Vainio et al 2009). The distribution of particles streaming along magnetic field lines produces resonant Alfven waves (Melrose 1982).…”