Particle acceleration at perpendicular shock waves: Model and observations

Abstract

[1] On the basis of a recently developed nonlinear guiding center theory for the perpendicular spatial diffusion coefficient k ? used to describe the transport of energetic particles, we construct a model for diffusive particle acceleration at highly perpendicular shocks, i.e., shocks whose upstream magnetic field is almost orthogonal to the shock normal. We use k ? to investigate energetic particle anisotropy and injection energy at shocks of all obliquities, finding that at 1 AU, for example, parallel and perpendicular shocks can inject protons with equal facility. It is only at highly perpendicular shocks that very high injection energies are necessary. Similar results hold for the termination shock. Furthermore, the inclusion of self-consistent wave excitation at quasiparallel shocks in evaluating the particle acceleration timescale ensures that it is significantly smaller than that for highly perpendicular shocks at low to intermediate energies and comparable at high energies. Thus higher proton energies are achieved at quasiparallel rather than highly perpendicular interplanetary shocks within 1 AU. However, both injection energy and the acceleration timescale at highly perpendicular shocks are sensitive to assumptions about the ratio of the two-dimensional (2-D) correlation length scale to the slab correlation length scale l 2D /l k . Model proton spectra and intensity profiles accelerated by a highly perpendicular interplanetary shock are compared to an identical but parallel interplanetary shock, revealing important distinctions. Finally, we present observations of highly perpendicular interplanetary shocks that show that the absence of upstream wave activity does not inhibit particle acceleration at a perpendicular shock. The accelerated particle distributions closely resemble those expected of diffusive shock acceleration, and observed at oblique shocks, an example of which is shown.

The Two Sources of Solar Energetic Particles

“…small θ Bn , probably were more likely to have knee energies below the energy interval of observation. Recently, Zank et al (2006) have suggested that "higher proton energies are achieved at quasi-parallel rather than highly perpendicular interplanetary shocks within 1 AU." The recent in situ observations (Reames 2012) seem to show the opposite; quasiperpendicular shocks are favored.…”

Numerical Simulations of Particle Acceleration at Interplanetary Quasi-perpendicular Shocks

“…The injection energy E K in j and E M in j from kappa and Maxwellian distributions, respectively, are shown in Table 4. We find that in each shock event E Zank et al (2006). Therefore, the Maxwellian distribution can produce an accelerated distribution that matches the data.…”

“…The turbulent magnetic fluctuations b are composed of a slab component and a 2D one (Matthaeus et al 1990;Zank & Matthaeus 1992;Bieber et al 1996;Gray et al 1996;Zank et al 2006),…”

“…The injection energy can be derived from diffusion models assuming small anisotropy in the particle distribution (Giacalone & Jokipii 1999;Giacalone & Kóta 2006;Zank et al 2006). Neergaard Parker & Zank (2012) and Neergaard Parker et al (2014) explored the injection energy at quasi-parallel and quasi-perpendicular shocks, respectively, through solving the steady-state transport equation.…”

Turbulence evolution and shock acceleration of solar energetic particles

“…Self-amplification of upstream AlfvCn wave turbulence is a powerful process that rapidly bootstraps shock acceleration of SEPs. There is likely to be more scattering than imposed by the ad hoc A > 3rg limit in our model [16]. Hence a > 2000 kmls coronal shocks is likely to accelerate protons to 100 MeV in < 5 minutes.…”