Electron acceleration at nearly perpendicular collisionless shocks 2. Reflection at curved shocks
Abstract
Electrons can be efficiently energized at interplanetary shocks and planetary bow shocks. The acceleration and reflection process is extremely sensitive to the angle θ_{Bn} between the upstream magnetic field and the shock normal, and is most prominent at θ_{Bn}~90°. The mechanism has been investigated by theoretical and simulation means, and can be interpreted as a fast Fermi process or as gradient drift acceleration. Previous work has been carried out for plane shocks only, and is expanded here to take into account the global curvature of a shock. Simple estimates suggest that this curvature may have a strong limiting effect on the acceleration to high energies, i.e., above several keV in case of the Earth's bow shock. We perform twodimensional test particle calculations to address this question, and evaluate the reflected electron flux as a function of θ_{Bn} at the shock surface. The shock profile is derived from hybrid code simulations, and modified to include the first order effects of a global curvature in the vicinity of θ_{Bn}=90°.
At low energies, the calculated fluxes exhibit a cutoff and a maximum, which can give rise to observed bumpontail distributions in the electron foreshock. Results at high energy show that while individual electrons gain less energy in a curved shock, concerning the flux this fact is largely offset by twodimensional focusing effects. Electrons that drift into the shock over a wide area converge and stream out within a narrow spatial area, thus greatly enhancing the flux of reflected electrons. A κ distribution of suprathermal solar wind electrons (of index κ=6) is capable of producing the observed large fluxes of reflected electrons at the Earth's bow shock up to energies of 10 to 15 keV, even when the global shock curvature is accounted for. Beyond this energy range observed spectra are harder, as has been found previously for a plane shock. As a likely reason, the solar wind speed population may be denser than modeled above several keV.
 Publication:

Journal of Geophysical Research
 Pub Date:
 January 1991
 DOI:
 10.1029/90JA01728
 Bibcode:
 1991JGR....96..143K
 Keywords:

 Collisionless Plasmas;
 Electron Acceleration;
 Flux Density;
 Shock Wave Propagation;
 Space Plasmas;
 Shock Spectra;
 Spatial Distribution;
 Velocity Distribution;
 Geophysics;
 Space Plasma Physics: Charged particle motion and acceleration;
 Space Plasma Physics: Numerical simulation studies;
 Space Plasma Physics: Shock waves