Shock drift acceleration of energetic protons at a planetary bow shock

Abstract

We present the results of numerical orbit integrations of the interaction of suprathermal charged particles (protons) with a planetary bow shock. The primary goal of this study is to analyze the effect of the changing geometry of the shock, due to its curvature, on the kinematics of the particle/shock interaction. The model bow shock is a conic section which has as free parameters the eccentricity and the distance from the planet to the subsolar point of the shock surface. We have considered both two‐ and three‐dimensional geometries for the bow shock. Protons of various suprathermal energies are considered (we make no assumptions as to the origin of these seed particles). The protons are released in such a fashion to best sample the quasi‐perpendicular region of the Earth's bow shock (i.e., 45° ≤ θBn ≤ 90°, where θBn is the angle between the local shock normal and the incident magnetic field). The results of the numerical orbit integrations are compared to an analytical model in which the charged particles conserve their first adiabatic invariant upon crossing each plane shock and it is assumed that they enter and exit at the same point on the shock. An important parameter is the ratio of the particle's initial gyroradius to the local radius of curvature of the shock. When this parameter is very small (∼ 10−4) the curved bow shock may be modeled in this fashion. For purposes of comparison with other bow shocks, we also discuss the application of this model to the bow shocks of Jupiter and Mercury. It is shown that the effect of introducing shock curvature to the shock in the numerical simulations is to increase the reflection probability of incident suprathermal protons. It is also shown that the curvature of the planetary bow shock allows protons to enter at a given value of θBn and exit at a different value. Since θBn is a very important variable concerning charged particle motion in collisionless shock waves, this result has consequences in the characteristics of the energetic charged particle environment in the planetary foreshock as well as the injection of near thermal energy protons into seed energies for further acceleration by either shock drift or Fermi acceleration.