Formation of the wave compressional boundary in the Earth's foreshock

Abstract

We analyze the interaction between energetic protons and hydromagnetic waves in the Earth's ion foreshock and locate compressional wave boundaries corresponding to interplanetary magnetic field (IMF) inclinations to the solar wind of θBV equal to 45° and 25°. Protons injected into the solar wind at the bow shock interact with MHD waves traveling along the IMF lines intersecting the shock. Starting with the quasi‐linear pitch angle diffusion equation, we obtain fluid equations for the densities and mean velocities of outward and inward streaming energetic protons. The excitation and damping of waves by these protons are described by linear growth rates for parallel propagation and evaluated using a model proton distribution function controlled by the local fluid variables. The coupled equations for the evolution of the wave intensities, proton densities, and mean velocities are solved numerically assuming a prescribed proton injection rate at the shock. The seed interplanetary waves are assumed to be unpolarized on average and to propagate predominantly away from the Sun, in the solar wind frame. We find that in the solar wind frame, (1) the dominant wave‐particle interaction in the outer foreshock is the damping of inward propagating (toward the shock) left‐polarized waves, producing a magnetically quiet region immediately downstream of the foreshock boundary; (2) excitation of outward propagating right‐polarized waves farther downstream leads to the recovery of δ|B| and to an upstream boundary for enhanced compressional wave activity; (3) at θBV = 45°, the calculated compressional boundary has a mean inclination of 78° from the Earth‐Sun axis, compared with the observed range of 85°±3°; and (4) at θBV = 25°, the calculated compressional boundary has a mean inclination of 42° from the Earth‐Sun axis, compared with the observed range of 42°±2°.