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Lee & Skadron 1985
Lee, M.A. and Skadron, G. (1985). A simple model for the formation of ‘‘Reflected,’’ ‘‘Intermediate,’’ and ‘‘Diffuse’’ Ion distributions upstream of earth’s bow shock. Journal of Geophysical Research 90: doi: 10.1029/JA090iA01p00039. issn: 0148-0227.

We present a simple model unifying the distinct energetic ion populations and their associated low-frequency hydromagnetic waves within earth's ion foreshock. Ions initially injected onto magnetic field lines at the shock excite hydromagnetic waves which pitch angle scatter the ions back toward the shock. The ions are represented by inhomogeneous inward (toward the shock) and outward traveling beams, and the transition rate between beams is determined by an effective quasi-linear pitch angle diffusion coefficient for the transition. The intensities of waves resonant with the beams are calculated from wave kinetic equations utilizing linear wave growth rates which in turn are determined by the instantaneous, local beam densities. The coupled equations for the spatial and temporal evolution of the ion densities and wave intensities along a given magnetic field line are solved numerically assuming steady injection of ions at the shock following the initial magnetic connection of the field line to the bow shock. The initial interplanetary waves are assumed to be unpolarized on average and to propagate predominantly away from the sun relative to the solar wind. We find that (1) the ion anisotropy near the shock decreases slowly during the initial minutes of magnetic contact, but then makes a rapid transition to a steady, ''diffuse'' distribution; (2) the diffuse ion density declines steeply away from the shock with a scale length of ~5 RE, forms a broad minimum, and then increases with increasing anisotropy to form an ''intermediate'' ion distribution; (3) upstream of the intermediate ions the density forms a broad ''reflected'' ion distribution with high anisotropy extending to the foreshock boundary; (4) the reflected and intermediate ion distributions are confined to spatial bands which are aligned with the foreshock boundary and have ~5--RE widths; and (5) the waves associated with intermediate ions are strongly right-hand polarized in the solar wind frame whereas the waves associated with diffuse ions exhibit a net polarization within a range about zero.

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Journal of Geophysical Research
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