Energetic particle spectra in finite shocks - The earth's bow shock

Particle acceleration and escape at the earth's bow shock wave are discussed in order to account for reported exponential fast particle spectra. A model is presented of particle acceleration in a finite two-dimensional shock perpendicular to the magnetic field, with particle parallel and perpendicular diffusion coefficients inversely proportional to each other. It is shown that the exponential particle energy per unit charge spectra observed by Ipavich et al. (1979) for the case of a radial solar wind magnetic field may be obtained if the fast particles escape the shock by means of resonant diffusion to unconnected field lines. The calculated e-folding value of the energy/charge ratio is found to be independent of the level of turbulence near the shock and in good agreement with observations. For the case of a nonradial solar wind magnetic field, the model is noted to predict that convection may be the dominant means of escape. It is also pointed out that the parallel and perpendicular diffusion coefficients may be measured indirectly at the bow shock.

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