Analytic MHD theory for Earth`s bow shock at low Mach numbers
- Univ. of Iowa City, IA (United States)
A previous MHD theory for the density jump at the Earth`s bow shock, which assumed the Alfven (M{sub A}) and sonic (M{sub s}) Mach numbers are both >> 1, is reanalyzed and generalized. It is shown that the MHD jump equation can be analytically solved much more directly using perturbation theory, with the ordering determined by M{sub A} and M{sub s}, and that the first-order perturbation solution is identical to the solution found in the earlier theory. The second-order perturbation solution is calculated, whereas the earlier approach cannot be used to obtain it. The second-order terms generally are important over most of the range of M{sub A} and M{sub s} in the solar wind when the angle {theta} between the normal to the bow shock and magnetic field is not close to 0 or 180{degrees} (the solutions are symmetric about 90{degrees}). This new perturbation solution is generally accurate under most solar wind conditions at 1 AU, with the exception of low Mach numbers when {theta} is close to 90{degrees}. In this exceptional case the new solution does not improve on the first-order solutions obtained earlier, and the predicted density ratio can vary by 10-20% from the exact numerical MHD solutions. For {theta}{approximately}90{degrees} another perturbation solution is derived that predicts the density ratio much more accurately. This second solution is typically accurate for quasi-perpendicular conditions. Taken together, these two analytical solutions are generally accurate for the Earth`s bow shock, except in the rare circumstance that M{sub A} {le} 2. MHD and gasdynamic simulations have produced empirical models in which the shock`s standoff distance {alpha}{sub s} is linearly related to the density jump ratio X at the subsolar point. Using an empirical relationship between {alpha}{sub s} and X obtained from MHD simulations, {alpha}{sub s} values predicted using the MHD solutions for X are compared with the predictions of phenomenological models. 21 refs., 9 figs.
- OSTI ID:
- 227166
- Journal Information:
- Journal of Geophysical Research, Journal Name: Journal of Geophysical Research Journal Issue: A10 Vol. 100; ISSN JGREA2; ISSN 0148-0227
- Country of Publication:
- United States
- Language:
- English
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