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Livesey et al. 1984
Livesey, W.A., Russell, C.T. and Kennel, C.F. (1984). A comparison of specularly reflected gyrating ion orbits with observed shock foot thicknesses. Journal of Geophysical Research 89: doi: 10.1029/JA089iA08p06824. issn: 0148-0227.

ISEE 1 and 2 flux gate magnetometer data has been used to measure the length or thickness of the ''foot'' of 60 quasi-perpendicular supercritical bow shocks along the shock normal. These bow shock crossings are contrasted with 10 quasi-perpendicular subcritical shocks which do not exhibit the precursor foot. For the supercritical shocks &THgr;Bn, the angle between the shock normal and the upstream magnetic field, ranges from 43¿ to 88¿. The range of &THgr;Bn for the laminar shocks is 56¿ to 76¿. The extent of the foot structure is compared to the orbit of an ion having solar wind velocity and undergoing simple specular reflection about the shock normal. Good quantitative agreement between the measured value of the foot and the predicted value of ~0.7 ion gyroradii [Woods, 1971> is evident. The foot thickness normalized to this predicted value is compared to M/Mc, the ratio of fast Mach number to critical fast Mach number. There is no dependence of the normalized foot thickness on Mach number other than at the transition point between subcritical and supercritical regime, M/Mc=1. No dependence of the normalized foot thickness on upstream ion &Bgr; is noted. The sole dependence of the normalized foot thickness on &THgr;Bn appears to be one of simple geometry, i.e., the determination of the component of the normal solar wind perpendicular to the upstream magnetic field.

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Journal of Geophysical Research
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