The motion of ions specularly reflected off a quasi‐parallel shock in the presence of large‐amplitude, monochromatic MHD waves

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Abstract
A test particle model is used to study the motion of ions specularly reflected off a shock in the presence of large‐amplitude, monochromatic, transverse MHD waves. The characteristics of the motion depend on the frequency, wavelength, phase, and amplitude of the wave that is being convected into the shock. For low wave frequencies and long wavelengths (ω′ ≪ ion gyrofrequency, λ ≫ ion gyroradius), the ion motion depends only upon θBn(ϕ0), the instantaneous angle between the total magnetic field at the shock (ambient + wave) and the shock normal. For high wave frequencies and short wavelengths (ω′ ≫ ion gyrofrequency, λ ≪ ion gyroradius), the ion motion depends only upon θBn0, the angle between the ambient magnetic field and the shock normal. For intermediate frequencies and wavelengths, including those of interest in the region upstream from the earth';s bow shock (ω′ ∼ ion gyrofrequency, λ ∼ ion gyroradius), no simple θBn0 or θBn(ϕ0)criterion for the ion motion is found. For example, at intermediate frequencies, the motion depends both on θBn(ϕ0) and θBn0 as well as upon b/B, the ratio of the wave amplitude to ambient magnetic field strength. In general, the presence of upstream waves inhibits the escape of specularly reflected ions from the shock, the effect being greatest when the wave amplitude is large. Other properties of ion motion that are affected by the presence of an MHD wave include the propagation time of an ion from the shock to a given upstream distance, the time variation of the gyrospeed and guiding center speed, and the energy upon return to the shock.