Transmission of Alfen waves through the earth's bow shock: Theory and observation

Alfven waves, propagating along the magnetic field, are considered to be interacting with strong fast MHD shocks. The wave-associated magnetic field perturbation is taken to lie in the magnetic field-shock normal plane. The interaction perturbs the shock surface and gives rise to transmitted waves consisting of a fast magnetoacoustic wave, forward and backward slow magnetoacoustic waves, and an entropy wave. To zeroth order in inverse upstream Mach numbers the wave vectors of the latter three waves are collinear and bend toward the normal, while the fast wave bends away from the normal, propagating parallel to the shock surface for incident angles of 610.To the same order, for incident angles of less than 610 and for γ=5/3, the magnetic field amplitude associated with one of the slow waves is roughly the same size as the incident amplitude, while that associated with the other slow wave is amplified 3 times.Magnetic field and plasma data from Explorer 35, taken in the vicinity of 14 bow shock crossings, are analyzed. On spacecraft time scales of 12-20 min the data suggest the presence of hydromagnetic waves on both sides of all the shocks; the presence of predominantly Alfvenic fluctuations is demonstrated in the upstream regions of atleast six of the crossings. Magnetic field fluctuations with frequencies of >1/100 Hz are found to be amplified across the shock by factors ranging from 0.9 through 2.5. It is suggested that the discrepancy in the observed and theoretical field amplifications is due to strong damping of any transmitted magnetoacoustic modes with relatively little damping of any transmitted Alfven waves