Simple magnetohydrodynamic waves

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Abstract
Large-amplitude magnetic field fluctuations often accompanied by density variations are frequently observed in front of the earth's bow shock and in the vicinity of comets by extraterrestrial in situ measurements. They are identified as a manifestation of magnetohydrodynainic (MHD) waves in space plasmas. Because of their large amplitudes (i.e. because the magnetic field amplitude is of the order of the ambient magnetic field, for instance), these fluctuations cannot be satisfactorily described by linear wave theory. In this paper the properties of one-dimensional MHD waves of arbitrary amplitude, i.e. so-called simple MHD waves, are investigated, and a relationship is derived between the enhancement of the magnetic field and the density as well as the propagation velocity. Fast large-amplitude magnetosonic waves exhibit wave steepening. Here the dependence of the steepening time on the wave amplitude is derived and illustrated numerically.

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