Coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks and Earth's bow shock revisited

A revised version of the self‐consistent theory of ion diffusive shock acceleration and the associated generation of hydromagnetic waves is presented. The theory generalizes and corrects the theory of Lee [1982, 1983]. Lee assumed a linear dependence of the anisotropic part of the ion distribution function on the cosine of the ion pitch angle. Here the wave growth or damping rate is again calculated using linear theory, but a more general ion anisotropy is calculated using the pitch angle diffusion equation. The wave intensity satisfies a wave kinetic equation, and the ion omnidirectional distribution function satisfies the energetic particle transport equation. These coupled equations are solved numerically and compared with an analytical approximation similar to that derived by Lee. The analytical approximation provides an accurate representation of both the proton distribution and the wave intensity. A comparison is made between the predicted wave magnetic power spectral density adjacent to the shock as a function of frequency and the wave spectrum measured by ISEE 3 at the November 11–12, 1978, interplanetary traveling shock. There is excellent agreement between the predicted and measured power spectral density in the frequency range of 0.03–0.3 Hz. A comparison is also made between the predicted total wave energy density and that observed upstream of Earth's bow shock by the AMPTE/IRM satellite for a statistical survey of ∼400 near‐to nose events from late 1984 and 1985. This comparison revises the result presented by Trattner et al. [1994]. The correlation between the observed wave power and that predicted, based on the observed energetic proton energy density, is very good with a correlation coefficient of 0.92. However, the average observed wave magnetic energy density is ∼63% of that predicted, suggesting possible wave dissipation which is not included in the theory.