Coupled hydromagnetic wave excitation and ion acceleration at interplanetary traveling shocks

A self‐consistent theory is presented for the excitation of hydromagnetic waves and the acceleration of ions upstream of interplanetary traveling shocks. The waves are excited by the ions by virtue of ion streaming relative to the solar wind; the ions are accelerated by being coupled to the compression of the shock via pitch angle scattering on the upstream waves and the downstream turbulence. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self‐consistently to yield analytical expressions for the differential wave intensity spectrum as a function of wave number k and distance z upstream of the shock and for the ion omnidirectional distribution functions and anisotropies as functions of energy E and z . In quantitative agreement with observations the theory predicts, for example, (1) power law ion spectra at the shock αE −r with 2 ≲ Γ ≲ 3, (2) a decrease in intensity and hardening of the ion spectra with increasing z , (3) upstream ion anisotropies (∼0.3 fo 30‐keV protons) away from the shock front in the frame of the solar wind, (4) an unpolarized enhanced wave intensity spectrum in the wave number range corresponding to 0.4–3×10 −2 Hz in the spacecraft frame, and (5) a decrease in the wave intensity spectrum with increasing z .