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 •E -r with 2 •< F •< 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 x 10-2 Hz in the spacecraft frame, and (5) a decrease in the wave intensity spectrum with increasing z.

A self-consistent theory is presented for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves the quasiequilibrium results from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions the quasi-equilibrium results from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, acceleration by compression at the shock front, loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. 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 frequency and distance from the bow shock z and for the ion omnidirectional distribution functions and anisotropies as functions of energy and z. In quantitative agreement with observations, the theory predicts (1) exponential ion spectra at the bow shock in energy per charge, (2) a decrease in intensity and hardening of the ion spectra with increasing z, (3) a 30-keV proton anisotropy parallel to z increasing from -0.28 at the bow shock to +0.51 as z --• • (4) a linearly polarized wave intensity spectrum with a minimum at ---6 x 10 -3 az and a maximum at ---2-3 x 10 -2 Hz, (5) a decrease in the wave intensity spectrum with increasing z, (6) a total energy density in protons with energies > 15 keV about eight times that in the hydromagnetic waves.

Energization at a quasi-perpendicular shock is described for ions which approach the shock with a speed much less than that of the incoming plasma. These ions may be trapped between the shock electrostatic potential and the upstream Lorentz force and accelerated by "surfing" along the shock surface, before eventually escaping the shock into the upstream or downstream plasma. The process is described in detail, extending previous work on the mechanism, and energy gains are calculated. It is pointed out that pickup ions in the solar wind are ideally configured, so that a reasonable fraction of the ions can be accelerated by this mechanism at cometary bow shocks, the solar wind termination shock, and interplanetary traveling shocks. The mechanism may provide the required "injection" or preacceleration at quasi-perpendicular shocks for subsequent diffusive shock acceleration.

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An analytical quasilinear theory is presented for the evolution of a ''gradual'' event consisting of solar energetic particles (SEPs) accelerated at an evolving coronal/interplanetary shock. The upstream ion transport is described by the two-stream moments of the focused transport equation, which accommodate the large streaming anisotropies observed near event onset. The proton transport equations and a wave kinetic equation are solved together for the coupled behavior of the hydromagnetic waves and the energetic protons. The theory includes diffusive shock acceleration, ion advection with the solar wind, spatial diffusion upstream of the shock, magnetic focusing, wave excitation by the energetic protons, and minor ions as test particles. A number of approximations are made for analytical tractability. The predictions reproduce the observed phases of most gradual SEP events: onset, a ''plateau'' with large streaming anisotropy, an ''energetic storm particle'' (ESP) enhancement prior to shock passage, and the decaying ''invariant spectra'' after shock passage. The theory treats naturally the transition from a scatter-dominated sheath adjacent to the shock where the wave intensity is enhanced to the nearly scatter-free ion transport in interplanetary space. The plateau is formed by ions that are extracted from the outer edge of the scatter-dominated sheath by magnetic focusing and escape into interplanetary space; it corresponds quantitatively to the ''streaming limit'' identified and interpreted in gradual events by D. V. Reames and C. K. Ng. The ion energy spectra at the shock have the standard power-law form dependent on shock strength, which is expected for diffusive shock acceleration, with a high-energy cutoff whose form is determined self-consistently by the ion escape rate. The increased shock strength, magnetic field magnitude, and injection energies close to the Sun account for the observed predominance of high-energy ions early in the event. The downstream ion transport is determined under two extreme assumptions: (i) vanishing diffusive transport and (ii) effective diffusive transport leading to small ion spatial gradients. The latter assumption reproduces the invariant spectra, spatial gradients, and exponential temporal decay observed in the late phase of many events. The minor ion distributions exhibit fractionation due to rigidity-dependent transport and acceleration. However, their energy spectra, spatial gradients, and high-energy cutoffs do not reproduce observed forms and lead to excessive fractionation. The origin of these discrepancies is probably the neglect of nonlinear processes. Although not easily incorporated in the theory, these processes could substantially modify the predicted wave intensity. An illustrative calculation assuming an arbitrary power-law form for the wave intensity demonstrates the sensitive dependence of ion fractionation on the power-law index. Subject headingg s: acceleration of particles -interplanetary medium -MHD -shock wavesSun: particle emission