REGULAR ACCELERATION OF PARTICLES AT THE FRONTS OF INTERPLANETARY SHOCK-WAVES

The regular acceleration of solar-wind protons by interplanetary shock waves in the inner heliosphere (r less than or equal to 1 AU) is stud ied. The theoretical description that is based on a quasi-linear appro ach includes a self-consistent allowance for the generation of Alfven waves by the accelerated particles and the assumption that a fraction of suprathermal particles are injected into the acceleration regime at the shock front. The equation for the diffusive transfer and the equa tion for the transfer of Alfven waves are solved numerically in the ap proximation of spherical symmetry. It is shown that allowance for the sphericity and adiabatic deceleration of particles in the expanding so lar wind results in a considerable softening of the spectrum of the ac celerated particles and in a decrease of their limiting energy. The ge neration of Alfven waves by the accelerated particles has no significa nt effect on the limiting energy of the particles, which is determined by the level of background Alfven turbulence in the solar wind. The t heory is in good agreement with experimental results.