The Influences of Shock Thickness and Alfven Waves on the Particle Acceleration by Diffusive Shocks

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3—10 MeV and from 2.5 to 5.0 in the high energy range of 20—60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3—10 MeV and from 11.6 to 5.0 in the high energy range of 20—60 MeV. At the same time, the turning point energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increases. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.