A Numerical Study on the Ion Acceleration in Parallel Shock Wave

Accompanied by flares and coronal mass ejections, the symbiotic coronal and interplanetary fast shock waves have become a hot topic in particle acceleration. Under the condition of quasi-parallel propagation, we construct a numerical method of solving one-dimensional transport equation, and thereby exploring the physical relationships between the distribution of the accelerated ions and the parameters of the shock waves and background plasmas. Considering the diffusive coefficient as a constant and a function of energy, respectively, the results of calculations of finite free escape boundaries show that (1) the energetic particles approximately exhibit a double power-law distribution and the spectral index decreases gradually from 10.2 to 2.4 in the low energy region of 3-10MeV with the increase of the acceleration time; (2) with the increase of the compression ratio of the shock from 2 to 4, the spectral index decreases from 3.2 to 2.2 at a given time and in the same energy range; (3) when the finite upstream and downstream escape boundaries decrease from 5 to 2, the spectral index of the particle energy spectrum increases from 2.4 to 3.3, and the acceleration efficiency of particles decreases; (4) the spectral index decreases from 2.4 to 0.9 with the increase of the initial inject energy of the particles; (5) when the diffusive coefficient is directly proportional to the energy of the particles, the spectral index increases from 2.2 to 4.3 as compared with the case of constant diffusive coefficient.