Abstract. Time-dependent solar energetic particle (SEP) acceleration is investigated at a fast, nearly parallel spherical traveling shock in the strongly non-uniform corona by solving the standard focused transport equation for SEPs and transport equations for parallel propagating Alfvén waves that form a set of coupled equations. This enables the modeling of self-excitation of Alfvén waves in the inertial range by SEPs ahead of the shock and its role in enhancing the efficiency of the diffusive shock acceleration (DSA) of SEPs in a self-regulatory fashion. Preliminary results suggest that, because of the highly non-uniform coronal conditions that the shock encounters, both DSA and wave excitation are highly time-dependent processes. Thus, DSA spectra of SEPs strongly deviate from the simple power-law prediction of standard steady-state DSA theory and initially strong wave excitation weakens rapidly. Consequently, the ability of DSA to produce high energy SEPs in the corona of ~1 GeV, as observed in the strongest gradual SEP events, appears to be strongly curtailed at a fast nearly parallel shock, but further research is needed before final conclusions can be drawn.
IntroductionWe report preliminary simulation results of time-dependent solar energetic particle (SEP) acceleration at a fast, nearly parallel spherical traveling shock in the corona by taking into account the strong radial dependence in background coronal plasma conditions that the shock encounters during the first hour of shock propagation. For this purpose a simple empirical coronal plasma model [1] is used as a first step. The model involves solving a set of coupled equations for SEPs and parallel propagating Alfvén waves. The standard focused transport equation is solved to simulate SEP acceleration at the traveling shock when SEPs are scattered by Alfvén waves in its vicinity [2,3], and standard transport equations for parallel propagating Alfvén waves are solved to model wave transport near the shock including self-excitation of waves in the inertial range by upstream SEPs undergoing shock acceleration [4,5,6,7,8]. Thus, enhanced scattering of SEPs by Alfvén waves is induced that enhances the efficiency of diffusive shock acceleration (DSA) of SEPs in a self-regulatory fashion at the nearly parallel shock [6,9,10]. For an excellent recent review of the current status of SEP modelling at traveling shocks, see Verkhoglyadova et al. [11]. Our calculations discussed below show that, because of the highly non-uniform coronal conditions that the shock encounters, both the DSA of SEPs and self-excitation of Alfvén waves by SEPs are highly time-dependent coronal processes. Thus, we find that the accelerated spectra of SEPs deviate strongly from the simple power-law prediction of standard