Acceleration of Solar Energetic Particles at a Fast Traveling Shock in Non-uniform Coronal Conditions

Abstract

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

Vlasov methods in space physics and astrophysics

“… 2015 , 2018 ; Hu et al. 2017 ; Kozarev and Schwadron 2016 ; Le Roux and Arthur 2017 ; Luhmann et al. 2010 ; Ng and Reames 2008 ; Sokolov et al.…”

“…Shock-particle interactions including kinetic effects have been modelled using various analytical and semiempirical methods (see, e.g. Afanasiev et al 2015Afanasiev et al , 2018Hu et al 2017;Kozarev and Schwadron 2016;Le Roux and Arthur 2017;Luhmann et al 2010;Ng and Reames 2008;Sokolov et al 2009;Vainio et al 2014), but drastic approximations are usually required in order to model the whole acceleration process, and Vlasov methods have not yet been utilised. The classic extension of hydrodynamic shocks into the MHD regime has been disproven by a number of hybrid models due to, e.g., shock reformation (Caprioli and Spitkovsky, 2013;Hao et al, 2017) and anisotropic pressure and energy imbalances due to non-thermal particle populations (Chao et al, 1995;Génot, 2009).…”

Acceleration of Solar Wind Particles by Traveling Interplanetary Shocks

“…However, this mutual independence of the SDE solutions also limits applications to the test-particle case. Non-linear effects of shock acceleration such as self-generated turbulence (Lee 1983;le Roux & Arthur 2017) or particle mediation of shock structures (Mostafavi et al 2017) can therefore not be considered. Moreover, any process that requires the calculation of particle intensity gradients becomes computationally expensive (e.g.…”

Simulating Three-Wave Interactions and the Resulting Particle Transport Coefficients in a Magnetic Loop

“…MHD wave spectra in magnetized plasmas determine the transport parameters of energetic charged particles [18], which are an important element of solar eruptions such as solar flares and coronal mass ejections; see, e.g., [19][20][21]. Under the weak turbulence approximation, wave-wave interactions can, to the lowest order, be treated as three-wave interactions [22], where two waves either coalesce to produce a single wave or a single wave decays to produce two waves.…”