1. Generation of Solar Energetic Particles (SEP) During May 2, 1998 Eruptive Event Igor V. Sokolov, Ilia I. Roussev, Tamas I. Gombosi (University of Michigan) Terry G. Forbes and Marty A. Lee (U. Hampshire) Jun-ichi Sakai (U. Toyama), Jozsef Kota (U. Arizona)

2. SEPs in Human Life Setup for evaluating the SEP influence consists of an astronaut body, shielded by the “standard screen”: of stopping length of g/cm 2 (Al, 2 mm), Fast proton motion through the “screen” is governed by: From here, the vitally important range of SEP energies is:

3. SEP Measurements for April-May 1998 Events

4. Diffuse-Shock-Acceleration Mechanism Diffusive kinetic equation (Dolginov & Toptygin,1966) governing the Diffuse- Shock-Acceleration Mechanism (Krymskii, 1997; Axford et al., 1997; Bell, 1998; Blandford & Ostriker, 1998): Here f is an isotropic part of the SEP distribution function ( ), u is the bulk plasma velocity, D is the diffusion tensor. Assume that the diffusion only occurs along the magnetic field line:. Assuming the magnetic field to be frozen into the plasma and introducing the Lagrangian coordinates along the magnetic field line, the kinetic equation can be written for each magnetic line separately: where  is the plasma density:

5. Dynamic Profiles of Plasma Density

6. Diffusion Through Magnetized Turbulent Plasma Estimate for diffusion along the magnetic field line is as follows: Steady-state distribution near parallel shock wave with :

7. Magnetic Field is Reasonably Strong Only for R<10R Sun !

8. Diffusion Length and Acceleration Rate Length of SEP upstream tail: Upper limit for cut-off kinetic energy (Bulanov & Sokolov,1984):

9. Computational Technology and Challenges High-resolution MHD simulation at the adaptive block grid: the better the spatial resolution at shock front, the smaller injection energies can be involved to analyze the SEP distribution, AW solver (Sokolov et al., 2000, 2002). SWMF coupling toolkit (Sokolov, 2003) can be used for tracing the Lagrangian meshes along particular magnetic field line. Employ fully implicit numerical scheme for SEP diffusion along the magnetic field line, and upwind implicit scheme for SEP advection along the energy coordinate.

10. Shock Wave Speed for May 2, 1998 Eruption Event

11. Cut-Off Kinetic Energy for SEPs

12. Conclusions SEP acceleration by Diffuse-Shock-Acceleration mechanism, up to energies sufficient for penetrating into spacecraft, occurs in low corona at and has comparatively short time scale (~1hour) To simulate this properly, high-resolution MHD simulation should be coupled with kinetic equation for SEP diffusion along magnetic field lines, including Fermi type- A acceleration. Magnetic field line(s) motion should be traced using Lagrangian coordinates. Physical requirements to numerical models of solar eruption: –Initial conditions should not produce shock wave as result of strong initial non- equilibrium; –However, solar eruption should be sufficiently energetic, rather violent, to form strong shock wave in Sun’s proximity.