1. Hybrid model of solar energetic particle acceleration and transport Hybrid model of solar energetic particle acceleration and transport Leon Kocharov, Rami Vainio, and Jens Pomoell University of Helsinki, Finland 32nd International Cosmic Ray Conference Beijing, China August 11-18, 2011 Rami.Vainio@helsinki.fi

2. Coordinate system for particle modeling Particle’s -coordinate change due to stretching/shortening of line i of evolving magnetic field should be added to particle’s physical advection caused by scattering-center flow and magnetic focusing. Particles are traced with Monte Carlo simulations in a hybrid coordinate system that is Lagrangian only in the direction perpendicular to magnetic field, with both diffusion approach and focused transport framework employed.

3. MHD modeling of CME liftoff and coronal shock propagation MHD modeling results: Snapshot of magnetic field structure and gas compression map after the first 4 min and 7 min of CME development. Vicinity of the Y-type neutral point: possible location of the accelerated particle escape Acceleration to high energies in highly oblique / quasi- perpendicular shock Low-threshold injection of seed particles into the shock acceleration

4. Shock-in-Loop Model Seed particle injection: Q~exp[-E th /E o ] Threshold energy by Sandroos & Vainio, ApJS, 181,183, 2009 Inside the shock:  2 2 Stochastic re-acceleration: Monte Carlo method: time stepping of quasi-particles [Shock upstream angle    ; compression ratio  X  ]

5. First modeling results Model parameters Loop height: R=1.2 Rsun Shock speed: u=3400 km/s Upstream of the shock: M A =10, =0.3,   װ (0.1MeV)= 10 7 km 2 /s,   /  װ =0.04 Seed particles: E o =10 keV SEP-escape site: around loop apex The escape sector: 30 deg The escape probability ~  (E) The escape period: 30 min Stochastic re-acceleration rate is proportional to the parameter 

6. Maximum re-acceleration No re-acceleration Inside the acceleration region Escaping particles Maximum re-acceleration No re-acceleration

7. 12 Sept 2000: S19W08 7 June 2011 SOHO/ERNE (preliminary) 4 Apr 2000: N16W66 Gradual SEP events in the deka-MeV energy range typically start with a weak hard-spectrum component [e.g., Kocharov et al., ApJ, 725, 2262 (2010)]

8. Conclusions  In magnetic environment of solar corona and with different seed particle populations, possible variety of shock accelerated particle spectra is wider than traditionally expected.  If the seed particle injection rate steeply declines with distance travelled by the shock, resulting SEP spectrum at the shock location can be very hard.  Weak, hard-spectrum ‘precursor’ of major SEP events observed in the deka-MeV range can be a signature of particle acceleration by coronal, CME- driven shock.  Stochastic re-acceleration after the shock passage cannot be ignored.

9. THANK YOU!

10. 20 Diffusive shock acceleration: Parallel shocks 12 Seed particles SEPs Stochastic re-acceleration Next to the shock:  =0.15, q=1.5 1 / 2 1/21/2

11. Diffusive shock acceleration: Oblique shocks Stochastic re-acceleration Comparison of stochastic acceleration effect and shock acceleration effect: Shock acceleration on (initially) semi-circular magnetic field line Kocharov et al., ApJ, vol. 735, Issue 1, article id. 4 (2011)