Generalized compound diffusion model of solar cosmic rays

1. Generalized compound diffusion model of solar cosmic rays accelerated in corotating interaction region VladimirUchaikin, RenatSibatov, Alexander Byzykchi Ulyanovsk State University, Russia The 2nd International Conference on Particle Physics and Astrophysics

2. Simulation of charged particle transport in turbulent MF Pucci, F. et al. (2016). MNRAS, 459(3), 3395-3406. Turbulent magnetic field The model builds up a turbulent magnetic field as a superposition of space-localized fluctuations at different spatial scales. The resulting spectrum is isotropic with an adjustable spectral index. The model allows them to reproduce a spectrum broader than four decades, and to regulate the level of intermittency through a technique based on the p-model.

3. Simulation of charged particle transport in turbulent MF Pucci, F. et al. (2016). MNRAS, 459(3), 3395-3406. Equations of motion The guiding center motion Resonant interactions and magnetic mirroring

4. Parallel and perpendicular diffusion coefficients Pucci, F. et al. (2016). MNRAS, 459(3), 3395-3406. Tempered Levy Walk for parallel transport

5. Levy walks and Brownian motion Distribution of path lengths between reflections Brownian motion Superdiffusion

6. Tempered Levy flights: space-time trajectories

7. Inverse problem Second moment of the random walk with finite velocity Second moment of the random walk with finite velocity

8. Parameters of tempered superdiffusion

9. Comparison of simulated and analytical results Tempered Levy Walk for parallel transport

10. Simulation of the tempered Levy walk: evolution of the diffusion packet

11. Magnetic field line random walk Bieber et al. Mean square displacement Fractional Brownian motion Perpendicular diffusion coefficient Pucci et al 2016

12. Parameters of perpendicular diffusion

13. Protons and electrons accelerated by corotating interaction region • Perri, S., & Zimbardo, G. (2007). • Perri, S., & Zimbardo, G. (2009). • Sugiyama, T., & Shiota, D. (2011). x

14. Superdiffusion from analysis of energetic particle profiles measured by spacecraft Normal diffusion – exponential decay of intensity Anomalous diffusion – power law decay of intensity

15. Superdiffusion from analysis of energetic particle profiles measured by spacecraft Electron transport is superdiffusive. Proton transport is normal diffusive. (Perri and Zimbardo, Adv. Spa. Res. 2009)

16. Superdiffusion of electrons Event of October 11, 1992 Dt=|t-tsh| Power law J=A(Dt)-g Exponential J=K exp(-GDt)

17. Specification of the Green function Uchaikin, V., Sibatov, R., & Byzykchi, A. (2014). Commun in Appl and Ind Math, 6(1).

18. Normal and anomalous diffusion of protons

19. Thank you for your attention!

20. Plasma and energetic particle profiles for the Ulysses shock crossing on 1992 October 11. From top to bottom, panels show 1 h averages of plasmaradial velocity, plasma temperature (from SWOOPS, PI D. McComas), proton fluxes and electron fluxes (from HI-SCALE LEFS 60, PI L. Lanzerotti).The vertical dashed line indicates the reverse shock crossing time. Energy channels as indicated.

21. The same technique was applied to CME driven shock waves by Sugiyama and Shiota, ApJL, 2011: ACE data for December 13, 2006 CME shock

22. Sugiyama, T., & Shiota, D. (2011). Gray curves in panels show the flux of the energetic particles in the upstream of the shock. The horizontal axis is the time interval |Δt| between the observation time t and the shock crossing time