MHD Turbulence: influences on transport and acceleration of energetic particles

1. MHD Turbulence: influences ontransport and acceleration of energetic particles W H Matthaeus Bartol Research Institute, University of Delaware Pablo Dmitruk Nirmal Seenu Gang Qin John Bieber Huntsville Workshop 2002: Astrophysical Particle Acceleration in Geospace and Beyond October 6-10, 2002 Chattanooga, Tennessee

2. MHD Turbulence effects on charged test particles • Magnetic shear/anisotropic cascade/reconnection • Structure of magnetic flux tubes • Transverse complexity and perpendicular transport • Acceleration by turbulent electric field

3. Three types of magnetic shear

4. Correlation/Spectral anisotropy MHD Correlation/Spectral Anisotropy:

5. K-space

6. Implication for energetic particle acceleration models: • Preferential cascade to high k-perp means it may be difficult to supply/re-supply power to resonant wave numbers at high k-parallel

7. Two component model:

8. Comparison of flux tubes

9. 80-20 turbulence labeled by local 2D vector potential

10. Implication for energetic particle transport: • In the presence of transverse structure, magnetic flux surfaces may not appear as they do in simple models  flux surfaces shred, become complex in a few correlation lengths.

11. G. Qin et al, 2002 GRL 2002 ApJL Perpendicular transport • Particle gyrocenters try to follow fields lines (“FLRW” limit) • Motion along field lines is inhibited by parallel (pitch angle) scattering • Low transverse complexity subdiffusion • Strong transverse complexity recovery of diffusion at lower level than FLRW

12. Two-dimensional turbulence and random-convection-driven reconnection

13. Acceleration of Charged Particles by Turbulence • Test particle approximation • Turbulent reconnection (2D) • Coherent and random contributions: • Coherent interaction with single reconnection site • Random v x b due to waves/nonlinearities • 2D turbulence • 3D turbulence Ambrosiano et al, JGR 1988 Gray and Matthaeus, PACP, 1992 Also see: Brown et al, ApJL, 2002 Lab. Exp. (SSX) Observation of Acceleration

14. Statistics of the induced electric field Milano et al, PRE, 2002 • For Gaussian v, b  Induced E is exponential or exponential-like • Ind. E is localized but not as localized as the reconnection zones themselves. • Kurtosis 6 to 9 Dashed lines are theoretical Values for Gaussian v, b Spectral MHD simulation t = 3 30 years of 1 hour SW data

15. Test particle acceleration by turbulent reconnection Ambrosiano et al, Phys. Fluids, 1988 • 2D MHD reconnection • Not equilibrium • Broadband fluctuations • - fast reconnection Particle speed distribution High energy particles Particles are accelerated (direct and velocity diffusion) in region between X- and O-points. Powerlaw/exponential distributions.

16. 2D turbulence • Scaling of energy depends upon  testparticleA  L/ (c/pi) Goldstein et al. GRL, 1986  219 B2 L/n1/2 (ev) Gray and Matthaeus, PACP, 1992

17. 3D • 1283or 2563 pseudospectral method compressible MHD code (parallel implementation) • MPI load balanced test particle code • 50,000 particles with a= 100 to 100,000 and accuracy of 10-9 • Nonrelativistic particles intially at rest

18. Magnetic field energy

19. MHD electric field

20. Particle energy distributions

21. Conclusions • MHD cascade produces transverse structure, associated with localized shear and reconnection sites. • Transverse structure produces “shredding” flux tubes • Transverse complexity “restores” perpendicular diffusion, but lower than FLRW • MHD turbulence produced broad band test particle distributions with Emax increasing with a= A

23. Spectral anisotropy in MHD

25. Perpendicular transport/diffusion • Field Line Random Walk (FLRW) limit is a standard picture. • K (v/2) D • When do you expect this: at low energy? At high energy? Fokker Planck coefficient for field line diffusion

26. Puzzling properties of perpendicular transport/diffusion Computed K’s fall Well below FLRW at low energy, but Above other Proposed explanations • Numerical results support FLRW at high energy, but no explanation for reported low energy behavior • K may be involved in explaining observational puzzles as well • Enhanced access to high latitudes • “chanelling” Slab/2D and Isotropic (Giacalone And Jokipii.) Slab (Mace et al, 2000)

27. Numerical Results: 0.9999 slab fluctuations:Parallel and perpendicular transport in the same simulation! • Running diffusion coefficient: K = (1/2) d<2>/dt • Parallel: free-streaming, then diffusion ( QLT) • Perpendicular: initially approaches FLRW, but is thwarted…behaves as t-1/2 i.e., subdiffusion Qin et al, 2002

28. IH Urch, Astrophys. Space Sci., 46, 389 (1977). J. Kota and J.R. Jokipii Ap. J. 531, 1067 (2000) Perpendicular Subdiffusion • In evaluating K~z/t  Dinstead of using z/t =v, assume that the parallel motion is diffusive, and z =(2 K t )1/2 •  K = D (K / t)1/2 • For this to occur, nearby field lines must be correlated. If the transverse structure sampled by the particle becomes significant, can diffusion be restored?

29. Numerical simulation using 2-component turbulence:80% 2D + 20% slab Qin et al, 2002 • Parallel: free stream, then diffuse, but at level < QLT • This appears to be nonlinear effect of 2D fluctuations • Perpendicular: movement towards FLRW, subsequent decrease, and then a “second diffusion” regime appears.