MHD Turbulence: influences on transport 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

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

Three types of magnetic shear

MHD Correlation/Spectral Anisotropy: Correlation/Spectral anisotropy

K-space

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

Two component model:

Comparison of flux tubes

80-20 turbulence labeled by local 2D vector potential

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.

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 G. Qin et al, 2002 GRL 2002 ApJL

Two-dimensional turbulence and random-convection-driven reconnection

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

Statistics of the induced electric field 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 Spectral MHD simulation t = 3 30 years of 1 hour SW data Dashed lines are theoretical Values for Gaussian v, b Milano et al, PRE, 2002

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

2D turbulence Scaling of energy depends upon  testparticle    L/ (c/  pi ) Gray and Matthaeus, PACP, 1992 Goldstein et al. GRL, 1986  219 B 2 L/n 1/2 (ev)

3D or pseudospectral method compressible MHD code (parallel implementation) MPI load balanced test particle code 50,000 particles with  = 100 to 100,000 and accuracy of Nonrelativistic particles intially at rest

Magnetic field energy

MHD electric field

Particle energy distributions

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 E max increasing with  A

Spectral anisotropy in MHD

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

Puzzling properties of perpendicular transport/diffusion 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” Computed K  ’s fall Well below FLRW at low energy, but Above other Proposed explanations Slab/2D and Isotropic ( Giacalone And Jokipii.) Slab ( Mace et al, 2000)

Numerical Results: slab fluctuations: Parallel and perpendicular transport in the same simulation! Running diffusion coefficient: K  = (1/2) d /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

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? IH Urch, Astrophys. Space Sci., 46, 389 (1977). J. Kota and J.R. Jokipii Ap. J. 531, 1067 (2000)

Numerical simulation using 2-component turbulence: 80% 2D + 20% slab 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. Qin et al, 2002