Turbulence, reconnection and particle acceleration

1. Turbulence, reconnection and particle acceleration W. H. Matthaeus, P. Dmitruk, N. Seenu Bartol Research Institute, University of Delaware M. R. Brown Swarthmore College SSX team members: C. Cothran. M. Landreman, D. Schlossburg 7th International Workshop on the Interrelationship between Plasma Experiments in Laboratory Space, Whitefish, Montana, June 29-July 3, 2003.

2. Test particles in 3D MHD turbulence • Test particle strategy (Ambrosiano et al, JGR 1988)

3. 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

4. 2D MHD turbulence • Magnetic field lines as contours • Electric current density as gray shades • Random reconnection events • 512 x 512 resolution spectral method code

5. 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.

6. Acceleration by 2D turbulence • In addition to acceleration by large scale 2D reconnection (with small scale turbulence), particles are accelerated in a very similar way by 2D homogeneous turbulence Test particles in 2D turbulence Gray and Matthaeus, PACP, 1992

7. Scaling of particle energy: • Scaling of energy depends upon  testparticleA  L/ (c/pi) Max energy Va B L  219 B2 L/n1/2 (ev) Goldstein et al. GRL, 1986 Note that: Energy containing scale/ ion inertial scale  bandwidth of the inertial range

8. “V-B-L” scaling of charged particle energies SSX From K. Nakishima, Astron. Nachr, 1999

9. Reconnection in SSX M. Brown, PI C. Cothran M. Landremann

10. SSX: Relative timing of MHD and energetic particle signals

11. SSX: detection of spectrum of energetic particles

12. Reconnection in driven 3D RMHD turbulence • A nice example of a randomly occurring reconnection event in nearly standard geometry

13. Electric field in 3D MHD turbulence Electric field Magnetic field magnitude

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 Solar Wind data

15. 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

16. Particle trajectories • 300 trajectories • Compare to locations of strong |E|

17. Acceleration of test particles by turbulent electric field a = tAlfven/tgyro • Particles start • with v=0 • Distribution after • 0.5 tAlfven • Two powerlaws

18. Scaling of particle energies Maximum energy Mean energy

19. Scaling of mean and maximum particle energy with alpha Energy ~ vBL or, a l E (alpha * E-correlation * typical electric field)

20. Conclusions • Charged test particles are accelerated by electric fields associated with turbulence and reconnection. • Phenomenon is very similar in • 2D turbulence • 3D turbulence • Reconnection in presence of small scale turbulence and large scale reconnection in the presence HD cascade produces transverse structure, associated with localized shear and reconnection sites. • V-B-L scaling seen in each case • SSX experimental results are consistent with the simulations. • Space and Astrophysical energy scalings are also consistent, including • Solar wind • Magnetosphere • Solar flares • Broad band test particle distributions are produced, with characteristic energies increasing with a= A