Turbulence reconnection and particle acceleration W H Matthaeus

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 7 th International Workshop on the Interrelationship between Plasma Experiments in Laboratory Space, Whitefish, Montana, June 29 -July 3, 2003.

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

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

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

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

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

Scaling of particle energy: • Scaling of energy depends upon testparticle A L/ (c/ pi) Max energy Va B L 219 B 2 L/n 1/2 (ev) Note that: Goldstein et al. GRL, 1986 Energy containing scale/ ion inertial scale bandwidth of the inertial range

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

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

SSX: Relative timing of MHD and energetic particle signals

SSX: detection of spectrum of energetic particles

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

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

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

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

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

Acceleration of test particles by turbulent electric field = Alfven/ gyro • Particles start with v=0 • Distribution after 0. 5 Alfven • Two powerlaws

Scaling of particle energies Maximum energy Mean energy

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

Conclusions • Charged test particles are accelerated by electric fields associated with turbulence and reconnection. • Phenomenon is very similar in – 2 D turbulence – 3 D 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