The Hall Current in Collisionless Reconnection and Reconnection in an Electron-Positron Plasma Manfred Scholer Max-Planck-Inst. Extraterrestrische Physik, Garching, Germany Queen MaryCollege, University London, UK Claus H. Jaroschek Rudolf A. Treumann

1.Hall physics and the importance for collisionless reconnection 2. Onset of reconnection in thin current sheets (PIC simulations) 3.PIC simulations of collisionless reconnection in an electron – positron plasma and particle acceleration 4.Recent PIC simulations of reconnection in large systems (Daughton et al.)

Mass conservation Energy conservation Ohm‘s+Ampere‘s law Sweet-Parker Reconnection

Sweet-Parker reconnection rate is magnetic Reynolds number (Lundquist number) L is of ambient system size and  small: Sweet/Parker rate is very small

Petschek Reconnection Petschek reconnection rate Because of logarithmic dependence on R m Petschek rate is much larger

Outer circle is the ion inertial domain. Inner circle (light blue) is the electron inertial region. Red arrows indicateinflow (of electrons) and reconnection jet outflow. Ions are unmagnetized on the ion inertial scale. Thin blue arrows are the Hall currents which generate quadrupolar Hall magnetic field. Schematic of Hall Current Systen in Reconnection

Two-Fluid-Simulation (left) and Cluster Observations (right) of Reconnection on Ion Scale Reconnecting B-component Out-of-plane B-component Normal B-component Vaivads et al., PRL 2004 Color-coded is out-of-plane magnetic field component (2D two-fluid simulation) Spaceraft configuration

Geospace Environmental Modeling Reconnection Challenge Results Dissipation region of the order of the electron skin depth and thus much smaller than the ion inertial length At this distance the Hall term in Ohm‘s law becomes important and introduces dispersion Below ions and electrons decouple. Electrons are frozen in. Whistler waves (and not nondispersive Alfven waves) control dynamics Electron frozen in condition boken at Electric field at X line supported by nongyrotropic electron pressure or electron inertia Scales Electron inertia Hall term whistler waves

Why is Wave Dispersion Important? Quadratic dispersion of whistler wave Smaller scales have higher velocities Shay and Drake, GRLett 1998 or since Electron diffusion region

When electron diffusion region of order of electron inertial scale d e (skin depth) electron outflow velocity is of order of electron Alfven velocity (Ion) Alfven velocity and length of ion diffusion region determines reconnection rate. 2-D fluid, hybrid, and PIC simulations show that length of ion diffusion region is about 10 d i (ion inertial length). Thus reconnection rate (inflow velocity) is about 0.1 v A (Claim of universal reconnection rate) Reconnection is independent of  and therefore of the mechanism by which the electron frozen in condition is broken (no bottleneck on electron scale) Shay and Drake, GRLett 1998

GEM Result – Reconnection Rate in Various Numerical Simulations 2-D Simulation - current sheet with anti-parallel magnetic field. In GEM challenge initial reconnection is enforced at by superposition of magnetic field disturbance Reconnection rate independent of dissipation mechanism. Whistler phase speed limits outflow speed. When diffusion region has electron scale the outflow velocity should be whistler speed based on electron skin depth = electron Alfven speed. MHD reconnection is too slow by orders of magnitude Reconnection rate is slope of reconnected flux vs time Birn et al., JGR 2001

Vlasov Codes Full particle codes PIC Hybrid Code MHD Code Kinetic DescriptionFluid Description Classification of Computer Simulation Models of Plasmas 2 Fluid MHD Code Electrons massless fluid Finite mass electron fluid Reconnection simulations need an artificial resistivity Reconnection electric field supported by either electron inertia or pressure tensor

PIC Simulation Industry Bhattacharjee, ………, Univ. New Hampshire Büchner,…., MPI Lindau, Germany Daughton, Scudder, Karimabadi, Univ. Iowa, UC San Diego Drake, Sitnov, Swisdak, Shay, Univ. Maryland Grauer, Schmitz,…, Univ. Bochum, Germany Hesse, Kutzentsova, Winske, NASA Goddard, Los Alamos Natl. Lab. Horiuchi, Pei, Sato, Kyoto Univ., Japan Hoshino, Shinohara, Fujimoto,..,Tokyo Univ., ISAS, Tokyo Inst. Techn., Japan Lapenta, Brackbill, Ricci, Los Alamos Natl. Lab. Pritchett, Coroniti, UCLA (MPI Garching)

3-D Full Particle Simulations (PIC) of Reconnection Double Harris-sheet Current sheet width = 1 ion inertial length Periodicity in all three directions particles of each species 3-D Particle-in-Cell code (relativistic): Multigrid algorithm for Poisson equation massively parallel Investigate reconnection onset

Thin Current Sheet with Antiparallel Magnetic Field Right: Reconnected flux versus time. The whole flux between the two current sheets is reconnected when Left: Magnetic field pattern at four different times (Isointensity contours of Scholer et al., Phys. Plasmas 2004 Explosive reconnection within a few ion times!

Lower Hybrid Drift Instability at the Current Sheet Edge Color coded electron density (left) and electric field (right) in the current directionin the plane perpendicular to the magnetic field. z is in the current direction – perp to magnetic field

Cuts of Various Parameters BEFORE Reconnection Starts Cuts of electron contribution to current density (top) and electron density across the current sheet. Profiles at t=0 are shown dashed for reference. Reduced electron distribution function f(v_z) verusus v_z in the current sheet gradient region (top) and in the center (bottom) of the current sheet exhibiting electron acceleration in the electric field of the LHD waves. t=0t=4

Thin Current Sheet with Antiparallel Field plus Guide Field (Sheared Field Configuration) B = 1 In the guide field case the LHDI develops as well, but it takes considerbly longer time for reconnection to set in. After reconnection onset the reconnection rate is about the same as in the exactly antiparallel case. z

Reconnection in a Pair Plasma: 2-D and 3-D Full Particle Simulations Jaroschek et al., Phys. Plasmas 2004 Simulation: Initial state: 1-D curent sheet, relativistic Maxwell-Juettner plasma (100 keV) Reconnection initialized by disturbance in center of current sheet Parameters: current sheet width (1 – 2 inertial lengths d o ) c / v Ao between 1 and  in a 3-D run about 2 x 10 9 particles Pair dominance in plasma of a)Relativistic extragalactic jets b)Pulsar outflows (Crab) c) Core of AGN‘s

EzEz n Current sheet and quasi-static acceleration region begin to sparate X-line at early times EzEz Reconnection rate after onset phase (electric field along X line) (E > 0.2)

Multiple X line and island coalescence phase Field lines E z Particle acceleration (  ) along center line Schematic of field topology y x y 

Temporal development 0 t on t coa t sep t equ Single X line Separation of X lines along current sheet Island coalescence t  c = X line buildup

Temporal development of the distribution function in the 2-D run

More (2-D) PIC Simulations of Reconnection in an Electron-Positron Plasma (From Bessho and Bhattacharjee, PRL 2005)

Reconnection rate Bessho and Bhattajarchee: High reconnection rate in pair plasma (E > 0.2) Note: there is no Hall current in a pair plasma!

Results from a 3-D PIC Simulation x y E z /B z x EzEz z x density Fast onset of relativistic drift kink instability due to RTSI Acceleration region about 20 electron inertial lengths in current direction (z). Limits  to 30. vzvz z Heating by a relativistic Buneman-type Instability (RTSI) Trapping

Total spectral synchrotron output as a function of  co (  co = cyclotron frequency) Application to Pair-Dominated Active Galactic Nucleus Core Regions (Extremely hard radio spectra, Power output of P ~ ergs/sec) Jaroschek et al., ApJ Lett Model assuming stochastic distribution of reconnection zones over the entire coronal souce region can explain power output and spectra

There is no Hall current system in a pair plasma, yet reconnection is fast Is Hall physics really the key mechanism for fast reconnection in an electron – proton plasma?

Large Scale PIC Simulation of Reconnection (Electron-Proton Plasma) Daughton et al. Phys. Plasmas 2006 Extent of electron diffusion region > 10 d i Island formation

Daughton et al.: The results are not consistent with the standard model of Hall mediated fast reconnection. Fast reconnection may still be possible so long as the process for generating secondary islands remains vigorous…

y-component of ion vorticityB y – field (out-of-plane) is frozen into ion fluid u. In the inflow region both terms are zero. Occurrence of vorticity has to be cancelled by B y Hybrid Simulation of Tail Reconnection Arzner and Scholer, JGR 2001

Reconnection in a pair plasma (no Hall physics involved) is fast In the late phase reconnection in a pair plasma is violent and particles are accelerated to high energies (>30 , also in 3-D) PIC simulations of (undriven) reconnection in an electron – proton plasma in a long system show that the electron diffusion region becomes very large, more than 10 ion inertial lengths long Hybrid simulations (massless electrons) with a large (resistive) diffusion region exhibit quadrupolar (Hall-type) magnetic fields. (Hall magnetic fields may only tell us that the plasma is collisionless) Summary

Physics of collisionless reconnection continues to be an open question

Electron Acceleration in Collisionless Reconnection

PIC Simulations of Reconnection – Electron Acceleration Drake et al., PRL 2005 Electron distibution at three times (Large Guide-Field Simulation) Stong parallel electric fields Electron holes

2-D PIC Simulations of Reconnection – Electron Acceleration by Surfing (Strongly driven inflow) E z polarization electric field near sepatarix Electric forcecan balance Lorentz force Hoshino, JGR 2005 Electron stays there and gains energy by moving in the y direction

Development of electron spectrum

Acceleration in Contracting Magnetic Islands Drake et al. Nature 2006 Test particle simulation of electron Fermi acceleration in squashed flux bubbles PIC reconnection simulation producing magnetic islands