William Daughton Plasma Physics Group, X-1 Los Alamos National Laboratory Presented at: Second Workshop on Thin Current Sheets University of Maryland April 19, 2004 The Onset of Magnetic Reconnection

Motivation for this work Current sheet geometry is often employed to study the basic physics of collisionless magnetic reconnection Kinetic Simulations are typically 2D with large initial perturbation: a. Does not allow instabilities in direction of current b. Avoids the question of onset completely www-spof.gsfc.nasa.gov Courtesy of Hantao Ji (PPPL)

Basic Approach For a given problem with fixed box size Explicit PIC must resolve all relevant scales 3D Simulations - Must choose very artificial parameters 2D Simulations - More realistic parameters are possible

Harris Current Sheet Main Distribution Background Distribution Anisotropy Thickness

2D Simulations of Tearing Consider 3 simulations - Only change the box length 1. Single island saturation 2. Two island saturation 3. Four island saturation Equilibrium Parameters Reduced by 30% for

Single Island Tearing Saturation Linear Growth Rate Mode Amplitude PIC Simulation

Two Island Coalescence Mode AmplitudesLinear Growth Rate M=1 M=2

Four Island Coalescence Onset Stage Central region of box Linear tearing islands Coalescence Very slow process Fast Reconnection Show entire box Large scale reconnection Saturation limited by box

Reconnection Onset from Tearing How might this change in 3D? LHDI is much faster than tearing 2D simulations in oblique plane Can the LHDI modify onset physics ? Single island tearing saturates at small amplitude Onset requires coalescence of many islands Finite B z is stabilizing influence Laval & Pellat 1968 Biskamp, Sagdeev, Schindler, 1970 Scholer et al, PoP 2003 Horiuchi Shinohara & Fujimoto Pellat, 1991 Pritchett, 1994 Quest et al, 1996 Sitnov et al, > can go unstable? Tearing is stable in magnetotail

Lower-hybrid Drift Instability (LHDI) Driven by density gradient Fastest growing modes Real frequency Growth rate Stabilized by finite beta Primarily electrostatic and localized on edge Example Eigenfunction Good Agreement Carter, Ji, Trintchouck, Yamada, Kulsrud, 2002 Davidson, Gladd, Wu & Huba, 1977 Huba, Drake and Gladd, 1980 Theory Experiment Bale, Mozer, Phan 2002 Observation

Established Viewpoint on LHDI Localized on edge of layer Small anomalous resistivity Wrong region to modify tearing Not relevant to reconnection New results challenge this conclusion 1. Direct penetration of longer wavelength linear modes 2. Nonlinear development of short wavelength modes

Penetration of LHDI t  ci =3 t  ci =11 t  ci =8 t  ci =13

2D Simulation of Lower-Hybrid Equilibrium Parameters Simulation Parameters: Thicker SheetColder Electrons More relevant to magnetospheric plasmas Background

Electrostatic Fluctuations Two fastest Growing modes Lower-Hybrid Drift Mode Fluctuations are confined to the edge of the sheet

Evolution of Current Density Initial Y-averaged Contours of

Initial Y-averaged Contours of Evolution of Ion Density

Initial Y-averaged Contours of Evolution of Ion Velocity

Initial Y-averaged Contours of Evolution of Electron Velocity

Y-averaged Contours of Evolution of Electron Anisotropy

Resonant Scattering of Crossing Ions Scale for Crossing Orbit Noncrossing Crossing Example of scattering Lower-hybrid fluctuations

Contours of Electrostatic Potential Net gain Net gain Net loss

Electron Acceleration Neglect Use Equilibrium Profiles

Inductive Heating of Electrons Evolution of current profile modifies magnetic field For electrons, magnetic field changes slowly Changes on the ion time scale How to construct adiabatic invariant for these orbits? Magnetic Moment Inductive Heating Adiabatic Invariant

Anisotropic Electron Heating Contours of Y-averaged

Physical Mass Plasma parameters are same but numerical requirements increase Results show same basic physics Details are described in preprint How big of a mass ratio is needed?

What about lower mass ratio?

1. Critical thickness for process to occur 2. Potential structure accelerates electrons 3. Enhances tearing mode New Model for Fast Onset of Reconnection Lower-hybrid drift instability 1. Current density 2. Anisotropy 4. Rapid onset of reconnection Critical Scale Tearing Growth Rate Forslund, 1968 J. Chen and Palmadesso, 1984

Test this idea at reduced mass ratio Tearing Growth Rate Factor of 17 increase in growth rate Fastest mode shifts to shorter wavelength Growth of small islands --> Coalescence Rapid onset of large scale reconnection Initialize previous 2-Mode case with

Electron Anisotropy Instabilities? Theory of Space Plasma Microinstabilities, S.P Gary 1. Whistler Anisotropy Instability 2. Electron Firehose Instability 1. Edge region is low beta 2. Center has complicated orbits 3. Does not appear in simulations? Should these occur in neutral sheet?

Neutralization of Electrostatic Potential Growth of LHDI Time scale for electrons to flow in and neutralize

Future Work Working with collaborators to simulate in 3D However, many things left to examine in 2D: 1. Does predicted critical thickness hold? 2. Role of guide field and/or normal component 3. Influence of background (lobe) plasma 4. More realistic boundary conditions Possible relevance to recent Cluster observations Runov et al, Cluster observation of a bifurcated current sheet, GRL, 2003