William Daughton

1
The Onset of Magnetic Reconnection

• 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

2
Motivation for this work
Current sheet geometry is often employed
to study the basic physics of collisionless
magnetic reconnection
www-spof.gsfc.nasa.gov
Courtesy of Hantao Ji (PPPL)

• 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
Focus on the onset problem
3
Basic Approach
Explicit PIC must resolve all relevant scales
For a given problem with fixed box size
3D Simulations - Must choose very artificial
parameters 2D Simulations - More realistic
parameters are possible
4
Harris Current Sheet
Background Distribution
Main Distribution
Anisotropy
Thickness
5
Can collisionless tearing explain onset?
6
2D Simulations of Tearing

• Consider 3 simulations - Only change the box
  length
• Single island saturation
• Two island saturation
• Four island saturation

Equilibrium Parameters
Reduced by 30 for
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Single Island Tearing Saturation
Mode Amplitude
Linear Growth Rate
PIC Simulation
8
Two Island Coalescence
Mode Amplitudes
Linear Growth Rate
M1
M2
9
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

10
Reconnection Onset from Tearing

• Single island tearing saturates at small
  amplitude
• Onset requires coalescence of many islands
• Finite Bz is stabilizing influence

Laval Pellat 1968 Biskamp, Sagdeev, Schindler,
1970
Pellat, 1991 Pritchett, 1994 Quest et al,
1996 Sitnov et al, 1998 -gt can go unstable?
Tearing is stable in magnetotail
Scholer et al, PoP 2003 Horiuchi Shinohara
Fujimoto
11
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
Carter, Ji, Trintchouck, Yamada, Kulsrud, 2002
Experiment
Good Agreement
Davidson, Gladd, Wu Huba, 1977 Huba, Drake and
Gladd, 1980
Theory
Bale, Mozer, Phan 2002
Observation
12
Established Viewpoint on LHDI
Standard Arguments

• Localized on edge of layer
• Small anomalous resistivity
• Wrong region to modify tearing
• Not relevant to reconnection

13
Penetration of LHDI
tWci3
tWci8
tWci13
tWci11
tWci13
14
Nonlinear Development in a Thicker Sheet ?
15
2D Simulation of Lower-Hybrid
Equilibrium Parameters
Thicker Sheet
Colder Electrons
Background
More relevant to magnetospheric plasmas
Simulation Parameters
16
Electrostatic Fluctuations
Two fastest Growing modes
Lower-Hybrid Drift Mode
Lower-Hybrid Drift Mode
Fluctuations are confined to the edge of the sheet
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Evolution of Current Density
Initial
Contours of
Y-averaged
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Evolution of Ion Density
Initial
Contours of
Y-averaged
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Evolution of Ion Velocity
Initial
Contours of
Y-averaged
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Evolution of Electron Velocity
Initial
Contours of
Y-averaged
21
Evolution of Electron Anisotropy
Contours of
Y-averaged
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Resonant Scattering of Crossing Ions
23
Electrostatic Potential
Net gain
Net loss - - - - - - - - -
Net gain
Contours of
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Electron Acceleration
Use Equilibrium Profiles
Neglect
25
Inductive Heating of Electrons
Evolution of current profile modifies magnetic
field
Changes on the ion time scale
For electrons, magnetic field changes slowly

Magnetic Moment
Adiabatic Invariant
Inductive Heating
How to construct adiabatic invariant for these
orbits?
26
Anisotropic Electron Heating
Y-averaged
Contours of
Y-averaged
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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?

28
What about lower mass ratio?
29
New Model for Fast Onset of Reconnection

1. Critical thickness for process to occur
2. Potential structure accelerates electrons
3. Enhances tearing mode

Lower-hybrid drift instability
Critical Scale
Lower-hybrid drift instability
1. Current density 2. Anisotropy
Tearing Growth Rate
Forslund, 1968 J. Chen and Palmadesso, 1984
4. Rapid onset of reconnection
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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 --gt Coalescence Rapid onset of large
scale reconnection
Initialize previous 2-Mode case with
31
Electron Anisotropy Instabilities?
Theory of Space Plasma Microinstabilities, S.P
Gary
1. Whistler Anisotropy Instability
2. Electron Firehose Instability
Should these occur in neutral sheet?

1. Edge region is low beta
2. Center has complicated orbits
3. Does not appear in simulations?

32
Neutralization of Electrostatic Potential
Growth of LHDI
Time scale for electrons to flow in and
neutralize
33
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
• More realistic boundary conditions
• Possible relevance to recent Cluster observations
  
• Runov et al, Cluster observation of a bifurcated
  current sheet, GRL, 2003