A Comparison of 2D PIC Simulations of Collisionless Reconnection

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A Comparison of 2D PIC Simulations of
Collisionless Reconnection

• Michael Harrison
• Thomas Neukirch
• Michael Hesse
• April 2, 2008

School of Mathematics and Statistics The
University of St. Andrews
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Investigate the transition from an anti-parallel
initial field Configuration through to a
Force-Free field configuration.
Investigate the Morphology of the Off-Diagonal
components of the Pressure Tensor.
Motivation
Compare the Differences in the Reconnection
process between Initial Configurations with
Constant guide-field and cases with spatially
varying shear fields
Compare the Reconnection Rates For different
initial magnetic field Configurations.
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Normalisations and Simulation Parameters

• Times are normalised to inverse ion cyclotron
  frequency.
• Lengths are normalised to the ion inertial
  length.
• The ratio of the electron plasma frequency and
  electron cyclotron frequency is set to a
  numerical value of 5.
• A time step is used.
• The mass ratio is set equal to 1. We are in the
  process of increasing this to more realistic
  values.

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Anisotropic Maxwellian DistributionFunction
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Extended Distribution Function

• Have to find periodic solutions of the
  differential equations.
• The case gives anti-parallel field
  configuration
• The case gives linear force-free
  equilibrium (Bobrova et al.)
• Can use the parameter to vary the shear
  field while keeping
  constant
• Can investigate the transition from a pressure
  balanced equilibrium to a force-free equilibrium.

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Case

• Magnetic field solution is a reverse field
  configuration at
• Force balance maintained by plasma pressure.
• Can add varying magnitudes of constant guide
  field.

We have investigated the reconnection process as
you make the transition from zero guide field
through to . Also
compared this to the linear force-free case.
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The Component of the Current Density with
the Flux Function Overplotted (Force-Free Case)
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The Structure of the Diffusion Region

• The electron equation of motion
• The y component of the electric field can be
  written as
• Is found that the gradients of the off-diagonal
  terms of the pressure tensor are the dominant
  contributions to at the X-Point.

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Example for Linear Force-Free Case
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Simulation Snapshots at Time of Max Reconnection
Rate
Force-Free
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The Off-Diagonal Components of the
PressureTensor -
Force-Free
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The Off-Diagonal Components of the
PressureTensor -
Force-Free
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Reconnected Flux and Reconnection Rates
We expect strong guide field cases to have a
slower reconnection rate than those with weak
guide field.
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Future Work

• Carry out comparison reconnection simulations for
  equilibria with spatially varying shear field
  .
• This can be done by using the extended
  distribution function for different values of
  and solving for periodic solutions.
• Carry out a similar investigation of the
  reconnection rates.
• Carry out a similar investigation of the
  off-diagonal components of the pressure tensor as
  you make the transition from no shear field to a
  force-free field.
• Carry out force free simulations with low
• Carry out simulations for higher mass ratios