A Comparison of 2D PIC simulations of Reconnection

1
A Comparison of 2D PIC simulations of Reconnection

• Michael Harrison
• Thomas Neukirch
• Michael Hesse
• 5th Cambridge Workshop on Magnetic Reconnection
• Bad Honnef
• August 17-22, 2008

2
Motivation

• To compare the reconnection process using 2.5D
  PIC simulations starting from different initial
  conditions.
• To investigate the morphology of the off-diagonal
  components of the electron pressure tensor as you
  go from weak to strong guide field using 2.5D PIC
  simulations to compare to previous results.
• To investigate this transition using
  Vlasov-Maxwell equilibria resulting from
  distribution functions that extend beyond the
  Harris sheet.
• To include in the investigation a comparison to
  the reconnection process starting from a
  self-consistent force-free Vlasov-Maxwell
  equilibria.
• Currently we carry out our simulations with mass
  ratio 1

3
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 (Hesse
  1999, 2001, Pritchett 2001, etc.).

4
Harris Sheet Cases
Flux Normalised Reconnection Rate
Reconnected Flux
movies\harriscxz.mpg
movies\harrisby05cxz.mpg
movies\harrisby1cxz.mpg
5
Pressure Tensor Component Comparisons
movies\harrisby05pxye.mp4
movies\harrispxye.mp4
movies\harrisby1pxye.mp4
6
Pressure Tensor Component Comparisons
movies\harrispyze.mp4
movies\harrisby05pyze.mp4
movies\harrisby1pyze.mp4
7
Anisotropic Bi-Maxwellian 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. 2001)
• 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.

8
The Two Cases
Numerical Solution
9
Anisotropic Bi-Maxwellian Cases
Flux Normalised Reconnection Rate
Reconnected Flux
movies\onlypy2cxz.mpg
movies\onlypy2by05cxz.mpg
movies\onlypy2by1cxz.mpg
movies\bobcxz.mpg
10
Pressure Tensor Component Comparisons
movies\onlypy2pxye.mp4
movies\onlypy2by05pxye.mp4
Force-Free
movies\onlypy2by1pxye.mp4
movies\bobpxye.mp4
11
Pressure Tensor Component Comparisons
movies\onlypy2pyze.mp4
movies\onlypy2by05pyze.mp4
Force-Free
movies\onlypy2by1pyze.mp4
movies\bobpyze.mp4
12
Conclusions

• We have investigated the morphology of the
  off-diagonal components of the electron pressure
  tensor as you make the transition from an initial
  condition with a weak guide field through to a
  strong guide field including a linear force-free
  initial configuration.
• In the initial stages of reconnection the
  structure of the electron pressure tensor
  components are similar for all initial conditions
  when compared to the previously known Harris
  sheet cases.
• It can be seen that in the case of the periodic
  equilibria resulting from an anisotropic
  bi-Maxwellian distribution function the structure
  of the electron pressure tensor components are
  drastically changed in the latter stages due to
  interaction of the multiple current sheets.
• The evolution of the periodic equilibria results
  in an almost complete change in the geometry of
  the field from initially having a
  structure to having a structure
  at the end.