Turbulent Reconnection in a Partially Ionized Gas

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Turbulent Reconnection in a Partially Ionized Gas
Alex Lazarian (U. Wisconsin) Jungyeon Cho
(Chungnam U.)
ApJ 603, 180-197 (2004)
Cracow October 2008
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How do Neutrals Affect the Dynamics of
Reconnection?

• Ambipolar Drift - this has
  a modest effect on reconnection. It allows some
  compression of the field.
• Anomalous damping - which can manifest itself as
  a drag or as an effective viscosity, depending on
  the scale and the rate of motion. This might
  reduce the inertial range of turbulence and
  produce laminar flows on smaller scales.

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Why is this important? What is stochastic
reconnection?

• The basic idea is that the reconnection speed
  falls out of the balance between inflow over the
  length of a reconnection sheet and outflow
  through a diffusion zone. The outflow speed is
  something like the Alfven speed of the
  reconnecting field component - set by the energy
  released by the relaxation of the magnetic field.
• For Sweet-Parker, ? is the width of the current
  sheet

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Suppose the field is turbulent?

• Two points, separated by some distance ?
  perpendicular to the mean field direction will
  see their mean square separation increase as one
  moves along the mean field, i.e.
• At every distance y along the field lines, there
  is some corresponding ? such that the local speed
  of reconnection is

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• However, since every segment of length y involves
  the reconnection of a separate flux element, the
  total reconnection rate is greater by a factor of
  (L/y) or
• The idea of stochastic reconnection is that it is
  equal to the minimum of this expression.
• In the inertial range of MHD turbulence there is
  a one to one correspondence between eddy length
  ? (along the field) and eddy thickness ?perp
  (across it).

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• Consequently the diffusion parameter D is just
• and ? is always about the thickness of an
  eddy of length ?. This means that the
  thickness of the current sheet has nothing to do
  with the thickness of the diffusion layer. Also
  the limit on the reconnection speed scales as
  ?-1/2. Smaller scales give a larger limit.
  Only the largest scale limit is relevant when the
  inertial range of the turbulence covers all
  scales of interest.

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Back to Neutral Damping!

• Now we see why neutral damping is important. By
  creating a range of scales where turbulence is
  suppressed it raises the possibility that the
  real limit on the reconnection speed could come
  from scales close to the current sheet thickness.
• When turbulence is suppressed we have
• where ? is the parallel damping scale. The
  mean square separation grows exponentially but
  from a small start (which it remembers).

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How likely is this? Neutral Damping and the
turbulent cascade.

• At large scales neutral damping acts like a
  viscosity. Damped turbulence produces strong,
  but intermittent magnetic perturbations and a
  power law decline in velocity. (Not
  exponentially damped, but not strong.)
• At smaller scales neutral damping acts like a
  uniform drag. The magnetic field perturbations
  decline again, but become less intermittent. The
  diffusion of field lines is more effective.

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• At very small scales ions are effectively
  decoupled from neutrals and the large scale
  shearing promotes regular turbulence, albeit in
  an intermittent manner. On these scales
  diffusion of field lines is as effective as on
  large scales.
• On very small scales (Larmor radii) the
  turbulence finally dies, but this is comparable
  to the thickness of the Sweet-Parker current
  sheet.

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So in realistic environments

• Many uncertainties attach to any attempt to
  define standard phases of the ISM. For a range
  of environments dominated by the Warm Neutral
  Medium to the dark cores of molecular clouds
  (densities from 0.4 to 104 and temperatures from
  about 6000 to about 10) we have calculated
  standard reconnection speeds.
• Neutral damping never suppresses reconnection by
  more than a factor of about 10.

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??

• Direct measure of the diffusion of field lines in
  complicated regimes are almost entirely absent.
• Calculations of how this affects really dense
  environments, relevant for the late stages of
  star formation, have not been done.

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