Turbulent Reconnection in a Partially Ionized Gas Cracow October 2008 Alex Lazarian (U. Wisconsin) Jungyeon Cho (Chungnam U.) ApJ 603, (2004)

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.

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

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

 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).

 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.

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).

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.

 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.

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 10 4 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.

??  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.