LIST of PAPERS on TURBULENT RECONNECTION

ANALYTICAL


Ichimaru (1975): Electric resistivity of electromagnetically turbulent plasma and reconnection rate of magnetic fields ApJ 202, 528.

Strauss (1988): Turbulent reconnection ApJ 326, 412.

Priest, ER (1986) 'Magnetic reconnection on the Sun', Mit. Astron. Ges. 65, 41-51.
[First suggestion of a regime of "impulsive bursty reconnection" in which the current sheet goes unstable to secondary tearing]

Forbes, TG and Priest, ER (1987) 'A comparison of analytical and numerical models for steadily driven reconnection', Rev. Geophys. 25, 1583-1607.
[Section 6 - a list of some numerical experiments showing turbulent reconnection - plus an estimate of the condition for tearing of a sheet and what it becomes for flux pileup or petschek reconnection]

Lazarian & Vishniac (1999): Reconnection in a Weakly Stochastic Field. ApJ 517, 700
[They call it "Turbulent reconnection" but actually it is just reconnection of a magnetic field with a random component. The magnetic fluctuations are assumed to follow the Goldreich & Sridhar (1997, ApJ 485, 680) model for MHD turbulence. A high reconnection rate (independent of Lundquist number) is predicted.]

Priest, ER and Forbes, TG (2000) Magnetic Reconnection: MHD Theory and Applications, Cambridge University Press, Cambridge.
[Just some qualitative comments on impulsive bursty reconnection on pages 152, 176, 201, 204]

Kim & Diamond (2001): On turbulent reconnection ApJ 556, 1052
[They show that in 2D and also in 3D reduced MHD the reconn.rate should scale like the Sweet-Parker rate only, i.e. no fast reconnection. This is analoguous to the well known result of Cattaneo & Vainshtein (1991, ApJ 376, L21) of a strong quenching of turbulent resistivity in 2D. The latter result is known to be invalid in 3D (Gruzinov & Diamond 1994, PhysRevLett 72, 1651).]

Lazarian, Vishniac & Cho (2004): Magnetic Field Structure and Stochastic Reconnection in a Partially Ionized Gas ApJ 603, 180
[They extend their previous work to partial ionization. They also reject Kim & Diamond's objection on the grounds that their mechanism is intrinsically 3D and that they do not actually need turbulent diffusion, or indeed turbulence at all, just a randomized magnetic field.]

NUMERICAL


Fan, Feng & Xiang (2004): Magnetohydrodynamic simulations of turbulent magnetic reconnection Phys.Plasmas 11, 5605.
[2D simulation, laminar flow, magn.field has random component. Constant diffusivity. Random component serves as seed for tearing instabilities, leading to formation of a series magnetic islands, separated by X-point-like configs. They find 2 phases: first a slower, then, as the islands develop, a faster regime.]

Fan, Feng & Xiang (2005): Magnetohydrodynamic simulations of turbulent magnetic reconnection Phys.Plasmas 12, 052901.
[They reiterate on the first paper, concentrating on the 2-phase behaviour.]

Baty, H., Priest, E.R. and Forbes, T.G. (2006) 'Effect of nonuniform resistivity in Petschek reconnection', Phys. of Plasmas 13, 022312/1-7.
[A technique for setting up fast reconnection numerically by overprescribing bcs on the edges of a box. They explore the conditions for setting up fast steady reconnection. It occurs when the diffusivity in the current sheet is enhanced -- eg they first set up a value in the sheet of 10^{-4} and an ambient value of 10^{-5} -- they then raise the ambient value slowly and find it goes unstable only when it is about 9 10^{-5}.
Code - VAC.
Box 100 x 600 points. Nonuniform grid.
Initial state B_{y} =B_{0} tanh(x/a) and equilibrium p(x) with uniform T.
Bc's - impose rho, v_{x}, v_{y}, B_{y}, energy density on inflow boundary x=1 and free conditions on outflow boundary y=1, and symmetry on x- and y-axes.]

Arber, TD and Haynes, M (2006) 'A generalized Petschek magnetic reconnection rate' Phys Plasmas 13, 112105.
[Their main aim is to study Hall reconnection, but before that they set up a resistive MHD experiment. The have a large enough box that it is essentially at infinity. They localise eta near X-point. The sheet goes impulsive and bursty with several islands which coalesce and are swept out of the sheet and eventually a fast steady state is set up.
Code - Lagrangian remap Lare2D.
Initial state B_{x} =B_{0} tanh(y/a), uniform T and p but with rho to give equilibrium. beta = 0.2.
Box 400 x 400 points with stretched grid.
Adiabatic energy.
Bcs - right and upper boundaries are free floating but simulations are stopped before slow shocks reach the boundary.