Ian J.D. Craig

Current singularities at finitely compressible three-dimensional magnetic null points

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the cu...

Particle acceleration scalings based on exact analytic models for magnetic reconnection

Observations suggest that particle acceleration in solar flares occurs in the magnetic reconnection region above the flare loops. Theoretical models for particle acceleration by the reconnection electric field, however, employ heuristic configurations for electric and magnetic fields in model current sheets, which are not solutions to the MHD reconnection problem. In the present study, particle acceleration is discussed within the context of a self-consistent MHD reconnection solution. This has the advantage of allowing poorly constrained local parameters in the current sheet region to be expressed in terms of the boundary conditions and electric resistivity of the global solution. The resulting acceleration model leads to energy gains that are consistent with those for high-energy particles in solar flares. The overall self-consistency of the approach is discussed.

Magnetic reconnection solutions based on a generalized Ohm's law

It is known that exact magnetic reconnection solutions can be constructed for collisionally dominated resistive plasmas. In this paper we refine the collisional resistive description by invoking an Ohms law that includes Hall current and plasma inertial contributions. We first demonstrate the surprising fact that the analytic treatment of both two and three dimensional current sheet reconnection remains valid for the generalized Ohms law description. A discussion of planar reconnection shows that while the influence of inertial effects is generally small, the Hall current is likely to be important in most physically realistic plasma regimes, even for turbulent current sheet models. In particular, by influencing the magnetic and electric fields within the current sheet, the Hall current can be expected to have a strong influence on the particle acceleration capabilities of magnetic merging solutions. We also address the extent to which the new solutions alleviate the need for enhanced, anomalous resistivities to moderate the large current densities that arise in collisional resistive merging.

Flare Energy Release by Flux Pile-up Magnetic Reconnection in a Turbulent Current Sheet

The power output of flux pile-up magnetic reconnection is known to be determined by the total hydromagnetic pressure outside the current sheet. The maximum energy-release rate is reached for optimized solutions that balance the maximum dynamic and magnetic pressures. An optimized solution is determined in this paper for a current sheet with anomalous, turbulent electric resistivity. The resulting energy dissipation rate Wa is a strong function of the maximum, saturated magnetic field Bs: Wa ~ B. Numerically, Wa can exceed the power output based on the classical resistivity by more than 2 orders of magnitude for three-dimensional pile-up, leading to solar flarelike energy-release rates of the order of 1028 ergs s-1. It is also shown that the optimization prescription has its physical basis in relating the flux pile-up solutions to the Sweet-Parker reconnection model.

Viscous effects in planar magnetic X-point reconnection

The impact of viscous dissipation is considered on magnetic reconnection in closed line-tied magnetic X-points. It is shown that viscous effects can provide fast energy dissipation for disturbances which do not alter the initial X-point topology. If the X-point topology is altered, then the rate of viscous dissipation depends on both the perturbed topology and the relative magnitudes of viscosity and electric resistivity. New solutions are demonstrated, which derive from the combination of resistive and viscous effects. The solutions are characterized by monotonically decaying modes which are qualitatively different from the previously known oscillatory modes in nonviscous resistive X-point reconnection. These results suggest that viscous heating in magnetic X-points may be an important effect in solar flares.

DYNAMIC PLANAR MAGNETIC RECONNECTION SOLUTIONS FOR INCOMPRESSIBLE PLASMAS

The planar magnetic reconnection problem for viscous, resistive plasmas is addressed. We show that solutions can be developed by superposing transient nonlinear disturbances onto quiescent ii background ˇˇ —elds. The disturbance —elds are unrestricted in form, but the spatial part of the back- ground —eld must satisfy +2K \( jK. This decomposition allows previous analytic reconnection solu- tions, based on one-dimensional disturbance —elds of ii plane wave ˇˇ form, to be recovered as special cases. However, we point out that planar disturbance —elds must be fully two-dimensional to avoid the pressure problem associated with analytic merging models, that is, to avoid unbounded current sheet pressures in the limit of small plasma resistivities. The details of the reconnection problem are then illus- trated using cellular background —eld simulations in doubly periodic geometries. The —ux pile-up rate is shown to saturate when the pressure of the current sheet exceeds the hydromagnetic pressure of the background —eld. Although the presaturation regime is well described by one-dimensional current sheet theory, the nonlinear postsaturation regime remains poorly understood. Preliminary evidence suggests that, although after saturation the early evolution of the —eld can be described by slow Sweet-Parker scalings, the —rst implosion no longer provides the bulk of the energy release. Subject headings: MHDplasmaswaves

Dynamic magnetic reconnection in three space dimensions: Fan current solutions

The problem of incompressible, nonlinear magnetic reconnection in three-dimensional “open” geometries is considered. An analytic treatment shows that dynamic “fan current” reconnection may be driven by superposing long wavelength, finite amplitude, plane wave disturbances onto three-dimensional magnetic X-points. The nonlinear reconnection of the field is preceded by an advection phase in which magnetic shear waves drive large currents as they localize in the vicinity of the magnetic null. Analytic arguments, reinforced by detailed simulations, show that the ohmic dissipation rate can be independent of the plasma resistivity if the merging is suitably driven.

Nonlinear development of the kink instability in coronal flux tubes

This paper describes a Lagrangian numerical scheme for simulating nonlinear evolution of ideal MHD equilibria and applies it to an unstable finite Gold-Hoyle flux tube, line-tied to perfectly conducting endplates. The ensuing kink instability develops considerably faster than linear theory would predict, and eventually (over typically 100 Alfven time scales) a new kinked equilibrium is attained in which current sheets appear to be present. Little magnetic energy is lost in the ideal MHD phase, but resistive instabilities in the current sheets could lead to much more explosive energy release. Numerical studies of nonlinear interactions indicate that growth of the unstable kink mode is suppressed by the presence of other modes, which offers a possible explanation of the observed longevity of coronal loops. 22 refs.

Magnetic Energy Release in Flux Pile-up Merging

The problem of pressure limitations on the rate of flux pile-up magnetic reconnection is studied. We first examine the recent suggestion of Jardine and Allen (1998) for moderating the build-up of magnetic pressure in the current sheet by considering inflows with nonzero vorticity. An analytic argument shows, however, that unbounded magnetic pressures in the limit of small resistivities can be avoided only at the cost of unphysical dynamic pressures in the plasma. Hence, the pressure limitation on the reconnection rate in a low-beta plasma cannot be avoided completely. Nevertheless, we demonstrate that reconnection can be more rapid in a new solution that balances the build-up in dynamic pressure against both the plasma and magnetic pressures. This exact MHD solution has the characteristics of merging driven by the coalescence instability. The maximum energy release rate of the model is capable of explaining a modest solar flare.

Exact solutions for steady‐state, planar, magnetic reconnection in an incompressible viscous plasma

The exact planar reconnection analysis of Craig and Henton [Astrophys. J. 450, 280 (1995)] is extended to include the finite viscosity of the fluid and the presence of nonplanar components in the magnetic and velocity fields. It is shown that fast reconnection can be achieved for sufficiently small values of the kinematic viscosity. In particular, the dissipation rate is sustained by the strong amplification of planar magnetic field components advected toward the neutral point. By contrast, nonplanar field components are advected without amplification and so dissipate energy at the slow Sweet–Parker rate.