Fast dynamic reconnection at X-type neutral points

Abstract

We consider the linear and nonlinear evolution of disturbed magnetic X-type neutral points. The problem is formulated within a unified analytic and computational framework which highlights the essence of the mag netic annihilation process, namely, the coupling of a global convection region to a localized diffusion region surrounding the neutral point. An analytic treatment is given for the case of small disturbances of the equilibrium field in the absence of gas pressure. This problem admits well-defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that reconnection can only occur in the case of purely radial (m = 0) disturbances: the reconnection process is oscillatory and "fast, " depending only logarithmically on the plasma resistivity (,,). We show that the linear theory supports the notion of an initial implosive stage which rapidly releases the bulk of the energy associated with reconnective field disturbances. This phase is initiated by the advective focusing of the perturbation energy into the neutral point and culminates in the formation of a cylindrical diffusion region of area A-17 and current density J-17i. This scaling provides a signature for fast linear reconnection. Next we consider the breakdown of the linear theory. Although fast reconnection is maintained for low amplitude disturbances in noncylindrical geometries, it is shown that finite gas pressure can stall the reconnec tion if sufficiently large. This effect, however, may not be critical in more complex X-point geometries. More seriously, for finite-amplitude displacements the cylindrical current structure close to the neutral point is dis torted into a quasi-one-dimensional current sheet whose thickness is limited by resistive diffusion. In this case fast reconnection is consistent with a flux pileup solution in which the bulk of the energy is released as heat rather than as the kinetic energy of mass motion.

Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields

“…In fact, the exponential growth of the current density indicates that the time for magnetic diffusion to become important will depend on ln η. This is in good agreement with Craig & McClymont (1991;1993) and Craig & Watson (1992) who had previously found that the reconnection rate scales as | ln η| 2 . This means that wave dissipation will be very efficient, and predicts that null points will be the natural locations of linear fast wave energy deposition and preferential heating.…”

“…Again, this result was the first to indicate a relationship between Alfvén wave propagation and the location of the separatrices. An alternative approach to the study of MHD wave behaviour in the neighbourhood of a 2D magnetic null point was investigated in a series of papers by Craig and co-workers (Craig & McClymont 1991;1993;Craig & Watson 1992) in which the authors considered perturbations of the flux function Az. Here, the focus was on applications for magnetic reconnection, specifically to investigate if null points (viewed as weaknesses in the magnetic field) could collapse in response to imposed boundary motions.…”

“…This is an important results as it shows that the damping of the fast wave is still highly significant even when the resistivity is small. Craig & Watson (1992) considered the radial propagation of the m = 0 mode and solved equation (15) using a mixture of analytical and numerical solutions. They demonstrated that the propagation of the m = 0 wave towards the null point generates an exponentially large increase in the current density and that magnetic resistivity dissipates this current in a time related to log η, in agreement with Craig & McClymont (1991).…”

“…assume β = 0). Under the β = 0 assumption, the plasma pressure plays no part in the dynamics of the system, and so the linearised equation of mass continuity has no influence on the momentum equation and so in effect the plasma is arbitrarily compressible (Craig & Watson 1992) and we assume the background gas density is uniform (ρ 0 ). A spatial variation in ρ 0 can cause phase mixing (Heyvaerts & Priest 1983;De Moortel et al 1999;Hood et al 2002).…”

MHD mode coupling in the neighbourhood of a 2D null point

“…Bulanov & Syrovatskii (1980) provided a detailed discussion of the propagation of fast and Alfvén waves using cylindrical symmetry. Craig & Watson (1992) mainly consider the radial propagation of the m = 0 mode (where m is the azimuthal wavenumber) using a mixture of analytical and numerical solutions. They show that the propagation of the m = 0 wave towards the null point generates an exponentially large increase in the current density and that magnetic resistivity dissipates this current in a time related to log η.…”