X-type Neutral Point Research Articles

The collapse of an X-type neutral point to form a reconnecting time-dependent current sheet

Abstract A general method for solving the two-dimensional time-dependent ideal MHD equations is developed when the Alfven-Mach number is small and the Mach number large in comparison with unity. The method is applied to the problem of the time-dependent nonlinear collapse of an X-type neutral point. A current sheet is formed which grows in a self-similar manner.

Linear theory of fast reconnection at an X-type neutral point

A complete analytic theory of dynamic linear reconnection at an X-type neutral point is developed. An eigenmode analysis, using cylindrical coordinates centered on the neutral point, extends the work of Craig & McClymont (1991) to include nonazimuthally symmetric perturbations on the flux function. It is demonstrated that all physically significant disturbances, both reconnective and nonreconnective, decay resistively on a 'fast' time scale. The significance of the linear theory is discussed within the general context of steady state and dynamic reconnection studies. Disturbances can be expected to focus explosively in the vicinity of the neutral point. This suggests the formation of a 'flux pile-up' current layer in which the bulk of the magnetic energy is released as heat rather than kinetic energy of mass motion.

Computer studies on development of the fast reconnection mechanism for different resistivity models

Computer simulations systematically study how the fast reconnection mechanism involving standing switch-off shocks can be established and sustained in a large-scale current sheet system. Initiated by a small disturbance, all the phenomena spontaneously grow from near the origin and propagate outward. Under the same initial boundary conditions, different resistivity models are assumed, where the resistivity is self-consistently determined by macroscopic quantities in the system. It is found that the reconnection process is strongly controlled by the resistivity model. Only when the resistivity is locally enhanced near an X-type neutral point in accordance with the global reconnection flow, the fast reconnection mechanism can rapidly build up and be sustained steadily. The steady fast reconnection mechanism works as an engine that drastically drives the overall system into catastrophe. Since this mechanism depends on the resistivity parameter very weakly, it may be applicable to large dissipative events in space plasmas. It is argued that local conditions near an X neutral point should be fundamental for the fast reconnection mechanism to be realized.

Fast dynamic reconnection at X-type neutral points

view Abstract Citations (57) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fast Dynamic Reconnection at X-Type Neutral Points Craig, I. J. ; Watson, P. G. Abstract The time evolution of disturbed X-type neutral points is considered. 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. Reconnection can only occur in the case of purely radial (m = 0) disturbances. The linear theory supports the notion of an initial implosive stage which rapidly releases the bulk of the energy associated with reconnective field disturbances. In the nonlinear problem, although fast reconnection is maintained for low-amplitude disturbances in noncylindrical geometries, finite gas pressure can stall the reconnection if sufficiently large. This effect may not be critical in more complex X-point geometries. More seriously, for finite-amplitude disturbances the cylindrical current structure close to the neutral point is distorted 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. Publication: The Astrophysical Journal Pub Date: July 1992 DOI: 10.1086/171512 Bibcode: 1992ApJ...393..385C Keywords: Magnetic Field Reconnection; Magnetohydrodynamics; Solar Corona; Solar Flares; Linear Equations; Scaling Laws; Solar Physics; MAGNETOHYDRODYNAMICS: MHD full text sources ADS |

Magnetic reconnection in incompressible fluids

The paper investigates the dynamical relaxation of a disturbed X-type magnetic neutral point in a periodic geometry, with an ignorable coordinate, for an incompressible fluid. It is found that the properties of the current sheet cannot be understood in terms of steady state reconnection theory or more recent linear dynamical solutions. Accordingly, a new scaling law for magnetic reconnection is presented, consistent with fast energy dissipation (i.e., the dissipation rate at current maximum is approximately independent of magnetic diffusivity (eta)). The flux annihilation rate, however, scales at eta exp 1/4, faster than the Sweet-Parker rate of sq rt eta but asymptotically much slower than the dissipation rate. These results suggest a flux pile-up regime in which the bulk of the free magnetic energy is released as heat rather than as kinetic energy of mass motion. The implications of our results for reconnection in the solar atmosphere and interior are discussed.

Dynamic magnetic reconnection at an X-type neutral point

The relaxation of a two-dimensional 'X-type' neutral point magnetic field disturbed from equilibrium is considered. Perturbations are shown to possess well-defined azimuthal modes which allow an exact determination of the magnetic annihilation rate. Free magnetic energy is dissipated by oscillatory reconnection which couples resistive diffusion at the neutral point to global advection of the outer field. The decay of azimuthally symmetric (m = 0) modes - the only modes associated with topological reconnection - is limited by the dissipation time scale of the 'fundamental' (n = 0) mode with no radial nodes. This mode decays over typically 100 Alfven times. An analytic treatment shows that the oscillation and decay time scales couple according to a given law.

The Evolution of Disturbed Neutral Point Equilibria

AbstractWe consider the linear and non-linear evolution of a perturbed X-type neutral point. A semi-analytic treatment is given for the case of small disturbances of the equilibrium field. This problem admits well defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that the longest lived modes are purely radial and decay of the timescale τ ≈ |ln η| where η defines the resistivity of the coronal plasma. Higher azimuthal modes decay much faster, generally on a fraction (O(m−1)) of the Alfvén timescale for the outer field.We go on to perform finite amplitude calculations that demonstrate the implosive current build-up that precedes the reconnective phase of the relaxation. In general both linear and non-linear studies support the idea of an initial implosive stage which rapidly releases the bulk of the energy associated with arbitrary field disturbances.

Application of the sine-Poisson equation in solar magnetostatics

Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.

Quantitative study of the self-consistent fast reconnection with anomalous resistivity

The quantitative feature of the fast reconnection development consistent with simultaneous growth of anomalous resistivity is numerically studied. An anomalous resistivity eta such that d eta (VD)/dVD(=kR))0 for VD)VC is assumed, where VD is the absolute value of the relative electron-ion drift velocity and VC the threshold value for occurrence of current-driven instability. It is found that: for the smaller value of kR the drift velocity VD becomes significantly larger so that effective anomalous resistivity grows locally near X-type neutral points; hence, the energy conversion rate associated with the fast reconnection process has a very weak dependence on kR. This implies, that, one the anomalous resistivity is available, the fast reconnection can build up by enhancing the anomalous resistivity, leading to rapid annihilation of initially antiparallel magnetic fields. It is hence concluded that the nonlinear coupling between the macroscopic reconnection flow and the microscopic plasma turbulence will be very fundamental for catastrophic events occurring in high-temperature plasmas.

On sheared magnetic field structures containing neutral points

This paper discusses the occurence of current sheets near the separatrix in sheared magnetic field structures containing an x-type neutral point, as suggested by a number of previous authors. Our approach is based on selfconsistent theory. In analogy to the theory of quasistatic convection by Grad, we interpret the break-down of the quasistatic theory near the separatrix as evidence for the occurence of a boundary layer. In particular, this picture suggests large (however integrable) current sheets, with the current flowing parallel to the poloidal magnetic field. This concept is also tested by numerical computations. Here the discretization procedure simulates those physical effects that in a real case would keep the current from becoming infinitely large. The results fully confirm the formation of current sheets. Our findings have potential applications to energy storage for solar flares and to the heating of the solar corona.

Magnetic reconnection across an x-type neutral point slow shocks versus current sheets

It is shown that Petschek's model of fast magnetic reconnection is not valid in the limit of small resistivity owing to the properties of the diffusion region. Instead the configuration resembles Syrovatsky's current sheet model.

Resistive MHD Processes

The problem of fast magnetic reconnection across an x-type magnetic neutral point is reconsidered. Several different numerical computations of the 2D incompressible MHD equations are presented concerning externally driven as well as spontaneous reconnection. The common result of these computations is that in the limit of small resistivity reconnection occurs in a diffusion layer of finite length, corresponding to the Sweet–Parker reconnection model. A Petschek type process is only obtained by assuming a strongly enhanced resistivity in the diffusion region.

Nonlinear development of magnetic reconnection in the tearing-type and the Petschek-type field geometries

Distinct hydromagnetic characteristics associated with the tearing-type and the Petschek-type field geometries are numerically studied. Both the tearing-type and the Petschek-type reconnections are initiated by local resistive disturbance and develop from an initially antiparallel magnetic field. In the tearing-type field geometry the current-sheet plasma, accelerated at X-type neutral points through reconnection, cannot be ejected away from the system but is confined in the resulting magnetic islands. It is found that the nonlinear saturation oscillates as a result of the interaction between the confined plasma and the surrounding magnetic field; the period of the oscillation is approximately given by the time required for an Alfven wave to cross one wavelength. On the other hand, in the Petschek-type field geometry the plasma can freely be ejected away from the system, so that the antiparallel field is allowed to collapse into the X-type neutral point.

Two dimensional magnetic merging and reconnection

Magnetic energy release is mergin flows in investigated by numerical integration of unsteady resistive MHD equations in two dimensions. No explosive magnetic energy release is found in two topologically distinct merging flow geometries, in the absence of imposed strong plasma inflows. The first geometry is the merging of straight field lines without magnetic reconnection, and the second is merging with reconnection at an x-type neutral point. In each geometry the merging energy release is compared with the diffusive energy release in the absence of plasma motion. It is found in both geometries that the merging energy release is less than the diffusive energy release. Magnetic island formation occurs in the reconnection simulation. The magnetic energy release appears mainly as thermal rather than kinetic energy, but the heating is not localized. These results indicate that two dimensional merging without strong forcing is not promising as a mechanism for explosive magnetic energy release, but is more promising for gradual plasma heating and magnetic field dissipation. It is suggested that similar results would apply to any merging geometry which is stable in ideal MHD.

Dynamics of a triple inverse pinch

Experiments show that plasma may be temporarily confined in a potential well created by three symmetrically spaced inverse pinches. X-type neutral points form at each of the three points of first contact of the inverse pinches and these three neutral points act as flux switches impulsively transferring flux into a central confinement region. The confinement is terminated by a transition to anomalous resistivity at the centre of the device resulting in rapid annihilation of the confining flux by resistive dissipation. The subsequent magnetic field pattern is much more like the vacuum field having only one hyperbolic neutral point.The plasma configuration can probably be made stable for longer periods of time and should also be of interest for studies of interactions between laser light and a plasma in a state of microturbulence.

Some comments on magnetic field reconnection

Some comments are made about how to determine the speed with which magnetic flux is carried towards an X-type neutral point and reconnected. Conditions in the diffusion region near the neutral point are also investigated, with the conclusion that the streamlines and magnetic field lines cannot both be locally hyperbolic. Instead, two distinct modes may be possible. In the first, the magnetic field lines are straight, and the diffusion region does not differ greatly from that described by Parker (1963). In the second, the fluid velocity components increase cubically away from the neutral point with the result that, for a given reconnection rate, the diffusion region is typically five times greater than in the Parker model.

Effect of obstacles on the rate of reconnection of magnetic field lines

Further results of a laboratory magnetic field line reconnection experiment are presented. In particular, it is found that the reconnection rate can be slowed by placing solid obstacles to impede the outflow of plasma from an x-type magnetic neutral point. Without the obstacles the reconnection rate is faster and more impulsive. The fastest reconnection event has strong similarities to solar flares and geomagnetic substorms. It is suggested that more stationary features of solar activity such as prominences may be the result of reconnection slowed by obstacles such as the photosphere.

Energy build-up and release mechanisms in solar and auroral flares

Flare phenomena in the solar atmosphere and in the terrestrial magnetosphere exhibit many similarities. The mechanical energy of enhanced photospheric motion is converted and stored in the form of magnetic potential energy in sunspot fields, which is analogous to the case of the growth phase of magnetospheric substorms. The energy release during the explosive phase is initiated by a sudden collapse in the magnetic field topology and the X-type magnetic neutral point is created in the corona. Subsequent electrical discharge takes place in the form of an intense electrojet current flowing in the base of the chromosphere at the altitude where the Cowling conductivity is a maximum. It is suggested that the field-aligned precipitation of hot electrons and the Ohmic heating in the chromosphere result in major features of solar flares.

Energy build-up and release mechanisms in solar and auroral flares

Flare phenomena in the solar atmosphere and in the terrestrial magnetosphere exhibit many similarities. The mechanical energy of enhanced photospheric motion is converted and stored in the form of magnetic potential energy in sunspot fields, which is analogous to the case of the growth phase of magnetospheric substorms. The energy release during the explosive phase is initiated by a sudden collapse in the magnetic field topology and the X-type magnetic neutral point is created in the corona. Subsequent electrical discharge takes place in the form of an intense electrojet current flowing in the base of the chromosphere at the altitude where the Cowling conductivity is a maximum. It is suggested that the acceleration of particles by field-aligned electric fields and the Ohmic heating in the chromosphere result in major features of solar flares.

Spectrum of turbulence at a magnetic neutral point

The spectral density of plasma waves generated at the x-type magnetic neutral point of a laboratory device known as the double inverse pinch has been measured using a double probe technique devised by Hamberger and Jancarik. The spectra peak at low frequencies and have no components above the ion plasma frequency. This is in general agreement with the ion-acoustic wave spectrum of Kadomtsev. No contribution is seen at frequencies characteristic of the two-stream instability. The plasma wave amplitude is estimated to be sufficient to produce the anomalous resistivity which has been observed in this device. A knowledge of the resistivity mechanism is essential in understanding neutral point phenomenon as the resistivity controls “the reconnection rate” or more precisely the flux transfer rate. Flux transfer is almost certainly a key element of solar flares and geomagnetic substorms. The flux transfer process also occurs in many laboratory plasma experiments.