Magnetic Neutral Point Research Articles

Chaos-induced Resistivity in Collisionless Magnetic Reconnection Region

Collisionless magnetic reconnection, which converts the magnetic energy into the kinetic energy of plasma particles via the heating or acceleration, has been believed widely to be able to explain various eruptive phenomena such as solar flares and geomagnetic storms. However, the microphysical mechanism of anomalous resistivity in the collisionless magnetic reconnection is still an unsolved fundamental problem. Among the many physical mechanisms of anomalous resistivity generation, chaos-induced resistivity based on the chaos of the charged particle orbits near the magnetic neutral point is not the most popular formation mechanism, but its microscopic physical picture is the clearest. This paper first briefly reviews the early research and physical model of the chaos-induced resistivity in collisionless magnetic reconnection region, introduces the recent research progress of the chaos-induced resistivity, and expounds the future research direction of the chaos-induced resistivity.

Conversion and Smoothing of MHD Shocks in Atmospheres with Open and Closed Magnetic Field and Neutral Points

Planar acoustically dominated magneto\-hydro\-dynamic waves are initiated at the high-$\beta$ base of a simulated 2D isothermal stratified atmosphere with potential magnetic field exhibiting both open and closed field regions as well as neutral points. They shock on their way upward toward the Alfv\'en-acoustic equipartition surface $a=c$, where $a$ and $c$ are the Alfv\'en and sound speeds respectively. Expanding on recent 1.5D findings that such shocks mode-convert to fast shocks and slow smoothed waves on passing through $a=c$, we explore the implications for these more complex magnetic geometries. It is found that the 1.5D behaviour carries over to the more complex case, with the fast shocks strongly attracted to neutral points, which are disrupted producing extensive fine structure. It is also observed that shocks moving in the opposite direction, from $a>c$ to $a<c$, split into fast and slow components too, and that again it is the slow component that is smoothed.

Mathematical models of magnetic circuits of sensors of functional diagnostic systems of electric carriers

The article discusses the magnetic circuit of the developed magnetoelastic sensors of mechanical forces used in the systems of functional diagnostics of electric locomotives is investigated, taking into account the distribution of the magnetic resistance of coaxially arranged ring cores, the magnetic capacitance of the ring gap between them, the section of magnetizing and measuring windings. It is shown that the magnetic voltage along the sensor magnetic circuit is nonlinearly distributed and changes its sign at the magnetic neutral point, and the magnetic flux is non-constant and has a minimum value at the magnetic neutral point, and with an increase in the magnetic flux attenuation coefficient in the magnetic conductor magnetic flux along the length of the magnetic circuit increases.

The dynamics and Lorentz transformation of magnetic nulls

Having previously treated the problem of the Lorentz transformation properties of static field lines around magnetic neutral points, it is time to explore the properties of dynamic nulls. We discuss the relativistic motion of magnetic nulls accounting for both the linear and the second order structure of the magnetic field. It is found that the dynamics of a magnetic null is given by a world line trajectory of the null point and the changing fieldline structure. The dynamics of magnetic null structure is also explored, showing the significance of both the null structure and the flow pattern. We describe relativistic transformation properties of the appearance and annihilation of magnetic nulls, where the previously proposed null region is used as an invariant identification of topological transition and bifurcation processes.

Description of second-order three-dimensional magnetic neutral points

Local configurations of three-dimensional magnetic nulls with pure second order expansions are investigated, both potentially and nonpotentially. The basic magnetic structures are classified and visualized according to the configurations of their electric current, which is of first order. A principle of constructing a 2nd order null is proposed.

Magnetic Neutral Points and Electric Lines of Force in Strong Gravity of a Rotating Black Hole

Magnetic field can be amplified and twisted near a supermassive black hole residing in a galactic nucleus. At the same time magnetic null points develop near the horizon. We examine a large-scale oblique magnetic field near a rotating (Kerr) black hole as an origin of magnetic layers, where the field direction changes abruptly in the ergosphere region. In consequence of this, magnetic null points can develop by purely geometrical effects of the strong gravitational field and the frame-dragging mechanism. We identify magnetic nulls as possible sites of magnetic reconnection and suggest that particles may be accelerated efficiently by the electric component. The situation we discuss is relevant for starving nuclei of some galaxies which exhibit episodic accretion events, namely, Sagittarius A* black hole in our Galaxy.

Consequences of spontaneous reconnection at a two-dimensional non-force-free current layer

Magnetic neutral points, where the magnitude of the magnetic field vanishes locally, are potential locations for energy conversion in the solar corona. The fact that the magnetic field is identically zero at these points suggests that for the study of current sheet formation and of any subsequent resistive dissipation phase, a finite beta plasma should be considered, rather than neglecting the plasma pressure as has often been the case in the past. The rapid dissipation of a finite current layer in non-force-free equilibrium is investigated numerically, after the sudden onset of an anomalous resistivity. The aim of this study is to determine how the energy is redistributed during the initial diffusion phase, and what is the nature of the outward transmission of information and energy. The resistivity rapidly diffuses the current at the null point. The presence of a plasma pressure allows the vast majority of the free energy to be transferred into internal energy. Most of the converted energy is used in direct heating of the surrounding plasma, and only about 3% is converted into kinetic energy, causing a perturbation in the magnetic field and the plasma which propagates away from the null at the local fast magnetoacoustic speed. The propagating pulses show a complex structure due to the highly non-uniform initial state. It is shown that this perturbation carries no net current as it propagates away from the null. The fact that, under the assumptions taken in this paper, most of the magnetic energy released in the reconnection converts internal energy of the plasma, may be highly important for the chromospheric and coronal heating problem.

The relation between ion temperature anisotropy and formation of slow shocks in collisionless magnetic reconnection

We perform a two‐dimensional simulation by using an electromagnetic hybrid code to study the formation of slow‐mode shocks in collisionless magnetic reconnection in low beta plasmas, and we focus on the relation between the formation of slow shocks and the ion temperature anisotropy enhanced at the shock downstream region. It is known that as magnetic reconnection develops, the parallel temperature along the magnetic field becomes large in association with the anisotropic plasma sheet boundary layer ion beams, and this temperature anisotropy has a tendency to suppress the formation of slow shocks. On the basis of our simulation result, we found that the slow shock formation is suppressed due to the large temperature anisotropy near the X‐type region, but the ion temperature anisotropy relaxes with increasing the distance from the magnetic neutral point. As a result, two pairs of current structures, which are the strong evidence of dissipation of magnetic field in slow shocks, are formed at the distance ∣x∣ ≥ 115 λi from the neutral point.

On spontaneous formation of current sheets: Untwisted magnetic fields

This is a study of the spontaneous formation of electric current sheets in an incompressible viscous fluid with perfect electrical conductivity, governed by the magnetohydrodynamic Navier–Stokes equations. Numerical solutions to two initial value problems are presented for a three-dimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozen-in condition and at characteristic fluid Reynolds numbers of the order of 500, from a nonequilibrium initial state with the fluid at rest. The evolution converts magnetic free energy into kinetic energy to be all dissipated away by viscosity so that the field settles into a minimum-energy, static equilibrium. The solutions demonstrate that, as a consequence of the frozen-in condition, current sheets must form during the evolution despite the geometric simplicity of the prescribed initial fields. In addition to the current sheets associated with magnetic neutral points and field reversal layers, other sheets not associated with such magnetic features are also in evidence. These current sheets form on magnetic flux surfaces. This property is used to achieve a high degree of the frozen-in condition in the simulations, by describing the magnetic field entirely in terms of the advection of its flux surfaces and integrating the resulting governing equations with a customized version of a general-purpose high-resolution (viz., nonoscillatory) hydrodynamical simulation code EULAG [J. M. Prusa et al., Comput. Fluids 37, 1193 (2008)]. Incompressibility imposes the additional global constraint that the flux surfaces must evolve with no change in the spatial volumes they enclose. In this approach, current sheet formation is demonstrated graphically by the progressive pressing together of suitably selected flux surfaces until their separation has diminished below the minimal resolved distance on a fixed grid. The frozen-in condition then fails in the simulation as the field reconnects through an effecting numerical resistivity. The principal results are related to the Parker theory of current-sheet formation and dissipation in the solar corona.

Magnetic layers and neutral points near a rotating black hole

Magnetic layers are narrow regions where the field direction changes sharply. They often occur in the association with neutral points of the magnetic field. We show that an organized field can produce these structures near a rotating black hole (BH), and we identify them as potential sites of magnetic reconnection. To that end, we study the field lines affected by the frame-dragging effect, twisting the magnetic structure and changing the position of neutral points. We consider oblique fields in vacuum. We also include the possibility of translational motion of the black hole which may be relevant when the black hole is ejected from the system. The model settings apply to the innermost regions around black holes with the ergosphere dominated by a super-equipartition magnetic field and loaded with a negligible gas content.

THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. I. SPONTANEOUS CURRENT SHEETS IN THREE-DIMENSIONAL FIELDS

We present mathematical models to demonstrate the inevitability of current-sheet formation in a cylindrical magnetic field governed by the ideal hydromagnetic induction equation, as described by the Parker theory. This process, central to the heating of the solar corona, is radically different in fully three-dimensional fields as compared with two-dimensional fields. Magnetic neutral points or separatrix flux surfaces are necessary for sheet formation in two-dimensional fields. In fully three-dimensional fields, current sheets form readily even in the complete absence of neutral points and separatrix surfaces, and these sheets can form densely throughout the field in response to changes in the magnetic volume. This general result is established for cylindrical fields that are topologically untwisted, including the first direct demonstration of sheet formation in the absence of any magnetic neutral point. We discuss simple implications of this basic result for solar flares and coronal heating. In subsequent papers, we apply our result to coronal mass ejections and solar flares.

Pulsed Dissipation of Spontaneous Current Sheets in the Solar Corona

A simple one-dimensional model of the pulsed dissipation of a spontaneous current sheet is presented. Parker has demonstrated that spontaneous current sheets, or magnetic tangential discontinuities, must inevitably form and dissipate in the electrically near-perfectly conducting solar corona. Under the simplifying assumption that the effects of magnetic diffusion and near-ideal MHD relaxation to equilibrium may be idealized to occur separately in time, exact analytical one-dimensional isothermal solutions for successive alternate equilibrium and diffused states are obtained showing explicitly the gradual removal of the magnetic discontinuity. For discontinuities between both parallel and antiparallel fields, this removal results in the liberation of energy stored in the field. Energy losses in the antiparallel cases are found to be larger than for the parallel cases, and this difference increases as the plasma β decreases. Diffusions of parallel fields are found to result in magnetic flux transfer across the current sheet during the evolution while discontinuities between parallel fields cause flux annihilation, the creation of magnetic neutral points, inflows, and localized plasma accumulations. Numerical solutions obtained using the Versatile Advection Code reproduce these basic properties under isothermal, nonisothermal adiabatic, and nonadiabatic conditions and with magnetic diffusion and MHD relaxation occurring simultaneously. The relevance of these models to more complicated systems is discussed.

Axisymmetric liquid-metal pipe flow through a non-uniform magnetic field containing a neutral point

Axisymmetric liquid-metal pipe flow passes through a quadrupole magnetic field that is generated by a pair of ‘oppositely sensed’ d.c. current coils. As a result of this arrangement, the flow experiences a degree of braking, mostly in the vicinity of the magnetic neutral point, owing to the effect of Lorentz forces acting upon the liquid-metal. Usefully, the system represents a practical and novel electromagnetic (e.m.) valve capable of regulating the flow of molten metal emanating from a tun-dish, for example. Linear theory predicts the development of a counter-intuitive unidirectional ‘slug-like’ profile throughout the liquid-metal pipe flow at large values of the Hartmann number, M, in the presence of an idealized axisymmetric neutral point that extends to infinity. We confirm that this behaviour is also apparent, but over a narrow region spanning the neutral point, in the case of a more realistic liquid-metal pipe flow acted upon by a pair of oppositely sensed d.c. current coils. The axial pressure gradient along the wall of this flow manifests a sharp peak at large M centred on the neutral point that is generated by the steep gradients in the slug profile there. In fact, the pressure drop developed across this region is approximately equal to the net braking effect of the e.m. valve.

Theory and Simulation of Reconnection

Reconnection is a major commonality of solar and magnetospheric physics. It was conjectured by Giovanelli in 1946 to explain particle acceleration in solar flares near magnetic neutral points. Since than it has been broadly applied in space physics including magnetospheric physics. In a special way this is due to Harry Petschek, who in 1994 published his ground breaking solution for a 2D magnetized plasma flow in regions containing singularities of vanishing magnetic field. Petschek’s reconnection theory was questioned in endless disputes and arguments, but his work stimulated the further investigation of this phenomenon like no other. However, there are questions left open. We consider two of them — “anomalous” resistivity in collisionless space plasma and the nature of reconnection in three dimensions. The Cluster and SOHO missions address these two aspects of reconnection in a complementary way — the resistivity problem in situ in the magnetosphere and the 3D aspect by remote sensing of the Sun. We demonstrate that the search for answers to both questions leads beyond the applicability of analytical theories and that appropriate numerical approaches are necessary to investigate the essentially nonlinear and nonlocal processes involved. Necessary are both micro-physical, kinetic Vlasov-equation based methods of investigation as well as large scale (MHD) simulations to obtain the geometry and topology of the acting fields and flows.

Stationary field-aligned MHD flows at astropauses and in astrotails

A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points of the magnetic field within these flows. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfven Mach number for the corresponding stationary equilibria is finite. The topological structure determines the geometrical structure of the interstellar gas - stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail region beyond the reverse shock. The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfven Mach numbers in the case of subalfvenic flows.

On the Topological Evolution of the Coronal Magnetic Field During the Solar Cycle

Using an axisymmetric model that includes the effects of flux emergence and surface transport processes, we calculate the evolution of the photospheric magnetic field over the solar cycle and derive a corresponding sequence of coronal configurations by means of a potential-field source-surface extrapolation. By identifying magnetic neutral points and tracking changes in the total flux within each topological domain, we construct an overall picture of how open and closed flux is transported as the coronal field reverses its polarity:

A model of partially open magnetosphere

The earth's magnetosphere is open but only partially open. Its cusped front part is filled by closed field lines with intense magnetopause current in deflecting the incident solar wind and its lobed rear part is filled by open field lines with quasi-steady reconnection between interplanetary and terrestrial field lines. The magnetopause is covered by solar wind streamlines that are closest to the earth. The front part of the magnetopause is covered by streamlines that proceed around a magnetic neutral point, carrying incident interplanetary field lines that are tangential to the magnetopause. The rear part of the magnetopause is covered by streamlines that proceed around an electric neutral point, carrying open field lines that pass through the magnetopause. The former closedness part of the magnetopause that separates oppositely-directed tangential field lines of interplanetary and terrestrial magnetic fields may be regarded as an electric equipotential surface of tangential discontinuity. The latter openness part that has open field lines passing through may be regarded as a magnetic equipotential surface of rotational dsicontinuity. The magnetopause current is intense on the closedness magnetopause and insignificant on the openness magnetopause. The closedness magnetopause has a pair of T-type magnetic neutral points on the exterior and interior faces of the current sheet. The openness magnetopause has a pair of electric neutral points on an X-type magnetic separator line where field-line reconnection takes place.

Magnetohydrodynamic Simulation of a Solar Flare with Chromospheric Evaporation Effect Based on the Magnetic Reconnection Model

Two-dimensional magnetohydrodynamic (MHD) simulation of a solar flare including the effect of anisotropic heat conduction and chromospheric evaporation based on the magnetic reconnection model is performed. In the simulation model, the coronal magnetic energy is converted to the thermal energy of plasma by magnetic reconnection. This energy is transported to the chromosphere by heat conduction along magnetic field lines and causes an increase in temperature and pressure of the chromospheric plasma. The pressure gradient force drives upward motion of the plasma toward the corona, i.e., chromospheric evaporation. This enhances the density of the coronal reconnected flare loops, and such evaporated plasma is considered to be the source of the observed soft X-ray emission of a flare. The results show that the temperature distribution is similar to the cusp-shaped structure of long-duration-event (LDE) flares observed by the soft X-ray telescope aboard the Yohkoh satellite. The simulation results are understood by a simple scaling law for the flare temperature described as where Ttop, B, ?, and ?0 are the temperature at the flare loop top, coronal magnetic field strength, coronal density, and heat conduction coefficient, respectively. This formula is confirmed by the extensive parameter survey about B, ?0, and L in the simulation. The energy release rate is found to be described as a linearly increasing function of time: |dEm/dt| ? B2/(4?)VinCAt ? B2/(4?)0.1Ct, where Em is the magnetic energy, Vin is the inflow velocity, and CA is the Alfv?n velocity. Thus, the second time derivative is found to be |d2Em/dt2| B4. We also find that the major feature of the reconnection inflow region is the expansion wave propagating outward from the magnetic neutral point. This expanded plasma has very low emission measure, which is 4 orders of magnitude smaller than that of the brightest feature in a flare. This explains the dimming phenomena associated with flares.

Solar Wind Streamlines in the Magnetospheric Noon-Midnight Plane

The magnetosphere formed in the interaction between the magnetized solar wind and the earth's magnetic field has a magnetopause that separates interplanetary and terrestrial plasmas. The self-closed magnetopause is covered by the solar wind streamlines that are closest to the earth. Solar wind streamlines are delineated by intersection curves of electric and magnetic equipotential surfaces. The front part of the magnetopause is an electric equipotential surface that interfaces between oppositely directed interplanetary and closed field lines. The fear part is a magnetic equipotential surface that has open field lines passing through. Thus the magnetopause current is intense on the former closedness part of the magnetopause, which is a tangential discontinuity, and insignificant on the latter openness part, which is a rotational discontinuity. The part of closedness magnetopause has a pair of T -type magnetic neutral points on the exterior/interior face of the current sheet. The part of openness magnetopause has an X-type magnetic neutral line, in the studied case of southward interplanetary field. The neutral line is manifested by its cross point in the noon-midnight plane in our two-dimensional elucidation. In the noon-midnight plane, which is an electric equipotential surface, solar wind streamlines are delineated by traces of magnetic equipotential surfaces.

Magnetic field structure at the diamagnetic cavity boundary (Numerical simulations)

A three‐dimensional adaptive grid MHD simulation of the solar wind interaction with comet Halley shows that the boundary of the diamagnetic cavity is a closed, well defined surface. On this surface magnetic field neutral points should exist, and indeed, two O‐type neutral points were found at the cavity boundary. In addition, the transition from closed magnetic field lines around the diamagnetic cavity to open field lines in the comet tail requires the formation of at least one X‐type neutral point. Such a neutral point was also found in the simulated cometary ionosphere downstream from the cavity. The results of numerical simulations show that the plasma density near the neutral points increases significantly. This increase seems to be indicative of plasma escape from the diamagnetic cavity in the neighborhood of the neutral points, resulting in plasma jets.