Finite‐Resistivity Instabilities of a Sheet Pinch
TL;DR: In this paper, the stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity, and the effect of a small layer curvature is simulated by a gravitational field.
Abstract: The stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity. The effect of a small layer curvature is simulated by a gravitational field. In an incompressible fluid, there can be three basic types of ``resistive'' instability: a long‐wave ``tearing'' mode, corresponding to breakup of the layer along current‐flow lines; a short‐wave ``rippling'' mode, due to the flow of current across the resistivity gradients of the layer; and a low‐g gravitational interchange mode that grows in spite of finite magnetic shear. The time scale is set by the resistive diffusion time τR and the hydromagnetic transit time τH of the layer. For large S = τR/τH, the growth rate of the ``tearing'' and ``rippling'' modes is of order τR−3/5τH−2/5, and that of the gravitational mode is of order τR−1/3τH−2/3. As S → ∞, the gravitational effect dominates and may be used to stabilize the two nongravitational modes. If the zero‐order configuration is in equilibrium, the...
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TL;DR: In this paper, the effect of weak, small-scale magnetic field structure on the rate of reconnection in strongly magnetized plasmas was examined and an upper limit of ~VA2 was derived by invoking both effects.
Abstract: We examine the effect of weak, small-scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich & Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find a lower limit for the reconnection speed ~VA-3/16L3/4, where VA is the Alfven speed, L is the Lundquist number, and is the large-scale magnetic Mach number of the turbulence. We derive an upper limit of ~VA2 by invoking both effects. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as -2/5L8/5, and the thickness of the current sheet scales as -3/5L-2/5. A significant fraction of the magnetic energy goes into high-frequency Alfven waves. The angle between adjacent field lines on the same side of the reconnection layer is ~-1/5L6/5 on the scale of the current sheet thickness. We claim that the qualitative sense of these conclusions, that reconnection is fast even though current sheets are narrow, is almost independent of the local physics of reconnection and the nature of the turbulent cascade. As the consequence of this the Galactic and solar dynamos are generically fast, i.e., do not depend on the plasma resistivity.
1,022 citations
932 citations
TL;DR: In this article, current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations, and a chain of plasmoid secondary islands is formed, whose number scales as S3∕8.
Abstract: Current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations. The instability is very fast: its maximum growth rate scales as S1∕4vA∕LCS, where LCS is the length of the sheet, vA the Alfven speed, and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S3∕8.
787 citations
TL;DR: In this paper, a general picture of magnetic reconnection in the framework of 2D incompressible resistive magnetohydrodynamic theory is presented, and a theory of the solution in the external and in the diffusion region is developed and analytical expressions in agreement with the simulation results are obtained by means of a variational principle.
Abstract: A general picture of magnetic reconnection in the framework of 2‐D incompressible resistive magnetohydrodynamic theory is presented. Numerical studies of (quasi‐) steady‐state driven reconnection reveal current sheet formation for Mach numbers M=u/vA exceeding the Sweet–Parker reconnection rate MSP=(η/LvA)1/2. Since the thickness δ of the current sheet is found to be invariant to a change of the resistivity η, its length Δ increases rapidly with decreasing η or increasing M, which can be written in the form Δ∼(M/MSP)4, so that Δ reaches the global system size L within a short range of the parameter M/MSP. The results are rather insensitive to the particular choice of boundary conditions. Because of the presence of a current sheet, the overall reconnection process is quite slow. This picture essentially agrees with Syrovatsky’s [Sov. Phys. JETP 33, 933 (1971)] theory and disproves Petschek’s [AAS/NASA Symposium on the Physics of Solar Flares, (NASA, Washington, DC, 1964) p. 425] mechanism of fast magnetic reconnection. A theory of the solution in the external and in the diffusion region is developed and analytical expressions in agreement with the simulation results are obtained by means of a variational principle. For sufficiently long current sheets the tearing mode becomes unstable in spite of the stabilizing effect of the inhomogeneous flow. The tearing mode contributes to the overall reconnection process, but a general assessment of this effect in the asymptotic regime of almost vanishing η is difficult.
752 citations
TL;DR: A short review of some of the basic concepts related to the origin of coronal mass ejections (CMEs) can be found in this paper, where various ideas which have been put forward to explain the initiation of CMEs are categorized in terms of whether they are force-free or non-force-free and ideal or nonideal.
Abstract: This paper provides a short review of some of the basic concepts related to the origin of coronal mass ejections (CMEs). The various ideas which have been put forward to explain the initiation of CMEs are categorized in terms of whether they are force-free or non-force-free and ideal or nonideal. A few representative models of each category are examined to illustrate the principles involved. At the present time there is no model which is sufficiently developed to aid forecasters in their efforts to predict CMEs, but given the current pace of research, this situation could improve dramatically in the near future.
732 citations
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TL;DR: In this article, the authors examined the stability of plasmas confined by magnetic fields and showed that the stability can be improved by paying more attention to the motions of individual particles.
487 citations
TL;DR: In this paper, a series of measurements over a wide range of data was carried out in the case of helium, argon, krypton, nitrogen, and hydrogen, showing that the potential drop along the column indicates a much higher diffusion rate across the magnetic field than that expected from the binary collision theory.
Abstract: Earlier results, by Lehnert, on the diffusion processes in the positive column in a longitudinal magnetic field have been confirmed in a new series of measurements over a wide range of data. Experiments with helium, argon, krypton, nitrogen, and hydrogen are described. In the case of helium good agreement is obtained between the collision diffusion theory and the experiment up to a certain critical magnetic field. For stronger fields the potential drop along the column indicates a much higher diffusion rate across the magnetic field than that expected from the binary collision theory. Account is taken, in the theory, of the presence of molecular ions and of charge exchange collisions. Abnormal voltage characteristics indicating an increased diffusion rate above a certain magnetic field strength have also been investigated in argon, krypton, nitrogen, and hydrogen. The transition from the normal to the abnormal branch of the characteristics seems to depend neither on the length of the discharge tube nor on the length of the magnetic field, provided that these lengths exceed some fifty tube diameters. On the other hand, the transition depends upon the gas density, the nature of the gas, the tube radius, and, also slightly, upon the discharge current. The transition is also indicated by an increasing noise level above the transition point. Finally, the product of the magnetic field strength and the tube radius seems to be constant at this point.
94 citations
TL;DR: In this article, the main features of Kadomtsev and Nedospasov's stability criterion are derived from simple physical arguments, and the mechanism responsible for instability is thus shown in a quantitative way.
Abstract: It is known that the positive column is unstable in a strong longitudinal magnetic field. The correct explanation of this phenomenon has been given by Kadomtsev and Nedospasov. However, the instability mechanism is not fully interpreted in their work. In this contribution, the main features of Kadomtsev and Nedospasov's stability criterion are derived from simple physical arguments, and the mechanism responsible for instability is thus shown in a quantitative way. In particular, the perturbed radial potential distribution can be related to the perturbed density distribution, and hence need not be assumed. It turns out that this screw instability is a new and important type of instability hitherto not considered. The instability mechanism is not very sensitive to the degree of ionization, and hence may also be expected to be operative in highly ionized plasma columns. Possible connections with the instabilities observed in the Stellarator and the Zeta machine are discussed. An attempt is also made to explain regular oscillations observed in a toroidal discharge in terms of the present theory.
40 citations
TL;DR: Inverse stabilized pinches yield perfectly reproducible magnetic probe traces at power levels several times those at which stabilized pinches are unstable as mentioned in this paper, and a technique for the study of plasma density distributions is given, based on the propagation of radial compressional waves.
Abstract: The hydromagnetic stability properties of ``hard‐core'' pinches are shown to be more favorable than those of conventional ``stabilized pinches.'' Linear ``hard‐core'' pinch experiments with a wide range of configurations show a basic consistency with hydromagnetic theory, but all configurations studied so far become unstable at sufficiently high current densities and low particle densities, even if possessed of theoretical hydromagnetic stability. Pinches with nulls in Bθ tend to be much less stable than those with nulls in Bz. ``Inverse stabilized pinches'' yield perfectly reproducible magnetic probe traces at power levels several times those at which ``stabilized pinches'' are unstable. A technique for the study of plasma density distributions is given, based on the propagation of radial compressional waves. The theory of the steady‐state pinch is enlarged to include convective effects and is documented by experiment. The role of electrodes is considered, and an anode‐cathode asymmetry in instability be...
39 citations