Instability Of Current Sheets Research Articles

Numerical simulation of three-dimensional reconnection due to the instability of collisionless current sheets

Based on analytical calculations we have currently argued that spontaneous reconnection through thin collisionless current sheets is an essentially three-dimensional (3 D) process (Büchner, 1996 a, b). Since 3 D kinetic PIC codes have become available, the three dimensional nature of the collisionless current sheet decay are now illustrated by numerical simulations (Büchner and Kuska, 1996; Pritchett and Coroniti, 1996; Zhu and Winglee, 1996). While the latter two claim a coupling to a longer wavelength kink mode as a main factor, destabilizing thin current sheets in 3 D, our simulations have revealed that even shorter scale perturbations in the current direction suffice to destabilize thin sheets very quickly. Since past simulation runs, however, were limited to mass ratios near unity, the influence of the electrons was not treated adequately. We have now investigated the stability of thin collisionless current sheets including 64 times lighter negatively charged particles. We can now show that while the two-dimensional tearing instability slows down for M = M p m e = 64 , the three-dimensional current sheet decay is a much faster process — practically as fast as the mass ratio M = 1 3 D sheet decay, even without kinking the sheet. We further conclude that, unlike the two-dimensional tearing instability, the three-dimensional decay of thin current sheets is not controlled by the electrons. For a sheet width comparable with the ion inertial length, we also recovered signatures of the Hall effect as predicted by Vasyliunas (1975) in the mass ratio M = 64 case. The ion inertial length seems to be the critical scale at which the sheet starts to decay.

MAGNETIC RECONNECTION IN MULTIPLE HELIOSPHERIC CURRENT SHEETS

Satellite observations of the heliospheric current sheet indicate that the internal structure of sector boundaries is a very complex structure with many directional discontinuities in the magnetic field. This implies that the heliospheric current sheet is not a single surface but a constantly changing layer with a varying number of current sheets. In this paper, we investigate magnetic reconnection caused by the resistive tearing mode instability in non-periodic multiple current sheets by using two-dimensional magnetohydrodynamic simulation. The results show that it is complex unsteady magnetic reconnection. Accompanying the nonlinear development of the tearing mode, the width of each magnetic island in multiple current sheets increases with time, and this leads to new magnetic reconnection. At the same time, the width of each current sheet increases, and the current intensity decreases gradually. Finally, the reverse current disappears, and a big magnetic island is formed in the central region. This process is faster when the separation between the current sheets is smaller. We suggest that the occurrence of multiple directional discontinuities observed at sector boundary crossings in the heliosphere may be associated with the magnetic islands and plasmoids caused by magnetic reconnection in multiple current sheets.

Coupling of Kelvin‐Helmholtz and current sheet instabilities to the ionosphere: A dynamic theory of auroral spirals

The Kelvin‐Helmholtz instability has often been invoked to describe transport at the magnetopause. However, recent observations of vortices in the postnoon sector of the auroral zone [Elphinstone et al., 1993] have indicated that structure of these vortices is inconsistent with the evolution of the standard Kelvin‐Helmholtz instability, and is instead consistent with the theory of auroral spirals proposed by Hallinan [1976]. Models of the Kelvin‐Helmholtz instability coupled to the ionosphere have generally neglected the effect of the field‐aligned current which is generated by the velocity shear. This current must close in the ionosphere, and leads to the presence of a magnetic shear in addition to the velocity shear. This magnetic shear is susceptible to a dynamic current sheet instability, which has many of the same properties as the Kelvin‐Helmholtz instability but produces vortices which are wound in a sense consistent with spiral observations. This instability, which may grow much faster than Kelvin‐Helmholtz, may provide a basis for a dynamic theory of auroral spirals.

On the ion‐tearing instability of forced current sheets

The ion‐tearing mode instability is studied in a magnetotail configuration, with an embedded thin current sheet at the center of the plasma sheet, taking into account the effects due to electron dynamics and perturbed electrostatic potential. It is found that the presence of trapped electrons in the forced current sheet has a strong stabilizing effect on thinner current sheets. The ion‐tearing instability can exist provided the trapped electron population density is less than about 10‐20% of the total electron number density. This can be achieved either by the background turbulence present in the plasma sheet or by the high ‐ frequency plasma instabilities excited by the strong current of the inner current sheet itself. Under such a situation, the configuration becomes progressively more ion‐tearing unstable as the forced current sheet becomes thinner. This eventually could lead to the disruption of the current sheet and to the onset of substorm expansion phase.

Resistive instability of periodic current sheets

The dispersion relation of the resistive tearing instability is derived and numerically solved for configurations characterized by periodic current sheets where a parameter-dependent resistivity can be included. Two unstable modes of different symmetry properties and different growth rates are identified, where the growth rates depend on the distance between the current layers. The results are relevant to a number of space and laboratory plasmas and the corresponding numerical simulations.

2-D, nonlinear spectral simulation of reconnective transitions on a periodic, planar current sheet with (1) smooth and (2) corrugated conducting wall boundary conditions with flow

A semi-implicit spectral/finite difference technique is used to evolve a reduced set of the visco-resistive MHD equations to investigate nonlinear processes involving reconnection on a planar current sheet. Two particular cases, of interest in astrophysical and magnetically confined plasmas, are discussed. An investigation of the time asymptotic behaviour of the basic current sheet with periodic boundary conditions and a cosh2x resistivity dependence has revealed a sequence of symmetry breaking bifurcations as a function of a parameter, Lp, defined as the ratio of the periodicity length of the system to the characteristic half-width of the current channel. Details are given of the dynamical behaviour involving coalescence and secondary current sheet instability. A method for periodically perturbing the edge magnetic field in the presence of flow without generating unphysical viscous boundary layers was then introduced to investigate forced reconnection in a stable plasma with finite flow along the current sheet. As the flow velocity was increased from zero, a transition from a state with force reconnected magnetic islands to one with negligibly small islands occured around a value of the velocity that depended on the Lunquist number and the viscosity.

Symmetry breaking bifurcations of a current sheet

Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh2 x resistivity model was used. For long periodicity lengths Lp, the resistivity gradient drives flows that cause forced reconnection at X point current sheets. Using Lp as a bifurcation parameter, two new symmetry breaking bifurcations were found: a transition to an asymmetric island chain with nonzero, positive, or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior, which involves a competition between secondary current sheet instability and coalescence.

The fine structure of the Saturnian ring system

A dust disc within a planetary magnetosphere constitutes a novel type of dust-ring current. Such an azimuthal current carrying dust disc is subject to the dusty plasma analog of the well known finite-resistivity ‘tearing’ mode instability in regular plasma current sheets, at long wavelengths. It is proposed that the presently observed fine ringlet structure of the Saturnian ring system is a relic of this process operating at cosmogonic times and breaking up the initial proto-ring (which may be regarded as an admixture of fine dust and plasma) into an ensemble of thin ringlets. It is shown that this instability developes at a rate that is many orders of magnitude faster than any other known instability, when the disc thickness reaches a value that is comparable to its present observed value.

Interplanetary gas. XXVI - On the reconnection of magnetic fields in cometary ionospheres at interplanetary sector boundary crossings

The reconnection process in the cometary ionosphere believed responsible for the disconnecting plasma tails phenomenon is studied through the basic equations of reconnection theory and current sheet instability criteria. It is proposed that reconnection occurs when the interplanetary magnetic fields incident on a comet that has gone just past a sector boundary are pressed into the fields captured from the previous sector. The fields are of opposite polarity, and the previously captured fields constitute the 'roots' of the plasma tail. An estimated duration of reconnection during a disconnection event (DE) of 0.75 days is used along with estimates of other cometary parameters to construct fusion region dimensions and resistivity with the adopted time scale.

Resistive instabilities of current sheets in the solar wind

We present some numerical results on resistive magnetohydrodynamic instabilities and discuss their relevance to current sheets of the type indicated by spacecraft observations in the interplanetary plasma.

Instabilities in charge sheets and current sheets and their possible occurrence in the aurora

An experimental demonstration has been given of the initiation of a vortex‐forming instability in sheets of charge by perturbations in the shape of the sheet. The net motion of charge along the sheet wherever the sheet is bent is shown to be related to displacement of the potential minimum in the sheet. These results suggest the existence of an instability in current sheets which also produces vortex forms. There is evidence that both of these instabilities result in the formation of vortexes in the aurora.

Thermal instability of coronal neutral sheets and the formation of quiescent prominences

It is argued that the quiscent prominences are a natural consequence of the formation and thermal instability of current sheets in the corona. Thus observation and theory of prominences can give vital information on the presence of currents and the topology of magnetic fields in the corona. Conversely by developing the theory of the structure and evolution of current sheets under coronal conditions we can attempt to gain a comprehensive understanding of the structure, evolution, and mass and energy balance of quiescent prominences. A stability analysis for coronal material permeated by a vertical magnetic field rooted in the photosphere, indicates that a condensation will take the form of a thin vertical wedge of cool matter. The development of a finite condensation is followed and it is shown that photospheric line tying is only important in the initial stages. A perturbation analysis of vertical motions at the neutral sheet shows that thermal instability can lead to overstable oscillations. Cooling of coronal material can lead to both upward and downward mass motions, and gravitational energy release is important to the thermal balance of prominences. Relevant optical and radio observations are discussed. Synoptic observations of the development of active regions and magnetic fields are needed to test the basic hypothesis of the formation of prominences from neutral sheets.