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NASA NTRS1981

Tearing at the dayside magnetopause

Initial observations of the dayside magnetopause thickness using magnetometers on board ISEE 1 (International Sun-Earth Explorer) and ISEE 2 indicate that this boundary may only be a few ion gyro-radii thick during periods of observed southward interplanetary magnetic field (IMF). Such a thin current layer can destabilize the collisionless tearing mode, a probable first step in the reconnection sequence. The linear growth rate is calculated assuming typical magnetopause parameters and it is found that it is a sensitive function of IMF orientation, magnetopause thickness, and electron number density. It is also shown that the finite size of the dayside magnetopause necessitates the existence of a two-dimensional tearing mode wave vector spectrum, a consequence of the inability of a thermal electron to maintain Landau resonance with the wave for a growth period. Implications regarding reconnection are discussed.

Quest, K. B.↗

NASA NTRS1990

Impulsive phase heating by uni-directional current systems in solar flares

The possibility of producing rapid heating of a substantial coronal volume by current dissipation, driven by a tearing instability associated with a single unidirectional current system, is investigated. For the fast tearing mode, it is found that, for initial growth rates gamma(f) equal or less than 0.3/s, the electron heating is offset by convective losses, resulting in a very slow temperature rise, and hard X-ray emitting temperatures are never realized. For the larger growth rates, heating from 10 to the 7th to 10 to the 8th K can be achieved in a few seconds; however, in this regime, the maximum volume heated is some three to five orders of magnitude less than the volume of heated material that is inferred from hard X-ray emission measures. The results suggest that to achieve the required heating for the fast tearing mode, a more complicated geometry involving multiple small-scale, oppositely directed current channels may be necessary.

La Rosa, T. N.↗

NASA NTRS1983

The effects of Ohmic heating and stable radiation on magnetic tearing

A study is made of the effect of a temperature-dependent Coulomb-like resistivity on the planar tearing mode. The local evolution of the temperature is described by an energy equation which includes Joule heating and optically thin radiation. The resulting system of coupled linear magnetohydrodynamic equations is solved numerically, and eigenfunctions and growth rates are obtained. In the absence of radiation, there are two distinct solutions above a critical value of the magnetic Reynolds number S, a tearing-like mode and a Joule-heating mode. Below this point, the growth rates coalesce into a conjugate-complex pair. When stable radiation (dR/dT greater than 0) is added, the heating mode disappears and a modified tearing excitation exists to much lower values of S before its growth is cut off by Ohmic heating. Examples are given for solar coronal parameters, and for those characteristic of fusion-research devices. The introduction of an effective value for the resistivity, in the presence of energy transport, allows a simple qualitative discussion of the different modes.

Tachi, T.↗

NASA NTRS1999

The Onset of Magnetic Reconnection in Tail-Like Equilibria

Magnetic reconnection is a fundamental mode of dynamics in the magnetotail, and is recognized as the basic mechanisms converting stored magnetic energy into kinetic energy of plasma particles. The effects of the reconnection process are well documented by spacecraft observations of plasmoids in the distant magnetotail, or bursty bulk flows, and magnetic field dipolarizations in the near Earth region. Theoretical and numerical analyses have, in recent years, shed new light on the way reconnection operates, and, in particular, which microscopic mechanism supports the dissipative electric field in the associated diffusion region. Despite this progress, however. the question of how magnetic reconnection initiates in a tail-like magnetic field with finite flux threading the current i.sheet remains unanswered. Instead, theoretical studies supported by numerical simulations support the point-of-view that such plasma and current sheets are stable with respect to collisionless tearing mode. In this paper, we will further investigate this conclusion, with emphasis on the question whether it remains valid in plasma sheets with embedded thin current sheets. For this purpose, we perform particle-in-cell simulations of the driven formation of thin current sheets, and their subsequent evolution either to equilibrium or to instability of a tearing-type mode. In the latter case we will pay particular attention to the nature of the electric field contribution which unmagnetizes the electrons.

Hesse, Michael↗

NASA NTRS1974

Fracture under combined modes in 4340 steel

An experimental investigation was conducted to study the interaction of combined modes of loading on crack instability in the presence of the opening and sliding modes of stress intensity factors, the opening and tearing modes of stress intensity factors, and all three modes of stress intensity factors. Through-cracked and surface-cracked flat and round specimens, and round notched bar specimens fabricated from high strength 4340 steel were used for the investigation. The results are evaluated to determine fracture criteria under the combined modes of stress intensity factors for the 4340 steel. These results are compared with the results of other investigators obtained for different materials.

Shah, R. C.↗

NASA NTRS1984

Radiative tearing - Magnetic reconnection on a fast thermal-instability time scale

Two energy modification mechanisms which are known to occur in sheared magnetic fields are the tearing and thermal instabilities. These processes can be studied separately with formalisms incorporating just the effective driving mechanism of interest (finite resistivity for the tearing mode and unstable radiation for the thermal mode). A model which includes both effects, and a temperature-dependent resistivity, indicates that modified forms of these two instabilities may coexist for identical physical conditions. When they are isolated computationally, one can show that their limiting growth rates are approximately those of the uncoupled instabilities. The spatial structure and energy content of these two new hybrid processes are then individually examined and are found to differ considerably from those obtained from separate treatments of the driving mechanisms. The faster radiative instability, which has a hydromagnetically scaled growth rate like the condensation mode of the thermal instability, is shown to involve a substantial amount of magnetic field reconnection. This can be partially explained by a large temperature drop (or resistivity rise) at the X-point. The island width of the Coulomb-coupled radiative mode is 30 percent of that produced by a comparable level of the slower tearing instability. In addition, the perturbed magnetic energy in the radiative instability is 5 times that of the perturbed thermal energy, indicating an appreciable modification of the initial magnetic structure.

Steinolfson, R. S.↗

NASA NTRS1991

Collisionless reconnection in two-dimensional magnetotail equilibria

A two-dimensional particle simulation model based on the Darwin approximation to Maxwell's equations for studying collisionless reconnection in the magnetotail has been developed. Simulations of the pure ion tearing mode in a thin current sheet with normal B(z) field component demonstrate that in this limit this mode grows more slowly than expected based on previous analytic estimates. The saturation level of the tearing instability greatly surpasses estimates based on a simple trapping argument. The effect of the normal field component on the evolution of the tearing instability is considered. It is found that a normal field of even a few percent on axis strongly inhibits the growth of the instability.

Pritchett, P. L.↗

NASA NTRS1984

Association between energetic particle bursts and Birkeland currents in the geomagnetic tail

IMP 8 observations in the geomagnetic tail of energetic particles at hundreds of keV and of the magnetic field are examined for a substorm period from 1700 to 1800 UT on Mar. 3, 1976. For this interval, it is found that bursts of energetic protons detected at a downstream distance of about 37 earth radii in the midnight tail region are accompanied by east-west magnetic field perturbations indicative of Birkeland current sheets. The magnitude of the magnetic field perturbations range from about 1 to 12 nT, corresponding to current densities of 1 to 9 mA/m when integrated over the current sheet thickness. These values are comparable to previous observations of Birkeland currents in the near-earth tail (X greater than -20 earth radii) and with the auroral-arc-associated Birkeland current densities at low altitudes scaled out to the tail region. The favorable comparison suggests that the closure of small-scale Birkeland current systems, at least in these instances, lies tailward of about 40 earth radii. The observed Birkeland current system and the magnitude of current densities are found to be consistent with ion tearing instability in the tail. The inferred wavelength of the tearing mode along the tail axis is about 2 to 17 earth radii. In the context of the tearing model, the presence of Birkeland currents and the occasional isotropic distribution of energetic electrons (of more than 0.22 MeV) suggest that the energetic particle events in this study occur on closed magnetic field lines, even though strong tailward streaming dominates the particle anisotropy in these events.

Lui, A. T. Y.↗

NASA NTRS1986

Can prominences form in current sheets

Two-dimensional numerical simulations of the formation of cold condensations in a vertical current sheet have been performed using the radiative, resistive MHD equations with line-tied boundary conditions at one end of the sheet. Prominence-like condensations are observed to appear above and below an X-line produced by the onset of the tearing-mode instability. Cooling in the sheet is initiated by Ohmic decay, with the densest condensations occurring in the region downstream of a fast-mode shock. This shock, which is due to the line-tied boundary conditions, terminates one of the two supermagnetosonic reconnection jets that develop when the tearing is fully developed. The condensation properties of shock waves, which may trigger or considerably enhance the conditions for thermal condensation are emphasized.

Malherbe, J. M.↗

NASA NTRS1989

Turbulent excitation of spontaneous reconnection

The long-term nonlinear evolution of a tearing-mode-unstable sheared-field plasma in a turbulent environment is explored. Two different physical configurations are modeled, and a different computational system is used for each. Results of both sets of calculations show that magnetic tearing arises spontaneously provided that the initial turbulence energy level is below the natural saturation level of the tearing instability. The relationship between these results and those of previous calculations are briefly discussed, concluding that there are no significant unexplainable disagreements.

Deeds, D.↗

NASA NTRS1994

Magnetotail dynamics under isobaric constraints

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

Birn, Joachim↗

NASA NTRS1992

Secondary instability in three-dimensional magnetic reconnection

We consider the transition to turbulence in three-dimensional reconnection of a magnetic neutral sheet. We find that the transition can occur via a three-step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two-dimensional quasi-steady state. Third, this secondary equilibrium is itself unstable when it is perturbed by three-dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three-dimensional linear stability properties of the two-dimensional saturated tearing layer. The numerical simulations are performed with a semi-implicit, pseudospectral-Fourier collocation algorithm. We identify a three-dimensional secondary linear stability which grows on the ideal timescale. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three-dimensional field, with the two-dimensional field acting as a catalyst.

Dahlburg, R. B.↗

NASA NTRS1985

The magnetohydrodynamics of current sheets

Examples of current sheets are summarized and their formation is described. A universal phenomenon in cosmic plasmas is the creation of sheets off intense current near X-type neutral points (where the magnetic field vanishes). These sheets are important as sites where the magnetic-field energy is converted efficiently into heat and bulk kinetic energy and where particles can be accelerated to high energies. Examples include disruptions in laboratory tokamaks, substorms in the earth's magnetosphere, and flares on the sun. The basic behavior of a one-dimensional sheet is presented, together with an account of the linear tearing-mode instability that can cause the field lines in such a sheet to reconnect. Such reconnection may develop in different ways: it may arise from a spontaneous instability or it may be driven, either from outside by motions or locally by a resistivity enhancement. Various processes are described that may occur during the nonlinear development of tearing, along with the many numerical and laboratory experiments that are aiding our understanding of this intriguing cosmical process.

Priest, E. R.↗

NASA NTRS1985

Electron acceleration in solar flares and the transition from nonthermal to thermal hard X-ray phases

Observations are reviewed which indicate that hard X-rays during the impulsive phase of a flare typically start with a primarily nonthermal phase which undergoes a transition to a primarily thermal phase as the flare progresses. Recent theoretical work on the modified two-stream instability as an efficient electron accelerator and modeling of thermal hard X-ray sources is considered. A scenario which is termed the dissipative thermal model is proposed to explain the observations. Fast tearing modes occurring in a loop give rise to cross-field ion motion. This in turn excites the modified two-stream instability which converts about 50 percent of the ion energy into accelerated electrons along the loop as long as the plasma beta is less than 0.3. These electrons impact the chromosphere and boil off a part of it which rises up the loop. This density increase coupled with the temperature increase due to tearing causes the beta to increase beyond 0.3 and efficient electron acceleration ceases. This leads to the primarily thermal phase.

Smith, D. F.↗

NASA NTRS1985

Collsionless tearing instability in a non-Maxwellian neutral sheet - An integro-differential formulation

In the present investigation, a general integro-differential formalism is derived for the study of the collisionless tearing mode in a highly non-Maxwellian neutral sheet in which both electrons and ions are treated kinetically. The obtained formalism is applied to a specific non-Maxwellian distribution. The dispersion relation for the considered system is determined, taking into account the fundamental harmonic of the orbital frequency. It is found that the dispersion relation is dominated by the electrons. The results are presented in a number of graphs. The growth rates of non-Maxwellian distributions are generally much greater than the growth rate of the conventional isotropic tearing instability.

Chen, J.↗

NASA NTRS1984

Fast collisionless tearing in an anisotropic neutral sheet

The collisionless tearing mode in a neutral sheet is studied in the presence of ion temperature (Ti) anisotropy, using Vlasov description for both ions and electrons. It is found that the growth rate of the instability is significantly enhanced if the ratio of Ti perpendicular to the equilibrium magnetic field to Ti parallel to the field is greater than one. For typical magnetotail parameters with modest temperature anisotropy, it is shown that the linear e-folding time is reduced to a small fraction of the time delays believed to precede the onset of reconnection. This enhancement of the growth rate is due to the Lorentz force acting on the ions that cross the neutral plane, traversing beyond the conventional electron-tearing layer.

Chen, J.↗

NASA NTRS1972

Magnetic models of solar flares.

A solar flare is interpreted as the explosive release of magnetic energy associated with a current sheet in the solar atmosphere. The release is due to field-line reconnection caused by the tearing-mode instability. Current sheets may be classified into closed and open, depending on whether the adjacent field lines are closed (contained in the sun's atmosphere) or open, extending into interplanetary space. A high-energy event requires an open current sheet. It is shown that certain types of photospheric motion may lead to the formation of current sheets. One of these is associated with high-energy events, another with filaments, and a third with surge flares.

Sturrock, P. A.↗

NASA NTRS1974

Instabilities connected with neutral sheets in the solar wind

A preliminary study is presented of two sets of data obtained by HEOS 1 and OGO 5 in the solar wind, which reveal the internal structure of two neutral sheets and their two-dimensional structure. HEOS 1 observations of the effects of the tearing mode instability in one of the sheets are described, including complicated structures connected with the sector boundary, sharp increases and decreases in the magnetic field intensity, and the presence of closed loops. HEOS 1 and OGO 5 observations of large oscillations due to plasma pressure imbalances are discussed, and it is concluded that an interchange instability may have been observed.

Formisano, V.↗