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Results for “Tearing instability”

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NASA NTRS1983

Computations of the current profile influence on tearing instability

Results of computations of tearing instability of a plasma column in a strong longitudinal magnetic field are presented for different current profiles. The power current profiles j=j sub 0(1-(r/a)(P))(nu) are considered and analyzed for various values of the parameters p and v. The tearing instability of the smoothed two-step profiles is studied. Optimal smoothed two-step profiles are constructed which are stable with respect to all helical largescale perturbations.

Blekher, P. M.↗

NASA NTRS1992

The beta dependence of the collisionless tearing instability at the dayside magnetopause

The beta dependence (where beta is the ratio between plasma pressure to magnetic pressure) of the collisionless tearing instability at the dayside magnetopause current sheet was investigated analytically for several current sheet models. The results show that, when the asymmetry of the dayside magnetopause current sheet is taken into account, the beta dependence of the collisionless tearing instability at the dayside magnetopause is controlled by the magnetic field profile across the magnetopause current sheet.

Ding, D. Q.↗

NASA NTRS1988

Streaming sausage, kink and tearing instabilities in a current sheet with applications to the earth's magnetotail

This paper investigates the growth rates and eigenmode structures of the streaming sausage, kink, and tearing instabilities in a current sheet with a super-Alfvenic flow. The growth rates and eigenmode structures are first considered in the ideal incompressible limit by using a four-layer model, as well as a more realistic case in which all plasma parameters and the magnetic field vary continuously along the direction perpendicular to the magnetic field and plasma flow. An initial-value method is applied to obtain the growth rate and eigenmode profiles of the fastest growing mode, which is either the sausage mode or kink mode. It is shown that, in the earth's magnetotail, where super-Alfvenic plasma flows are observed in the plasma sheet and the ratio between the plasma and magnetic pressures far away from the current layer is about 0.1-0.3 in the lobes, the streaming sausage and streaming tearing instabilities, but not kink modes, are likely to occur.

Lee, L. C.↗

NASA NTRS1989

Linear, collisionless, bi-Maxwellian neutral-sheet tearing instability

The problem of linear bi-Maxwellian neutral-sheet tearing instability has been solved, using neither an approximation of the orbits nor the constant-psi approximation. The present method has a larger range of validity than the best previous approximation, the three-region approximation. It is found that as the temperature anisotropy is increased, the growth rate increases and the wavelength associated with the peak growth decreases. It is suggested that if small-island formation is experimentally observed, then temperature anisotropy may be present.

Burkhart, G. R.↗

NASA NTRS1988

Does the resistive tearing instability nonlinearly evolve to a fast reconnection mode

A fundamental problem in applying linear tearing instability theory to the rapid processes (particle acceleration, heating) in flares was the characteristically slow rate of reconnection. This problem can be at least partially overcome if the tearin mode nonlinearly evolves to a regime in which the reconnection rate is substantially enhanced, such as that for the Petschek configuration. This possibility was often suggested, and some numerical simulations appear to provide support for such a view. Numerical simulation are used to study the nonlinear evolution of the tearing stability and show that a fast Petschek-like regime may not be achieved. This conclusion follows when there are sufficient grid points within the diffusion region to completely resolve the nonlinear dynamic interactions in the diffusion layer. When the numerical resolution is not adequate, the solution does appear to approach a Petschek configuration. The resolved solution contains reverse flow vortices and current sheets, terminated with a current reversal, similar to those obtained by Syrovatsky (JEPT, 33, 933, 1971).

Steinolfson, R. S.↗

NASA NTRS1989

Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.

Burkhart, G. R.↗

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 NTRS1986

Collisional tearing instability in the current sheet with a low magnetic Lundquist number

An MHD model is used to calculate the growth rate of the collisional tearing mode instability in a current layer with a Lundquist number in the range 3-100,000. The maximum growth rate is found to be a function of the Alfven transit time in the current sheet and the Lundquist number. When the Lundquist number is below 50, the growth rate asymptotically approaches a value of about -0.075/transit time. The discovery of the dependence of the asymptotic value is considered to be of use in studies of the current sheet in the diffusion region of a magnetic reconnection configuration, where the Lundquist number will be in the range 2-100.

Lee, L. C.↗

NASA NTRS1976

High conductivity magnetic tearing instability

Linearized equations of magnetohydrodynamics are used to investigate the tearing mode, for arbitrary values of the conductivity, through a consideration of the additional effect of the electron-inertia contribution to Ohm's law. A description is provided of the equilibrium and subsequent instability in the magnetohydrodynamic approximation. A method for solving the perturbation equations in the linear approximation is discussed and attention is given to the results in the high conductivity limit.

Cross, M. A.↗

NASA NTRS1988

Nonlinear 3-D evolution of bounded kinetic Alfven waves due to shear flow and collisionless tearing instability

The three-dimensional nonlinear simulation of the evolution of a kinetic Alfven wave is presented for simple boundary conditions that resemble those of a discrete auroral breakup arc. The model used is a variant of the reduced megnetohydrodynamic description that includes, in addition, the important dispersive effect of electron inertia. It is found that with a 'generator' boundary condition corresponding to a current generator and a fully conducting 'load' boundary, the wave evolves three-dimensionally through a combination of shear flow and collisionless tearing mode instability.

Seyler, Charles E., Jr.↗

NASA NTRS1990

Collisionless tearing instability in magnetotail plasmas

The problem of the linear stability of collisionless tearing modes in the earth's magnetotail is revisited. It is found that the collisionless tearing mode is linearly unstable with wavelengths of the order of 10 R(E). It is shown that an important feature neglected in earlier theories is a nonzero equilibrium B(y)-field. The physics of the instability is elucidated in the context of a simple slab model and a sheared parabolic model which is representative of the magnetotail in which all three components of the magnetic field are nonzero. The dispersion equation for the instability is obtained by a boundary-layer analysis. The implications of the theory for recent observations on current disruption and diversion during substorms is discussed.

Wang, Xiaogang↗

NASA NTRS1984

Tearing instability in an anisotropic neutral sheet

A study is made of the collisionless tearing-mode stability properties of a field-reversed plasma layer whose temperature distribution is anisotropic. The plasma is confined by its self magnetic field with no external field. A kinetic description is used for both ions and electrons. The effects of the axis-crossing and nonaxis-crossing orbits are discussed. It is found that the conventional technique of matching the inner and outer asymptotic solutions at the electron inner-region is inadequate for the anisotropic case. An intermediate region in which the axis-crossing ion orbits are important is identified. The eigenvalue equation is solved using both analytic approximations and numerical methods to obtain the eigenmode structure and the linear dispersion relation. Previously announced in STAR as N84-14920

Chen, J.↗

NASA NTRS1988

Spectral analysis of turbulent effects on resistivity and the tearing instability

A spectral numerical-simulation code and ancillary diagnostics are used here to analyze the behavior of resistive magnetic tearing in the presence of short-wavelength turbulence. It is found that, in general, the anomalous resistivity defined by Biskamp and Welter (1983) due to short-wavelength turbulence tends to return quickly towards zero even when artificially supported away from zero, and that its effect on tearing-mode behavior is not consistent with its interpretation as a resistivity. The behavior reported by Biskamp and Welter and the behavior observed here are analyzed. It is argued that, while not meaningful as a true resistivity, the anomalous resistivity parameter is a useful diagnostic showing the energy balance of the system.

Deeds, D.↗

NASA NTRS1987

Effect of a localized minimum in equatorial field strength on resistive tearing instability in the geomagnetotail

A two-dimensional, resistive-MHD computer code is used to investigate the spontaneous reconnection of magnetotaillike configurations. The initial conditions adopted in the simulations are of two types: (1) in which the equatorial normal magnetic field component B(ze) declines monotonically down the tail, and (2) in which B(ze) exhibits a deep minimum in the near-earth plasma sheet. To represent the case where the earthward convection stops before the X line forms, zero-flow boundary conditions are imposed at the edges of the computational box. The initial configurations are in equilibrium and table within ideal MHD. The dynamic evolution of the system starts after the resistivity is turned on. The main results of these simulations basically support the neutral-line model of substorms and confirm Birn's (1980) computer studies. Spontaneous formation of an X-type neutral point and a single O-type plasmoid with strong tailward flow on the tailward side of the X point is found. The time interval from the turning on of the resistivity to the formation of a plasmoid is much shorter in the case where there is an initial deep minimum. A simple analytic calculation is also carried out to demonstrate why the configuration with a deep minimum is more susceptible to the development of the neutral point.

Hau, L.-N.↗

NASA NTRS1990

Linear and non-linear studies of Alfven waves in space. Stationary and dynamic processes in magnetospheric plasmas

The Final Technical Report on linear and non-linear studies of Alfven waves in space is presented. Areas of research included relaxation of magnetotail plasmas with field-aligned currents; the equilibrium dayside magnetosphere; macroscale particle simulation of kinetic Alfven wave physics; ballooning stability of plasmas with sheared equilibrium flows; theory of the drift-mirror instability; collisionless tearing instability in magnetotail plasmas; and nonadiabatic behavior of the magnetic moment of a charged particle in a dipole magnetic field and the development of stochastic webs.

Bhattacharjee, A.↗

NASA NTRS1983

Hall current effect on tearing mode instability

From a linear 2-D eigenmode analysis, it is found that the Hall current effect on collisional tearing mode instability becomes important for the thin magnetic reversal layer whose width is comparable to the ion inertia length; Hall currents produce a three-dimensional field structure and increase the reconnection (growth) rate. Since the magnetaic reversal layer widths both in the magnetopause and in the magnetotail are reported to become as thin as the ion inertial length (several hundred km) when the reconnection process is supposed to occur, the Hall current effect may explain the appearance of the dawn-dusk component of the magnetic field in the magnetotail reconnection region.

Terasawa, T.↗

NASA NTRS1994

Tearing mode instability in a multiple current sheet system

The tearing mode and magnetic reconnection are studied for multiple current sheet systems by two-dimensional magnetohydrodynamic (MHD) simulations. Both the linear and nonlinear evolution of this process are anaylsed for laminar perturbations. The results illustrate the existence of a linear regime with a symmetric and antisymmetric mode and agree with previous analytic results (Otto and Birk, 1992). The nonlinear evolution shows a number of interesting new features and may explain some properties in corresponding studies of turbulent reconnection. For wavelengths larger than twice the current sheet separation the evolution of antisymmetric modes leads to an entire reconfiguration of the magnetic field and converts a major portion of the magnetic energy into kinetic energy. Antisymmetric modes with smaller wavelengths and symmetric modes are found to saturate. The influence of the value of the resistivity on the reconnection rate decreases in the nonlinear evolution, and the ratio of current sheet separation to wavelength seems to be of major importance. A comparion of the dynamics of periodic current sheets with the evolution of only two current sheets indicates that some of the results for the periodic system also apply to the evolution of only two interacting current sheets. The results are discussed with respect to observations of large-scale plasma and magnetic field reconfigurations in the magnetosheath and near the Earth's bow shock.

Yan, M.↗

NASA NTRS1983

Energy dynamics in stressed magnetic fields - The filamentation and flare instabilities

The thermal and tearing instabilities are believed to be the two primary temperature modification mechanisms in sheared astrophysical magnetic fields. The former gives rise to the formation of cool filaments and the latter to the release of magnetic energy. It has long been known that these processes are interrelated, most conspicuously in the case of the solar corona where prominences often precede flares within the same magnetic structure. It is also clear, from first principles, that the energy transport underlying the thermal instability should have a strong effect on the resistivity which facilitates magnetic tearing, and that the energy release of the latter should affect the temperature drop of the former. This paper describes some results of the first calculations which attempt to unify the dynamic treatment of these two coexisting instabilities. Growth rates as a function of resistivity, and examples of the primary mode structures are provided, along with a discussion of some critical aspects of the interaction of these two astrophysical energy flux mechanisms.

Van Hoven, G.↗