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NASA NTRS1985

Force-free equilibria of magnetized jets

Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.

Koenigl, A.↗

NASA NTRS1995

Cross-tail magnetic flux ropes as observed by the GEOTAIL spacecraft

Ten transient magnetic structures in Earth's magnetotail, as observed in GEOTAIL measurements, selected for early 1993 (at (-) X(sub GSM) = 90 - 130 Earth radii), are shown to have helical magnetic field configurations similar to those of interplanetary magnetic clouds at 1 AU but smaller in size by a factor of approximately = 700. Such structures are shown to be well approximated by a comprehensive magnetic force-free flux-rope model. For this limited set of 10 events the rope axes are seen to be typically aligned with the Y(sub GSM) axis and the average diameter of these structures is approximately = 15 Earth radii.

Lepping, R. P.↗

NASA NTRS1988

Driven, steady-state RFP computations

The pseudospectral three-dimensional MHD code of Dahlburg et al. (1986 and 1987) is used to compute the dynamical behavior of a channel of magnetofluid carrying an axial current and magnetic flux. This situation contains the essential MHD behavior of the reversed-field pinch (RFP). An externally imposed electric field is applied to an initially current-free magnetofluid and drives currents that rise and eventually fluctuate about values corresponding to pinch ratios Theta of about 1.3, 2.2, and 4.5. A period of violent turbulence leads to an approximately force-free core, surrounded by an active MHD boundary layer that is not force-free. A steady state is reached that can apparently be sustained indefinitely (for several hundred Alfven transit times or longer). The turbulence level and time variability in the steady state increase with increasing Theta. The average toroidal magnetic field at the wall reverses for Theta = 2.2 and 4.5, but not for Theta = 1.3. Negative toroidal current filaments are observed. The Lundquist numbers are of the order of a few hundred.

Dahlburg, J. P.↗

NASA NTRS1994

Three-dimensional force-free looplike magnetohydrodynamic equilibria

Computations of three-dimensional force-free magnetohydrodynamic (MHD) equilibria, del x B = lambdaB with lambda = lambda(sub 0), a constant are presented. These equilibria are determined by boundary conditions on a surface corresponding to the solar photosphere. The specific boundary conditions used correspond to looplike magnetic fields in the corona. It is found that as lambda(sub 0) is increased, the loops of flux become kinked, and for sufficiently large lambda(sub 0), develop knots. The relationship between the kinking and knotting properties of these equilibria and the presence of a kink instability and related loss of equilibrium is explored. Clearly, magnetic reconnection must be involved for an unknotted loop equilibrium to become knotted, and speculations are made about the creation of a closed hyperbolic field line (X-line) about which this reconnection creating knotted field lines is centered.

Finn, John M.↗

NASA NTRS1990

Self-similar evolution of the nonlinear magnetic buoyancy instability

A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.

Shibata, K.↗

NASA NTRS1991

Laboratory experiments on the electrodynamic behavior of tethers in space

The transient current systems between tethered plasmas in a large magnetoplasma are investigated experimentally for extrapolation to electrodynamic tethers in space. The studies measure the perturbed magnetic fields and the current density associated with pulsed currents to electrodes in three-dimensional space and time. The electrodes excite electron whistlers because they produce fields that dominantly couple to electrons, allowing pulsed currents to propagate and disperse as whistler wave packets. The wave packets evolve into force-free, flux-ropelike field configurations, and a whistler 'wedge' is formed in the plasma due to 'eddy' currents caused by insulated tethers with dc currents. Substantial radiation into the whistler mode happens with moving VLF antennas as well as tethers, and the wave spread within the ray cone is the most significant characteristic event. The wave spread widens the current channel, incites current closure, and is also associated with a 'phantom loop' phenomenon.

Stenzel, Reiner L.↗

NASA NTRS1990

Filament cooling and condensation in a sheared magnetic field

Thermal instability driven by optically thin radiation in the corona is believed to initiate the formation of solar filaments. The fact that filaments are observed generally to separate regions of opposite, line-of-sight, magnetic polarity in the differentially rotating photosphere suggests that filament formation requires the presence of a highly sheared magnetic field. The coupled energetics and dynamics of the most important condensation modes, those due to perpendicular thermal conduction at short wavelengths are discussed. Linear structure in the sheared field and their growth rates is described, and 2D, nonlinear, MHD simulations of the evolution of these modes in a force-free field are conducted. The simulations achieve the fine thermal structures, minimum temperatures and maximum densities characteristic of observed solar filaments.

Van Hoven, Gerard↗

NASA NTRS2004

KINEMATIC TREATMENT OF CORONAL MASS EJECTION EVOLUTION IN THE SOLAR WIND

We present a kinematic study of the evolution of coronal mass ejections (CMEs) in the solar wind. Specifically, we consider the effects of (1) spherical expansion and (2) uniform expansion due to pressure gradients between the interplanetary CME (ICME) and the ambient solar wind. We compare these results with an MHD model that allows us to isolate these effects h m the combined kinematic and dynamical effects, which are included in MHD models. They also provide compelling evidence that the fundamental cross section of so-called "force-free" flux ropes (or magnetic clouds) is neither circular or elliptical, but rather a convex-outward, "pancake" shape. We apply a force-free fit to the magnetic vectors from the MHD simulation to assess how the distortion of the flux rope affects the fit. In spite of these limitations, force-free fits, which are straightforward to apply, do provide an important description of a number of parameters, including the radial dimension, orientation, and chirality of the ICME. Subject headings: MHD - solar wind - Sun: activity - Sun: corona - Sun: coronal mass ejections (CMEs) - On-line material color figures Sun: magnetic fields

Riley, Pete↗

NASA NTRS1978

The exterior source surface for force-free fields

Consideration is given to the exterior source surface for force-free fields. The spherical harmonic expansion is presented for boundary values on two concentric spheres. An upper limit on a constant which measures the strength of coronal currents is found to be a function of the lowest multipole moment of the prescribed boundary values. The solar atmosphere is in the class of magnetic fields for which the study is applicable.

Barbosa, D. D.↗

NASA NTRS1992

A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds

We contrast two different solutions of the constant alpha, force-free MHD equation, both of which have been suggested as models for magnetic clouds: a solution in cylindrical coordinates and one in spherical coordinates. In line with the observation that magnetic clouds expand, we generalize these static models and construct their expanding counterparts. We find that expansion introduces in both cases a large asymmetry in the field strength signature which is in the same sense as that seen the the data, i.e. towards the leading edge of the cloud. We then do a least squares fit of the respective models to one-spacecraft data on a magnetic cloud. We find that the fitting routine converges in both cases. However, while purely formally we cannot distinguish between the two models using data from one spacecraft, the field components in the 'spherical' model have features not compatible with data on magnetic clouds.

Farrugia, C. J.↗

NASA NTRS1975

The calculation of force-free fields from discrete flux distributions

This paper presents particularly simple mathematical formulas for the calculation of force-free fields of constant alpha from the distribution of discrete sources on a flat surface. The advantage of these formulas lies in their physical simplicity and the fact that they can be easily used in practice to calculate the fields. The disadvantage is that they are limited to fields of 'sufficiently small alpha'. These formulas may be useful in the study of chromospheric magnetic fields by the comparison of high-resolution H-alpha photographs and photospheric magnetograms.

Sheeley, N. R., Jr.↗

NASA NTRS1980

The stability properties of cylindrical force-free fields - Effect of an external potential field

A large-scale potential field with an embedded smaller-scale force-free structure gradient x B equals alpha B is studied in cylindrical geometry. Cases in which alpha goes continuously from a constant value alpha 0 on the axis to zero at large r are considered. Such a choice of alpha (r) produces fields which are realistic (few field reversals) but not completely stable. The MHD-unstable wavenumber regime is found. Since the considered equilibrium field exhibits a certain amount of magnetic shear, resistive instabilities can arise. The growth rates of the tearing mode in the limited MHD-stable region of k space are calculated, showing time-scales much shorter than the resistive decay time.

Chiuderi, C.↗

NASA NTRS2003

Observed Helicity of Active Regions in Solar Cycle 21

We report the results of a study of helicity in solar active regions during the peak of activity in solar cycle 21 from observations with the Marshall Space Flight Center's solar vector magnetograph. Using the force-free parameter alpha as the proxy for helicity, we calculated an average value of alpha for each of 60 active regions from a total of 449 vector magnetograms that were obtained during the period 1980 March to November. The signs of these average values of alpha were correlated with the latitude of the active regions to test the hemispheric rule of helicity that has been proposed for solar magnetic fields: negative helicity predominant in northern latitudes, positive in the southern ones. We have found that of the 60 regions that were observed, 30 obey the hemispheric rule and 30 do not.

Hagyard, M. J.↗

NASA NTRS2003

Observed Helicity of Active Regions in Solar Cycle 21

We report the results of a study of magnetic helicity in solar active regions during solar cycles 21 and 22 from observations with the Marshall Space Flight Center's solar vector magnetograph. Using the force-free parameter a as the proxy for helicity, we calculated an average value of a for each of 91 active regions from a total of 683 vector magnetograms that were obtained during the period March 1980 to July 1993. The signs of these average values of a were correlated with the latitude of the active regions to test the hemispherical rule of helicity that has been proposed for solar magnetic fields: negative helicity predominant in northern latitudes, positive in the southern ones. We have found that of the 65 regions that were observed in cycle 21,49% obey the hemispherical rule and 51% do not. On the other hand, for the 26 regions in cycle 22,65% do exhibit this correlation. In addition, our results seem to support the findings of Hagino and Sakurai (2002) which indicate evidence for a time variability in the hemispheric rule.

Hagyard, M. J.↗

NASA NTRS2003

Using an MHD simulation to interpret the global context of a coronal mass ejection observed by two spacecraft

In late February 1999 the ACE spacecraft observed a coronal mass ejection (CME) at 1 AU, in the ecliptic plane. Thirteen days later, Ulysses observed a CME at 5 AU and 22"s. We present a detailed analysis of the plasma, magnetic field, and composition signatures of these two events. On the basis of this comparison alone, it is not clear that the two spacecraft observed the same solar event. However, using a generic MHD simulation of a fast CME initiated at the Sun by magnetic flux cancellation and propagated out into the solar wind, together with additional evidence, we argue that indeed the same CME was observed by both spacecraft. Although force-free models appear to fit the observed events well, our simulation results suggest that the ejecta underwent significant distortion during its passage through the solar wind, indicating that care should be taken when interpreting the results of force-he models. Comparison of composition measurements at the two spacecraft suggests that significant spatial inhomogeneities can exist within a single CME.

Riley, Pete↗

NASA NTRS1993

Nonlinear evolution of magnetic flux ropes. I - Low-beta limit

We study the nonlinear self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial and azimuthal. We restrict ourselves to the case of a plasma of low beta. Introducing a special class of configurations we call 'separable fields', we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong repulsive term and a weak restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.

Osherovich, V. A.↗

NASA NTRS1978

Measurement and analysis of magnetic field variation during a class 2b flare

A digital analysis of high-time-resolution videomagnetograms taken during a class 2b flare that occurred at 60 deg east is reported. The data were obtained at the Big Bear Observatory and calibrated by a Mt. Wilson magnetogram. Changes of weak magnetic fields (less than 100 G) with an amplitude of 30% to 100% have been detected over 55% of the optical flare region, apparently taking place at the initial phase of the flare. Statistical considerations suggest a real flare association with most of these changes. H-alpha observations show that large changes took place over the footpoints of heavily inclined structures like penumbral fibrils, while smaller changes took place over the plage region. An apparent polarity reversal was found at the feet of erupted fibrils. Based on force-free field calculations these changes can be reasonably explained as a transformation of the current-carrying fields to potential fields which produced large changes in the field-line inclination and rotation.

Tanaka, K.↗

NASA NTRS2010

3D Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability: Instability of a Static Column - 1

We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.

Mizuno, Yosuke↗