Engineering topics

Finn, John M.

Publications and source records attributed to Finn, John M..

13 records

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 NTRS1993

Long-term containment of energetic particles in coronal loops

Recent observation from the Compton Gamma-Ray Observatory shows that gamma-ray emission after a solar flare can last for as long as 8 hours. There is also evidence that electrons and protons are accelerated only during the impulsive phase of the flare and are subsequently mirror trapped in coronal magnetic loops. This poses the following dilemma: if the magnetic field lines in the loop are simple plane arches, the protons will drift across the cross section of the loop in seconds to minutes, rather than hours. To solve the dilemma, we use guiding center theory to show that long-term containment of energetic protons in a coronal loop is possible if magnetic field lines have enough twist. We also find that in the trapped region of the loop, the twist angle of field lines between the mirror points of a bounce orbit is approximately 2 pi.

Lau, Yun-Tung↗

NASA NTRS1993

Loss of equilibrium and reconnection in tearing of two-dimensional equilibria

Two-dimensional tearinglike behavior is studied in reduced resistive magnetohydrodynamics (MHD) with flux conserving boundary conditions on a rectangular box. The tearinglike perturbations do not destroy the symmetries of the initial state, either discrete or continuous. In such cases, in which the perturbation does not break a symmetry of the equilibrium, linear instability is typically not directly observed. However, there can be a loss of equilibrium associated with the existence of a tearing unstable state. These ideas are illustrated with three examples: a very elongated tokamak, a tokamak with pinching coils to elongate its flux surfaces, and a model for the magnetotail or for solar arcades. The loss of equilibrium is demonstrated by means of a nonlinear energy functional. The importance of the fact that the dynamics shows a loss of equilibrium is that a large amount of free energy can be released, in the form of reconnection, and that there is a possibility of hysteresis.

Finn, John M.↗

NASA NTRS1993

Fast dynamos with finite resistivity in steady flows with stagnation points

Results are presented of a kinematic fast dynamo problem for two classes of steady incompressible flows: the ABC flow and the spatially aperiodic flow of Lau and Finn (1992). The numerical method used to find the solutions is described, together with convergence studies with respect to the time step and the number of points N of the spatial grid. It is shown that the growth rate and frequency can be extrapolated to N = infinity. Results are presented indicating that fast kinematic dynamos can exist in both these flows and that chaotic flow is a necessary condition. It was found that, for the ABC flow with A = B = C, there are two dynamo modes: an oscillating mode and a purely growing mode.

Lau, Yun-Tung↗

NASA NTRS1992

Three-dimensional kinematic reconnection of plasmoids with nulls

The global nonlinear dynamics of magnetic field lines in plasmoids with a pair of nulls, where B = 0, is studied. The aim of this analysis is to describe the separatrix surfaces on which singularities can occur in ideal magnetohydrodynamics because of topological changes in the field. These separatrix surfaces should locate the boundary layers associated with 3D reconnection in the presence of resistivity or inertia. It is found that the field lines exhibit chaotic scattering with several properties in common with plasmoid models without nulls (in which one component of the magnetic field never changes sign). In particular, the singular surfaces can be fractal, implying complex current density structures down to the dissipation scale. These generic features are expected to exist in typical coronal magnetic geometries exhibiting three-dimensional reconnection and the formation of current sheets.

Lau, Yun-Tung↗

NASA NTRS1992

Generation of magnetic fields by chaotic fluid convection - The fast dynamo problem

In the kinematic fast dynamo problem, the underlying nonlinear dynamics of the flow play a critical role in the behavior of a dynamo field. It is presently noted that the two important facets of the problem are the approximately lognormal distribution of vector lengths, and the presence of partial cancellation. It is suggested that these features may be reflected in the magnetic fields observed on the sun.

Finn, John M.↗

NASA NTRS1991

Magnetohydrodynamic equilibria in the vicinity of an X-type neutral line specified by footpoint shear

Consideration is given to a class of 2D magnetohydrodynamic (MHD) equilibria with hyperbolic, X-line-type geometry and with footpoint displacement field lines arbitrary near the separatrix. The scale-invariant, or similarity, solutions are presented to specification of the footpoint displacement that is finite as the separatrix is approached. They are appropriate near the X-line on length scales intermediate between the boundary layer width because of resistivity and the macroscopic length scale. Force balance across the separatrix implies identical radial dependence in all four quadrants and continuity of Bz squared across the separatrix. It is found that the general solutions can have arbitrary separatrix angle and ratio of flux between the quadrants.

Finn, John M.↗

NASA NTRS1991

Fractal dimension in nonhyperbolic chaotic scattering

In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.

Lau, Yun-Tung↗

NASA NTRS1991

Three-dimensional kinematic reconnection of plasmoids

The kinematic reconnection model of Lau and Finn (1990) is applied in a theoretical investigation of three-dimensional plasmoid morphology, as seen in the solar corona and earth magnetotail. The derivation of the governing equations is outlined; long, short, and periodic plasmoid models are developed; and the evolution of the stable and unstable manifolds in these models is presented graphically. It is inferred that sheet currents and tangential discontinuities can form on surfaces topologically identical to those where Delta(phi) about equal to Delta(z) singularities occur in the kinematic reconnection model, and can be broadened in a similar way by nonideal effects. Two such surfaces exist in long plasmoids, and also in short plasmoids in the presence of finite resistivity; the intertwined surfaces characteristic of the periodic plasmoid form a fractal set but merge in the presence of finite resistivity, producing structures similar to those proposed by the sheet-current theory of Parker (1983).

Lau, Yun-Tung↗

NASA NTRS1990

The fast kinematic magnetic dynamo and the dissipationless limit

The evolution of the magnetic field in models that incorporate chaotic field line stretching, field cancellation, and finite magnetic Reynolds number is examined analytically and numerically. Although the models used here are highly idealized, it is claimed that they display and illustrate typical behavior relevant to fast magnetic dynamic behavior. It is shown, in particular, that consideration of magnetic flux through a finite fixed surface provides a simple and effective way of deducing fast dynamo behavior from the zero resistivity equation. Certain aspects of the fast dynamo problem can thus be reduced to a study of nonlinear dynamic properties of the underlying flow.

Finn, John M.↗

NASA NTRS1990

Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines

The present investigation of three-dimensional reconnection of magnetic fields with nulls and of fields with closed lines gives attention to the geometry of the former, with a view to their gamma-line and Sigma-surface structures. The geometric structures of configurations with a pair of type A and B nulls permit reconnection across the null-null lines; these are the field lines which join the two nulls. Also noted is the case of magnetostatic reconnection, in which the magnetic field is time-independent and the electrostatic potential is constant along field lines.

Lau, Yun-Tung↗

NASA NTRS1989

Do steady fast magnetic dynamos exist?

This paper considers the question of the existense of a steady fast kinematic magnetic dynamo for a conducting fluid with a steady velocity field and vanishingly small electrical resistivity. The analysis of examples of steady dynamos, found by considering the zero-resistivity dynamics, indicated that, for sufficiently small resistivity, dynamo action can indeed occur in steady smooth three-dimensional chaotic fluid flows and that fast dynamos should consequently be a typical occurrence for such flows.

Finn, John M.↗

NASA NTRS1988

Chaotic flows and fast magnetic dynamos

The kinematic dynamo problem is considered in the R(m) approaching infinity limit. It is shown that the magnetic field tends to concentrate on a zero volume fractal set; moreover, it displays arbitrarily fine-scaled oscillations between parallel and antiparallel directions. Consideration is given to the relationship between the dynamo growth rate and quantitative measures of chaos, such as the Liapunov element and topological entropy.

Finn, John M.↗