Engineering topics

Van Hoven, G.

Publications and source records attributed to Van Hoven, G..

At least 37 records · Page 2

NASA NTRS1985

The physics of thermal instability in two dimensions

Previous studies of a thermal (radiative) instability in a sheared magnetic field have shown that, under solar coronal conditions, cool condensations can form in a small neighborhood about the shear layer. Such results have served to model the formation of solar filaments (or prominences) observed to occur above photospheric magnetic polarity-inversion lines. A surprising conclusion of these studies is that the width of the condensation does not depend on the thermal conductivity. By examining the mass-flow patterns of two-dimensional condensations in the absence of thermal conduction, it is demonstrated that local plasma dynamics and the constraints imposed by boundary conditions are together sufficient to explain the size of the condensation width. In addition the results of a series of numerical calculations are presented which illustrate the characteristic mode structure of sheared-field condensations.

Sparks, L.↗

NASA NTRS1985

Radiative and reconnection instabilities - Compressible and viscous effects

Filaments and flares are prominent indicators of the magnetic fields of solar activity. These instability phenomena arise from the influence of weak transport effects (radiation and resistivity, respectively) on coronal magnetodynamics and energy flow. It has been shown that the filament and flare (tearing or reconnection) mechanisms are resistively coupled in sheared magnetic fields of the kind existing in active regions. The present paper expands this treatment to include the effects of compressibility and viscosity, which are most prominent at short wavelengths. The results show that compressibility affects the radiative mode, including a modest increase of its growth rate, and that viscosity modifies the tearing mode, partially through a decrease of its growth rate. A comprehensive discussion of the mode structures and flows is presented. The strongest effect found is a reversal, at very long wavelengths, of the radiative cooling of the resistive interior layer of the tearing mode, caused by compressional heating.

Tachi, T.↗

NASA NTRS1985

A unified treatment of the filament and flare instabilities

An integrated theory of cooling and resistive reconnection processes in flares and filaments of a sheared magnetic structure is proposed. Thermal and tearing phenomena in the structure were coupled by means of a temperature-dependent Coulomb instability, and the relevant linearized equations were solved numerically over a range of parameters. It is shown that an increase in the growth rate of instabilities in the structure was associated with a significant amount of magnetic reconnection, particularly at shorter wavelengths. Long wavelength reconnection was abetted by an increase in Coulomb resistivity due to the dominance of cooling at the X-point. Some implications of the above results for current models of solar coronal reconnection processes are discussed.

Van Hoven, G.↗

NASA NTRS1984

Nonlinear computations of a solar flare model

A cylindrical axisymmetric tearing mode model for solar flares is investigated numerically. Large magnetic energy release only occurs when there are at least two mode rational surfaces in the current-carrying plasma.

Strauss, H.↗

NASA NTRS1984

The thermal instability in a sheared magnetic field - Filament condensation with anisotropic heat conduction

The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.

Van Hoven, G.↗

NASA NTRS1984

Radiative and reconnection instabilities - Filaments and flares

The way in which the initial development of solar filament radiative cooling and the magnetic reconnection of a solar flare can occur in the center of a field-shear layer is demonstrated. Since the present treatment unites these two mechanisms, it indicates the common as well as the disparate features they possess. Unstable radiation serves to increase the Coulomb resistivity at the X-point, so that the reconnection is not self-quenching. The surprising dominance of the magnetic component of the perturbation in the midwavelength range indicates the need to examine the nonlinear saturation of the energy transport of the radiative mode, taking the accompanying magnetic reconnection and potential-energy release into account, for comparison with observations of filaments as well as for clues to the character of the preflare state.

Van Hoven, G.↗

NASA NTRS1984

Nonlinear evolution of the resistive tearing mode

The nonlinear behavior of the tearing instability is investigated with the aid of numerical solutions of the resistive incompressible magnetohydrodynamic equations. This study is directed toward solar applications, such as flares. Simulations were carried out for values of the Lundquist number S from 100 to 1,000,000 and wavelength parameter alpha from 0.042 to 0.5. The influence of linear conditions, such as the constancy of psi, on nonlinear growth characteristics is investigated. For high S and low alpha, secondary-flow vortices, opposite in direction to the linear vortices, were found to generate a new magnetic island centered at the initial X point. The nonlinear spatial distributions of the physical variables differ greatly from the linear behavior, and growth slows considerably once nonlinear effects become important.

Steinolfson, R. S.↗

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 NTRS1984

Flare precursors and onset

A report on the progress of a search for precursors that have direct physical connections to the start of subsequent solar flares is presented. The discussion includes recent results at radio, visible, ultraviolet, and X-ray wavelengths, which are relevant to the preimpulsive (onset) phase. Relationships between various aspects of a theoretical scenario are also established, based on magnetic reconnection with transport-coefficient phase changes, in order to explain flare onset. The pertinent time scales for preimpulsive temporal developments are discussed.

Van Hoven, G.↗

NASA NTRS1984

Fast spontaneous reconnection by the resistively coupled radiative instability

The thermal and tearing instabilities give rise to the development of filaments and flares in sheared magnetic fields. The coexistence of these physical mechanisms in the case when Coulomb resistivity couples the energy evolution to the plasma dynamics is investigated, and it is found that the analog of the thermal mode, which still develops on the radiative time scale, involves significant magnetic-field reconnection. When compared on the basis of equal magnitudes of nonlinear terms, the fast radiative mode provides some 30 percent of the reconnected magnetic flux associated with the much slower (less than 0.01 in growth rate for solar coronal conditions) tearing mode. This finding opens the possibility for a more rapid initiation of magnetic reconnection, with resulting energy release, than had previously been thought feasible.

Steinolfson, R. S.↗

NASA NTRS1984

The nonlinear tearing mode

A series of nonlinear computations of tearing-mode development have been performed which achieve higher values of the magnetic Reynolds number and larger wavelengths than previously considered. A prime candidate for the realization of dynamic reconnection is the resistive magnetic tearing mode, a spontaneous instability of a stressed magnetic field. Typical simulations are described for a magnetic Lundquist number S of 10 to the 4th and wavelength parameters alpha from 0.05 to 0.5. In all cases, the nonlinear mode initially evolves at the linear growth rate, followed by a period of reduced growth. Another common feature is the formation of secondary flow vortices, near the tearing surface, which are opposite in direction to the initial linear vortices.

Van Hoven, G.↗

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 NTRS1983

The stability of coronal loops - Finite-length and pressure-profile limits

Results are described from a quickly converging, necessary-and-sufficient, MHD-stability test for coronal-loop models. The primary stabilizing influence arises from magnetic line tying at the photosphere, and this end conditions requires a series expansion of possible loop excitations. The stability boundary is shown to quickly approach a limit as the number of terms increases, providing a critical length for the loop in proportion to its transverse magnetic scale. Several models of force-free-field profiles are tested and the stability behavior of a localized current channel, embedded in an external current-free region, is shown to be superior to that of other, broader, current profiles. Pressure-gradient effects, leading to increased or decreased stability, are shown to be amplified by line tying. Long loops must either conduct low net current, or exhibit an axial-field reversal coexisting with a low-pressure core. The limits on stability depend on the magnetic aspect ratio, the plasma-to-magnetic pressure ratio, and the field orientation at the loop edge. Applications of these results to the structure of coronal loops are described.

Einaudi, G.↗

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.↗

NASA NTRS1983

The growth of the tearing mode - Boundary and scaling effects

A numerical model of resistive magnetic tearing is developed in order to verify and relate the results of the principal approximations used in analytic analyses and to investigate the solutions and their growth-rate scalings over a large range of primary parameters which include parametric values applicable to the solar atmosphere. The computations cover the linear behavior for a variety of boundary conditions, emphasizing effects which differentiate magnetic tearing in astrophysical situations from that in laboratory devices. Eigenfunction profiles for long and short wavelengths are computed and the applicability of the 'constant psi' approximation is investigated. The growth rate is computed for values of the magnetic Reynolds number up to a trillion and of the dimensionless wavelength parameter down to 0.001. The analysis predicts significant effects due to differing values of the magnetic Reynolds number.

Steinolfson, R. S.↗

NASA NTRS1982

A boundary-coupled generalization of the Newcomb stability criterion

In magnetohydrodynamic problems in which there are boundaries in the axial or azimuthal symmetry directions, the energy principle involves multiple nonorthogonal trial perturbations. The subsequent Euler-Lagrange coupling of these allowed excitations necessitates a generalization of the Newcomb necessary-and-sufficient stability criterion. This extension, in which the absence of a conjugate point (instead of a simple zero) provides stability, is described in this paper. An important aspect of the proof involves the treatment of certain asymmetries which arise in the presence of the anisotropy caused by the magnetic field. The general method described here has applications to finite-length axial laboratory pinches and to astrophysical plasmas with rooted magnetic fields.

Ray, A.↗

NASA NTRS1982

Hydromagnetic stability of coronal arcade structures The effects of photospheric line tying

A model is given of the magnetic-field equilibrium and possible dynamic excitations of a solar coronal arcade. Such structures are well observed in the spectral range from H-alpha to X-rays and often give rise to two-ribbon flares. However, the preflare state must be stable to ideal magnetohydrodynamic disturbances, and this problem is treated with particular attention to the necessary foot-point boundary conditions. With reasonably general perturbation set, an energy-principle analysis is used to show the strong stabilizing influence of inertial field-line tying at the photosphere.

Ray, A.↗

NASA NTRS1982

The structure, stability and flaring of solar coronal loops

A review is given of recent progress in the theory of the magnetohydrodynamic behavior of coronal loops, beginning with a brief characterization of thy observations. The equilibrium magnetic field is described, along with the consequences of the empirical requirement for short-term, or infinite-conductivity, stability which is shown to be dominated by the end-effect influence of thy quasi-rigid photosphere. A new loop-flare model is then developed, which takes account of the finite loop length. The primary resistive-sausage-mode instability exhibits the necessary threshold behavior, and produces a number of spatially and energetically distinct flare-release manifestations.

Van Hoven, G.↗