Engineering topics

Steinolfson, R. S.

Publications and source records attributed to Steinolfson, R. S..

At least 55 records · Page 3

NASA NTRS1985

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Steinolfson, R. S.↗

NASA NTRS1985

Study of the formation, evolution, and decay of shocks in the heliosphere between 0.5 and 30.0 AU

The spatial and temporal evolution of corotating interaction regions is examined between 0.5 and 30 AU using a solar-wind simulation with a continuous sinusoidally varying velocity, density, and temperature input pulse train. The well-known formation of forward-reverse MHD shock ensembles is followed by their interaction, which results in a highly nonlinear 'pressure' wave that eventually reforms into a new but more irregular set of forward-reverse shock pairs. As a result of these compound interactions, the overall temperature decays much more slowly than the classical steady-state adiabatic radial dependency of R BXP -4/3.

Smith, Z. K.↗

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 NTRS1984

Thermal ripples in a resistive and radiative instability

The development of the resistive tearing instability in the case of sheared magnetic fields is considered, taking into account also the occurrence of a radiatively driven thermal instability. It is pointed out that thermal conduction has generally been neglected in theories similar to those discussed. The present investigation is concerned with a consideration of both parallel and perpendicular thermal conduction, in addition to finite resistivity and radiative loss. Attention is given to the equations and the model, the spatial singularity which arises with consideration of only the parallel heat conduction, the removal of this singularity and the formation of temperature oscillations (thermal ripples) by inclusion of the perpendicular heat-flux component, and details regarding the numerical procedure. A brief explanation is provided of the conditions required for the oscillations, and potential implications of the results with respect to the solar flare are discussed.

Steinolfson, R. S.↗

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

Resonant absorption of phase-mixed Alfven surface waves in ideal and resistive magnetohydrodynamics - Initial-value problem

An initial-value approach to the study of Alfven surface waves, in which the linearized MHD equations are solved numerically in time and space, is considered. A disturbance of a particular wavelength is excited in a nonuniform plasma and its temporal evolution is simulated with numerical solutions of the ideal and resistive MHD equations in slab geometry. This procedure generates a continuous spectrum and therefore simulates phase-mixing and subsequent resonant absorption. Energy in the phase-mixed surface waves resistively dissipates with the absorption time and width scaling as resistivity to the -1/3 and 1/6 powers, respectively.

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

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

Modeling of transient disturbances in coronal-streamer configurations

Numerical simulations of the formation and propagation of mass ejection, loop transients in coronal streamers are discussed. The simulations are accomplished with numerical solutions of the single fluid, ideal MHD equations of motion in the meridional plane. The streamer is produced by simulating the relaxation of an initially radial hydrodynamic flow coupled with a dipole magnetic field. The simulated transient then results from an energy release at the base of the streamer. The legs of the loop transient produced remain essentially stationary while the loop expands mainly in the radial direction with velocities of 400 to 750 km s-1. Once the leading edge of the transient has passed out of the lower corona, the initial streamer configuration is restored after 15 to 24 hours. A second energy release 2 hours later than, and with an energy release identical to, the first does not produce a significant coronal disturbance.

Steinolfson, R. S.↗

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

Energetics and the resistive tearing mode - Effects of Joule heating and radiation

The contribution of energy flux to the dynamics of magnetic field reconnection is analytically studied in order to determine the influence of Joule heating and radiation on the linear development of the tearing instability in slab geometry. A temperature-dependent Coulomb-like resistivity is used to provide the coupling between the dynamics and the energy equation. Analytical expressions are derived for the growth rates utilizing constant-psi and long-wavelength approximations. The solutions indicate the occurrence of several modes in addition to the usual tearing mode, several of which have relatively slow, complex growth rates. At large values of the magnetic Reynolds number, there are at least two modes with purely exponential growth when the radiative loss decreases with increasing temperature. If the radiation is neglected, the Joule heating alone also results in two modes with real, positive growth at large S. Below a particular value of S, all the modes are generally stabilized.

Steinolfson, R. S.↗

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

Closed and open magnetic fields in stellar winds

A numerical study of the interaction between a thermal wind and a global dipole field in the sun and in a giant star is reported. In order for closed field lines to persist near the equator (where a helmet-streamer-like configuration appears), the coronal temperature must be less than a critical value Tc, which scales as M/R. This condition is found to be equivalent to the following: for a static helmet streamer to persist, the sonic point above the helmet must not approach closer to the star than 2.2-2.6 stellar radii. Implications for rapid mass loss and X-ray emission from cool giants are pointed out. The results strengthen the case for identifying empirical dividing lines in the H-R diagram with a magnetic topology transition locus (MTTL). Support for the MTTL concept is also provided by considerations of the breakdown of magnetostatic equilibrium.

Mullan, D. J.↗

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

The steady global corona

The formation of the steady coronal structure which consists of coronal streamers and holes is seen in terms of a model employing numerical solutions of time-dependent, dissipationless, magnetohydrodynamic equations of motion applicable to the meridional plane. A coronal streamer consists of closed magnetic field lines near the solar surface with overlying and adjacent open field lines, and the atmosphere, which is stationary in the closed region, flows outward in the open region, or coronal hole. The steady coronal structure is obtained by starting the numerical calculation with a state comprising a polytropic, hydrodynamical solution to the steady-state radial equation of motion coupled with a dipole magnetic field. Global coronal configurations are calculated for values of the plasma beta which vary from 0.1 to 100. It is found that the height and lateral extension of the closed region are only weakly dependent on the data.

Steinolfson, R. S.↗

NASA NTRS1981

Magnetohydrodynamic models of coronal transients in the meridional plane. IV - Effect of the solar wind

A two-dimensional, time-dependent magnetohydrodynamic model in the meridional plane with and without an ambient solar wind in an ambient radial magnetic field has been used to investigate mass motions associated with coronal transients. It is shown that the solar wind does not significantly affect the general dynamic characteristics of the mass motion. The ambient solar wind, however, increases the velocity of the mass motion and produces a moderate change in the thermodynamic properties of the coronal plasma.

Wu, S. T.↗