Engineering topics

Zweibel, Ellen G.

Publications and source records attributed to Zweibel, Ellen G..

At least 19 records

NASA NTRS1998

Fast Reconnection of Weak Magnetic Fields

Fast magnetic reconnection refers to annihilation or topological rearrangement of magnetic fields on a timescale that is independent (or nearly independent) of the plasma resistivity. The resistivity of astrophysical plasmas is so low that reconnection is of little practical interest unless it is fast. Yet, the theory of fast magnetic reconnection is on uncertain ground, as models must avoid the tendency of magnetic fields to pile up at the reconnection layer, slowing down the flow. In this paper it is shown that these problems can be avoided to some extent if the flow is three dimensional. On the other hand, it is shown that in the limited but important case of incompressible stagnation point flows, every flow will amplify most magnetic fields. Although examples of fast magnetic reconnection abound, a weak, disordered magnetic field embedded in stagnation point flow will in general be amplified, and should eventually modify the flow. These results support recent arguments against the operation of turbulent resistivity in highly conducting fluids.

Zweibel, Ellen G.↗

NASA NTRS1995

Changes in the upper turning point due to magnetism

It was observed that the p-mode power is substantially suppressed in magnetic regions. One possible explanation is that the upper turning point, the acoustic cut-off point of the solar p-modes is lowered in the presence of a magnetic field. A related possibility is that the attenuation length scale in the evanescent region is reduced in the presence of a magnetic field. It is likely that the observations sample a different position in the evanescent tails of the eigenfunctions in magnetic regions because of different temperature structures in these regions. A model is used to quantify the first of these effects.

Jain, Rekha↗

NASA NTRS1995

Is there a seismic signature of the sun's magnetic field?

Both weak magnetic fields and latitudinally dependent acoustic perturbations remove the degeneracy of the azimuthal quantum number, m, of acoustic modes of otherwise spherically symmetrical solar model. In the case of acoustic perturbations, the degeneracy is removed because the range of latitude in which a mode propagates depends on m, and therefore modes of like principle order n and degree l sample the aspherical scalar sound speed distribution differently. In the magnetic case, the removal of the degeneracy is caused by the same geometrical effect, and is influenced by the anisotropy of the Lorentz forces. Asymptotic analysis is used to show that the frequency splittings cannot be unambiguously attributed to the direct effect of a magnetic field, and that the effect of such a field on frequency splittings can be reproduced by a perturbation to the sound speed.

Zweibel, Ellen G.↗

NASA NTRS1995

Driven acoustic oscillations within a vertical magnetic field

The effects of a vertical magnetic field on p-mode frequencies, line widths, and eigenfunctions, are examined. A solar model, consisting of a neutrally stable polytropic interior matched to an isothermal chromosphere, is applied. The p-modes are produced by a spatially distributed driver. The atmosphere is threaded by a constant vertical magnetic field. The frequency shifts due to the vertical magnetic field are found to be much smaller than the shifts caused by horizontal fields of similar strength. A large vertical field of 2000 G produces shifts of several nHz. It is found that the frequency shifts decrease with increasing frequency and increase with field strength. The coupling of the acoustic fast mode to the escaping slow modes is inefficient. Constant vertical magnetic field models are therefore incapable of explaining the high level of absorption observed in sunspots and plage.

Hindman, Bradley W.↗

NASA NTRS1995

Magnetic merging in colliding flux tubes

We develop an analytical theory of reconnection between colliding, twisted magnetic flux tubes. Our analysis is restricted to direct collisions between parallel tubes and is based on the collision dynamics worked out by Bogdan (1984). We show that there is a range of collision velocities for which neutral point reconnection of the Parker-Sweet type can occur, and a smaller range for which reconnection leads to coalescence. Mean velocities within the solar convection zone are probably significantly greater than the upper limit for coalescence. This suggests that the majority of flux tube collisions do not result in merging, unless the frictional coupling of the tubes to the background flow is extremely strong.

Zweibel, Ellen G.↗

NASA NTRS1995

Equiparatition of energy for turbulent astrophysical fluids: Accounting for the unseen energy in molecular clouds

Molecular clouds are observed to be partially supported by turbulent pressure. The kinetic energy of the turbulence is directly measurable, but the potential energy, which consists of magnetic, thermal, and gravitational potential energy, is largly unseen. We have extended previous results on equipartition between kinetic and potential energy to show that it is likely to be a very good approximation in molecular clouds. We have used two separate approaches to demonstrate this result: For small-amplitude perturbations of a static equilibrium, we have used the energy principle analysis of Bernstein et al. (1958); this derivation applies to perturbations of arbitary wavelength. To treat perturbations of a nonstatic equilibrium, we have used the Lagrangian analysis of Dewar (1970); this analysis applies only to short-wavelength perturbations. Both analysis assume conservation of energy. Wave damping has only a small effect on equipartition if the wave frequency is small compared to the neutral-ion collision frequency; for the particular case we considered, radiative losses have no effect on equipartition. These results are then incorporated in a simple way into analyses of cloud equilibrium and global stability. We discuss the effect of Alfvenic turbulence on the Jeans mass and show that it has little effect on the magnetic critical mass.

Zweibel, Ellen G.↗

NASA NTRS1994

The effects of a hot outer atmosphere on acoustic-gravity waves

We examine the effects of a hot chromosphere and corona on acoustic-gravity waves in the Sun. We use a simple solar model consisting of a neutrally stable polytrope smoothly matched to an isothermal chromosphere or corona. The temperature of the isothermal region is higher than the minimum temperature of the model. We ignore sphericity, magnetic fields, changes in the gravitational potential, and nonadiabatic effects. We find a family of atmospheric g-modes whose cavity is formed by the extremum in the buoyancy frequency at the transition region. The f-mode is the zero-order member of this family. For large values of the harmonic degree l, f-mode frequencies are below the classic f-mode frequency, mu=(gk)(exp 1/2), whereas at small values of l, the f-mode is identical to the classical f-mode solution. We also find a family of g-modes residing in the low chromosphere. Frequency shifts of p-modes can be positive or negative. When the frequency is less than the acoustic cutoff frequency of the upper isothermal atmsophere, the frequency of the upper isothermal atmosphere, the frequency shift is negative, but when the frequency is above this cutoff, the shifts can be positive. High-frequency acoustic waves which are not reflected by the photospheric cutoff are reflected at the corona by the high sound speed for moderate values of l and v. This result is independent of the solar model as long as the corona is very hot. The data are inconsistent with this result, and reasons for this discrepancy are discussed.

Hindman, Bradley W.↗

NASA NTRS1994

Shock propagation and the generation of magnetohydrodynamic wave fields in inhomogeneous molecular clouds

We develop a simple one-dimensional model for the interaction of a steady, thin, planar shock wave with a nonrigid cloud which may be in motion relative to the surrounding medium, and we apply the model to shocks impinging on, and propagating through, molecular clouds. Both 'adiabatic' (gamma = 5/3) and radiative (gamma = 1) shocks are considered and we allow for the presence of a uniform magnetic field directed either parallel or perpendicular to the shock normal. The former field orientation is equivalent to the hydrodynamic case, and the latter involves only fast MHD shocks. We focus on the manner in which such shocks can generate internal kinetic motions in the cloud on a range of size and density scales through the direct acceleration of cores and clumps by shocks transmitted into them and through the generation of an MHD wavefield via the reflection of the incident shock at clump boundaries. We find that stronger incident Mach numbers and smaller density contrasts lead to more efficient cloud acceleration, as do isothermal intercloud shocks and small intercloud magnetic field strengths. The acceleration efficiency is insensitive to the adiabatic index and the magnetic field strength in the cloud itself. For typical parameter choices, the direct acceleration of clouds and clumps by strong shocks is found to be substantial and could at least in part account for their observed velocity dispersions. If the shocks are moderately weak, the final velocity of the cloud is linearly related to its initial velocity, with higher acceleration giving shallower slopes (i.e., final velocity distributions which are less sensitive to the initial distribution). Compared to the kinetic energy of the postshock cloud, the energy given to the wavefield at each encounter is small, and the heating of the interclump medium by the dissipation of this wavefield is found to be insufficient to balance the cooling rate in the cloud as a whole (although it may be important in particular regions), even if this medium is warm, unless it is also extremely tenuous (n approximately less than 0.1/cu cm). Nevertheless, the correction for the velocity imparted to the cloud leads to a substantial increase in the critical incident Mach numner for wave emission over that reported by Spitzer for the rigid case. The implications of our model for shock-induced star formation are discussed briefly.

Miesch, Mark S.↗

NASA NTRS1994

Acoustic instability driven by cosmic-ray streaming

We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.

Begelman, Mitchell C.↗

NASA NTRS1994

The formation of sharp structures by ambipolar diffusion

The effect of ambipolar diffusion is investigated using simple numerical models. Examples are shown where sharp structures develop around magnetic nulls. In contrast to the case of ordinary diffusion, the magnetic field topology is conserved by ambipolar diffusion. This is demonstrated in an example where differential rotation winds up an initially uniform magnetic field and brings oppositely oriented field lines close together. It is argued that ambipolar diffusion produces structures of scales small enough for reconnection to occur.

Brandenburg, Axel↗

NASA NTRS1993

Magnetic fields in star-forming regions - Observations

We review the observational aspects of magnetic fields in dense, star-forming regions. First we discuss ways to observe the field. These include direct methods, which consist of the measurement of both linear and circular polarization of spectral line and continuum radiation; and indirect methods, consisting of the angular distribution of H2O masers on the sky and the measurement of ambipolar diffusion. Next we discuss selected observational results, focusing on detailed discussions of a small number of points rather than a generalized discussion that covers the waterfront. We discuss the Orion/BN-KL region in detail, both on the small and large scales. Next we discuss the derivation of the complete magnetic vector, including both the systematic and fluctuating component, from a large sample of Zeeman and linear polarization measurements for the L204 dark cloud. We examine the virial theorem as it applies to dark clouds in general and one dark cloud, Barnard 1, in particular. We critically discuss the numerous claims for alignment of cloud structural features with the plane-of-the-sky component of the magnetic field, and find that many of these have not been definitively established.

Heiles, Carl↗

NASA NTRS1992

On the virial theorem for turbulent molecular clouds

An Eulerian, rather than Lagrangian, form of the virial theorem is derived for a turbulent, magnetized cloud embedded in a steady, turbulent, low-density intercloud medium. The role of turbulent pressure in cloud confinement is clarified, and it is shown that, in the absence of a magnetic field, a cloud can be at a somewhat lower pressure than the intercloud medium. Simple forms for the magnetic term in the virial equation are obtained. Radiation pressure is considered; its effects are relatively small under average conditions in the interstellar medium. Under typical conditions, external pressure and magnetic fields are shown to have a relatively small effect on virial estimates of the mass of self-gravitating clouds.

Mckee, Christopher F.↗

NASA NTRS1991

Magnetized supernova remnants with cosmic rays

The effects of interstellar magnetic fields and cosmic rays on the dynamics of an SNR expanding into a warm H I gas are examined. As long as the shock wave driven by the SN explosion propagates faster than 110 km/s, the vicinity of the shock front is fully ionized, and cosmic rays are well coupled to the thermal fluid. They are first accelerated at the adiabatic front, and further compressed in the postshock cooling zone. When the shock velocity drops below 110 km/s, ion-neutral collisions in the vicinity of the shock dissipate the waves which couple cosmic rays to the thermal gas, and impede cosmic-ray acceleration. It is found that magnetic and cosmic-ray pressures together dominate over thermal pressure away from the magnetic poles. As a result, most of the shell becomes considerably thicker, and the shock wave propagates somewhat faster than in the nonmagnetic case. At late times, the transverse mass motions which take place from the poles to the equator create H I holes at the polar caps. This theory leads to a simple interpretation of the 'barrel-shaped' distribution of radio emission observed in some SNRs.

Ferriere, Katia M.↗

NASA NTRS1991

Cosmic-ray heating of cooling flows - A critical analysis

It is shown that a combination of MHD wave-mediated cosmic ray heating and thermal conduction could balance cooling in intracluster media and substantially reduce the rate of inflow. The appropriate system of steady state equations is solved, including a new self-consistent formulation for the cosmic-ray diffusivity. Models which can produce substantial positive temperature gradients in static configurations are found when conduction is reduced by a factor of 10 or more. These models have too-flat thermal pressure profiles compared with observations. It is found that cosmic-ray heating is unlikely either to stabilize positive density perturbations against condensation or to contribute appreciably to the powering of the optical filaments.

Loewenstein, Michael↗

NASA NTRS1991

Evolution to nonequilibrium in simple models of prominence filaments

The support of cold plasma against gravity by a line-tied magnetic field is considered. The normal component of the field at the boundaries, the mass/unit flux, and the magnetic shear are all specified. Fixing the first two of these quantities, and varying the third leads to evolutionary sequences. When the magnetic shear is less than a critical value, an infinite number of solutions exist. When the magnetic shear is sufficiently large, there are no solutions with the desired topology. These results support the idea that prominences erupt as a result of evolution to magnetic nonequilibrium.

Zweibel, Ellen G.↗

NASA NTRS1991

Expansion of a superbubble in a uniform magnetic field

The effects of interstellar magnetic fields on the evolution and structure of superbubbles are investigated. First, the governing equations for propagation of a radiative shock are derived and solved analytically in the limit of high expansion velocity. A numerical code able to solve them in the general case and discuss the numerical results is then presented. It is found that magnetic fields of the strength present in the Galactic disk do not significantly modify the overall shape and dimensions of a superbubble. They reduce the volume of the interior cavity by one-third on average during the expansion phase. The shell elongates slightly in the direction of the external field. Magnetic pressure dominates over gas pressure in most of the shell and forces it to thicken substantially. Finally, because of the transverse mass motions which take place from the magnetic poles to the equator, the column density at the poles is reduced by typically a factor of 10.

Ferriere, Katia M.↗

NASA NTRS1990

Electron acceleration by magnetosonic waves in solar flares

Results of a simulation of electron acceleration by magnetosonic waves in a solar coronal loop are presented. The dependence of the energization rate on the strength and shape of the wave spectrum is discussed. Comparisons are made with the predictions of quasilinear theory and of a model describing stochastic acceleration by waves as isotropic diffusion in momentum space.

Zweibel, Ellen G.↗

NASA NTRS1990

Evolution of a superbubble blastwave in a magnetized medium

Researchers investigate the effects of interstellar magnetic fields on the evolution and structure of interstellar superbubbles, using both analytic and numerical magnetohydrodynamic (MHD) calculations. These cavities of hot gas, surrounded by shells of cold dense material preceded by a shock wave result from the combined action of stellar winds and supernova explosions in OB associations. If the medium in which a superbubble goes off is homogeneous and unmagnetized, the blast wave expands isotropically. As the interstellar gas flows through the shock, it cools significantly and gets strongly compressed such that thermal pressure remains approximately equal to ram pressure. Hence, the swept up material is confined to a very thin shell. However, if the ambient medium is permeated by a uniform magnetic field B sub o approx. 3 mu G (typical value for the interstellar matter (ISM)), the configuration loses its spherical symmetry, and, due to magnetic pressure, the shell of swept up material does not remain thin. Researchers found the following qualitative differences: (1) Except in the immediate vicinity of the magnetic poles, the shell is supported by magnetic pressure. (2) The refraction of field lines at the shock and the thermal pressure gradient along the shell both contribute to accelerating the gas toward the equator. The resulting mass flux considerably decreases the column density at the magnetic poles. (3) Away from the poles, magnetic tension in the shell causes the field lines (particularly the inner boundary) to elongate in the direction of B sub o. In contrast, the shock wave radius increases with increasing theta. (4) The reduced inertia of a parcel in the polar neighborhood makes it easier to decelerate, and accounts for the dimple which appears at the poles in numerical simulations. This dimple also results from the necessity to call on intermediate shocks in order to insure a smooth transition between a purely thermal shock at the poles and a magnetic shock in the rest of the shell. (5) The shock wave propagates faster than in the absence of magnetic field, except near the poles where the reduced mass of the shell allows it to be more efficiently decelerated.

Ferriere, Katia M.↗