Showing papers on "Magnetic flux published in 1983"

Steepest‐descent moment method for three‐dimensional magnetohydrodynamic equilibria

Abstract: An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representation x=x(ρ, θ, ζ). Here, θ are ζ are poloidal and toroidal flux coordinate angles, respectively, and p=p(ρ) labels a magnetic surface. Ordinary differential equations in ρ are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition of x. A steepest‐descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive‐definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter λ is introduced to ensure the rapid convergence of the Fourier series for x, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self‐consistent value for λ.

Magnetic Neutral Sheets in Evolving Fields - Part Two - Formation of the Solar Corona

Abstract: It is shown in the previous paper that whenever twisted flux tubes are bundled together, they are subject to dynamical nonequilibrium and internal neutral point reconnection, causing rapid dissipation of their torsion. In the present paper we explore the consequences of this general dynamical dissipation in the magnetic fields that produce the active corona of the Sun. The footpoints of the field are continually manipulated by the subphotospheric convection, so that the lines of force are continually wrapped and rotated about each other. The dynamical dissipation of the wrapping and rotation transfers the work done on the footpoints directly into heat in the corona, at a rate estimated to be of the order of 10/sup 7/ ergs cm/sup -2/ s/sup -1/. The effect appears to be the principal source of heat to the visible corona. This general picture implies that all magnetic fields extending outward from convecting astronomical bodies produce intense heating of the tenuous outer atmospheres of these bodies, in general agreement with the observed fact of the universal activity of stars and galaxies.

Centrifugally driven winds from contracting molecular disks

Abstract: We suggest that bipolar outflows in dense molecular clouds associated with young stellar objects are steady, centrifugally driven, hydromagnetic winds that arise from molecular disks (on scales < or =10/sup 16/ cm) in which the infrared source(s) embedded. A disk of mass approx.100 M/sub sun/ and rotational speed of approx.10/sup 6/ cm s/sup -1/ provides a resevoir of 10/sup 47/ ergs, which could power the most energetic outflows observed. Acceleration to supersonic speeds is accomplished by the magnetic field embedded in the disk (paralllel rotational and magnetic axes) and extending outward beyond the wind region to join the galactic field. The wind carries angular momentum and energy from the disk out to large distances. Our analysis treats the problem of magnetic braking and energy transport in a partially ionized (two-fluid) wind. The basic parameter which is shown to govern the flow is the coupling parameter ..beta.. = T/sub n/-i/T/sub n/, the ratio of the characteristic neutral-ion collision time to flow time. A general analysis of angular momentum and energy transport is given, and the wind equation is solved along flux tubes in the strongly coupled (..beta..<<1) limit. The centrifugally driven wind forms when an embedded protostar begins to ionize themore » disk core region. A disk envelope forms at the wind base at a pressure which adjusts to the wind requirements. Envelope heating may be maintained by magnetic flux loss from the dense core (which has a field approx.10/sup -3/ gauss) that is preferentially along the rotation axis for flattened disks. The structure of the field at the disk core surface is derived. The observational implications are discussed; in particular, we emphasize that such molecular disks with double profiles should be observed.« less

Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona

Abstract: The problem of the hydrostatic equilibrium of a large-scale magnetic field embedded in a fluid with infinite electrical conductivity is considered. It is pointed out that a necessary condition for static equilibrium is the invariance of the small-scale pattern in the field along the large-scale direction. A varying topological pattern implies that no fluid pressure distribution exists for which the field is everywhere static. Magnetic neutral sheets form, and dynamical reconnection of the field takes place. It is shown here that the invariance is also a sufficient condition for the existence of a fluid pressure distribution producing static equilibrium. Even in the simplest cases, however, the requirements on the fluid pressure are extreme and, a priori, are unlikely. It is concluded that almost all twisted flux tubes packed together produce dynamical nonequilibrium and dissipation of their twisting. This is the basic effect underlying the long-standing conjecture that the shuffling of the footpoints of the bipolar magnetic fields in the sun is responsible for heating the active corona. Attention is then given to the consequences of this general dynamical dissipation in the magnetic fields that produce the active corona of the sun. The footpoints of the field are continually manipulated by the subphotospheric convection in such a way that the lines of force are continually wrapped and rotated about one another.

Combined position sensor and magnetic motor or bearing

Abstract: A combined magnetic sensor and actuator device for applying a magnetic force to a magnetizable body and for sensing the distance between the device and the magnetizable body. The device includes a magnetizable pole piece separated from the magnetizable body by gaps. The pole piece, gaps, and magnetizable body form a magnetic circuit with the gaps preferably being the major reluctance of the circuit. Separate means are provided for generating a relatively large time-varying magnetic actuating flux in the magnetic circuit and for generating a relatively small time-varying magnetic sensing flux in the magnetic circuit. Each magnetic flux follows a flux path, such that the two flux paths have at least a portion in common. Detection means measure the relatively small magnetic flux in the magnetic circuit, and thereby measure the distance between the device and the magnetizable body.

The equilibrium and stability of rotating plasmas

Abstract: In a rotating equilibrium state, the velocity and magnetic fields are shown to share the same flux surfaces. A simplified derivation is given of a second‐order (not necessarily elliptic) partial differential equation which determines axisymmetric equilibrium states. For general configurations, equations on flux surfaces which determine the Alfven and cusp continuous spectrum are derived and the stability investigated. These equations are written without the use of any particular coordinate system. Similar equations yield a sufficient condition for global stability of axisymmetric equilibria if the flow is parallel to the magnetic field up to a rigid rotation of the plasma. This condition is also necessary for stability in a mirror configuration with no toroidal field and a pure rigid rotation.

A Method of Including the Effects of Main Flux Path Saturation in the Generalized Equations of A.C. Machines

Abstract: This paper shows how the effects of saturation of the main flux path can be incorporated in the generalized equations of alternating current machines in which the currents are deliberately chosen as the state variables. In the conventional equations linear magnetic conditions are assumed and the forms taken by these equations in various reference frames are well known. When saturation of the main flux path is taken into account, some parameters have to be modified and additional terms introduced; stator (and rotor) self inductances in orthogonal axes are no longer equal. These are the consequence of intersaturation - sometimes called cross-saturation; a phenomenon which has been mentioned in the literature but has not been subjected to general analysis. New forms of generalized equations are derived and their application to the analysis of induction motor starting transients described.

Magnetic flux tubes on the Sun

Abstract: Magnetic fields are the cause of almost all forms of solar activity. Near the solar surface, and possibly in the entire convection zone, these fields occur in the form of isolated flux tubes. In recent years, new views have been developed (and older ones revived) in which this property plays a central role. Here we review these ideas, dealing with the nature of the solar cycle, sunspot structure, the origin of spicules and the source of mechanical heating in the solar atmosphere. The ideas are illustrated with the aid of a simple mathematical model for the behaviour of thin magnetic flux tubes. The properties of inhomogeneities in the corona (coronal loops) are also discussed.

Sawteeth, magnetic disturbances, and magnetic flux regeneration in the reversed-field pinch

Abstract: A comparison of experimental data and theoretical results is presented that may help to explain the underlying causes of the flux regeneration mechanism (‘‘dynamo’’) in the reversed‐field pinch (RFP). Discrete events are seen on many diagnostic measurements which are coincident with observable increases in toroidal magnetic flux in discharges where the pinch parameter θ (θ≡Bθwall/〈Bφ〉) exceeds the value 1.6. By observing the relative timing and the θ dependence of these events as the discharge is returned to lower values of θ, a case may be made for associating the m=1 tearing mode with the RFP dynamo.

Magnetic flux ropes in the Venus ionosphere: Observations and models

Abstract: Pioneer Venus Orbiter data are used as evidence of naturally occurring magnetic field filamentary structures which can be described by a flux rope model. The solar wind is interpreted as piling up a magnetic field on the Venus ionosphere, with the incident ram pressure being expressed as magnetic field pressure. Currents flowing at the ionopause shield out the field, allowing magnetic excursions to be observed with magnitudes of tens of nT over an interval of a few seconds. A quantitative assessment is made of the signature expected from a flux rope. It is noted that each excursion of the magnetic field detected by the Orbiter magnetometer was correlated with variations in the three components of the field. A coordinate system is devised which shows that the Venus data is indicative of the presence of flux ropes whose parameters are the coordinates of the system and would yield the excursions observed in the spacecraft crossings of the fields.

Investigations of the magnetic structure and the decay of a plasma‐gun‐generated compact torus

Abstract: The results of a series of experimental measurements of compact toroidal (CT) plasmas produced by a magnetized coaxial plasma gun injecting into a flux‐conserving metallic liner are reported. The experiments were performed on the Beta II facility at Lawrence Livermore National Laboratory. The magnetic equilibria are well described by a force‐free eigenmode structure that results from an extension of Taylor’s theory of the reversed‐field pinch. Consideration of helicity conservation during relaxation of the composite plasma‐gun flux‐conserver system to the final state equilibrium yields theoretical expressions that are compared with the experiment. In particular the CT poloidal flux (ψpol) and the overall electrical efficiency for producing the CT are predicted to be functions of the plasma gun inner‐electrode flux (ψgun) and the volt‐seconds input to the gun discharge (∫∞0 V dt). Away from a cutoff at too low values of ∫∞0 V dt or too high values, ψgun ,ψpol scales linearly with the square root of the product of ψgun and ∫∞0 V dt, whereas the electrical efficiency equals about 13% for ∫∞0 V dt/ψgun ≊10. For an electrical energy input Win =45 kJ, CT’s are produced with poloidal plus toroidal field energy up to WB =8 kJ and toroidal plasma current Itor =330 kA. The chord‐averaged plasma density is 2–4×1014 cm−3, and the plasma volume equals 150 liters. The radius of the flux conserver is 37.5 cm, and the axial length is 40 cm. If a bias flux ψb is superimposed on the flux conserver, n=1 tilting is observed when ψb/ψpol exceeds a ratio of about 0.20 to 0.25. Impurity radiation measured by a pyroelectric detector accounts for all of the plasma magnetic energy if uniform volume emission of radiation is assumed. The dominant impurities observed are carbon and oxygen. Helium‐like lines are not observed, indicating that the plasma has not ‘‘burned through’’ the low electron temperature radiation maxima. The experimentally observed decay times (defined by the e‐folding time of plasma magnetic fields) are 80 to 160 μsec—consistent with Zeff =2 and Te in the range 5–10 eV if classical resistivity is assumed. A zero‐dimensional rate equation model of impurity radiation loss gives a reasonably good account of the experimental observations and predicts that the carbon concentration must be reduced to the level of a few percent to allow burnthrough of the low‐Te carbon radiation barrier. Glow discharge cleaning of the gun electrodes and flux conserver resulted in a 20% increase of the e‐folding time of plasma magnetic fields (from an average value 115 to 140 μsec). The CT plasma density was observed to scale linearly with the electrical energy input to the gun discharge and to be only weakly dependent on the filling pressure and timing of pulsed deuterium gas valves. It seems likely that further improvements in increasing plasma lifetime can be made by improving the vacuum conditions and discharge cleaning methods and experimenting with the gun electrode materials.

Planar magnetron sputtering device

Abstract: A planar magnetron sputtering device having a movable magnetic source which is hydraulically moved with respect to a target and substrate to cause lines magnetic flux parallel to the surface of the target to sweep over the surface of the target during the sputtering process.

Steepest descent moment method for three-dimensional magnetohydrodynamic equilibria

Abstract: An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representation x=x(ρ, θ, ζ). Here, θ are ζ are poloidal and toroidal flux coordinate angles, respectively, and p=p(ρ) labels a magnetic surface. Ordinary differential equations in ρ are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition of x. A steepest‐descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive‐definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter λ is introduced to ensure the rapid convergence of the Fourier series for x, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self‐consistent value for λ.

Magnetic reconnection driven by the coalescence instability

Abstract: A detailed study of magnetic reconnection at an X point driven by the coalescence instability is presented. In particular, the effects of plasma compressibility and the magnitude of the toroidal field on the rate of reconnection are explored. For large toroidal fields, the plasma is almost incompressible and the destruction of magnetic flux proceeds linearly with time. However, when the attractive force between two neighboring islands is strong, and when the poloidal and the toroidal fields are comparable in magnitude, the reconnection rate is found to be faster. Implications for the steady‐state models of magnetic reconnection are discussed.

Observation of recorded magnetization pattern by electron holography

Abstract: Electron holography was employed for experiments involving a high‐density magnetic recording, in which it was possible to directly observe streams of magnetic flux. The magnetic flux distribution in recorded films, and the maximum packing density in high‐coercivity evaporated cobalt film were investigated. With magnetic longitudinal recording the resultant highest density was 170 000 bits per inch. This experiment has proven that electron holography is useful for the study of magnetic recording.

Doubly diffusive magnetic buoyancy instability in the solar interior

Abstract: An investigation of the buoyancy of diffuse magnetic fields has shown that in the presence of rotation, static equilibrium configurations of the toroidal magnetic field and ambient plasma can exist In that case, the escape of toroidal magnetic flux from the solar interior may be determined by the growth of instabilities which the equilibrium configuration may be subject to In connection with the present investigation, it is assumed that in the region of toroidal magnetic flux amplification, the magnetic field has not as yet filamented into flux ropes, and is therefore 'diffuse' A study is conducted of the MHD stability of an electrically conducting and differentially rotating gas in the presence of a toroidal magnetic field, an external constant gravitational field, and radiance pressure The full dispersion relation for the magnetic buoyancy problem is developed, and the solutions of the dispersion relation are discussed

Sensing system for measuring a parameter

Abstract: A parameter, such as the current flowing through a conductor, is measured by initially passing an energizing magnetic flux through a hall element to produce a hall voltage proportional to the sensed parameter. To eliminate temperature, aging and non-linear effects normally associated with a hall element, the amplitude of the hall voltage is effectively ignored and only its polarity is detected and employed to control the operation of an integrator to develop a cancelling current to establish an equal, but opposite direction, cancelling flux in the hall element. With a zero net flux, the integrator will hold the cancelling current at the level required to balance out and cancel the initial energizing flux. Since the cancelling current needed to null the energizing flux will be proportional to that flux, the current may be used to produce a control voltage to represent the measured parameter.

Sources of acoustic emission in superconducting magnets

Abstract: Origins of acoustic emission (AE) in superconducting wires have been investigated. Our experimental results indicate that wire motion is a dominant source of AE in current‐carrying wires, both superconducting and nonsuperconducting. Furthermore, the results show that flux motion, except during flux jumping, produces no discernable acoustic signals. Both of these conclusions differ from the conclusions of earlier AE results which attributed the major source of AE signals in superconductors and superconducting magnets to flux motion. A simple model based on frictional sliding of conductor is presented to interpret acoustic data; agreement between theory and experiment is good.

Finite‐Larmor‐radius magnetohydrodynamic equations for microturbulence

Abstract: A set of nonlinear fluid equations which includes the effect of finite ion Larmor radius is derived to describe microturbulence [k⊥ ρs ≂O(1), k∥R≂O(1), n1/n0≂ ρs/Ln, and B1/B0≂ρs/R ] in an inhomogeneous plasma with a strong magnetic field of general geometry. Here ρs is the ion Larmor radius at the electron temperature, Ln is the density gradient scale length, R is the radius of curvature of the magnetic line of force, k is the wave vector, and n1/n0 and B1/B0 are relative levels of density and magnetic field perturbations.

Permanent magnet rotary dynamo electric machine

Abstract: A permanent magnet rotary dynamo electric machine wherein each permanent magnet pole (13) is equipped with a flux shunt (18) which provides a direct flux path between the airgap at the strong tip region of the pole and the iron circuit (12) upon which the pole is supported, the direct flux path shunting magnetic flux to the iron circuit when the current in the associated windings is low, but being saturated by flux flowing in the opposite direction at high values of winding current.

Moat-guarded Josephson SQUIDs

Abstract: We report experimental investigations of a simple structure, called a moat, which significantly reduces the probability of flux-trapping in Josephson SQUIDs. Proper operation of Josephson logic and memory circuits requires that the SQUIDs be free of stray magnetic flux that may become trapped in the superconducting groundplane upon cooling through the critical temperature. The problem is particularly severe for so-called holey SQUIDs which rely on holes in the groundplane to obtain suitably large device inductances. Moats are rectangular channels in the groundplane surrounding the SQUID's which provide preferred sites for trapping flux, thus preventing such flux from coupling to the SQUID. We have measured the effectiveness of moats by monitoring the flux trapped in the moats and comparing it to the flux trapped in the associated SQUID as a function of applied field. The number of flux quanta in the moat is determined by measuring the shift of the threshold curve of a two-junction SQUID coupled to the moat. The data indicates that at fields on the order of a mG, moats reduce the sensitivity of holey SQUIDs to trapped flux by at least several orders of magnitude. As the chips are cooled through T c , transient magnetic fields are produced in the metallic sample holder parts surrounding the chip by thermal-gradient-induced EMF's. The effects of such magnetic fields on the flux trapping behaviour of the SQUIDs are also reported.

A model of anisotropic grain-oriented steel

Abstract: In this work the magnetic flux distribution in the grain-oriented steel core transformer is investigated with the finite element method. A mathematical model (Model II) is obtained for the reluctivity tensor. The model, optimized by means of experimental values of the B-H curve, predicts different directions of the magnetization field, not just along the rolling and transverse directions of the material. The results are the flux maps, as well as the reactance values and the electrodynamic forces on the windings. These results, obtained by means of the isotropic model and the anisotropic first model [1], are compared with the experimental ones.

Dynamics and spectroscopy of asymmetrically heated coronal loops

Abstract: We investigate numerical models of steady flows along coronal magnetic flux tubes of varying cross sectional area. The flows are induced by altering the spatial symmetry of the heating. In two cases the flux tube geometry is symmetric about the top of the loop, but the spatial dependence of the heating rate is changed from a symmetric deposition which supports a stationary equilibrium to a time-independent asymmetric deposition. In a third case the volumetric heating rate is uniform, but one half of the loop is larger in volume that the other. The resulting velocity structure varies significantly with changes in the flux tube geometry. Calculations of the ionization balance and line emission for a number of ionization states of oxygen suggest that heating induced flows may be responsible for the redshifts seen in spectral lines formed in the network at transition region temperatures.

Magnetic field line reconnection experiments 5. Current disruptions and double layers

Abstract: An investigation is conducted of the stability of a large laboratory plasma current sheet, which has been generated in the process of magnetic field line reconnection, with respect to local current increases. Magnetic flux variations in regions remote from the current sheet generate an inductive voltage in the current loop that drops off inside the plasma in the form of a potential double layer, leading to particle acceleration with velocities much larger than those expected from the steady state electric fields in the plasma. A model for the mechanism of the current disruptions is formulated in which the potential structure leads to ion expulsion, creating a localized density drop. The associated current drop in an inductive circuit drives the potential structure, providing feedback for the disruptive instability. Similarities to, and differences from, magnetospheric substorm phenomena are noted.

Induced mass and wave motions in the lower solar atmosphere. I. Effects of shear motion of flux tubes

Abstract: Observations indicate that various dynamic solar phenomena lead to enhanced emission of electromagnetic waves from radio to X-ray wavelengths which can be traced to magnetic activity in the photospheric level. A number of previous investigations have ignored the dynamic responses in the solar atmosphere. On the other hand, Nakagawa et al. (1978, 1981) have studied the atmospheric responses in the frame of MHD in the supersonic super-Alfvenic region. Studies of the slowly varying dynamic response (subsonic) have been unsuccessful because of the requirements of high accuracy in the numerical scheme in which a rigorous mathematical treatment of the boundary conditions is necessary. Recently, a numerical MHD model was constructed by using the full implicit continuous eulerian method. The present investigation makes use of a method which is written in a more convenient numerical code. A two-dimensional, time-dependent, nonplanar MHD model is used to investigate the induced mass and wave motions in the lower solar atmosphere due to the shear motion of flux tubes.

The kinematics of hexagonal magnetoconvection

Abstract: Calculations are presented for the evolution of a magnetic field which is subject to the effect of three-dimensional motions in a convecting layer of highly conducting fluid with hexagonal symmetry. The back reaction of the field on the motions via the Lorentz force is neglected. We consider cases where the imposed field is either vertical or horizontal. In the former case, flux accumulates at cell centres, with subsidiary concentrations at the vertices of the pattern. In the latter, topological asymmetries between up- and down-moving fluid regions generate positive flux at the base of the layer and negative flux at the top, though the system is actually an amplifier rather than a self-excited dynamo. Spiral field lines form in the interiors of the cells, and the phenomenon of “flux expulsion” found in two-dimensional solutions is somewhat altered when the imposed field is horizontal. Applications for stellar magnetic fields include a possible mechanism for burying flux at the base of a convectio...

The structure of twisted magnetic flux tubes

Abstract: The equilibrium structure of an axisymmetric twisted magnetic flux tube, confined by an external plasma pressure p/sub e/(z) which varies along the tube, is studied. Previous results for cylindrical twisted tubes, and for untwisted tubes in an inhomogeneous atmosphere, are generalized to take into account the effect of twist, of a varying pressure and of a radial field component.

Global characteristics of magnetic flux ropes in the Venus ionosphere

Abstract: An examination is undertaken of global characteristics of Venus ionosphere magnetic flux ropes, whose maximum spatial occurrence at 165-km altitude occupies more than half of the ionospheric volume. Ropes above 200 km altitude in the low zenith angle regions appear to have quasi-horizontal orientations, while those below that altitude tend to be quasi-vertical. High zenith angle cases tend to be horizontal above 300 km, and randomly oriented below that altitude. Ropes may be more tightly 'twisted' at low than at high altitudes, especially in the low zenith angle regions. Rope field strengths are highest near the altitudes where their occurrence is greatest, and scale with the square root of the ambient thermal pressure. The global polarities of flux rope field-aligned currents seem to be random and do not support a steady, nonturbulent global formation mechanism.