Position Of Sheet Research Articles

Self‐consistent magnetotail theory: General solution for the quiet tail with vanishing field‐aligned currents

The three‐dimensional theory of the quiet magnetotail by Birn et al. (1977a) is revised and generalized. The general static solution is presented for the case of vanishing field‐aligned currents holding for quiet times with small bulk velocities and negligible pressure anisotropy. Since the knowledge of particle entry, transport, and loss and of the interaction of the magnetosphere with the solar wind is too small to determine the solution by appropriate initial and boundary conditions, the free functions of the general solution have been adjusted to the observational material inside the tail. It is shown that the quiet tail data can be fitted by a self‐consistent model without flux loss through the boundary (closed magnetosphere). Restrictions following from self‐consistency provide further (indirect) evidence for plasma sheet thickening towards the flanks. The effect of dipole tilt on the neutral sheet position and tail aberration can also be included in the model. It turns out that the curvature of the field lines in the x, y plane is connected with the occurence of field‐aligned currents.

ILLIQUIDITY, THE DEMAND FOR RESIDENTIAL HOUSING, AND MONETARY POLICY

IN ANALYZING THE EFFECTS of monetary policy on the demand for tangible consumer assets, such as consumer durables and residential housing, primary attention has been focused on interest rate and credit rationing effects. Recent work (Mishkin (21)) takes a different approach by studying the previously neglected illiquid aspect of consumer durable asset. The following results are derived: the consumer durable is a less desireable portfolio asset if (a) the consumer's debt holdings are high, (b) gross financial asset holdings are low, (c) income variance is high, or (d) expected income is low. These results stem from the illiquidity of the consumer durable asset which causes a rise in the effective opportunity cost of holding the consumer durable as the consumer's probability of encountering financial distress increases. As a result, the balance sheet position of households plays an important role in the demand for durables, and as monetary policy affects the balance sheet it also affects the demand for durables. The results of this were tested in a standard stock-adjustment model of consumer durable expenditure on postwar quarterly data; and the empirical results were quite favorable to the hypothesis.' Residential housing is also an illiquid consumer tangible asset, differing from consumer durables in that its illiquidity stems from slightly different sources. The liquidity hypothesis should thus apply to the housing asset as well. This paper adapts the liquidity theory to the housing asset and tests the hypothesis on postwar quarterly U.S. data with a model of residential housing demand. The empirical results do indeed support this hypothesis. In previous studies of the demand for residential housing, monetary policy has its major impact either through the availability of credit or the cost of financing the housing purchase.2 In addition, two novel potent channels of monetary influence

An evaluation of recent quantitative magnetospheric magnetic field models

Recent quantitative magnetospheric field models contain many features not found in earlier models. Magnetopause models which include the effects of the dipole tilt have been presented. More realistic models of the tail field include tail currents which close on the magnetopause, cross‐tail currents of finite thickness, and cross‐tail current models which model the position of the neutral sheet as a function of tilt. Finally, models have attempted to calculate the field of currents distributed in the inner magnetosphere. As the purpose of a magnetospheric model is to provide a mathematical description of the field that reasonably reproduces the observed magnetospheric field, several recent models have been compared with the observed ΔB(Bobserved ‐ Bmain field) contours. Models containing only contributions from magnetopause and tail current systems are able to reproduce the observed quiet time field only in an extremely qualitative way. The best quantitative agreement between models and observations occurs when currents distributed in the inner magnetosphere are added to the magnetopause and tail current systems. However, the distributed current models are valid only for zero tilt. Even the models which reproduce the average observed field reasonably well may not give physically reasonable field gradients. Three of the models evaluated contain regions in the near tail in which the field gradient reverses direction. One region in which all the models fall short is that around the polar cusp, though most can be used to calculate the position of the last closed field line reasonably well.

A Discussion on the physics of the solar atmosphere - Current sheets

Current sheets are believed to be of prime importance in the solar atmosphere. Low down they may form at supergranulation boundaries, whereas up in the corona they have been suggested as a prominence formation site. In addition, they may occur when rapidly emerging flux presses up against pre-existing magnetic fields: if rapid magnetic field annihilation and reconnection is then triggered, a surge or a flare may be produced. Comments are given about three aspects of general current sheet theory. The position and shape of the current sheet which forms between two-dimensional dipole sources is calculated. The thermal instability which occurs when the length of the sheet exceeds a critical value is described. Finally, a simple model of magnetic field annihilation is presented.

The formation of current sheets during the emergence of new magnetic flux from below the photosphere

Solar flares are frequently observed to occur where new magnetic flux is emerging and pressing up against strong active region magnetic fields. Since the solar plasma is highly conducting, current sheets develop at the boundary between the emergent and ambient flux, provided the two magnetic fields are inclined at a non-zero angle to one another. The present paper gives a simple two-dimensional model for the development of such sheets under the assumptions that no reconnection occurs and that the surrounding field remains a potential one. By using complex variable techniques, the position, orientation and shape of a current sheet may be determined, as well as the excess magnetic energy associated with it. Two examples are considered. The first, in which the ambient field is bipolar, may model new flux emergence near the edge of an active region, while the second example assumes a constant ambient field and may approximate the so-called ‘fibril crossings’ which occur prior to some flares. In each case, the current sheets are curved, and the magnetic energy which is stored in excess of potential is sufficient to supply a solar flare when the sheets are long enough.

Prediction of the secondary and tertiary structure of plastocyanin.

The amino acid sequences of nine plastocyanins were examined using four published methods for the prediction of secondary structure in proteins. The results of the four methods were combined in such a way as to maximize agreement, and the position of alpha helices, beta sheets, and beta turns in plastocyanin was predicted. From this result and other information, such as the position of conserved residues and the requirements for coordination of copper, a preliminary model for the mainchain folding of the molecule was presented.

Complete plasma dropouts at vela satellites during thinning of the plasma sheet

Five satellite years of Vela data are examined for plasma sheet thinnings. Complete proton disappearances (plasma dropouts) are the main subject here. During such times, the Vela satellite is temporarily in the high-latitude tail lobe. The distribution of such plasma dropouts within the magnetotail suggests that the semithickness of the plasma sheet near midnight seldom reaches less than 1 RE during substorms and that the dawn and dusk portions of the plasma sheet remain thicker than the midnight portion. But it is also shown that the plasma sheet occasionally becomes very thin near the dusk magnetopause. This seems to occur when the magnetopause near the dawn and dusk meridians lies further away from the earth than is normal. Extension of the magnetopause to these greater distances does not seem to be related to magnetically quiet periods nor to the Z component of the interplanetary magnetic field (IMF). No such severe thinnings of the plasma sheet are found near the dawn magnetopause. Plasma dropouts can occur regardless of the sign of the Z component of the IMF, but their frequency of occurrence seems to be greater when the Z component is negative. The decreased frequency of occurrence with northward IMF may reflect weaker thinning of the plasma sheet at ∼ 18 RE during the weaker substorms that occur then. Weaker thinning of the plasma sheet may also imply a greater than normal distance from the earth to the magnetic neutral line thought to form in the magnetotail at substorm onset. Three plasma dropouts which occurred in the midnight sector at unusually large distances from the estimated position of the neutral sheet were observed during geomagnetic storms. It is likely that the midnight sector of the plasma sheet can become very thick (∼18 RE) at certain times during the main phase of storms. Detailed measurements in the plasma sheet were obtained near the beginning of a geomagnetic storm whose sc triggered a substorm. A compression of the plasma sheet at XSM ≈ −15 RE occurred about 10 min after the sc onset at the earth and about 5 min after the start of plasma sheet thinning associated with the sc-related substorm. If compression-thinning of the plasma sheet initiated this substorm, the triggering action must have occurred earthward of XSM ≈ −15 RE.

The influence of the direction of the geomagnetic dipole on the position of the neutral sheet

An analysis of neutral sheet crossings detected by the NASA-Goddard Space Flight Center magnetometer on the Explorer 34 satellite has shown that the diurnal wobble of the geomagnetic dipole measurably influences the position of the neutral sheet at 30 RE. Viewed in the solar-ecliptic coordinate system, the dipole wobble originates from the 11° angle between the earth's spin axis and the dipole axis, has a period of 24 hours, and can be resolved into components of motion perpendicular and parallel to the earth-sun line. The perpendicular component exerts a torque on the magnetotail and causes the neutral sheet to pivot about an axis approximately parallel to the solar wind direction. The parallel component encourages the neutral sheet to move above and below the solar-magnetospheric equatorial plane with an amplitude of 1 RE. This latter motion is consistent with the neutral sheet's being hinged at a geocentric distance of 5.25 RE. Although hinging is not as dominant a feature of neutral sheet motion as pivoting at 30 RE, both are in phase with the 24-hour precession of the dipole axis about the earth's spin axis.

Kpdependence of the plasma sheet boundary

An empirical relationship has been obtained between the location of the inner boundary of the plasma sheet along the geostationary orbit and Kp. Through the use of an analytical expression for the shape of the boundary and a relationship between the convection electric field and Kp this result is extended to yield the radial position of the boundary versus Kp. The result illustrates the high degree of sensitivity of measurements in the geostationary orbit region to shifts in the plasma sheet position arising from geomagnetic activity or an increasing convection electric field.

Limiting currents for the relativistic planar diode with space-charge neutralization

The electrons produced by cathode emission in a plane diode generate positive ions by collisions in their passage through a thin sheet of neutral particles situated between and parallel to the electrodes. An expression is developed relating the electron current to the density of the neutral sheet, the position of the sheet, the electrode separaation, the cathode electric field and the electrode potential difference up to a value of 10 MV. The electron current density is conveniently defined as a multiple of the nonrelativistic Child-Langmuir limiting current density J0. Evaluation of the maximum electron current density shows that it ranges from 4·59 J0 for nonrelativistic potentials to 1·63 J0 for an anode potential of 10 MV, representing a factor of between 4·59 and 3·30 times the unneutralized limiting current. In all cases this maximum occurs for optimum values of the neutral sheet density and position.

The neutralization of space charge in the planar diode: II. By the injection of neutral particles

The electrons produced by cathode emission in a plane diode generate positive ions by collisions in their passage through a thin sheet of neutral particles situated between and parallel to the electrodes. A nonrelativistic treatment of the charged particle motion enables the electron current to be calculated as a function of the electrode separation, the electrode potential difference, the density of the neutral sheet, the position of the sheet, and the cathode electric field. The maximum possible electron current is 4·59 times the electron Child-Langmuir limit and occurs for unique values of the position and density of the neutral sheet and also for zero cathode field. Cathode fields equal to several multiples of the average interelectrode field accompanied by currents equal to several multiples of the Child-Langmuir limit can be obtained by suitable choice of the neutral sheet parameters. Finally, it is shown that a neutral sheet of the required specifications can be formed by the effusion of mercury vapour through a suitably positioned slit.

Space-Charge Flow with Unrestricted Variation of Current Density and Energy Range

A fast but accurate relativistic method for determining the time variation of potential and field distributions, electron trajectories, and space-charge-limited current between parallel conducting walls is described. No limit is placed on how broad the energy spectrum of the emitted electrons may be, or in what manner the energy distribution and intensity may vary with time. A major simplification results from performing the basic calculations in terms of scalar potentials rather than vector fields. The emission of a group of charge sheets representing the existing energy spectrum is assumed for each closely spaced time interval. The incremental advance of each sheet is found from its starting velocity and acceleration as functions of the momentary potential distribution curve and of its past variations by a procedure which also compensates for ``self-field'' effects. The new sheet positions define a new potential curve and the process is repeated. Trajectories calculated for monoenergetic electrons agree with previous analytic solutions. For the first time trajectories are calculated for electrons injected with rapidly varying current density and a broad energy range. The method was developed for electron emission resulting from energetic photons but has general applicability.

Plasma-sheet ions at lunar distance preceding substorm onset

During the partial lunar eclipse of August 17, 1970, four intense, transient bursts of kV-energy positive ions were detected at the lunar surface by the Rice University ALSEP Suprathermal Ion Detector Experiment. The eclipse happened to occur during a main-phase geomagnetic storm while the Moon was within a few Earth radii of the calculated position of the neutral sheet. The two most intense ion bursts were each followed roughly 1 2 hr later by the sudden onset of a several thousand gamma polar magnetic substorm at the Earth's surface. Two smaller ion enhancements were also followed by smaller magnetic disturbances. This observation is interpreted in terms of a downstream escape of plasma-sheet particles associated with the substorm growth phase.

Fibers from Polyhexamethylene Terephthalamide

On treatment with a variety of swelling agents, polyhexamethylene terephthalamide (nylon 6-T) fibers undergo char acteristic changes in tensile properties, x-ray pattern, and dyeability. Microscopically visible voids are permanentlv removed and the uptake of acid and disperse dyestuffs is increased in that portion of the fiber penetrated by the swotting agent. The molecular rearrangement which occurs during this "relaxation" consists of disorientation and probably in volves a change in the relative positioning of successive hydrogen-bonded sheets. It is suggested that the change in dyeing behavior on relaxation consists in general of an increase in extent of the so-called "overdyeing" resulting from the genera tion of additional "vacancies."

Magnetic field variations in the near geomagnetic tail associated with weak substorm activity

Magnetic field observations obtained with the UCLA Ogo 5 fluxgate magnetometer on an inbound pass, during which the satellite remained close to the magnetic meridian and traveled almost parallel to and approximately 2 RE above the expected position of the neutral sheet, are used to illustrate the variations in the configuration of the tail field during weak substorm activity. Beyond 10 RE from the earth, changes to dipolar fields are accompanied by a reduction in field strength presumably due to plasma sheet expansion. Within approximately 10 RE changes to a more dipolar field are accompanied by no change or by an increase in field strength. In both regions, these changes are accompanied by turbulence or noise. Occasional twisting of the field out of the usual magnetic meridian is also observed.

Configuration of the geomagnetic tail during substorms

Geomagnetic tail configuration during substorms from Imp 4 magnetic field and auroral index measurements

Some remarks on the position and shape of the neutral sheet

Position and shape of neutral sheet in geocentric solar magnetospheric coordinate system from geomagnetic tail measurements

Calculations on Shock Tubes with Current Crowbarring

Current crowbarring in electromagnetic shock tubes is analysed in terms of the snowplough model. The analysis has a bearing upon the crowbar action of secondary discharges which may give rise to decoupled current loops. Expressions relating current sheet position to time, sheet speed and current are given in nondimensional form. It is shown that the speed may continue to increase after crowbarring.

Synthesis of Multiple Resistance Networks from Single Resistive Films

A design procedure is described whereby multiple resistance networks can be synthesized from a single layer, monolithic, resistive structure. The method is illustrated by detailing the design of attenuators operating on an image-impedance basis. The single sheet geometry used is a rectangle with conducting tabs placed on its boundary. Conformal transformation techniques are applied to facilitate the computation of the required open-circuit resistance values which characterize a given rectangular geometry. Two SchwarzChristoffel transformations and a bilinear transformation permit the rapid design of a monolithic resistive network meeting prescribed specifications. The mapping of critical points is diagrammed to help the reader clearly visualize the transformations involved. Specific analytical examples are carried out, and curves are presented showing the dependence of network characteristics upon the parameters of sheet resistivity, geometric ratios, and position and size of the conducting tabs. The synthesis of two pads is described to illustrate graphical techniques involved. Both attenuators are designed to operate between 75 \Omega characteristic impedances, and to have 2 db of insertion loss. The first pad is realized by holding tab size constant and deriving the necessary rectangular geometry and resistivity. In the second case, the resistivity is held constant while the required geometry is determined. In general, alternative physical embodiments which are electrically equivalent afford a desirable flexibility from the viewpoint of network fabrication. The above synthesis techniques have been substantiated by the construction and measurement of laboratory models. Experimental data are given which represent the results obtained using tantalum film designs. Excellent correlation with theory is noted. Possible advantages which monolithic single-sheet networks offer over the discrete multiple resistor circuits which they replace are reduction of the number of components, better HF performance, ease of manufacture, and higher reliability due to the need for fewer interconnections. The single-sheet resistive components are notable for their compatibility with current thin-film fabrication techniques.

X. The Tertiary Composite Sill of South Bute

The Tertiary composite sill of South Bute has already been described,1 but as the evidence brought to light by the present work will entail fundamental alterations, not only in the description but in the conclusions to be drawn therefrom, it will be advisable to give a short resume of previous work. The sill has been described as consisting of three sheets, a thick inner sheet of dolerite flanked by two marginal sheets of quartz-porphyry. In two places a fourth sheet is observed, a thin basic sheet interposing between the lower acid sheet and the country rock. The acid sheets make very irregular junctions with the dolerite core, and contain xenoliths torn from it, while the dolerite contains xenocrysts of quartz and felspar obviously similar to the crystals in the acid rock. The conclusion arrived at was that an earlier acid sill had been eviscerated by a doleritic magma working along the centre, thus accounting for the marginal position of the acid sheets, the xenocrysts in the dolerite, and the irregular junctions. This theory has three weak points—(1) It fails to explain the xenoliths in the acid rock, (2) it ignores the two occurrences of a fourth sheet, (3) it forms a complete exception to the order of events found to persist in the composite sills of Skye of the same age. This reversal of the usual order of intrusion has rendered this sill quite remarkable, and has thus called for two references from Harker2 & 3. Though thus quoted as This 250-word extract was created in the absence of an abstract