Sheath Currents Research Articles

Computer Simulation of an Ion Beam Antenna

The feasibility of using a modulated beam of ions as an antenna in the magnetosphere is discussed briefly. A computer simulation of an ion beam in a plasma is presented in which the motion of the ions is prescribed while the electrons in the surrounding plasma are represented by concentric charged shells, each of which moves in the self-consistent field set up by the beam and the other shells. By following the motion of the shells on a computer, an attempt is made to estimate the sheath current that is induced in the plasma by the beam.

Protecting CATV Equipment Against the Effects of Longitudinal Sheath Currents

The advantages and disadvantages of various protection devices which are used in CATV systems are explored. The interrelated effects of other components related to system reliability, such as time-delay relays, standby power supplies, and system grounds are then discussed.

Cable Shielding Performance and CW Response

We show that the reference for the measurement of the shielding performance of a cable sheath should be the sheath current. However, unless the phase length of the cable is short, the response at the ends of the line will be sensitive to frequency even if the sheath current is uniform, and the coaxial line formed by the core wires and the sheath is matched at both ends. This is because the driving field in the coaxial line and the waves that it generates have different phase speeds and directions. We present supporting experimental data. Because of this effect it is not meaningful simply to state that a cable provides a specifled attenuation, except for a cable that is short at the highest frequency of interest. We discuss the effects of connectors and of cracks or holes in the sheath. Because the total leakage is proportional to the sum of leakages through the sheath (the connectors and the cracks) and not to their product, it is necessary to assign these contributions with some arbitrariness in order to compare them in decibels. We give an example that shows the importance of RF-tight connectors.

Nonlinear Sheath Admittance, Currents, and Charges Associated With High Peak Voltage Drive on a VLF/ELF Dipole Antenna Moving in the Ionosphere

We consider a bare antenna consisting of two line elements driven by a VLF source and immersed in the ionosphere. Nonlinear effects associated with high voltages up to 1000 volts and with an additional induced v×B·1 voltage are included. The applied voltage is visualized as a dc effect. For various instantaneous voltage values, we obtain the distribution along the antenna of voltage and resis'ive current, sheath size, and charge per unit length. At the feed points, waveforms for the charge and both resistive and displacement currents are illustrated, assuming an applied cosine voltage form. Averaging over a cycle yields, as a function of peak bias voltage, the average power dissipated in collection of particles from the medium, the average work done in moving charge between the two half‐antennas, and the average sheath conductance and capacitance. Numerical results are given for three altitudes and two antenna lengths.

Stability of supercurrents in flat films of tin

Using pulsed, 80-nsec-currents the stability of supercurrents in flat films of tin with compensating current return has been investigated. It is found that the voltage along the film rises with timet approximately asV=b+a[t′/2(t−c))1/2], whereb represents the (almost instantaneous) flux-flow voltage in a perpendicular field and the time constantt′ is an exponentially decreasing function ofJ(1+420/d)/[1−(T/Tc4][1−H⊥/Hc⊥]. HereJ is the current density in the film of thicknessd in A,T/Tc is the reduced temperature, andH⊥/Hc⊥ is the reduced magnetic field. It is suggested that this instability is of the type investigated by Kramer and by Fink and Presson for currents in a superconducting surface sheath. At lower temperatures a second instability is found which is distinctly different from the one dominant at the higher temperatures.

Normal precipitates in type II superconducting eutectic alloys

The effect of a second phase on the sheath current carrying capacity of type II superconductors is investigated by measurements on suitable binary eutectic alloys. The results show that the presence of a normal second phase increases the sheath current. Furthermore, the orientation of the second phase with respect to the applied field is shown to affect the value of the sheath current. The results are explained by postulating surface sheath superconductivity occurring at the interfaces of the superconducting matrix with the second phase.

Stability of supercurrents in cylindrical films of tin

Using pulsed currents of 80-nsec duration the stability of supercurrents in cylindrical films with current return through the center has been investigated. It is found that the voltage along the film rises with timet approximately asV = a[1 − erf(t′/2(t − c))1/2] where the time constantt′ is an exponentially decreasing function ofi(1 + 420/d)/(1 −(T/Tc)4). Herei is the current through the sample,d the thickness of the film in angstroms, andT/Tc the reduced temperature. Comparison with older data by Mydosh and Meissner and by Hagedorn indicates that it is indeed the currenti, rather than the current densityJ, which determinest′. It is suggested that the instability is of the nature of those investigated by Kramer and by Fink and Presson for currents in a superconducting surface sheath.

Anisotropy of the Surface Impedance in the Surface-Sheath Regime as Evidence for Fluctuations of the Superconducting Order Parameter

In the surface-sheath regime, the high-frequency surface impedance of a superconductor is a function of the angle between the polarization plane of the incident wave's electric vector ${\mathbf{E}}_{\ensuremath{\omega}}$ and the steady magnetic field H. This anisotropy arises from collective fluctuations of the superconducting order parameter $\ensuremath{\Delta}(x)$. In the ground state $\ensuremath{\Delta}(x)$ is a modeless function. When ${\mathbf{E}}_{\ensuremath{\omega}}$ and H are perpendicular, the incident electromagnetic wave can couple to the intrinsic sheath currents and excite $\ensuremath{\Delta}(x)$ into states with a finite damping coefficient. No such excitations are possible when ${\mathbf{E}}_{\ensuremath{\omega}}$ and H are parallel. The extra absorption predicted by theory in the dirty limit explains experimental data obtained from two lead-based alloys very well. These experiments should, therefore, be considered as direct evidence for the existence of collective fluctuations of the order parameter in the surface-sheath regime of superconductors.

Superconductivity in the lead-bismuth system

The magnetic behaviour of superconducting lead-bismuth alloys (in the range 0 – 56.5 at.% Bi) has been correlated with composition and microstructure Critical fields H C1, H C2 and H C3 have been measured. Irreversible magnetic effects have been interpreted in terms of the Irie and Yamafuji model modified in some cases by the existence of a surface barrier for Type II alloys, and in terms of flux-tube energetics and surface sheath currents for Type I.

Generalized critical-state model of type II superconductors

A modified form of the critical-state model of type II superconductors is described which takes account of Hc1 and surface sheath currents. The penetrating flux, hysteresis loop characteristics, a.c. losses and rate of penetration of flux into the superconductor when exposed to a sinusoidal magnetic field are evaluated. The model implies zero power dissipation for peak applied fields less than Hc1+ΔH and rapidly increasing dissipation just above this region, asymptotically approaching that derived from the Bean-London model.

Comparative steady-state performance of crossbonded cable systems

The paper gives a universal system of steady-state analysis for any crossbonded and/or transposed cable system with unequal lays. It first introduces a nomenclature which enables any conductor or sheath to be identified in geometric and/or longitudinal position in any lay and/or section both for the general case and for four specific cases of crossbonding. It is then shown that the effect of unequal lays on sheath voltages, currents and losses may always be analysed, provided that there is rigorous adherence to the system of nomenclature. The paper is restricted to cases of unbalanced conductor currents in the steady state and does not deal with the additional variables and complexities when the various crossbonded systems have multiple-earthed points and are under external or internal unbalanced fault conditions. A large selection of graphical results is presented for sheath currents, losses and longitudinal sheath voltages of the three main cases of crossbonding. In the particular case of trefoil spacing, taken as an example, the influence of variation of lay length between 0.6 and 1.4 p.u. on the sheath currents and longitudinal induced voltages is shown. The results are discussed in detail since comparative performances for these various systems have not previously been presented. The conclusions extend also the analytical methods, it being shown that all crossbonded systems of whatever complexity can be analysed by the use of rotation matrices and the notation for nonuniform lay length; it follows en passant that normal symmetrical-component methods do not yield a solution, owing to the crossbonded systems having multiple unbalances and six degrees of freedom.

Determination of the open-circuit sheath voltages of cable systems

The literature of the crossbonded a.c. cable systems is sparse and is mainly of Japanese and American origin. Recent work in the UK has indicated the need for precise numerical data on sheath conditions of these systems. The paper gives the numerical magnitudes of steady-state voltages and overvoltages to be expected on these systems, since they do not appear to have been formulated comprehensively in the literature.The sheath voltages can be found by identical methods for any cable system, whether it be transposed, crossbonded or normally laid. The system of calculation in the paper is thus part of a method for determining overall cable behaviour in terms of sheath voltages, currents and losses, and for either single or double circuits. Attention is drawn to the complexity of calculations for many modern systems with crossbonding, transposition and unequal lay lengths, from which it follows that more powerful mathematical methods, allied to fast large-store-capacity computers, become necessary.An economical system of notation, avoiding the use of multiple suffixes, is used, even though 3 × 3 × 3 × 2 × 2 variables must be permuted.Furthermore, in any lay (or section in the more complex cases) it is necessary to locate a particular sheath relative to a particular conductor, as well as locating each one geographically in the cable trench at any particular junction in a barrel of lays and sections.Results are presented for all the practical cases, together with single and double 3-phase circuits representing the theoretical limits. All results are given to the same base of induced voltages per 1000ft per 100A in the reference conductor; comparison of results is thus facilitated.

Extreme currents in the superconducting surface sheath

The one-dimensional Ginzburg-Landau equation for a superconducting half-space in a parallel magnetic field H o > H C2 have been solved numerically in order to determine the extreme or “critical” currents in the surface sheath. A comparison to earlier calculations shows that the asymmetry of the critical current can be much greater than previously reported.

Critical Currents in the Superconducting Surface Sheath

Results are presented of magnetization measurements on Pb-Tl cylinders in axial magnetic fields of such magnitude that superconductivity is confined to the superconducting surface sheath. Specimens whose Ginzburg-Landau $\ensuremath{\kappa}$ values range from 0.6 to 1.4 have been investigated. For these cylindrical specimens a nonzero magnetization exists beyond the upper critical field ${H}_{c2}$ up to a field ${H}_{c3}$ (1.7 to 1.75 ${H}_{c2}$) identifiable with the surface nucleation field (1.695 ${H}_{c2}$). Evidence is presented that indicates the observed magnetization results from partial shielding of the interior of the cylinders by critical currents induced in the multiply-connected surface sheath. Our experimental results are in quantitative accord with recent theoretical calculations of Fink and Barnes concerning the influence of critical sheath currents on the effective bulk-magnetization characteristics of a cylinder. It is observed that diamagnetic ($M<0$) and paramagnetic ($M>0$) shielding occur in uniformly increasing and decreasing fields, respectively, which is consistent with the existence of a multiconnected superconducting region which can carry a total current. The surface localization of the superconductivity involved is demonstrated by the proximity effects of electroplated normal metals on the specimens. Cu plating reduces both the magnetization and ${H}_{c3}$ (\ensuremath{\sim}1.4 ${H}_{c2}$). Owing, perhaps, to their magnetic properties, electroplated Ni and Cr have a much more drastic effect than electroplated Cu. To the limit of experimental sensitivity, all traces of superconductivity above ${H}_{c2}$ are removed by Ni and Cr platings.

Sheilding properties of the superconducting surface sheath

Properties of the surface sheath of type I (κ > 0.42) and type II superconducting plates ( 1 √2 < κ < 2 ) in a parallel magnetic field are investigated. It is shown that the changing external magnetic field induces currents in the surface sheath which lead to hysteretic behaviour in the real part of the surface impedance R as a function of the applied field. The shielding of the bulk is most pronounced near the thermodynamical critical field H c, in qualitative agreement with recent work by Fink. The shielding properties in decreasing field seem to break down at H c, even in type II material with κ below a critical value. In an increasing field the bulk type I superconductor remains ideally diamagnetic up to a field higher than H c.

Induced voltages in the sheaths of crossbonded a.c. cables

When groups of single-conductor concentric cables are used in power systems, it is necessary both to bond the sheaths together at the various joint shells and to earth them at intervals to ensure that there are no large potentials present on them. This arrangement leads to large circulating sheath currents and losses.Various arrangements have been devised to eliminate the sheath losses, the one which is probably most in favour in Britain being the Kirke-Searing scheme. In this scheme, the cable conductors are transposed at regular intervals along a run, and the sheaths are bonded and transposed at the same intervals. While the arrangement eliminates the circulating currents and losses under balanced conditions, it does not prevent relatively large potentials from being present at intermediate points, and it causes appreciable voltages to be present across the insulators inserted in the sheaths at the joints.It is of interest to know the magnitudes of the sheath voltages which are likely to be present in the absence of voltage limiting devices. Some analytical work has been done on this subject for both balanced and unbalanced steady-state conditions, and there are also some experimental results relating to transient conditions. There is, however, little analytical work available on the latter topic. This paper extends the analysis of steady-state conditions by the use of symmetrical-component techniques, and explains the underlying reasons for the high transient sheath voltages which have been detected in the past.

Solution of the Vlasov Equations for a Plasma in an Externally Uniform Magnetic Field

An exact solution of the collisionless Boltzmann equation is presented that describes a slab of plasma contained in a magnetic field that is uniform external to the slab. The magnetic field dips in the plasma due to the diamagnetic currents in the plasma sheath separating the region of nearly constant density from the vacuum region. The currents are given by the distribution functions for ions and electrons and the fields obey Maxwell's equations. The solution has the qualitative features of real collisionless laboratory plasma distributions. The problem of a cylindrical plasma with axial magnetic field is also treated, and a solution presented for a limiting case. The solution to the slab problem is charge neutral. The limiting case in the cylindrical problem is also charge neutral, but the general cylindrical problem is not, and contains radial electric fields. The solutions have the merit of being substantially more simple than others that have previously been found for the plasma sheath problem.

Study of a-c sheath currents and their effect on lead-cable-sheath corrosion

Study of a-c sheath currents and their effect on lead-cable-sheath corrosion

Study of A-C Sheath currents and their effect on lead-cable-sheath corrosion

The destruction of lead sheaths on underground cables by electrolysis usually is caused by the action of direct currents which originate from one or several well-defined sources. Little information is available concerning a-c electrolysis, and since the extent of its destructive action is less widespread than that produced by direct current it is considered generally to be relatively less important in the field of cable-sheath corrosion. This paper discusses two cases of electrolysis in which the lead sheaths on single-conductor power cables were corroded through, causing cable breakdowns; and describes field observations and laboratory tests which show that at first the corrosive action was accelerated greatly by rectified alternating currents which were induced in the sheaths by the load current. A method of protecting the sheaths against such electrolytic corrosion also is described.

Study of A-C Sheath Currents and Their Effect on Lead-Cable-Sheath Corrosion

The destruction of lead sheaths on underground cables by electrolysis usually is caused by the action of direct currents which originate from one or several well-defined sources. Little information is available concerning a-c electrolysis, and since the extent of its destructive action is less widespread than that produced by direct current it is considered generally to be relatively less important in the field of cable-sheath corrosion. This paper discusses two cases of electrolysis in which the lead sheaths on single-conductor power cables were corroded through, causing cable breakdowns; and describes field observations and laboratory tests which show that at first the corrosive action was accelerated greatly by rectified alternating currents which were induced in the sheaths by the load current. A method of protecting the sheaths against such electrolytic corrosion also is described.