An overview of Earth's global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Air-earth current density measurements at Lerwick; implications for seasonality in the global electric circuit

Atmospheric electricity measurements were made at Lerwick Observatory in the Shetland Isles (60°09′N, 1°08′W) during most of the 20th century. The Potential Gradient (PG) was measured from 1926 to 84 and the air-earth conduction current (Jc) was measured during the final decade of the PG measurements. Daily Jc values (1978–1984) observed at 15 UT are presented here for the first time, with independently-obtained PG measurements used to select valid data. The 15 UT Jc (1978–1984) spans 0.5–9.5 pA/m2, with median 2.5 pA/m2; the columnar resistance at Lerwick is estimated as 70 PΩm2. Smoke measurements confirm the low pollution properties of the site. Analysis of the monthly variation of Lerwick Jc data shows that winter (DJF) Jc is significantly greater than the summer (JJA) Jc by 20%. The Lerwick atmospheric electricity seasonality differs from the global lightning seasonality, but Jc has a similar seasonal phasing to that observed in Nimbostratus clouds globally, suggesting a role for non-thunderstorm rain clouds in the seasonality of the global circuit.

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.

Optimal inverter design for an induction machine using resonant frequency matching

The frequency responses of two 50 Hz and one 400 Hz induction machines have been measured experimentally over a frequency range of 1 kHz to 400 kHz. This study has shown that the stator impedances of the machines behave in a similar manner to a parallel resonant circuit, and hence have a resonant point at which the Input impedance of the machine is at a maximum. This maximum impedance point was found experimentally to be as low as 33 kHz, which is well within the switching frequency ranges of modern inverter drives. This paper investigates the possibility of exploiting the maximum impedance point of the machine, by taking it into consideration when designing an inverter, in order to minimize ripple currents due to the switching frequency. Minimization of the ripple currents would reduce torque pulsation and losses, increasing overall performance. A modified machine model was developed to take into account the resonant point, and this model was then simulated with an inverter to demonstrate the possible advantages of matching the inverter switching frequency to the resonant point. Finally, in order to experimentally verify the simulated results, a real inverter with a variable switching frequency was used to drive an induction machine. Experimental results are presented.

An overview of Earth’s global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Torque in mooring chain. Part 1: Background and theory

Chain in both its forms - common (or stud-less) and stud-link - has many engineering applications. It is widely used as a component in the moorings of offshore floating systems, where its ruggedness and corrosion resistance make it an attractive choice. Chain exhibits some interesting behaviour in that when straight and subject to an axial load it does not twist or generate any torque, but if twisted or loaded when in a twisted condition it behaves in a highly non-linear manner, with the torque dependent upon the level of twist and axial load. Clearly an understanding of the way in which chains may behave and interact with other mooring components (such as wire rope, which also exhibits coupling between axial load and generated torque) when they are in service is essential. However, the sizes of chain that are in use in offshore moorings (typical bar diameters are 75 mm and greater) are too large to allow easy testing. This paper, which is in two parts, aims to address the issues and considerations relevant to torque in mooring chain. The first part introduces a frictionless theory that predicts the resultant torques and 'lift' in the links as non-dimensionalized functions of the angle of twist. Fortran code is presented in an Appendix, which allows the reader to make use of the analysis. The second part of the paper presents results from experimental work on both stud-less (41 mm) and stud-link (20.5 and 56 mm) chains. Torsional data are presented in both 'constant twist' and 'constant load' forms, as well as considering the lift between the links.

Torque in mooring chain. Part 2: Experimental investigation

Chain is a commonly used component in offshore moorings where its ruggedness and corrosion resistance make it an attractive choice. Another attractive property is that a straight chain is inherently torque balanced. Having said this, if a chain is loaded in a twisted condition, or twisted when under load, it exhibits highly non-linear torsional behaviour. The consequences of this behaviour can cause handling difficulties or may compromise the integrity of the mooring system, and care must be taken to avoid problems for both the chain and any components to which it is connected. Even with knowledge of the potential problems, there will always be occasions where, despite the utmost care, twist is unavoidable. Thus it is important for the engineer to be able to determine the effects. A frictionless theory has been developed in Part 1 of the paper that may be used to predict the resultant torques and movement or 'lift' in the links as non-dimensional functions of the angle of twist. The present part of the paper describes a series of experiments undertaken on both studless and stud-link chain to allow comparison of this theoretical model with experimental data. Results are presented for the torsional response and link lift for 'constant twist' and 'constant load' type tests on chains of three different link sizes.