Illustrating field emission theory by using Lauritsen plots of transmission probability and barrier strength

This technical note relates to the theory of cold field electron emission (CFE). It starts by suggesting that, to emphasize common properties in relation to CFE theory, the term 'Lauritsen plot' could be used to describe all graphical plots made with the reciprocal of barrier field (or the reciprocal of a quantity proportional to barrier field) on the horizontal axis. It then argues that Lauritsen plots related to barrier strength (G) and transmission probability (D) could play a useful role in discussion of CFE theory. Such plots would supplement conventional Fowler-Nordheim (FN) plots. All these plots would be regarded as particular types of Lauritsen plot. The Lauritsen plots of -G and lnD can be used to illustrate how basic aspects of FN tunnelling theory are influenced by the mathematical form of the tunnelling barrier. These, in turn, influence local emission current density and emission current. Illustrative applications used in this note relate to the well-known exact triangular and Schottky-Nordheim barriers, and to the Coulomb barrier (i.e., the electrostatic component of the electron potential energy barrier outside a model spherical emitter). For the Coulomb barrier, a good analytical series approximation has been found for the barrier-form correction factor; this can be used to predict the existence (and to some extent the properties) of related curvature in FN plots.Comment: Based on a poster presented at the 25th International Vacuum Nanoelectronics Conference, Jeju, S. Korea, July 2012. Version 3 incorporates small changes made at proof stag

Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope

The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the onset condition of solar eruptions.Comment: V2: update to conform to the published article; new choice for internal inductance of torus; updated Fig. 2; new Figs. 3, 5, and

Simulated Gas Turbine Casing Response to Rotor Blade Pressure Excitation

Non-intrusive measurement of blade condition within gas turbines is of major interest within all areas of their use. It is proposed that the measurement of the casing vibration, due to the aerodynamic-structural interaction within the turbine, could provide a means of blade condition monitoring and modal parameter estimation. In order to understand the complex relationship between blade vibrations and casing response, an analytical model of the casing and simulated pressure signal associated with the rotor blades is presented. A mathematical formulation is undertaken of the internal pressure signal due to both the rotating bladed disk as well as individual blade vibrations and the solution of the casing response is formulated. Excitation by the stator blades and their contribution to the casing response is also investigated. Some verification of the presented analytical model is provided by comparison with Finite Element Analysis results for various rotor rotational speeds

Atherosclerotic carotid plaque composition: a 3T and 7T MRI-histology correlation study

Background and Purpose Carotid artery atherosclerotic plaque composition may influence plaque stability and risk of thromboembolic events, and non-invasive plaque imaging may therefore permit risk stratification for clinical management. Plaque composition was compared using non-invasive in-vivo (3T) and ex-vivo (7T) MRI and histopathological examination. Methods Thirty three endarterectomy cross sections, from 13 patients, were studied. The datasets consisted of in-vivo 3T MRI, ex-vivo 7T MRI and histopathology. Semi-automated segmentation methods were used to measure areas of different plaque components. Bland- Altman plots and mean difference with 95% confidence interval were carried out. Results There was general quantitative agreement between areas derived from semi-automated segmentation of MRI data and histology measurements. The mean differences and 95% confidence bounds in the relative to total plaque area between 3T versus Histology were: fibrous tissue 4.99 % (-4.56 to 14.56), lipid-rich/necrotic core (LR/NC) with haemorrhage - 1.81% (-14.11 to 10.48), LR/NC without haemorrhage -2.43% (-13.04 to 8.17), and calcification -3.18% (-11.55 to 5.18). The mean differences and 95% confidence bounds in the relative to total plaque area between 7T and histology were: fibrous tissue 3.17 % (-3.17 to 9.52), LR/NC with haemorrhage -0.55% (-9.06 to 7.95), LR/NC without haemorrhage - 12.62% (-19.8 to -5.45), and calcification -2.43% (-9.97 to 4.73). Conclusions This study provides evidence that semi-automated segmentation of 3T/7T MRI techniques can help to determine atherosclerotic plaque composition. In particular, the high resolution of ex-vivo 7T data was able to highlight greater detail in the atherosclerotic plaque composition. High field MRI may therefore have advantages for in vivo carotid plaque MR imaging

Indeterminacy and instability in Petschek reconnection

We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the X-line that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, Sweet-Parker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the X-line. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate

Distinguishing Solar Flare Types by Differences in Reconnection Regions

Observations show that magnetic reconnection and its slow shocks occur in solar flares. The basic magnetic structures are similar for long duration event (LDE) flares and faster compact impulsive (CI) flares, but the former require less non-thermal electrons than the latter. Slow shocks can produce the required non-thermal electron spectrum for CI flares by Fermi acceleration if electrons are injected with large enough energies to resonate with scattering waves. The dissipation region may provide the injection electrons, so the overall number of non-thermal electrons reaching the footpoints would depend on the size of the dissipation region and its distance from the chromosphere. In this picture, the LDE flares have converging inflows toward a dissipation region that spans a smaller overall length fraction than for CI flares. Bright loop-top X-ray spots in some CI flares can be attributed to particle trapping at fast shocks in the downstream flow, the presence of which is determined by the angle of the inflow field and velocity to the slow shocks.Comment: 15 pages TeX and 2 .eps figures, accepted to Ap.J.Let