Physical electrostatics of small field emitter arrays/clusters

This paper improves understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays. Using the "floating sphere at emitter-plate potential" (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. On need consider only the effects of sphere charges and (for separated emitters) image charges. For the 2-emitter system, formulas are found for "charge-blunting" and "neighbour-field" effects, for widely spaced and "sufficiently closely spaced" emitters. Mutual charge-blunting is always dominant, with a related (negative) fractional AFEF-change {\delta}_two. For sufficiently small emitter spacing c, |{\delta}_two| varies as 1/c; for large spacing, |{\delta}_two| decreases as 1/c^3. In a 3-emitter linear array, differential charge-blunting and differential neighbor-field effects occur, but the former are dominant, and cause the "exposed" outer emitters to have higher AFEF ({\gamma}_0) than the central emitter ({\gamma}_1). Formulas are found for the exposure ratio {\Xi}={\gamma}_0/{\gamma}_1, for large and for sufficiently small separations. The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge models (LCMs) are an alternative, but an apparent difficulty with recent LCM models is identified. Better descriptions of array electrostatics may involve developing good fitting equations for AFEFs derived from accurate numerical solution of Laplace's equation, perhaps with equation form(s) guided qualitatively by FSEPP-model results. In existing fitting formulas, the AFEF-reduction decreases exponentially as c increases, which differs from FSEPP-model formulas. FSEPP models might provide a useful guide to the qualitative behaviour of small field emitter clusters larger than those investigated.Comment: 34 pages, including 3 figures, with an extra 7 pages of Supplementary Material (giving details of algebraic analysis); v3 is slightly revised version, submitted after reviewin

The Murphy-Good plot: a better method of analysing field emission data

Measured field electron emission (FE) current-voltage Im(Vm) data are traditionally analysed via Fowler-Nordheim (FN) plots, as ln{Im/(Vm)**2} vs 1/Vm. These have been used since 1929, because in 1928 FN predicted they would be linear. In the 1950s, a mistake in FN's thinking was found. Corrected theory by Murphy and Good (MG) made theoretical FN plots slightly curved. This causes difficulties when attempting to extract precise values of emission characterization parameters from straight lines fitted to experimental FN plots. Improved mathematical understanding, from 2006 onwards, has now enabled a new FE data-plot form, the "Murphy-Good plot". This plots ln{Im/(Vm)**(2-({\eta}/6)} vs 1/Vm, where {\eta} depends only on local work function. Modern ("21st century") MG theory predicts that a theoretical MG plot should be "almost exactly" straight. This makes precise extraction of well-defined characterization parameters from ideal I_m(V_m) data much easier. This article gives the theory needed to extract characterization parameters from MG plots, setting it within the framework of wider difficulties in interpreting FE Im(Vm) data (among them, use of the "planar emission approximation"). Careful use of MG plots could also help remedy other problems in FE technological literature. It is argued MG plots should now supersede FN plots.Comment: Intended articl

Examples of mesoscale structures and short-term wind variations detected by VHF Doppler radar

The first of three wind profilers planned for operation in central and western Pennsylvania began full-time, high-quality operation during July 1985. It is located about 20 km south-southeast of University Park and operates at 50 MHz. Another 50-MHz radar and a 400-MHz radar are to be installed over the next few months, to complete a mesoscale triangle with sides of 120 to 160 km. During the period since early July, a number of weather systems have passed over the wind profiler. Those accompanied by thunderstorms caused data losses either because the Department computer system lost power or because power went out at the profiler site. A backup power supply and an automatic re-start program will be added to the profiler system to minimize such future losses. Data have normally been averaged over a one-hour period, although there have been some investigations of shorter-period averaging. In each case, preliminary examinations reveal that the profiler winds are indicative of meteorological phenomena. The only occasions of bad or missing data are obtained when airplane noise is occasionally experienced and when the returned power is nearly at the noise level, at the upper few gates, where a consensus wind cannot be determined. Jets streams, clouds, and diurnal variations of winds are discussed

Compatible Weighted Proper Scoring Rules

Many proper scoring rules such as the Brier and log scoring rules implicitly reward a probability forecaster relative to a uniform baseline distribution. Recent work has motivated weighted proper scoring rules, which have an additional baseline parameter. To date two families of weighted proper scoring rules have been introduced, the weighted power and pseudospherical scoring families. These families are compatible with the log scoring rule: when the baseline maximizes the log scoring rule over some set of distributions, the baseline also maximizes the weighted power and pseudospherical scoring rules over the same set. We characterize all weighted proper scoring families and prove a general property: every proper scoring rule is compatible with some weighted scoring family, and every weighted scoring family is compatible with some proper scoring rule