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Carbon fibers passing current are subject to resistive heating. When failure occurs, this is related to their local temperature. The failure temperature and its location are estimated. The temperature variation is calculated using analytical models for electrical and thermal conductivities based on the temperature dependent electron–phonon relaxation time. In the absence of radiative heat loss, an analytic expression of temperature along the fiber is given from which a maximum possible emission current is derived and is governed by a single introduced parameter ω o. A method of treating the radiative heat loss is developed and is governed by a second parameter γ , which allows a rapid numerical means to calculate the correction to the analytic form. Heat variation along a thick carbon fiber is contrasted to that along a multi-walled carbon nanotube (MWNT): it is shown that the relative magnitude of ω o compared to γ determines that the analytical formula is a good approximation for MWNTs but requires numerical correction for fibers. Furthermore, it is shown that the analytical form of ω o specified a maximum current beyond which the carbon emitter fails due to thermal runaway. The theoretical models are used to interpret observed behavior of field emission from carbon fibers and the resulting damage they endure when the extracted field-emission current is high. Results from implementing the developed temperature variation model into the MICHELLE beam optics simulation code are presented, with an example application predicting the conditions for stable equilibrium operation as well as for the onset of fiber failure. [ABSTRACT FROM AUTHOR]

A methodology for implementing the recently developed reformulated general thermal-field equation describing simultaneous thermal and field emission contributions to electron emission is developed, with modifications directed to enhancing speed and accuracy of computation as demanded by emitter characterization and electron beam simulations. An accurate factor to correct both thermal-field (T F) and high field (Fowler-Nordheim or FN) predictions based on a rapid Lorentzian fit model is given. The analytic protrusion model is constructed from modifications to a point dipole model that allow surface elements and field enhancement factors to be rapidly evaluated. The model is applied to an analytical model of a protrusion on a bump in a diode configuration to characterize how current-voltage I (V) relations are affected by T F emission conditions. In addition, it is also shown (i) how aggressively Schottky's conjecture is undermined as the protrusion dimensions become larger; (ii) how the total current in the T F regime can be substantially larger than predicted by canonical [FN and Richardson-Laue-Dushman (RLD)] formulations; (iii) how an optimal protrusion size may exist; and (iv) how the inference of field enhancement, notional emission area, and work function are poorly predicted using conventional methods relying on the canonical FN and RLD equations even outside the thermal-field regime, even though data can be linear on FN and RLD plots. [ABSTRACT FROM AUTHOR]

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A methodology of modeling nonplanar surfaces, in which the microscale features of the emission sites can be orders of magnitude smaller than the mesoscale features defining the active emission area, has been developed and applied to both ordered arrays of identical emitters and random variations characteristic of a roughened surface. The methodology combines a general thermal-field-photoemission model for electron emission, a point charge model for the evaluation of field enhancement factors and surface geometry, and a Ballistic-Impulse model to account for the trajectories of electrons close to the cathode surface. How microscale and mesoscale features can both undermine the estimation of thermal-field emission parameters, such as characteristic field enhancement and total current predictions, as well as give rise to changes in the distribution of transverse velocity components used to estimate beam quality features such as emittance that are important to photocathodes, is quantified. The methodology is designed to enable both the proper characterization of emitters based on experimental current-voltage data and the development of a unit cell model of emission regions that will ease the emission model demands in beam optics codes. [ABSTRACT FROM AUTHOR]

The strengths of beam current and velocity modulation produced in gridded electron gun are calculated. It is shown that under normal conditions, the initial modulation is dominated by density variation rather than velocity variation.

Quantum tunneling by field emission from nanoscale features or sharp field emission structures for which the anode-cathode gap is nanometers in scale (“nano diodes”) experience strong deviations from the planar image charge lowered tunneling barrier used in the Murphy and Good formulation of the Fowler-Nordheim equation. These deviations alter the prediction of total current from a curved surface. Modifications to the emission barrier are modeled using a hyperbolic (prolate spheroidal) geometry to determine the trajectories along which the Gamow factor in a WKB-like treatment is undertaken; a quadratic equivalent potential is determined, and a method of shape factors is used to evaluate the corrected total current from a protrusion or wedge geometry. [ABSTRACT FROM AUTHOR]

Although Fowler and Nordheim developed the basics of field emission nearly one century ago with their introduction of the Fowler-Nordheim equation (FNE), the topic continues to attract research interest particularly with the development of new materials that have been proposed as field emitters. The first order analysis of experiments typically relies upon the FNE for at minimum a basic understand of the physical emission process and its parameters of emission. The three key parameters in the FNE are the work function, emission area, and field enhancement factor, all of which can be difficult to determine under experimental conditions. This paper focuses in particular, on the field enhancement factor β. It is generally understood that β provides an indication of the surface roughness or sharpness of a field emitter cathode. However, in this paper, we experimentally and computationally demonstrate that cathodes with highly similar surface morphologies can manifest quite different field enhancements solely through having different emission regions. This fact can cause one to re-interpret results in which a single sharp emitter is proposed to dominate the emission from a field emitting cathode. [ABSTRACT FROM AUTHOR]

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects of both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat the meso-scale diode region separate from the micro-scale regions characteristic of the emission sites. The consequences of discrete emission events are given for both one-dimensional (sheets of charge) and three dimensional (rings of charge) models: in the former, results converge to steady state conditions found by theory (e.g., Rokhlenko et al. [J. Appl. Phys. 107, 014904 (2010)]) but show oscillatory structure as they do. Surface roughness or geometric features are handled using a ring of charge model, from which the image charges are found and used to modify the apex field and emitted current. The roughness model is shown to have additional constraints related to the discrete nature of electron charge. The ability of a unit cell model to treat field emitter structures and incorporate surface roughness effects inside a beam optics code is assessed. [ABSTRACT FROM AUTHOR]

An oft used approximation to predict quantum efficiency (QE) from bare metals or those with a low work function coating such as cesium is to assume that photo-excited electrons have not scattered prior to their emission. Monte Carlo simulations are used to assess that approximation, and show that, while good for bare metals, for cesiated metals a photoexcited electron may undergo several scattering events and yet be emitted. Neglecting scattered electrons therefore underestimates QE. Emitted electrons that have undergone scattering before emission elongate the response time by giving rise to a long time tail, low energy contribution to the faster non-scattered emission, for which a model is developed. The theory is applied to study variations in QE as a function of wavelength measured from cesiated metal surfaces. The extension of the findings to semiconductor photocathodes is briefly discussed. [ABSTRACT FROM AUTHOR]

Passing an electron beam through an aperture can serve to reduce the beam current or change the transverse beam profile. For a sufficiently intense beam, space charge will drive a radial expansion of the beam, which may cause the current passing through the aperture to decrease even though the current arriving at the aperture is increasing. When a gridded electron gun is used, this may be expressed by stating that the transconductance of the apertured gun is negative. Here, we explain this effect and explore some of the key factors governing when it can occur and influencing its strength. [ABSTRACT FROM AUTHOR]