J. R. Harris

Edge enhancement control in linear arrays of ungated field emitters

In arrays of ungated field emitters, the field enhancement factor of each emitter decreases as the distance between the emitters decreases, an effect known as screening. At the edge of these arrays, emitters experience reduced screening, leading to higher field enhancement factors than emitters at the array center, causing nonuniform emission across the array. Here, we consider this effect in linear arrays of ungated field emitters spaced at distances comparable to their heights, which is the regime that generally maximizes their average current density. A Line Charge Model is used to assess the degree to which these edge effects propagate into the array interior, and to study the impact of varying the height, location, and tip radius of emitters at the ends of an array on the edge enhancement. It is shown that each of these techniques can accomplish this edge enhancement control, but each has advantages and disadvantages that will be discussed.

Dependence of optimal spacing on applied field in ungated field emitter arrays

In ungated field emitter arrays, the field enhancement factor β of each emitter tip is reduced below the value it would have in isolation due to the presence of adjacent emitters, an effect known as shielding or screening. Reducing the distance b between emitters increases the density of emission sites, but also reduces the emission per site, leading to the existence of an optimal spacing that maximizes the array current. Most researchers have identified that this optimal spacing is comparable to the emitter height h, although there is disagreement about the exact optimization. Here, we develop a procedure to determine the dependence of this optimal spacing on the applied electric field. It is shown that the nature of this dependence is governed by the shape of the β(b) curve, and that for typical curves, the optimal value of the emitter spacing b decreases as the applied field increases.

Practical considerations in the modeling of field emitter arrays with line charge distributions

Predictive models of field emission remain elusive, in part, due to the sensitivity of this process to emitter surface details at length scales ranging from macroscopic to atomic. Moving towards more fully predictive models requires that we develop techniques to disentangle contributions of features on the largest length scales, which can be easily measured and controlled, from contributions on smaller length scales, which are generally difficult to measure or control. Here, specific challenges are addressed, with an emphasis on comparisons between a Line Charge Model (LCM) and experimental measurements of ungated carbon fiber field emitter arrays. The LCM with appropriate corrections is used to understand the macroscale contributions to field enhancement and emission current for physical emitters, with contributions from the microscale structure isolated using suitable approximations. We will show that excellent agreement can be obtained between the LCM and experiments when the net contributions of the m...

Field emission characteristics of a small number of carbon fiber emitters

This paper reports an experiment that studies the emission characteristics of small number of field emitters. The experiment consists of nine carbon fibers in a square configuration. Experimental results show that the emission characteristics depend strongly on the separation between each emitter, providing evidence of the electric field screening effects. Our results indicate that as the separation between the emitters decreases, the emission current for a given voltage also decreases. The authors compare the experimental results to four carbon fiber emitters in a linear and square configurations as well as to two carbon fiber emitters in a paired array. Voltage-current traces show that the turn-on voltage is always larger for the nine carbon fiber emitters as compared to the two and four emitters in linear configurations, and approximately identical to the four emitters in a square configuration. The observations and analysis reported here, based on Fowler-Nordheim field emission theory, suggest the ele...

Current from a nano-gap hyperbolic diode using shape-factors: Theory

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.

Propagation of modulated electron and X-ray beams through matter and interactions with radio-frequency structures

The generation and evolution of modulated particle beams and their interactions with resonant radiofrequency (RF) structures are of fundamental interest for both particle accelerator and vacuum electronic systems. When the constraint of propagation in a vacuum is removed, the evolution of such beams can be greatly affected by interactions with matter including scattering, absorption, generation of atmospheric plasma, and the production of multiple generations of secondary particles. Here, we study the propagation of 21 MeV and 25 MeV electron beams produced in S-band and L-band linear accelerators, and their interaction with resonant RF structures, under a number of combinations of geometry, including transmission through both air and metal. Both resonant and nonresonant interactions were observed, with the resonant interactions indicating that the RF modulation on the electron beam is at least partially preserved as the beam propagates through air and metal. When significant thicknesses of metal are plac...

Modeling behavior of Computer Generated Forces with Machine Learning Techniques, the NATO Task Group approach

Commercial/Military-Off-The-Shelf (COTS/MOTS) Computer Generated Forces (CGF) packages are widely used in modeling and simulation for training purposes. Conventional CGF packages often include artificial intelligence (AI) interfaces, but lack behavior generation and other adaptive capabilities. We believe Machine Learning (ML) techniques can be beneficial to the behavior modeling process, yet such techniques seem to be underused and perhaps under-appreciated. This paper aims at bridging the gap between users in academia and the military/industry at a high level when it comes to ML and AI. We address specific requirements and desired capabilities for applying machine learning to CGF behavior modeling applications. The paper is based on the work of the NATO Research Task Group IST-121 RTG-060 Machine Learning Techniques for Autonomous Computer Generated Entities.

Propagation and detection of RF-modulated electron and X-ray beams in air

Electron beams produced in RF linear accelerators will naturally be modulated at the RF frequency. Here we report measurements of the RF harmonic content of a 21.6 MeV electron beam coasting in air, as well as the RF harmonic content of x-rays produced from that electron beam, and the effects of these modulated electron and x-ray beams on several fast detection systems. The RF fundamental and its higher harmonics were found to be impressed onto the x-rays generated from the electron beam, and the response of an RF waveguide to passage of the modulated x-ray signal indicated that this harmonic content was also impressed onto the secondary electrons produced by the passage of the x-rays through the waveguide. An unexpected, interference-like effect was observed, which was particularly prominent in the case of the waveguide when struck by the modulated x-rays. The participation of secondary electrons produced by passage of the x-rays through the x-ray converter upstream of the waveguide was ruled out as a si...

Photonic Crystal-Based High-Power Backward Wave Oscillator

An electron beam traversing a slow wave structure can be used to either generate or amplify electromagnetic radiation through the interaction of the slow space charge wave on the beam with the slow wave structure modes. Here, a cylindrical waveguide with a periodic array of conducting loops is used for the slow wave structure. This paper considers operation as a backward wave oscillator. The dispersion properties of the structure are determined using a frequency-domain eigenmode solver. The interaction of the electron beam with the structure modes is investigated using a 2-D particle-in-cell (PIC) code. The operating frequency and growth rate dependence on beam energy and beam current are investigated using the PIC code and compared with analytic and scaling estimates where possible.

Field emission properties of arrays of carbon-nanotube-based fibers

Recently, we presented a multiscale model of field emission (FE) from carbon nanotube fibers (CBFs) taking into account Joule heating within the fiber and radiative cooling and the Nottingham effect at the tip of the individual carbon nanotubes in the array located at the fiber tip [1]. The model was used to predicts the fraction of carbon nanotubes (CNTs) being destroyed as a function of the applied external electric field and reproduces many experimental features observed in some recently investigated carbon nanotube fibers such as, order of magnitude of the emission current (mA range), low turn on electric field (fraction of V/μm), deviation from pure Fowler-Nordheim behavior at large applied electric field, hysteresis of the FE characteristics, and a spatial variation of the temperature along the CNF axis with a maximum close to its tip of a few hundred °C. In this work, we report the simulations of the field emission properties from small arrays of carbon nanotube fibers in the presence of shielding effects. The latter are modeled using the line charge model recently developed by Harris et al. [2-5]. The average total emission current and its variance for linear arrays composed of seven carbon nanotube fibers are calculated to show their sensitivity to the morphology of the apex of the individual fibers which are modeled as random arrays of CNTs. In practice, the FE properties of the latter can be strongly dependent of the cutting technique used to form the fiber apexes.