Emitter Height Research Articles

Supression of Shielding Effect of Large Area Field Emitter cathode in Radio Frequency Gun environment

Abstract Using large area field emitters (LAFE) as cathodes for RF gun injectors offers significant potential for creating compact, high-power, and high-brightness electron beams, crucial for advanced accelerator technologies. However, when subjected to DC electric fields, LAFEs face significant challenges due to the shielding effect, which limits emission from central emitters and decreases overall current density. Overcoming the shielding effect in an RF gun environment is essential to meet the required beam quality in accelerators. The current distribution of LAFE under DC conditions is influenced by several geometric parameters, such as emitter height, inter-emitter distance, aspect ratio, and the number of emitters. Moreover, in an RF gun setup, LAFEs experience varying macroscopic electric fields at different emitter positions, altering the current distribution compared to DC fields. In this study, we have systematically examined the impact of various LAFE parameters on their field emission performance in an RF gun environment. We have adopted a semi-analytical approach to estimate the current distribution of LAFE, combining analytically calculated field enhancement factors (γ) with numerically calculated applied RF field values. After validating the method with COMSOL simulations, we have applied it to estimate the current distribution of an LAFE cathode integrated into a ½ cell S-band (2856 MHz) gun. The simulation results indicate that, under favorable conditions, a Gaussian spatial beam distribution can be achieved with LAFE, thus mitigating the shielding effect typical in DC fields. By optimizing various LAFE parameters, the desired current and beam distribution patterns can be attained. This study highlights a promising approach for designing LAFE cathodes for RF guns, which could advance accelerator-related technologies.

Statistical Characterization of Emitter Fabrication over Electrospray Array Thruster

A method for characterizing the variance in fabrication of emitters and extractors in a porous conical electrospray array thruster is presented. Coherence scanning interferometry is used to produce topographic maps of 543 of 576 sites within the array. The emitter and extractor geometries, features of size a few hundred micrometers, are modeled as a spherically capped cone recessed from a circular aperture. Regressing this model against the topographic maps yields a set of salient parameters that describe the geometry of a site, including the tip radius and height of the emitter and its offset from the extractor aperture. Statistics over the emitter geometries are computed, which represent manufacturing tolerances. It is found that key parameters like the emitter tip radius are highly variable (mean 25.8 μm and standard deviation 20.9 μm), highlighting the stochastic nature of the manufacturing process. Correlations between the tip radius and emitter height indicate that this variability arises from blunting of the emitters during fabrication, and the observation that emitters are shorter than nominal is explained by an increase in effective cutting diameter of the tools. Further analysis indicates that determining the mean emitter tip radius of the entire population within 5% error requires over 300 individual emitter measurements. These results indicate that accurately quantifying emitter variability at scale requires rigorous and extensive analysis, and the implications of this emitter variability for device performance and design are discussed.

Semi-analytical modeling of large area field emitters having non-identical pins

The Line Charge Model (LCM) is an excellent analytical tool to model vertically aligned nano-tips in large area field emitters (LAFE). The linear line charge model is exact for isolated hemi-ellipsoidal nano-tips placed in a uniform external electric field. It has recently been used to model a LAFE with randomly placed identical emitters. The results are accurate when the mean spacing c is moderate to large compared to the emitter height h. In a closely packed LAFE (c⪅0.75h), the LCM underpredicts the apex enhancement factor. We introduce a heuristic correction in the LCM result that yields a better accuracy in predicting the apex enhancement factor over a wider range of mean spacing. The corrected LCM model is then used to simulate emitter shapes having a distribution in the height of emitters and apex radius of curvature Ra. A hybrid approach is adopted for non-ellipsoidal shapes where the line charge density is nonlinear and, hence, harder to implement. Predictions for the apex enhancement factor and the net emission current are found to be reasonably accurate for a LAFE with a wide variation in h and Ra values.

Evaluation of electron currents from cesium-coated tungsten emitter arrays with inclusion of space charge effects, workfunction changes, and screening

Evaluations of electron current output from tungsten emitter arrays with Cs and CsI coatings are carried out. The approach is based on first-principles calculations of the material physics including evaluation of the internal potentials, electronic wavefunctions, tunneling probabilities, and work function to predict field emission currents. This is coupled to time-dependent kinetic simulations for the assessment of emitter array currents with an inclusion of many-body Coulomb contributions from the electron swarm, geometric field enhancements with shielding based on a line charge model and dynamic screening from the swarm. Our numerical evaluations for arrays with a hexagonal lattice show the expected role of field screening with reductions in emitter separation. For scaling with emitter number, the results indicate nearest neighbor separations of more than 2.5 times the emitter height, in keeping with previous reports.

Numerical investigation of the effects of geometry and materials on the onset voltage of electrospray emitters

Guidelines for the design of 2D electrospray emitter arrays that operate at minimal emission onset voltage are established by analyzing the dependence of the emission onset voltage on key emitter dimensions. The electrostatic field, and resulting onset voltage, are determined numerically for different configurations. The relative permittivity of the medium surrounding the emitters is varied between 1 and 10 to consider two types of emitters: capillary emitters standing in vacuum, and capillary emitters embedded in a dielectric material. Results for single electrospray emitters are compared to those of an analytical model. Trends in the data imply minimal onset voltage when using dielectrics with low relative permittivity, small-diameter emitters tall enough to escape shielding from the surrounding features of the device, and a small extractor distance. However, these relationships are complex and are discussed in detail. The data also agrees with previous numerical research into arrays of emitters showing that at an emitter spacing of approximately 2.5 times the emitter height, shielding effects become negligible. These design guidelines and the specific results reported herein are particularly relevant to the rapid development of miniaturized electrospray chips holding hundreds, or even thousands, of emitters that are expected to reach market in the near future.

Mitigation of Geostationary Lightning Mapper Geolocation Errors

AbstractThe geolocation of lightning flashes observed by spaceborne optical sensors depends upon a priori assumptions of the cloud-top height (or, more generally, the height of the radiant emitter) as observed by the satellite. Lightning observations from the Geostationary Lightning Mappers (GLMs) on Geostationary Operational Environmental Satellite 16 (GOES-16) and GOES-17 were originally geolocated by assuming that the global cloud-top height can be modeled as an ellipsoidal surface with an altitude of 16 km at the equator and sloping down to 6 km at the poles. This method produced parallax errors of 20–30 km or more near the limb, where GLM can detect side-cloud illumination or below-cloud lightning channels at lower altitudes than assumed by the ellipsoid. Based on analysis of GLM location accuracy using a suite of alternate lightning ellipsoids, a lower ellipsoid (14 km at the equator, 6 km at the poles) was implemented in October and December 2018 for GLM-16 and GLM-17, respectively. While the lower ellipsoid slightly improves overall GLM location accuracy, parallax-related errors remain, particularly near the limb. This study describes the identification of optimized assumed emitter heights, defined as those that produce the closest agreement with the ground-based reference networks. Derived using the first year of observations from GOES-East position, the optimal emitter height varies geographically and seasonally in a manner consistent with known meteorological regimes. Application of the optimal emitter height approximately doubles the fraction of area near the limb for which peak location errors are less than half a GLM pixel.

Verification of shielding effect predictions for large area field emitters

A recent analytical model for large area field emitters [D. Biswas and R. Rudra, Phys. Plasmas 25, 083105 (2018)], based on the line charge model (LCM), provides a simple approximate formula for the field enhancement on hemiellipsoidal emitter tips in terms of the ratio of emitter height to pairwise distance between neighboring emitters. The formula, verified against the exact solution of the linear LCM, was found to be adequate, provided that the mean separation between emitters is larger than half the emitter height, h. In this paper, we subject the analytical predictions to a more stringent test by simulating (i) an infinite regular array and (ii) an isolated cluster of 10 random emitters, using the finite element software COMSOL v5.4. In the case of the array, the error in the apex field enhancement factor (AFEF) is found to be less than 0.25% for an infinite array when the lattice constant c ≥ 1.5h, increasing to 2.9% for c = h and 8.1% for c = 0.75h. For an isolated random cluster of 10 emitters, the error in large AFEF values is found to be small. Thus, the error in the net emitted current is small for a random cluster compared to a regular infinite array with the same (mean) spacing. The LCM thus provides a reasonable analytical tool for optimizing a large area field emitter.

The anode proximity effect for generic smooth field emitters

The proximity of the anode to a curved field electron emitter alters the electric field at the apex and its neighborhood. A formula for the apex field enhancement factor, γa(D), for generic smooth emitters is derived using the line charge model when the anode is at a distance D from the cathode plane. The resulting approximately modular form is such that the anode proximity contribution can be calculated separately (using geometric quantities such as the anode-cathode distance D, the emitter height h, and the emitter apex radius of curvature Ra) and substituted into the expression for γa(∞). It is also shown that the variation of the enhancement factor on the surface of the emitter close to the apex is unaffected by the presence of the anode and continues to obey the generalized cosine law. These results are verified numerically for various generic emitter shapes using COMSOL Multiphysics®. Finally, the theory is applied to explain experimental observations on the scaling behavior of the I–V field emission curve.

Shielding effects in random large area field emitters, the field enhancement factor distribution, and current calculation

A finite-size uniform random distribution of vertically aligned field emitters on a planar surface is studied under the assumption that the asymptotic field is uniform and parallel to the emitter axis. A formula for field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of field lines. The distribution of field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area field emitter.

Mathematical modelling of conjugate heat transfer and fluid flow inside a domain with a radiant heating system

This study deals with the numerical investigation of combined heat transfer by conduction, turbulent natural convection, and surface thermal radiation in a closed square air-filled cavity with a local radiant heater. The turbulent flow was computed within the quasi (pseudo) direct numerical simulation approach. The governing equations were solved by means of the finite difference method. Developed numerical code was validated by comparison of temperature profiles obtained experimentally and numerically. The effect of time, buoyancy force, walls emissivity, and emitter height on local and mean heat transfer characteristics was studied. For the first time it was found that the mean convective Nusselt number at the bottom solid-fluid interface was slightly altered in the cavity with the local radiant heater when varying the governing parameters. An increase in the Rayleigh number led to a significant rise in the overall temperature. The isotherms and streamlines were significantly altered with time. However, the mean radiative Nusselt number was slightly changed over the time.

A universal formula for the field enhancement factor

The field enhancement factor (FEF) is an important quantity in field emission calculations since the tunneling electron current depends very sensitively on its magnitude. The exact dependence of FEF on the emitter height h, the radius of curvature at the apex Ra, as well as the shape of the emitter base are still largely unknown. In this work, a universal formula for the field enhancement factor is derived for a single emitter. It depends on the ratio h/Ra and has the form γa=(2h/Ra)/[α1ln(4h/Ra)−α2], where α1 and α2 depend on the charge distribution on the emitter. Numerical results show that a simpler form γa=(2h/Ra)/[ln(4h/Ra)−α] is equally valid with α depending on the emitter-base. Thus, for the hyperboloid, conical, and ellipsoid emitters, the value of α is 0, 0.88, and 2, while for the cylindrical base, α ≃ 2.6.

Monte Carlo simulation of temporal behavior of surface charging across insulator at flashover initial stage in vacuum

The temporal behaviors of charging on insulator surface at flashover initial stage is studied under dc voltage in vacuum. It suggests that the surface charging process develops synchronously with multipactor phenomena. A saturated region is firstly formed nearby the cathode triple junction (CTJ), and the insulator surface is charged gradually from cathode toward anode as the multipactor develops forward. The surface charge density increases linearly with applied electric field, but a stronger applied electric field will slow down the charging velocity as the results of violent collisions of secondaries with dielectric surface due to the stronger normal field built by surface charges. The charging velocity mainly depends on the secondary electron yield (SEY) for dielectric, i.e., the higher SEY, the greater the charging velocity is. The emitter height from CTJ has great influence on surface charging at areas adjacent to cathode, but little effect on charging behaviors at other areas. Once the multipactor is triggered by adequate initial electrons released from cathode, the surface will be charged spontaneously even if the field emission process at cathode is terminated, implying the generation of secondary electrons turns into a self-sustaining process. This study strongly supports the speculation in our previous publications regarding the mechanisms of stable luminescence preceding flashover, which is attributed to be initialized by Fowler-Nordheim emission of electrons at CTJ and finally generated by the radiative de-excitation of excited atoms/molecules in the self-stabilizing secondary electron emission (SSEE) process.

Assessment of the AERMOD dispersion model over complex terrain with different types of meteorological data: Tracy Power Plant experiment

The accuracy of air pollutants dispersion modelling results depends on the quality of the input data, including the representativeness of the meteorological data. The paper presents the results of the AERMOD model validation using data from Tracy Power Plant experiment (Nevada, USA) with various meteorological data sources, including WRF modelling system outputs. The highest efficiency of the AERMOD model performance was found using site-specific meteorological data and the results from the WRF model. In general, the AERMOD modelling system inadequately represents the concentration levels of tracer gas (SF6 ) at receptors situated below the emitter height in areas of complex topography.

Multi-field electron emission pattern of 2D emitter: Illustrated with graphene

The mechanism of laser-assisted multi-field electron emission of two-dimensional emitters is investigated theoretically. The process is basically a cold field electron emission but having more controllable components: a uniform electric field controls the emission potential barrier, a magnetic field controls the quantum states of the emitter, while an optical field controls electron populations of specified quantum states. It provides a highly orientational vacuum electron line source whose divergence angle over the beam plane is inversely proportional to square root of the emitter height. Calculations are carried out for graphene with the armchair emission edge, as a concrete example. The rate equation incorporating the optical excitation, phonon scattering, and thermal relaxation is solved in the quasi-equilibrium approximation for electron population in the bands. The far-field emission patterns, that inherit the features of the Landau bands, are obtained. It is found that the optical field generates a characteristic structure at one wing of the emission pattern.

Simulation of the enhancement factor from an individual 3D hemisphere-on-post field emitter by using finite elements method

This paper presents a 3D computational framework for evaluating electrostatic properties of a single field emitter characterized by the hemisphere-on-post geometry. Numerical simulations employed the finite elements method by using Ansys-Maxwell software. Extensive parametric simulations were focused on the threshold distance from which the emitter field enhancement factor (γ) becomes independent from the anode-substrate gap (G). This investigation allowed demonstrating that the ratio between G and the emitter height (h) is a reliable reference for a broad range of emitter dimensions; furthermore, results permitted establishing G/h≥2.2 as the threshold condition for setting the anode without affecting γ.

Modelling field emitter arrays using line charge distributions

Field emitter arrays are high-brightness electron sources with important current and future applications in vacuum electronics, particle accelerators, and directed energy. The current produced by individual emitters in these arrays is controlled by the total electric field on their surfaces, which depends on the background field, the space charge field from previously-emitted electrons, and field enhancements due to geometric features at the macro-, meso-, and micro-scales. To facilitate the study of shielding and space charge effects in these arrays, we have developed a mathematical model using tapered line charges to generate equipotential surfaces which approximate the geometry of high aspect ratio field emitters. This model provides an analytic approach for studying contributions to array performance due to macro-scale and meso-scale features such as array geometry, emitter height, and emitter tip radius. Here we present this model and use it to assess the impact of these parameters on the field enhancement factor of individual field emitters and emitters in 1D and 2D arrays.

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.

Multiplexing and scaling-down of nanostructured photon-triggered silicon field emitter arrays for maximum total electron yield

Femtosecond ultrabright cathodes with spatially structured emission are a critical technology for applications such as free-electron lasers, tabletop coherent x-ray sources, and ultrafast imaging. In this work, the optimization of the total electron yield of ultrafast photon-triggered field emission cathodes composed of arrays of nanosharp, high-aspect-ratio, single-crystal silicon pillars is explored through the variation of the emitter pitch and height. Arrays of 6 nm tip radius silicon emitters with emitter densities between 1.2 and 73.9 million tips cm−2 (hexagonally packed arrays with emitter pitch between 1.25 and 10 μm) and emitter height between 2.0 and 8.5 μm were characterized using 35 fs 800 nm laser pulses. Three-photon electron emission for low-energy (<0.3 μJ) light pulses and strong-field emission for high-energy (>1 μJ) light pulses was observed, in agreement with the literature. Of the devices tested, the arrays with emitter pitch equal to 2.5 μm produced the highest total electron yield; arrays with larger emitter pitch suffer area sub-utilization, and in devices with smaller emitter pitch the larger emitter density does not compensate the smaller per-emitter current due to the electric field shadowing that results from the proximity of the adjacent tips. Experimental data and simulations suggest that 2 μm tall emitters achieve practical optimal performance as shorter emitters have visibly smaller field factors due to the proximity of the emitter tip to the substrate, and taller emitters show marginal improvement in the electron yield at the expense of greater fabrication difficulty.

Shielding in ungated field emitter arrays

Cathodes consisting of arrays of high aspect ratio field emitters are of great interest as sources of electron beams for vacuum electronic devices. The desire for high currents and current densities drives the cathode designer towards a denser array, but for ungated emitters, denser arrays also lead to increased shielding, in which the field enhancement factor β of each emitter is reduced due to the presence of the other emitters in the array. To facilitate the study of these arrays, we have developed a method for modeling high aspect ratio emitters using tapered dipole line charges. This method can be used to investigate proximity effects from similar emitters an arbitrary distance away and is much less computationally demanding than competing simulation approaches. Here, we introduce this method and use it to study shielding as a function of array geometry. Emitters with aspect ratios of 102–104 are modeled, and the shielding-induced reduction in β is considered as a function of tip-to-tip spacing for emitter pairs and for large arrays with triangular and square unit cells. Shielding is found to be negligible when the emitter spacing is greater than the emitter height for the two-emitter array, or about 2.5 times the emitter height in the large arrays, in agreement with previously published results. Because the onset of shielding occurs at virtually the same emitter spacing in the square and triangular arrays, the triangular array is preferred for its higher emitter density at a given emitter spacing. The primary contribution to shielding in large arrays is found to come from emitters within a distance of three times the unit cell spacing for both square and triangular arrays.

Advances on Ultrafast Silicon Field Emitter Array Photocathodes for Coherent Radiation Sources Based on Inverse Compton Scattering

Low-cost, compact, and coherent X-rays sources would enable exciting applications such as biomedical imaging of soft tissue and real-time visualisation of molecules at a widespread scale. A promising approach to implement such an X-ray source is based on inverse Compton scattering of a series of nanostructured electron sheets accelerated to relativistic speeds. Photon-triggered field emission arrays can readily produce planar arrays of electron bunches with pC-level sheet charge at high repetition rates using intense laser pulses. In this article, the performance of single-crystal, ultrafast, photon-actuated silicon field emitter arrays is investigated for varying emitter height. Charge vs. incident photon pulse energy characteristics and quantum efficiency of the devices are reported.