John R. Harris

Effective field enhancement factor and the influence of emitted space charge

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.

Discrete space charge affected field emission: Flat and hemisphere emitters

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.

Expansion of a Surface Flashover Plasma

A strong electric field applied parallel to the surface of a dielectric in vacuum can lead to the formation of a vacuum surface flashover discharge, which will produce light, neutral gas, and plasma. Plasma formed in this way can be used for a number of applications, including as a source of electrons, but the plasmas expansion away from the discharge site will impact its usefulness for those applications. Here, we report measurements on the expansion of a surface flashover plasma generated from a pulsed discharge in vacuum, using electric fields on the order of 10 MV/m applied across a Plexiglas sample. Expansion velocity and energy distribution measurements were made using a moveable, biased detector probe. The temporal structure of the plasma arriving at the probe was found to have a characteristic shape, indicating the presence of three different components of the plasma having different velocities in the range of 1-9 cm/μs. The pulser charging voltage was found to have a noticeable effect on the plasma energy distributions, but only a small effect on the plasma expansion velocity.

2D/3D image charge for modeling field emission

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbon nanotube and carbon fiber field emitters is discussed.

Electron Back-Bombardment and Mitigation in a Short Gap, Thermionic Cathode RF Gun

When an un-gated thermionic cathode is operated in a radio-frequency gun, some fraction of the emitted electrons will return to the cathode due to the change in sign of the electric field in the gun. This back-bombardment current causes heating of the cathode, and this reduces the ability of the cathode heater to control the bunch charge. In this paper, we investigate the fundamental factors in single-frequency back-bombardment for a short-gap electron gun. Simulations revealed that the back-bombardment power depends strongly on the operating frequency and the bunch charge. Additionally, the use of a two-frequency TM010/TM020 electron gun to mitigate this effect was investigated which revealed that the effectiveness of this technique depends strongly upon single-frequency back-bombardment power but with the optimal reduction in back-bombardment power (62% of the baseline) occurring in the low-frequency limit.

Linear permittivity tapering in a Cerenkov microwave source with a pre-bunched beam

Cerenkov microwave sources use a dielectric-lined waveguide to reduce the velocity of the electromagnetic wave and provide efficient energy transfer between the wave and the driving electron beam. Tapering the permittivity of the dielectric to maintain synchronism between the beam and the wave as the beam loses energy can increase the efficiency of these devices. Here, we consider such a structure driven by an electron beam with a harmonic density perturbation. Particle-In-Cell (PIC) simulations and a macro-particle model based on the slowly varying envelope approximation are first used to examine an un-tapered baseline case. PIC simulations of the source with linear tapers over the entire amplifier length as well as over only a section of the amplifier where the beam executes synchrotron oscillations are examined. The efficiency for the baseline un-tapered source is 18%, while efficiencies up to approximately 48% are found using a taper in dielectric permittivity. Results of the best performing cases are presented. Detailed examination of longitudinal phase space, particle energy distributions, evolution of longitudinal wavenumber, and phase dynamics are presented from the PIC simulations.

Transport of Electron Beams with Initial Transverse-Longitudinal Correlation

When an electron beam whose current varies in time is extracted from a DC gun, the competition between the time-dependent space charge force and the time-independent focusing force will cause a correlation between radius, divergence, current, and position along the beam. This correlation will determine the beams configuration in trace space, and together with the design of the downstream transport system, will determine the quality of the transport solutions that can be obtained, including the amplitude of the mismatch oscillations occurring in each slice of the beam. Recent simulations of a simplified diode with Pierce-type focusing operating at nonrelativistic voltages indicated that the radius and divergence of beams extracted from such guns can be approximated to high accuracy as linear functions of current. Here, we consider the impact of this dependence on the beam configuration in trace space and investigate the implications for matching and transport of such correlated beams in uniform linear foc...

Transverse-longitudinal correlations in electron guns

When a modulated beam is produced in a DC electron gun, the time-dependent space charge force and the time-independent focusing force produce a correlation between current, position along the beam, and the beam’s radius and divergence. This has implications for beam extraction and downstream beam transport. Here, we simulate an electrostatically-focused DC electron gun to study this correlation. Beam radius and divergence at the anode are found to be approximately linear functions of beam current, and the consequences for beam loss and extraction are considered.

Control of bulk and edge screening effects in two-dimensional arrays of ungated field emitters

In arrays of ungated field emitters, nearby emitters introduce a screening effect, reducing each emitters field enhancement factor below its value in isolation. At the edge of the array, however, the strength of this screening effect is reduced because the number of nearby emitters is reduced, leading to a variation in the emitted current with position in the array. This may have detrimental effects on the emitted beam properties and lead to increased damage to the emitters near the edge due to increased current, heating, and ion bombardment. In this work, the authors apply line and point charge models to study the impact of screening on the performance of two-dimensional field emitter arrays, with an emphasis on quantifying the extent of the edge enhancement effect, and on assessing potential means to control it.

Generation and focusing of electron beams with initial transverse-longitudinal correlation

In charged particle beams, one of the roles played by space charge is to couple the transverse and longitudinal dynamics of the beam. This can lead to very complex phenomena which are generally studied using computer simulations. However, in some cases models based on phenomenological or analytic approximations can provide valuable insight into the system behavior. In this paper, we employ such approximations to investigate the conditions under which all the slices of a space charge dominated electron beam with slowly varying current could be focused to a waist with the same radius and at the same location, independent of slice current, and show that this can be accomplished approximately if the initial transverse-longitudinal correlation introduced onto the beam by the electron gun is chosen to compensate for the transverse-longitudinal correlation introduced onto the beam in the drift section. The validity of our approximations is assessed by use of progressively more realistic calculations. We also consider several design elements of electron guns that affect the initial correlations in the beams they generate.