Wilkin Tang

Experimental study of electric field screening by the proximity of two carbon fiber cathodes

This paper describes the first experiments that use only two carbon fiber field emitters with different separations to quantify and isolate the effect of electric field screening. Experiments show that when the separation between the two carbon fiber cathodes decreases, both the effective field enhancement factor, βeff, and the current emission decreases. For a two-emitter geometry, our experiment suggests a height of approximately 1.5 times the separation between the two cathodes as the optimum ratio to optimize the emitted current. The paper shows the analysis of the turn on voltage of the field emitters for different separations. The authors compare experimental data with Fowler–Nordheim field emission theory and particle-in-cell simulation, showing good agreement between experiment, theory, and modeling.

Experimental validation of a higher dimensional theory of electrical contact resistance

The increased resistance of a cylindrical conducting channel due to constrictions of various radii and axial lengths was measured experimentally. The experimental data corroborate the higher dimensional contact resistance theory that was recently developed.

A re-examination of the Buneman–Hartree condition in a cylindrical smooth-bore relativistic magnetron

The Buneman–Hartree condition is re-examined in a cylindrical, smooth-bore, relativistic magnetron using both the conventional, single particle model, and the Brillouin flow model. These two models yield the same result for the Buneman–Hartree condition only in the limit of a planar magnetron. When b/a=1.3, where a is the cathode radius and b (>a) is the anode radius, the difference in the two models becomes significant. When b/a=4 the difference is acute, the Buneman–Hartree magnetic field at a given voltage in the Brillouin flow model exceeds four times that in the single particle model. Such a difference is always present, whether the voltage is relativistic or not. These results are quantified for b/a⪢1 using Davidson’s model, conveniently cast in terms of the normalized gap voltage and normalized magnetic flux imposed on the cylindrical magnetron. A comparison with the University of Michigan/L-3 relativistic magnetron experiment is given.

Heating of a particulate by radio-frequency electric and magnetic fields

With the use of a highly symmetrical model, the heating of a spherical particulate by a predominantly radio-frequency electric field and by a predominantly rf magnetic field is solved exactly using the Maxwell equations. It is found that, in general, heating by the rf magnetic field is dominant whenever δ<a, where δ is the resistive skin depth and a is the radius of the particulate, which may either be nonmagnetic or magnetic. The known analytic scaling laws in the various regimes are recovered, from the static case to very high frequency, subject to λ⪢a, where λ is the free space wavelength of the rf field. The analysis may form a theoretical basis in the heating phenomenology of particulates.

Effect of soft metal gasket contacts on contact resistance, energy deposition, and plasma expansion profile in a wire array Z pinch.

Soft metal gaskets (indium and silver) were used to reduce contact resistance between the wire and the electrode in an aluminum wire Z pinch by more than an order of magnitude over the best weighted contact case. Clamping a gasket over a Z-pinch wire compresses the wire to the electrode with a greater normal force than possible with wire weights. Average contact resistance was reduced from the range of 100-3000 Omega (depending on wire weight mass) to 1-10 Omega with soft metal gaskets. Single wire experiments (13 microm Al 5056) on a 16 kA, 100 kV Marx bank showed an increase in light emission (97%) and emission volume (100%) of the plasma for the reduced contact resistance cases. The measured increases in plasma volume and light emission indicate greater energy deposition in the ablated wire. Additionally, dual-wire experiments showed plasma edge effects were significantly decreased in the soft metal gasket contact case. The average height of the edge effects was reduced by 51% and the width of the edge effects was increased by 40%, thus the gasket contact case provided greater axial uniformity in the plasma expansion profile of an individual wire.

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.

The Ohmic heating of particulates in a lossless medium

This paper provides a general theory on the Ohmic dissipation of electromagnetic energy by a spherical particulate that is embedded in a lossless medium. The particulate may possess an arbitrary electrical conductivity, and both the medium and the particulate may assume general values of permittivity and permeability. Under the assumption that the wavelength of the electromagnetic field in the medium is large compared with the particulate size, we provide an accurate account of the degree of Ohmic heating by the radio frequency (rf) electric field and by the rf magnetic field of the electromagnetic field. It is found that, in general, heating by the rf magnetic field is dominant whenever δ<a, where δ is the resistive skin depth and a is the radius of the particulate. Analytic scaling laws in the various regimes are derived, from the static case to very high frequency, and for ratios of δ∕a ranging from zero to infinity. The calculation is extended to a transient electromagnetic pulse. Also constructed is ...

MAIZE: a 1 MA LTD‐Driven Z‐Pinch at The University of Michigan

Researchers at The University of Michigan have constructed and tested a 1‐MA Linear Transformer Driver (LTD), the first of its type to reach the USA. The Michigan Accelerator for Inductive Z‐pinch Experiments, (MAIZE), is based on the LTD developed at the Institute of High Current Electronics in collaboration with Sandia National Labs and UM. This LTD utilizes 80 capacitors and 40 spark gap switches, arranged in 40 “bricks,” to deliver a 1 MA, 100 kV pulse with 100 ns risetime into a matched resistive load. Preliminary resistive‐load test results are presented for the LTD facility.Planned experimental research programs at UM include: a) Studies of Magneto‐Raleigh‐Taylor instability of planar foils, and b) Vacuum convolute studies including cathode and anode plasma.

Field enhancement for fiber emitters in linear and rectangular arrays

One of the key issues for understanding the emission physics of field emitters is the determination of the field enhancement factor β. Quantifying β is complicated by determining accurate values for the work function and emission area. In this article, the authors consider two and four carbon fiber emitters in linear and square arrays in which the geometry, hence β, can be carefully controlled, while computational methods allow an estimate of the emission area. In order to reduce the effects of work function variation between different fibers, all the carbon fiber cathodes the authors use are made with the same materials and underwent the same manufacturing process. This approach reduces the influence of work function and emission area on experimental results. While single emitter tips and large arrays of emitters (∼1000 s) have been studied in the past, this article addresses the emission of low numbers (<10) of field emitters in carefully controlled geometries. Studying such configurations allows us to ...

Nonlinear transmission line based electron beam driver

Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.