John J. Petillo

The MICHELLE three-dimensional electron gun and collector modeling tool: theory and design

The development of a new three-dimensional electron gun and collector design tool is reported. This new simulation code has been designed to address the shortcomings of current beam optics simulation and modeling tools used for vacuum electron devices, ion sources, and charged-particle transport. The design tool specifically targets problem classes including gridded-guns, sheet-beam guns, multibeam devices, and anisotropic collectors, with a focus on improved physics models. The code includes both structured and unstructured grid systems for meshing flexibility. A new method for accurate particle tracking through the mesh is discussed. In the area of particle emission, new models for thermionic beam representation are included that support primary emission and secondary emission. Also discussed are new methods for temperature-limited and space-charge-limited (Childs law) emission, including the Longo-Vaughn formulation. A new secondary emission model is presented that captures true secondaries and the full range rediffused electrons. A description of the MICHELLE code is presented.

Recent developments to the MICHELLE 2-D/3-D electron gun and collector modeling code

Recent developments to the MICHELLE electron gun and collector design tool are reported in this paper. The MICHELLE code is a new finite-element (FE) two-dimensional and three-dimensional electrostatic particle-in-cell code that has been designed to address the recent beam optics modeling and simulation requirements for vacuum electron devices, ion sources, and charged-particle transport. Problem classes specifically targeted include depressed collectors, gridded-guns, multibeam guns, sheet-beam guns, and ion thrusters. The focus of the development program is to combine modern FE techniques with improved physics models. The code employs a conformal mesh, including both structured and unstructured mesh architectures for meshing flexibility, along with a new method for accurate, efficient particle tracking. New particle emission models for thermionic beam representation are included that support primary emission, with an advanced secondary emission model. This paper reports on three significant advances to MICHELLE over the past year; hybrid structured/unstructured mesh support, a time-domain electrostatic algorithm, and an ion plasma model with charge exchange.

Intense Sheet Electron Beam Transport in a Uniform Solenoidal Magnetic Field

In this paper, the transport of intense sheet electron beams in a uniform solenoidal magnetic field in high-power vacuum electronic devices is theoretically examined with the 3-D beam optics code MICHELLE. It is shown that a solenoidal magnetic field can be an effective transport mechanism for sheet electron beams, provided the beam tunnel is matched to the beam shape, and vice versa. The advantage of solenoidal magnetic field transport relative to periodic magnetic transport resides in the feasibility of transporting higher current density beams due to the higher average field strength achievable in practice and the lower susceptibility to field errors from mechanical misalignments. In addition, a solenoidally transported electron beam is not susceptible to voltage cutoff as in a periodic magnetic focusing system; hence, device efficiency is potentially higher.

High-power four-cavity S-band multiple-beam klystron design

We develop a methodology for the design of multiple-cavity klystron interaction circuits. We demonstrate our approach with the detailed design of a collector and a four-cavity circuit for a multiple-beam klystron (MBK) operating in the fundamental mode at a center frequency of 3.27 GHz (S-band). These elements are designed to be used with a 32-A 45-kV magnetically shielded eight-beam electron gun currently under fabrication . Upon integration of the gun, circuit, and collector, the MBK will be used for beam transport and beam-wave interaction studies and to validate developmental design codes and design methodologies. The device has a predicted gain of 33 dB at a peak pulsed output power of 750 kW with a corresponding electronic efficiency of 52%. For the present design, broad bandwidth is not a design objective, and the 3-dB bandwidth is 2.5%. Downstream of the output cavity, the magnetic field profile and the interior surface profile of the collector are carefully shaped to minimize the space-charge potential depression at the entrance to the collector, minimizing reflected electrons. The maximum calculated instantaneous power density on the walls of the collector is approximately 55 kW/cm/sup 2/; at low duty cycles (<1.8%), the average power density is well within the limits for liquid cooling for pulse lengths up to 1.3 ms.

Electron gun design for fundamental mode S-band multiple-beam amplifiers

This paper describes the detailed design of an eight-beam electron gun for use in S-band multiple-beam amplifiers operating in the fundamental mode. The gun operating voltage is 45 kV with a total beam current of 32 A, evenly divided among the beamlets. Each individual beam has a perveance of 0.42 mpervs making a total beam perveance of 3.35 mpervs. The optimized electron gun is singly convergent using a four-fold symmetry with the four inner and four outer emitters interlaced 90/spl deg/ apart. The emitter current density has been kept below 10 A/cm/sup 2/ (space-charge limited). The cathode is magnetically shielded and the longitudinal magnetic field in the interaction region is in the range of 1.1-1.8 kG. The design of the magnetic focusing system minimizes beam corkscrewing as well as electron interception on the tunnel walls. Beam optics simulations of the gun indicate excellent beam transport characteristics with a final beam-to-tunnel radial fill factor of less than 0.45. The primary computational tools used in the design process were the three-dimensional gun code MICHELLE, and the magnetostatics code MAXWELL-3D.

Sheet-Beam 90 GHz and 220 GHz Extend-Interaction-Klystron Designs

Circuit designs for 91 GHz and 220-GHz sheet-beam extended-interaction klystrons (EIKs) are presented. The W-band circuit employs a relatively simple two-cavity configuration to demonstrate beam transport and high peak power RF generation, which will serve as the basis for future scaling to higher gain and frequencies. Uniform (solenoidal) magnetic focusing is employed in both cases. Simulations with MAGIC-3D indicate peak RF powers of 10.5 kW and >400 W are feasible with a 3 A, 19.5 kV beam and a 0.5 A, 16.5 kV beam at 91 GHz and 220 GHz, respectively. Proof of principle experimental demonstrations are planned.

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.

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.

Wide band Ka-band Coupled-Cavity Traveling Wave Tube (CCTWT) development

A series of Ka-band Coupled-Cavity Traveling-Wave Tubes (CCTWTs) has been successfully developed, built, and tested at Communications and Power Industries (CPI) in collaboration with the Naval Research Laboratory (NRL) and SAIC. These devices represent a significant advance in the state-of-the-art of millimeter-wave CCTWTs, exploring the limits of power, bandwidth, and stability. We discuss the design and successful demonstration of the series of CCTWTs, including the VTA-6430N1 prototype which achieved over 700-W (879-W maximum power) over a 5-GHz range in Ka-band.

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.