Simon J. Cooke

A Leapfrog Formulation of the 3D ADI-FDTD Algorithm

We introduce a new, alternative form of the 3D alternating direction implicit finite-difference time-domain (ADI- FDTD) algorithm that has a number of attractive properties for electromagnetic simulation. We obtain a leapfrog form of the time advance equations, where the E- and H- fields are staggered at half-integer and integer time steps respectively, that preserves the unconditional stability of the ADI-FDTD method. The resulting equations resemble the explicit leapfrog FDTD method, but the field update equations are modified to include the solution of sets of tridiagonal equations at each step, similar to the original ADI- FDTD scheme, so that the scheme is not constrained by the Courant-Friedrichs-Lewy (CFL) limit. The algorithm is simpler than the ADI-FDTD method but algebraically equivalent, allowing a reduction in computation to achieve the same numerical solution. We discuss the advantages of the formulation over the original FDTD and ADI-FDTD methods, and confirm our results numerically.

Parallel Simulation of Independent Beam-Tunnels in Multiple-Beam Klystrons Using TESLA

We present an extension of the klystron simulation code TESLA to model multiple-beam klystrons (MBKs) in which interaction parameters may vary significantly from beam-tunnel to beam-tunnel. In earlier work, the single-beam code was applied to model the MBK by assuming that all electron beams and beam-tunnels were identical and all electron beams interacted identically with the fields of the resonant cavities, using averaged values of R/Q to represent interaction with each resonant cavity. To overcome the limitations of this approach and to take into account the effects from nonidentical beams and/or beam-tunnels, we have modified the code to use a parallel algorithm for multiple beams. The implementation of the parallel version of TESLA is based on the latest Fortran-95 version of the serial code and uses the message-passing interface library for communication. For testing and verification purposes, the new version of the code is applied to simulate an experimental four-cavity, eight-beam klystron amplifier, which was designed and successfully tested last year at the Naval Research Laboratory. The results of modeling using the new parallel TESLA and their comparison with experimental data are discussed in detail.

Wave coupling in sheet- and multiple-beam traveling-wave tubes

To increase the power level of the sources of coherent electromagnetic radiation at frequencies from 100 GHz up to the terahertz range it makes sense to develop devices with a spatially extended interaction space. Sheet-beam and multiple-beam devices belong to the category. In the present paper the small-signal theory of traveling-wave tubes with sheet-beam and multiple sheet-beam configurations is developed. It is shown that in such tubes the wave coupling on electron beams may occur even in small-signal regimes. The wave coupling and its role for amplification of forward and excitation of backward waves in such amplifiers is studied. Also the effect of transverse nonuniformity of the electromagnetic field on the device operation is analyzed and illustrated by several examples.

Characterization of a Ka-band Sheet-Beam Coupled-Cavity Slow-Wave Structure

This paper investigates the properties of a three-slot doubly periodic staggered-ladder sheet-beam coupled-cavity slow-wave structure (SWS) developed at the U.S. Naval Research Laboratory. The structure is overmoded with complicated mode crossings and field structures. The staggered-ladder structure is compared to round-beam structures via full-wave electromagnetic simulations and experimental measurements. We explore the application of this SWS in a traveling-wave tube amplifier.

Validation of the large-signal klystron Simulation code TESLA

We demonstrate the effectiveness of the Telegraphists Equations Solution for Linear-beam Amplifiers code for simulation of a range of klystron amplifier designs. Simulation results are compared to both particle-in-cell (PIC) simulations and experimental data, with good agreement obtained in each case. Specific features and optimizations included in the model are discussed and shown to allow a significant reduction in simulation times over the general PIC approach.

Modeling and Design of Millimeter Wave Gyroklystrons

A series of high power, high efficiency Ka-band and W-band gyroklystron experiments has been conducted recently at the Naval Research Laboratory (NRL). Stagger tuning of the cavities for bandwidth enhancement is commonly used in the conventional multicavity klystrons. The desired stagger tuning is usually achieved via mechanical tuning of the individual cavities. However, in the millimeter wave regime, particularly, in the case of the high average power operation, it is desirable to be able to achieve the required stagger tuning by design. The NRL gyroklystron experiments explored the tradeoffs between power, bandwidth, efficiency, and gain to study the effects of large stagger tuning in millimeter wave without resorting to mechanical tuning of the cavities. Both, Ka-band and W-band, experiments demonstrated a record power-bandwidth product. The success of the experiments was due in large part to a battery of improved large-signal, stability, and cold test codes employed in the modeling and design stage. ...

Demonstration of a Wideband 10-kW Ka-Band Sheet Beam TWT Amplifier

A sheet-beam coupled-cavity traveling wave tube has produced over 10 kW of peak power at a center frequency of 34 GHz, with a 3-dB bandwidth of almost 5 GHz. The power of this amplifier is an order of magnitude higher than state-of-the-art conventional amplifiers of comparable frequency, bandwidth, and operating voltage (<;20 kV). This unprecedented performance is made possible by a unique, Naval Research Laboratory (NRL)-developed sheet electron beam along with a novel slow-wave interaction structure. High-current, low-voltage operation provides high gain per unit length and allows an interaction structure<;5-cm long to be used to achieve the desired gain of 15 dB at saturation. Measured performance agrees well with 3-D particle-in-cell simulations.

Simulation of Klystrons With Slow and Reflected Electrons Using Large-Signal Code TESLA

The problem of modeling slow and reflected electrons that appear during operation of high-power klystrons is discussed. These electrons are not only problematic for the operation of real klystrons but also present a numerical challenge for simulation codes that solve the equations of motion with axial distance rather than time as the independent parameter. To meet this challenge, particles with axial velocity below some threshold are treated using an alternative algorithm. This approach has been implemented in the simulation code TESLA. The method is verified by comparison with PIC simulation. The effect of these particles on the efficiency of a hypothetical device is also presented.

Design Methodology and Experimental Verification of Serpentine/Folded-Waveguide TWTs

The general electromagnetic properties and design methodology for serpentine/folded-waveguide (FW) amplifiers are presented. In addition, hybrid-waveguide circuit topologies, which permit greater design flexibility than the basic serpentine/FW topologies, are also introduced, and their dispersion characteristics are discussed. Experimental validation of design methodology and tools is provided via test results of the recently demonstrated wideband 220-GHz serpentine amplifier, which embodies the design methodology described herein. Particular attention will be paid to the comparison between code prediction and experimental data, which are in excellent agreement.

A finite integration method for conformal, structured-grid, electromagnetic simulation

We describe a numerical scheme for solving Maxwells equations in the frequency domain on a conformal, structured, non-orthogonal, multi-block mesh. By considering Maxwells equations in a volume parameterized by dimensionless curvilinear coordinates, we obtain a set of tensor equations that are a continuum analogue of common circuit equations, and that separate the metrical and metric-free parts of Maxwells equations and the material constitutive relations. We discretize these equations using a new formulation that treats the electric field and magnetic induction using simple basis-function representations to obtain a discrete form of Faradays law of induction, but that uses finite integral representations for the displacement current and magnetic field to obtain a discrete form of Amperes law, as in the finite integration technique [T. Weiland, A discretization method for the solution of Maxwells equations for six-component fields, Electron. Commun. (AE U) 31 (1977) 116; T. Weiland, Time domain electromagnetic field computation with finite difference methods, Int. J. Numer. Model: Electron. Netw. Dev. Field 9 (1996) 295-319]. We thereby derive new projection operators for the discrete tensor material equations and obtain a compact numerical scheme for the discrete differential operators. This scheme is shown to exhibit significantly reduced numerical dispersion when compared to the standard linear finite element method. We take advantage of the mesh structure on a block-by-block basis to implement these numerical operators efficiently, and achieve computational speed with modest memory requirements when compared to explicit sparse matrix storage. Using the Jacobi-Davidson [G.L.G. Sleijpen, H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 401-425; S.J. Cooke, B. Levush, Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm, J. Comput. Phys. 157 (1) (2000) 350-370] and quasi-minimal residual [R.W. Freund, N.M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315-339] iterative matrix solution algorithms, we solve the resulting discrete matrix eigenvalue equations and demonstrate the convergence characteristics of the algorithm. We validate the model for three-dimensional electromagnetic problems, both cavity eigenvalue solutions and a waveguide scattering matrix calculation.