Large-signal Code Research Articles

From 2.5-D to 1.5-D: Fast, Reduced-Order Simulations With the TESLA-Family of Large-Signal Codes

From 2.5-D to 1.5-D: Fast, Reduced-Order Simulations With the TESLA-Family of Large-Signal Codes

Increasingly Accurate Stability Study of the Experimental W-Band TWT Using Code TESLA-Z Stability Analysis Framework

We present the results of our comprehensive numerical stability study of the experimental, high-power, two-stage Serpentine <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${W}$ </tex-math></inline-formula> -band traveling-wave tube (TWT) with ~10% working bandwidth. This device demonstrated an output power level of ~215 W at 92 GHz at the nominal beam voltage of 20 kV and ~285 W at an increased beam voltage of 20.8 kV. The experimental device was observed to be stable in all cases when operated within the designed beam voltage range. The onset of instability near the lower band edge was observed at higher beam voltages approaching a threshold value of ~21.0 kV. We use the recently developed stability analysis framework, based on the Naval Research Laboratory (NRL) 2-D large-signal code TESLA-Z, to find the predicted threshold of zero-drive instabilities, which could develop near the lower band edge of the experimental <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${W}$ </tex-math></inline-formula> -band TWT. An initial study was done by using a simplified model for geometry of the experimental electrodynamic structure of the TWT, which ignored all interface elements. TESLA-Z predictions for onset of instability, in this case, were found much higher in beam voltage than its measured value. Next, an advanced TESLA-Z-based stability study was performed using a more accurate, detailed model for geometry of the experimental electrodynamic structure of the TWT, including important elements such as couplers (transformers), lossy load (sever), and windows. This more detailed analysis gave more accurate results for the onset of instability, in good agreement with the measurements.

Numerical Determination of Vacuum Electronic Device Stability

We present a new approach to the study of the stability of vacuum electronic devices (VEDs) using the Naval Research Laboratory (NRL) large-signal code TESLA-Z. The approach combines a precomputed complex impedance matrix, $\hat {Z}$ , describing the structure with a TESLA-Z computed admittance matrix, $\hat {Y}_{ \boldsymbol {bt}}$ , characterizing the electron beam and beam tunnel. The gain matrix $\hat {G}$ for a given device then can be found as the product of the reduced $Z$ -matrix of the structure and admittance matrix $\hat {Y}_{ \boldsymbol {bt}}$ of the beam tunnel. Subsequent analysis of the eigenvalues of the gain matrix $\hat {G}$ using Nyquist’s method determines the stability of the device. We discuss the details of the new algorithm and illustrate its application to an experimental G-band serpentine TWT.

Nonlinear study of injection process types into the traveling wave tube with hollow electron beam

In this paper, examples of all types of signal injection such as different signal , harmonic signal and multiple signal injections in a TWT including hollow electron beam near frequency 1800 MHz and within input powers lower than TWT saturation power has been analyzed using approximate analytical solution of S-MUSE model. Later, the results obtained from approximate analytical solution with large signal code LATTE, that is a Lagrangian model, have been tested and simulated so that the effect of input phase difference between drive and injected wave and the effect of input powers on the amplification value of drive and generated second-order harmonic waves were investigated. The phase difference between drive and harmonic waves is a key parameter in harmonic injection for increasing the output power of drive and second-order harmonic frequencies.

KlyC: 1.5-D Large-Signal Simulation Code for Klystrons

The High Efficiency International Klystron Activity (HEIKA) was initiated at CERN in 2014 to evaluate and develop new klystron bunching technologies for high-efficiency klystrons in application to the large-scale scientific projects such as the Compact Linear Collider (CLIC) and the Future Circular Collider (FCC). The success of such development strongly depends on the availability of the specialized klystron computer codes. Unfortunately, the accurate and efficient 2-D large-signal codes are proprietary and are not freely available to the wide klystron community. The new 1.5-D klystron code called KlyC has been developed as an attempt to bridge the gap between fast, but approximate 1-D models and time/resources consuming particle-in-cell (PIC) codes. KlyC simulates the specific physical processes such as the current emission from the metal surface, the space charge depression along the klystron, and the residual RF current modulation of the spent beam. KlyC internal eigenmode solver allows fast simulations of the 2-D complex electromagnetic (EM) field in the axis-symmetrical cavity with the arbitrary cavity profile. The internal KlyC optimizer module can help the designer to speed up the klystron development process. In this paper, the theoretical model, general review of the code performance, and benchmarking between KlyC, AJDisk/1-D, PIC code MAGIC/2-D, and CST/3-D are presented using FCC klystrons as an example.

3-D Nonlinear Theory for Sheet-Beam Folded-Waveguide Traveling-Wave Tubes

A 3-D frequency-domain nonlinear model for sheet beam (SB) traveling-wave tubes (TWTs) based on folded waveguides (FWs) is presented in this paper. The SB with finite thickness is a 3-D asymmetric system. To characterize such a system, an accurate description of the radio frequency (RF) fields and the space charge (SC) fields in the interaction gap in all three dimensions is required. An analytical expression for the interaction electric fields is derived. Beside of the interaction electric fields, a modified analytical model for the dispersion and interaction impedance is also imbedded in our code predicting the cold characteristics of the waveguide, which agrees with the results of the 3-D simulation code CST. As a result, the model provides a through predictive capability from the geometrical parameters to the device performance, such as saturation power and gain. Due to the short computing time, our code is very useful for the large-scale optimizations of TWTs. For the calculation of the SC field, a particle-in-cell method is used by solving the 3-D Helmholtz equation and the motion equation. Such analytical technology is much more preferable to interpret the complicated beam–wave interaction than the conventional electron beam models, which attributes to the ever-increasing computing capacity of the computers. These features have been incorporated in the development of our large-signal code SB-FWTWT-3-D. The validation of the model is performed and comprehensive results are presented.

Quasi-3-D Modeling of Higher Order Mode Instability in a Two-Gap Input Cavity of Broadband MBK

We present the results of our comprehensive study of the stability of a two-gap input cavity used in an experimental broadband multiple-beam klystron (MBK) with 18 beams and 7 cavities, which was designed for projected >500 kW maximum output power and ~13% bandwidth (so-called NRL MBK-3 design). The device was experimentally observed to be prone to self-excitation at all beam voltages below its designed operational value of ~42 kV. Postexperiment examination of the two-gap input cavity revealed traces of breakdown on its face. Detailed simulations performed using a 3-D computational electromagnetic code HFSS have shown presence of a few high-Q higher order modes (HOMs), which could explain self-excitation of the two-gap input cavity in a wide range of beam voltages. To explore HOM instability of the two-gap input cavity of the MBK in greater details, we applied the code TESLA-MB, which represents a parallel extension of the 2-D large-signal klystron code TESLA and which is suitable for an accurate modeling of multiple-beam devices with unique distributions of R/Qs over gaps in all its beam-tunnels.

Nonlinear analysis of beam-wave interaction in a planar THz travelling-wave tube amplifier

Large-signal analysis is presented for analysing non-linear beam-wave interaction in a planar THz TWT with a sheet electron beam. The sheet beam within one RF beam wavelength is represented by uniform rectangular charged discs for confined flow of the beam, and the discs are tracked in small distance steps of forward integration. For a planar THz TWT, a staggered double-vane loaded rectangular waveguide slow-wave structure (SDVSWS) is used. Frequency-domain analysis is used to define the RF circuit field in the SDVSWS and the interaction of the RF circuit field with the electron beam is carried out for steady-state TWT operation. The RF circuit field is considered to be continuous as in a helix SWS and it is represented by transmission line theory at each integration plane. A large-signal analysis code of a helix TWT with pencil beam (SUNRAY-1D) was modified for a planar TWT with a sheet beam. The accuracy of the modified SUNRAY code was checked against the 3D e.m. field simulator (CST-PS) by comparing the output performance for a 0.22-THz planar TWT. The results for the gain and the output power over the operating band given by the two codes were found to be comparable. A significant advantage of the SUNRAY code is that it is very fast compared to the CST code. It takes less than a minute to simulate the RF performance of a typical THz TWT at a single frequency and drive power on a standard PC. The SUNRAY code can therefore, be used interactively for design a complete SWS with input/output couplers, sever, loss profiles and phase velocity taper for a high efficiency high gain THz TWT.

Modeling Vacuum Electronic Devices Using Generalized Impedance Matrices

We have developed a general approach to modeling a large class of vacuum electronic devices (VEDs) by using impedance matrices to characterize the circuit structure. Our approach can treat VEDs that have an arbitrary number of interaction gaps, severs, and input and/or output ports that may incorporate arbitrarily complex matching and/or tuning elements and windows. To find the impedance matrix for a given structure, we use the computational electromagnetics 3-D finite-element code HFSS to compute the response of the entire structure to an excitation of each individual port and gap. We define voltages and currents as certain integrals over the electric and magnetic fields, respectively, the ratios of which are elements of the generalized impedance matrix. This matrix is then imported into a beam-wave interaction code, which is used to compute VED performance (gain, output power, bandwidth, and so on). We have implemented this capability in a new 2-D code TESLA-Z, which has been verified by comparison with the large-signal code TESLA-FW and then validated by comparison with measured data from a Ka-band folded-waveguide power-booster TWT. Similar capability was also implemented in the 1-D interaction code CHRISTINE-CC.

Large-Signal 2.5-D Steady-State Beam-Wave Interaction Simulation of Folded-Waveguide Traveling-Wave Tubes

A large-signal beam-wave interaction code for folded-waveguide traveling-wave tubes is presented. Formulation in frequency domain yields fast results of the steady state. The slow-wave structure is described by an equivalent circuit, while the electrons of the beam are modeled by means of a particle-in-cell approach. The latter exploits the periodicity of the electromagnetic fields in the beam tunnel region, thus allowing to work with a relatively low number of injected particles compared to conventional implementations. Physically consistent solutions are then obtained iteratively by incorporating the well-established Broyden’s method. Further improvement in terms of computation time is achieved by initializing the iterative algorithm with results from previous simulations. The approach is verified by a comparison with published interaction simulation results. Single-frequency responses are obtained within a few minutes, which compares favorably with other specialized simulation packages and enables device optimization with acceptable effort.

Large-Signal 2-D Modeling of Folded-Waveguide Traveling Wave Tubes

A new computationally efficient 2-D large-signal code TESLA-FW has been developed to model traveling wave tubes (TWTs) using folded (or serpentine) waveguide (FW) slow-wave structures. The code incorporates a recently published shunt-loaded transmission line model of the structure and takes advantage of a new time advance algorithm recently implemented in the code TESLA-CC. The new code has been applied to modeling $G$ -band (220 GHz) serpentine and FW TWTs. Results compare very favorably with those obtained from the 3-D particle-in-cell (PIC) code MAGIC3D and with experimental data. Typical running times of TESLA-FW are 1–2 orders of magnitude less than those of 3-D PIC codes.

Simulation of Drive-Induced Oscillation in Coupled-Cavity TWTs

Drive-induced oscillation (DIO) is an instability that limits the achievable output power in wideband coupled-cavity traveling wave tubes (CC-TWTs). It occurs under large-signal conditions, when the electron beam is slowed as a result of its interaction with the circuit at the drive frequency. DIO occurs at a frequency very near the $2\pi $ point (band edge) of the lower branch of the cold circuit dispersion diagram. It is commonly accompanied by a sudden increase in the body current and a flattening of the power transfer curve at the drive frequency. The accurate prediction of the conditions for onset of DIO would be useful to the designers of CC-TWTs. In this paper, we present an approach to the prediction of DIO thresholds using the multifrequency large-signal simulation code TESLA-CC.

Nonlinear Investigation and 3-D Particle Simulation of Second-Harmonic Gyro-TWT With a Mode Selective Circuit

The beam-wave interaction behavior of a second-harmonic Ku-band high-power gyro-TWT comprising a mode selective RF interaction circuit has been investigated using a 3-D particle simulation code. The mode-selective RF circuit has been cut axially into four slices to restrain the electromagnetic modes not having m = 2 symmetry. A self-consistent nonlinear large signal code has been developed to compute the field amplitude, power, energy, and phase of the gyrating beam. The amplifier gives a saturated peak power of ~230 kW at 15.8 GHz for beam parameters of 80 kV and 20 A having a pitch of 1.1. The large signal gain of the device has been calculated as ~16 dB for the beam spread of 14%. Further, the nonlinear findings have been validated against the Particle-in-Cell code that predicts the saturated output power of ~193 kW in a circular TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> mode at the desired operating frequency.

A 3-D Large Signal Model for Sheet Beam Traveling Wave Tubes

A 3-D frequency domain large signal code called sheet beam traveling-wave tube 3-D (SBTWT3-D) for illustrating the nonlinear beam-wave interaction in the SBTWT is presented in this paper. A recent published field theory model for illustrating the staggered double-grating arrays waveguide (SDGAW) slow-wave structure is adopted in the code to obtain the RF circuit fields' distribution and ohmic loss. The sheet beam is simulated by a set of discrete rays. The ac and dc space-charge fields are obtained by solving the discrete Helmholtz equations and the discrete Poisson equation, respectively. A 3-D nonlinear beam-wave interaction analysis for a W-band SDGAW SBTWT is performed and the calculation results are compared with those obtained from time-domain 3-D particle-in-cell simulations.

Design of Folded Waveguide Slow-Wave Structure for &lt;inline-formula&gt; &lt;tex-math notation="TeX"&gt;\(W\) &lt;/tex-math&gt;&lt;/inline-formula&gt;-Band TWT

Design of RF structure for W-band folded waveguide traveling-wave tube was accomplished using electromagnetic simulation codes CST-MWS and GdfidL. The parameters characterizing the folded waveguide structure were optimized through a detailed analysis. CST-MWS and GdfidL simulated dispersion results have been compared and found in a close agreement. The CST-particle studio and in-house developed a large-signal analysis code SUNRAY 1-D were used for a large-signal analysis. The results of the parametric analysis and large-signal analysis are presented in this paper. Dimensions have been fixed for getting a gain ~18 dB and 7% bandwidth (95-102 GHz) corresponding to a 16-kV beam line for a uniform section. A gain of nearly 24 dB was obtained by employing pitch tapering near the output section of the tube of same length. Design of folded waveguide RF structure with a simple but efficient waveguide coupler yielding a return loss better than -15 dB has been obtained in the desired band (90-105 GHz).

Recent Developments to the Microwave Tube Simulator Suite

Recent developments to microwave tube simulator suite (MTSS) are reported in this paper. The MTSS is a full-featured tightly integrated software package for microwave tube analysis and design. It includes a commercial grade user interface and three physics simulators. The electron optics simulator is a finite-element (FE) 2-D and 3-D electrostatic steady-state beam trajectory code that has been used to design beam optics, including electron gun and collector. High-frequency circuit simulator is a full 3-D FE computational electromagnetic code that aims to get the accurate electromagnetic wave character spreading in high-frequency structures, such as dispersion, coupling impedance, and attenuation. Beam wave interaction simulator is a large-signal simulation code for helix traveling wave tubes (TWTs), coupled-cavity TWTs, and klystrons. The first version of MTSS was released in 2007, and all of these three physics simulators and user interface are improved and updated over the past six years. This paper reports on some significant advances to MTSS; new Ribbon style user interface, a lot of component modeling templates, more abundant postprocessing features, parallel version, full 64-bit version, more physics, and computation methods improvement.

1-D Large Signal Model of Folded-Waveguide Traveling Wave Tubes

A recently published hybrid circuit model for folded-waveguide slow wave structures has been implemented in the 1-D large signal code CHRISTINE. The resulting code is applied to a design for a G-band (220 GHz) folded-waveguide traveling wave tube. Results of small and large signal gain are compared with those from TESLA, a 2-D code using the same circuit model. Conditions for accuracy of the 1-D model are illustrated and explained. The effects of an offset beam tunnel on circuit dispersion and amplifier stability are illustrated using the CHRISTINE code.

Design of the RF Circuit for a Coaxial Cavity High-Power Multiple-Beam Klystron

This paper presents the design methodology and detailed design of the interaction circuit for use in an L-band 10-MW MBK, which operating in the fundamental mode at a center frequency of 1.3 GHz. Coaxial cavities are adopted to give adequate space for the use of multiple large cathodes, which has a low cathode loading and thereby facilitate a long lifetime. The emphasis for the present design is on efficiency and high-peak output power. The initial design was carried out using the large signal code KLY. To calculate the beam-wave interaction characters conveniently with cavities present, we developed a 2-D single-beam equivalent design methodology, in which the multitunnel coaxial cavities are replaced by the conventional single-tunnel cylindrical cavities with transformed RF parameters. The 3-D PIC simulations with actual coaxial cavity geometries are carried out at last to check on the large signal and the 2-D PIC simulations. The 3-D simulation results indicate that the equivalent design methodology is effective. The final RF circuit consists of six coaxial cavities including a second-harmonic cavity to reduce the device length. The circuit has a predicted gain of 50 dB at a peak pulsed output power of 10.4 MW with a corresponding electronic efficiency of more than 68%. The design and test results of the output system with two windows are also presented.

Parallel Frequency-Domain Simulation of Hyperspectral Waveforms in Nonlinear Power Amplifiers With Memory

We present a parallelization framework prototype for efficient physics-based computer simulation of hyperspectral time-dependent waveforms (i.e., wideband with a large number of frequency components) in nonlinear power amplifiers with memory. It relies on an adaptive algorithm for signal splitting and splicing in the time domain and uses a well-established pseudospectral multifrequency large-signal code, CHRISTINE, as its underlying simulation engine. Included in the model, and calculated from first-principles, are memory effects, such as dispersion and wave reflections. We validate our approach on a specific class of hyperspectral waveforms and study the effect of modifying a set of critical preprocessing parameters on the fidelity and the performance characteristics of the simulation.

Enhanced Stability of Second- and Fourth-Harmonic Gyrotrons Driven by a Frequency-Doubled Prebunched Beam

There is currently considerable interest in operating gyrotrons at the second and higher cyclotron harmonics in order to access the near-terahertz regime while reducing magnetic field requirements. High-frequency gyrotrons have successfully operated at the second harmonic. However, competition from the fundamental harmonic increasingly limits operation in the higher order modes needed for the near-terahertz regime. Savilov recently proposed a scheme for frequency-doubled phase bunching of gyrating electron beams in a waveguide resonator formed from Bragg reflectors and with the drive frequency equal to the cyclotron frequency. The advantages of phase prebunching at twice the cyclotron frequency include suppression of the fundamental harmonic, enhanced second-harmonic operation, and increased likelihood of fourth-harmonic operation. We have investigated the use of this phase bunching technique to enhance higher harmonic operation in gyrotron oscillators with annular beams. We compute the frequency-doubled bunching produced by a Bragg-type prebunching cavity and use a large-signal, multimode, and multiharmonic gyrotron oscillator code to simulate the effect of this bunching on a highly overmoded output cavity. Regimes of stable operation are predicted for the second- and fourth-harmonic point designs.