Periodic Focusing System Research Articles

Design and analysis of a hundred-watt G-band traveling wave tube

In this paper, a hundred-watt level traveling wave tube operating in the G-band is designed and analyzed. A non-semi-arc folded waveguide (FW) slow wave structure (SWS) is adopted to achieve high output power. Compared with the conventional FW, this structure has a higher coupling impedance, which is beneficial for beam–wave interaction. To further improve the efficiency of beam–wave interaction, phase velocity taper technology is adopted in SWS. A diamond pill-box output window is designed for electromagnetic wave input and output in SWS. In addition, the electron optics including a Pierce electron gun and a periodic permanent magnet focusing system are designed for emitting and constraining the electron beam. Using CST PIC solver for simulation, the results show that under a 23 kV and 80 mA electron beam, the maximum output power of the SWS is 132.7 W and the saturated gain is 36.5 dB. The bandwidth for output power greater than 100 W is 12 GHz. A pill-box window is designed and fabricated, and experimentally measured S11 is better than −13 dB and S21 is better than −1.3 dB in 213–229.5 GHz. The electron optics generate 79 mA current at 23 kV voltage.

Compact E-Band Sheet Beam Folded Waveguide Traveling Wave Tube for High Data Rate Communication

The design of a compact <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{E}$</tex-math> </inline-formula> -band (71–76 GHz) sheet beam (SB) folded waveguide (FWG) traveling wave tube (TWT) for high data rate communications is presented in this article. The round beam tunnel for a pencil FWG slow wave structure (SWS) has been redesigned with a rectangular beam tunnel to be suitable for the SB with increased beam current. A novel periodic permanent magnet (PPM)–periodic quadrupolar magnet (PQM) focusing system has been developed to reduce the beam ripple and improve the transmission ratio. A multistep side-out coupler is designed to import and extract the RF power from the SWSs and be compatible with the planar periodic magnetic focusing system. Particle-in-cell (PIC) simulations are employed to evaluate the performance of the high-frequency circuit. Driven by a 1 W signal, the 30-period circuit is estimated to produce more than 100 W power and achieve a 21 dB gain with a less than 0.4 dB variation over 71–76 GHz. Moreover, phase and linearity analysis show a less than 6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> in-band phase distortion and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim$</tex-math> </inline-formula> 30 dB third-order intermodulation distortion (C/3IM) at 30 W of output power, meeting the requirements of a communications-focused TWT. Over 5% circuit efficiency and 40% overall efficiency when equipped with a single-stage collector can be achieved by the compact TWT over the target band.

Electron-optical system for dual radial sheet beams for Ka-band cascaded angular log-periodic strip-line traveling wave tube

A novel electron-optical system is proposed for dual azimuthally stacked radial sheet electron beams (ARSEBs). The two sheet beams are emitted from curved surfaces of two cathodes and are focused by a focusing electrode, which is carefully designed to produce a symmetric field distribution for the two beams and to avoid interference between the beams. A common tunable periodic cusped magnetic focusing system is also designed to focus the two ARSEBs. The dual sheet beams are used in a traveling wave tube (TWT) consisting of a cascade of two azimuthally supported angular log-periodic strip-line (ASALS) slow-wave structures (SWSs). The transmission efficiency in the presence of beam–wave interaction is 93%. The particle-in-cell simulation results show that for a beam voltage of 4400 V and a current of 0.39 A, the proposed cascaded TWT has a maximum gain of 32.5 dB at 35 GHz and a maximum output power of 180 W; this is a significant gain improvement over a TWT using a single ASALS SWS.

Stability Analysis of 300-GHz Sheet Electron Beam Transport in a Periodic Rectangular Quadrupole

A novel periodic magnetic focusing system is proposed. The stability of elliptical sheet beam transport in the magnetic field of a periodic rectangular quadrupole (PRQ) is studied and compared with that in the magnetic field of periodically cusped magnets (PCMs). Theoretically predicted matching conditions are verified by numerical simulations. An 11.7- kV, 35-mA, 0.32 mm $\times $ 0.06 mm elliptical sheet beam is confined in a 0.53 mm $\times $ 0.08 mm beam tunnel and transported over a distance of 30 mm. Both the PCM and PRQ have similar characteristics of electron beam distribution change, beam emittance, and beam transmission. The results of the initial stability analysis indicate that PCMs are preferable to PRQs because of their ability to confine the beam with a long magnet period.

Development of a compact coaxial cusped periodic permanent magnet focusing system.

To achieve the application of a periodic permanent magnet in high power microwave, a compact coaxial cusped periodic permanent magnet (CPPM) focusing system is constructed. The system consists of permanent magnets with different magnetization directions and soft magnets. Taking the required magnetic field performance and the effect of demagnetization into account, NdFeB and FeCoV are selected as the permanent and soft magnet materials. After the system is constructed, the magnetic field is measured. The results show that the guiding magnetic field strength and period of the CPPM are about 0.29 T and 26 mm, respectively, and the magnetic field distribution of measurement shows good agreement with the simulation results. However, there are some differences between the measurement and simulation results, and the differences are compared and analyzed here.

Linear beam stability in periodic focusing systems: Krein signature and band structure

The general question of how a beam becomes unstable has been one of the fundamental research topics among beam and accelerator physicists for several decades. In this study, we revisited the general problem of linear beam stability in periodic focusing systems by applying the concepts of Krein signature and band structure. We numerically calculated the eigenvalues and other associated characteristics of one-period maps, and discussed the stability properties of single-particle motions with skew quadrupoles and envelope perturbations in high-intensity beams on an equal footing. In particular, an application of the Krein theory to envelope instability analysis was newly attempted in this study. The appearance of instabilities is interpreted as the result of the collision between eigenmodes of opposite Krein signatures and the formation of a band gap.

Transportation of Electronic Flows in Magnetic Periodic Focusing Systems with an Anharmonic Magnetic Field Distribution Designed for Millimeter-Range Wave Traveling Lamps

Abstract—The paper considers theoretical and practical problems on developing electron-optical systems of traveling wave tubes (TWTs) that focus an intense electron flow via a magnetic periodic focusing system (MPFS) upon advancement into the millimeter-wave range. An analytical solution has been found for the magnetic field distribution in an MPFS TWT combined with a retarding system with magnetically soft inserts that form a passage channel with a diameter substantially less than the internal diameter of the tip. The stable focusing zones of the electron flow are determined for the considered MPFS, which makes it possible to focusing the flow with magnetic field parameters exceeding the critical values of a conventional MPFS.

Дополнительные требования к параметрам магнитных периодических фокусирующих систем для ЛБВ с малым диаметром пролетного канала.

Дополнительные требования к параметрам магнитных периодических фокусирующих систем для ЛБВ с малым диаметром пролетного канала.

Study on Radial Sheet Beam Electron Optical System for Miniature Low-Voltage Traveling-Wave Tube

Angle log-periodic meander line microstrip radial sheet beam traveling-wave tube is one kind of novel minimized vacuum device with low beam voltage. To generate and focus the radial sheet electron beam, a novel radial divergent sheet beam electron optical system, including the tractable radial sheet electron beam gun and miniaturized and feasible radial small tunable periodic cusped magnetic focusing system, is proposed in this paper. The fan-shaped radial sheet beam is emitted from the cylindrical surface cathode, compressed in axial direction, and confined in azimuthal direction by the focusing electrode. Simulation results show that the total emission of the angular radial sheet beam gun is 51.2 mA with the dimensions of $0.26~\text {mm} \times 8$ ° under the voltage of 1.7 kV, and the fan-shaped radial sheet beam can totally pass through the fan-shaped drift tunnel under the magnetic field. The experimental results are good in agreement with the simulation results. The tested angular radial sheet beam transmission efficiency is >90% in an 18.8-mm-length beam tunnel with the fill factor of 50%.

Parametric instabilities in 3D periodically focused beams with space charge

Parametric resonances of beam eigenmodes with a periodic focusing system under the effect of space charge---also called structural instabilities---are the collective counterparts to parametric resonances of single particles or of mechanical systems. Their common feature is that an exponential instability is driven by a temporal modulation of a system parameter. Thus, they are complementary to the more commonly considered space charge single particle resonances, where space charge pseudo-multipole terms are assumed to exist already at finite level in the initial distribution. This article elaborates on the characteristics of such parametric instabilities in 3D bunched beams---as typical in linear accelerators---for modes of second (envelope), third and fourth order, including the transverse coupled ``sum envelope instabilities'' recently discovered for 2D beams. Noteworthy results are the finding that parametric resonances can be in competition with single particle resonances of twice the order due to overlapping stopbands; furthermore the surprisingly good applicability of the stopband positions and widths obtained from previously published 2D linearised Vlasov stability theory to the 3D non-Kapchinskij-Vladimirskij particle-in-cell code studies presented here.

Design and Measurement of a Nonlinear-Curve Directional Coupler for Sheet Beam Traveling Wave Tube

A new type of input/output coupler for sheet beam traveling wave tube is designed, analyzed, and measured in this paper. In the design, a special sloped coupling aperture distributed between two paralleled rectangular waveguides in ${H}$ -plane is employed for compact dimensions, ease of fabrication, attainment of high power capacity, and more convenience for periodic cusped magnet focusing system. A nonlinear-curve profile with Chebyshev-curve distribution is applied to extend the operating frequency bandwidth while suppressing reflections to avoid generating oscillation in the slow-wave structure. Based on the analytical investigation and numerical simulation, an optimized sloping angle of the coupling aperture is obtained to improved performance. Simulations imply that the coupler achieves a broadband bandwidth ( $S_{11} dB) of 23 and 10 GHz in $W$ - and $Q$ -band, respectively, with coupling coefficient above −0.2 dB. Cold test results satisfactorily agree with simulations.

Near equilibrium distributions for beams with space charge in linear and nonlinear periodic focusing systems

A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.

Temperature stability of magnetic field for periodic permanent-magnet focusing system

In this study, finite element analysis based on an Ansoft Maxwell software was used to reveal the temperature stability of a magnet ring and the equivalent structural periodic permanent-magnet (PPM) focusing system. It is found that with the temperature increasing, the decrease rate of magnetic induction peak (B z)max of single magnet ring is greater than that of remanence B r of magnet in the range from room temperature to 200 °C, however, the PPM focusing system do have the same temperature characteristics of permanent-magnet materials. It indicates that the magnetic temperature properties of the PPM system can be effectively controlled by adjusting the temperature properties of the magnets. Moreover, the higher permeability of the magnets indicates the less H cb, giving rise to lower magnetic induction peak \( ( {B_{\text{z}} })^{\prime }_{\hbox{max} }. \) Finally, it should be noted that the magnetic orientation deviation angle θ (<15°) of permanent magnets has little effect on the focusing magnetic field of the PPM system at different temperatures and the temperature stability. The obtained results are beneficial to the design and selection of permanent magnets for PPM focusing system.

Optimization of the parameters of a virtual-cathode oscillator with an inhomogeneous magnetic field

A two-dimensional numerical model is used to study the generation of powerful microwave radiation in a vircator with an inhomogeneous magnetic field applied to focus a beam. The characteristics of the external inhomogeneous magnetic field are found to strongly affect the vircator generation characteristics. Mathematical optimization is used to search for the optimum parameters of the magnetic periodic focusing system of the oscillator in order to achieve the maximum power of the output microwave radiation. The dependences of the output vircator power on the characteristics of the external inhomogeneous magnetic field are studied near the optimum control parameters. The physical processes that occur in optimized virtual cathode oscillators are investigated.

An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system

In this paper, we point out an error in the paper: Positive periodic solution for Brillouin electron beam focusing system, Discrete Contin. Dyn. Syst. Ser. B, 16(2011), 385-392. Meanwhile, it is pointed out that, for $0 < a < 1$, the conjecture that the Brillouin electron beam focusing system $x''+a(1+\cos 2t)x=1/x$ admits positive periodic solutions is still an open problem.

Particle Simulation of Slow-Wave System in Multi-Beam Traveling Wave Tube

A time-dependent particle code has been developed to simulate the motion and changing regularity of particles in multi-beam traveling wave tube. Magnetic focusing and interaction models of multi-beam traveling tube were established, and static magnetic field was calculated. The process of bunching particles by periodic permanent magnetic focusing system and beam-wave interaction was also simulated. The results show that particle simulation can really reflect the motion of particles in multi-beam traveling wave tube, which can provide some references for particle study of traveling wave tube.

Influence of external nonuniform magnetic field on the spectral characteristics of a virtual cathode oscillator’s output radiation

The influence of an external non-uniform magnetic field created using a periodic magnetic focusing system on the spectral characteristics of a virtual cathode oscillator’s output radiation is investigated by means of numerical simulation. It is shown that raising the magnetization intensity of a single magnetic ring or the number of magnetic rings leads to an increase in the output microwave radiation power spectrum’s irregularity. As consequence, the output microwave signal exhibits wide-band oscillations with a bandwidth close to one octave.

Structure and magnetic field of periodic permanent magnetic focusing system with open magnetic rings

The magnetic field along the central axis for an axially magnetized permanent magnetic ring was investigated by analytical and finite element methods. For open magnetic rings, both calculated and measured results show that the existence of the radial magnetic field creates a remarkable cosine distribution field along the central axis. A new structure of periodic permanent magnet focusing system with open magnetic rings is proposed. The structure provides a satisfactory magnetic field with a stable peak value of 120 mT for a traveling wave tube system.

带开口磁环的周期永磁聚焦系统的轴向磁场

带开口磁环的周期永磁聚焦系统的轴向磁场

X波段耦合腔行波管周期永磁聚焦系统

X波段耦合腔行波管周期永磁聚焦系统