Beam-wave Interaction Research Articles

The coherent THz Smith-Purcell radiation from a three-dimensional open holes array structure

Coherent Smith-Purcell radiation from multiple electron beam excitation in a three-dimensional open holes array structure has been proposed. The electron beam passes through the holes, which can be coupled with each other to enhance surface wave fields, so that the multiple electron beam injection can interact with the surface wave field efficiently. And the Smith-Purcell radiation will be enhanced due to an increasement in dipole oscillations occurring when the electrons pass through the holes. Therefore, a high beam-wave interaction efficiency is yielded and very strong coherent terahertz radiation can be generated. This multi-beam system is expected to provide a favorable way to excite the coherent Smith-Purcell radiation, which would be used to generate terahertz radiation.

Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian ρz-plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a (TEϕ,TMϕ) field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.

170-GHz, 2-MW Coaxial-Cavity Gyrotron Design for Plasma Fusion System

Multimegawatt RF power in millimeter waveband (30–300 GHz) is required in the magnetically confined plasma fusion reactors. In this paper, the design of 170-GHz, 2-MW gyrotron with coaxial-cavity configuration is discussed. The mode selection and optimization of corrugation geometry of the coaxial insert are performed and discussed in detail. The beam-wave interaction computation and interaction cavity design are carried out using a particle-in-cell code. The beam-wave interaction analysis confirms 2.2-MW RF power at the 170.07-GHz frequency with more than 40% interaction efficiency. A 5.5-MW coaxial magnetron injection gun (C-MIG) is designed to launch the gyrating electron beam at the first radial maxima of the electric field peak of the selected operating mode in the interaction cavity. The magnetic system consisting of auxiliary coils and superconducting coils is also designed as per the requirement in MIG design.

The Nonlinear Analysis on a 210/240/270-GHz Megawatt-Class Gyrotron for DEMOs

In this paper, a multifrequency, multimode, megawatt-class gyrotron has been analyzed, which can operate at frequencies of 210, 240, and 270 GHz with corresponding modes TE−35.15, TE−40.17, and TE−45.19, respectively. With the help of a time-dependent, multimode, self-consistent code, the startup scenarios have been investigated with considering ideal and realistic electron beam, respectively. In the analysis, the frequency-dependent effective conductivity was considered for the calculations of ohmic losses and beam-wave interaction. Meanwhile, to satisfy the multifrequency, multimode operation, a triode magnetron injection gun was employed, in which the electron parameters varying with the modulation voltage have been investigated. In the startups, the pitch factor and beam current varying with the beam voltage and modulation voltage have been discussed and investigated in theory and simulation. The results show that gyrotron can steadily operate at every operating mode under considerations of ideal and realistic beams.

Study of Performance Improvement for a <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math> </inline-formula>-Band Sheet-Beam Traveling-Wave Tube

The study of performance improvement for a ${Q}$ -band sheet-beam traveling-wave tube (SB-TWT) based on an improved double-staggered grating waveguide slow-wave structure (SWS) is presented. To enhance the tube performance, such as reducing the driving power requirement and increasing the electronic efficiency, three approaches were combined together in the tube design, including making the operating frequency be closer to the cutoff frequency of the SWS, improving the SWS with a curved beam tunnel, and introducing the phase velocity tapering technique. Beam–wave interaction simulations predicted that great improvements have been achieved. The output power, gain, and electronic efficiency at 42.5 GHz have, respectively, increased from 7.5 to 20.2 kW, from 23.7 to 60 dB, and from 13.9% to 30.3%, in comparison with a previously designed SB-TWT.

Theoretical Design and Numerical Simulation of Beam-Wave Interaction for <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math> </inline-formula>-Band Unequal-Length Slots EIK With Rectangular Electron Beam

A beam-wave interaction model for G-band rectangular beam extended-interaction klystron (EIK) with unequal-length slots is proposed and analyzed to achieve high output power and broad bandwidth. The length ratio of long slot with short slot is carefully optimized to obtain a large effective characteristic impedance and wide mode separation. The influence of beam tunnel size on the effective characteristic impedance is studied with the beam aspect ratio of 2.3:1. The beam conductance for 5-gap, 7-gap, and 11-gap cavities are analyzed theoretically to optimize the beam-wave interaction stability. Furthermore, beam current and input power are investigated to obtain high performance. The analysis of fabrication tolerance and alignment tolerance indicates that less than 5- $\mu \text{m}$ machining precision is required. With beam current of 0.40 A and voltage of 16.5 kV, 3-D PIC simulation predicts peak power of 1139 W and 3-dB bandwidth of 1.15 GHz, with efficiency of 17.3% and gain of 37.5 dB. In addition, PIC simulations are compared with 1-D AJDISK calculations, the approximate results with similar tendencies indicate that our proposed beam-wave interaction model for G-band EIK is relatively reliable.

Power enhancement via an ion-channel in a Raman free-electron laser

As a high-power and high-efficiency coherent radiation source, the free-electron laser extends to two unique spectra: the region in the ultra-violet, x- and -rays, and the range in the millimeter- and terahertz-waves. Based on credible simulations, it is shown that the nonlinear power of a Raman free-electron laser in a millimeter wave range goes up and gets an increase of at least 9% when an ion-channel is applied to the beam-wave interaction chamber. A physical explanation is that the ion-channel weakens the velocities spread over the electron beam and, therefore, improves the electron-beam transportation quality and the beam-wave interaction.

Analytic Exploration of the Accuracy of Pierce’s Three-Wave Beam-Wave Interaction Theory of Traveling-Wave Tubes

As it is well known that the simplified classical Pierce's three-wave theory can provide scaling insights into traveling-wave tube (TWT) operation for its close-form solutions, and thus becomes a useful guide for TWT design. However, the classical Pierce's three-wave theory shows poor agreement with Lagrangian theory, so determining how to achieve a more accurately Pierce's three-wave theory from Pierce's four-wave theory becomes an open problem. In this paper, a more accurately revised Pierce's three-wave dispersion relation is deduced by using an approximate treatment on the nonlinear term of the dispersion relation of Pierce's four-wave beam-wave interaction theory. Meanwhile, the boundary conditions of classical Pierce's three-wave theory are revised by theoretical analysis. Thus, the revised Pierce's three-wave theory is established. The Pierce small-signal theories are compared to each other and Lagrangian theory on a set of TWT parameters which are based on a single pitch section of C- and Ku- bands TWTs. It is found that the revised Pierce's three-wave theory agrees extremely well with Lagrangian theory and gains more accuracy than the classical Pierce's three-wave theory in the small-signal beam-wave interaction region. Finally, the phase difference between Pierce's four-wave theory and revised Pierce's three-wave theory is discussed.

Study of the Mechanism and Suppression of Group Delay Distortion of a Traveling-Wave Tube Using Eulerian Hydrodynamic Analysis

In this paper, a simplified Eulerian nonlinear beam-wave interaction (BWI) theory of a helix traveling-wave tube (TWT) is developed. Derived from this model, analytic solutions are first obtained by the method of successive approximation. Then, the linear analytic solution of group delay distortion (GDD) is obtained. Subsequently, the mechanism of group delay is studied. It is found that the main mechanism of GDD is the propagation time difference between the wave group and electron beam throughout the BWI region. Furthermore, a series of group delay suppression schemes is discussed by using the mechanism. Finally, the Eulerian formation and the suppression schemes are validated by an in-house code based on the Lagrangian theory. Results show that the analytic solutions of Eulerian model and GDD agree well with the Lagrangian theory in small-signal region. In addition, the suppression schemes are applied to a high-efficiency Ku-band space TWT. The GDD is greatly reduced by approximately 50% with a slightly drop of output power.

Magnetic Field Tapering Approaches for Backward-Wave Oscillation Suppression in Helix Traveling-Wave Tubes

Two magnetic field tapering concepts for the suppression of backward-wave oscillations in helix traveling-wave tubes (TWTs) are presented. Therefore, the beam-wave interaction in a homogeneous helix section is modified. Increasing the field strength reduces the beam diameter and consequently the beam-wave coupling, while an additional offset in the focusing field alters the synchronism between both. The theoretical background is introduced and results from a 1-D small-signal and a 3-D particle-in-cell code are presented and compared. Furthermore, a concept to apply the suppression techniques to a complete TWT is presented, and the influence on the amplifier output characteristics is analyzed.

Numerical Simulation and Experimental Study of Sub-THz and THz CW Clinotron Oscillators

Results of computer modeling for the sub-THz and THz continuous-wave clinotrons are presented together with the results of their experimental investigations. Presented simulation results are obtained with both the computation methods and the statistical processing of real device operational parameters. This combination provides relevant output results. The effect of weakly inhomogeneous magnetic field on the electron beam adjustment in clinotron oscillator is clearly shown with the carried out 3-D particle tracking modeling. The effect of the surface roughness and thermal heating of the grating structure on a clinotron operation is also considered, and obtained results were considered during computer modeling. The 3-D thermal heating analysis in clinotron was performed, and its influence on ohmic losses was analyzed. Comparison of beam–wave interaction simulation and experimental results has been presented and discussed.

Efficient Calculation of Impedance Matrices for Vacuum Electronic Device Circuit Structures

We present a computationally efficient method for the calculation of impedance matrices of a large class of standing- and traveling-wave structures used in klystrons, traveling-wave tubes, and other vacuum electronic (VE) devices. By treating the gaps as “lumped ports,” this method avoids the time and disk spaces consuming steps employed in [1] , which required postprocessing the electromagnetic fields from a finite-element (FE) simulation. By applying analytical transformations to the impedance matrix, we show that it may be cast in a form suitable for the large-signal 1-D and 2-D beam-wave interaction codes CHRISTINE-CC [4] , [5] and TESLA-Z [1] . These transformations are formulated in a way to avoid numerical errors near structure resonance frequencies (singularity points). We also derive and apply formulas by which the impedance matrix of a structure may be constructed from the impedance matrices of its component parts, without additional FE simulations; by inverting the algebraic operations, we show that the impedance matrix of a structure from which a selected subsection has been removed may also be computed. Application of these formulas greatly facilitates the accurate calculation of the impedance matrices of large complex circuits that are difficult or impossible to model whole in a single FE simulation.

Impact of Thermal State on Backward-Wave Oscillation in Helix TWT Under Operation

The impact of thermal state on backward-wave oscillation (BWO) in a helix traveling-wave tube (TWT) under operation is explored, considering total thermal losses induced by high-frequency electromagnetic field power dissipation on helix, output port, carbon-coating attenuators, support rods, inner wall of the barrel, and the electron beam collision on the helix. By numerically solving the Maxwell equations, the electron motion equation, the heat conduction equation, and the thermal expansion equation, we analyze integrally the beam-wave interaction process and the resulting thermal distribution as well as thermal deformation of both slow wave structure and the output port. The simulation results for a broadband (8–18 GHz) helix TWT show the temperature on the last 20 turns of the helix is the highest, with a peak value of 347 °C at the end of helix. The greatest thermal deformation (0.0151 mm) is located on the inner conductor of the output port. The experimental result for the saturated output power of the TWT prototype shows a BWO power hole at 11 GHz, which is not found in simulation without considering thermal deformation. We find also that, considering the thermal deformation of helix and output port, BWO occurs at 22.4 GHz with the amplitude of 0.0708 V, which is over 5 times of that without considering thermal deformation, and it induces the same power hole as the experimental one at 11 GHz. Thermal deformation is one of the contributing factors for BWO in the helix TWT.

A megawatt-level surface wave oscillator in Y-band with large oversized structure driven by annular relativistic electron beam

High power vacuum electronic devices of millimeter wave to terahertz regime are attracting extensive interests due to their potential applications in science and technologies. In this paper, the design and experimental results of a powerful compact oversized surface wave oscillator (SWO) in Y-band are presented. The cylindrical slow wave structure (SWS) with rectangular corrugations and large diameter about 6.8 times the radiation wavelength is proposed to support the surface wave interacting with annular relativistic electron beam. By choosing appropriate beam parameters, the beam-wave interaction takes place near the π-point of TM01 mode dispersion curve, giving high coupling impedance and temporal growth rate compared with higher TM0n modes. The fundamental mode operation of the device is verified by the particle-in-cell (PIC) simulation results, which also indicate its capability of tens of megawatts power output in the Y-band. Finally, a compact experimental setup is completed to validate our design. Measurement results show that a terahertz pulse with frequency in the range of 0.319–0.349 THz, duration of about 2 ns and radiation power of about 2.1 MW has been generated.

Study on W-band sheet-beam traveling-wave tube based on flat-roofed sine waveguide

A W-band sheet electron beam (SEB) traveling-wave tube (TWT) based on flat-roofed sine waveguide slow-wave structure (FRSWG-SWS) is proposed. The sine wave of the metal grating is replaced by a flat-roofed sine wave around the electron beam tunnel. The slow-wave characteristics including the dispersion properties and interaction impedance have been investigated by using the eigenmode solver in the 3-D electromagnetic simulation software Ansoft HFSS. Through calculations, the FRSWG SWS possesses the larger average interaction impedance than the conventional sine waveguide (SWG) SWS in the frequency range of 86-110 GHz. The beam-wave interaction was studied and particle-in-cell simulation results show that the SEB TWT can produce output power over 120 W within the bandwidth ranging from 90 to 100 GHz, and the maximum output power is 226 W at typical frequency 94 GHz, corresponding electron efficiency of 5.89%.

Design and cold test of period-tapered double-ridge-loaded folded waveguide slow wave structure for Ka band TWTs

A double-ridge-loaded folded waveguide (DRL-FW) travelling wave tube (TWT) based on period-tapered structure is proposed. Through analysing the dispersion characteristics of the DRL-FW slow wave structure (SWS), the physical mechanism of the band-edge oscillation is obtained. Period-tapered SWS is proposed and analysed for verifying the feasibility in suppressing upper-band-edge oscillation and increasing the output power. Then the electromagnetic characteristics and the beam-wave interaction of TWT based on the period-tapered DRL-FW SWS are investigated. The calculation results predict that it potentially could provide continuous wave power over 600W from 29 GHz to 32 GHz without upper-band-edge oscillation. The bandwidth expands from 29-31GHz to 29-32GHz and electron efficiency is increased from more than 8.3% to more than 11%, while the range of operating voltage expands from 22kV-22.5kV to 22kV-24kV. The corresponding saturated gain can reach over 36.8 dB. In addition, we have carried out experimental tests on the transmission characteristics of period-tapered DRL-FW SWS. The cold test results show that the voltage stand-wave ratio (VSWR) is below 1.8 in the range of 29-32GHz. Good transmission characteristics greatly reduce the risk of reflection wave oscillation, thus improving the stability of DRL-FW TWT.

Study on the Effect of Electron Beam Quality on a Continuously Frequency-Tunable 250-GHz Gyrotron

The effect of the electron beam quality, including the variation of the velocity spread, the guiding center radius spread, and the pitch factor when the operating frequency of a 250-GHz TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">52</sub> mode continuously frequency-tunable gyrotron used for dynamic nuclear polarization (DNP) enhanced nuclear magnetic resonance (NMR) spectroscopy is tuned by changing the operating voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or the operating magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , on the operating frequency, the frequency-tunable range and the beam-wave interaction efficiency, has been studied based on a selfconsistent nonlinear beam-wave interaction theory. It is found that the velocity spread changes from 2.2% to 7.3% and the guiding center radius spread varies from 0.6% to 1.5%, when the operating voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> changes between 8 and 15 kV at an operating magnetic field of 9.24 T, the velocity spread varies from 4.1% to 6% and the guiding center radius spread changes from 0.8% to 1.4%, when the operating magnetic field B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> changes between 9 and 9.3 T at an operating voltage of 10.1 kV. The variation of the velocity spread and guiding center radius spread with respect to the operating voltage or the magnetic field have a significant effect on the beam-wave interaction efficiency and the frequency-tunable range of the 250-GHz TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">52</sub> mode continuously frequency-tunable DNP/NMR gyrotron,and the effect of the variation of the velocity spread and the guiding center radius spread should be taken into account in a frequency-tunable gyrotron design.

Investigation on heat transfer analysis and its effect on a multi-mode, beam-wave interaction for a 140 GHz, MW-class gyrotron

The interaction cavity of a 140 GHz, 1 MW continuous wave gyrotron developed in UESTC will be loaded with a very large heat load in the inner surface during operation. In order to reduce the heat, the axial wedge grooves of the outside surface of the cavity are considered and employed as the heat radiation structure. Thermoanalysis and structural analysis were discussed in detail to obtain the effects of heat on the cavity. In thermoanalysis, the external coolant-flow rates ranging from 20 L/min to 50 L/min were considered, and the distribution of wall loading was loaded as the heat flux source. In structural analysis, the cavity's deformation caused by the loads of heat and pressure was calculated. Compared with a non-deformed cavity, the effects of deformation on the performance of a cavity were discussed. For a cold-cavity, the results show that the quality factor would be reduced by 72, 89, 99 and 171 at the flow rates of 50 L/min, 40 L/min, 30 L/min and 20 L/min, respectively. Correspondingly, the cold-cavity frequencies would be decreased by 0.13 GHz, 0.15 GHz, 0.19 GHz and 0.38 GHz, respectively. For a hot-cavity, the results demonstrate that the output port frequencies would be dropped down, but the offset would be gradually decreased with increasing coolant-flow rate. Meanwhile, the output powers would be reduced dramatically with decreasing coolant-flow rate. In addition, when the coolant-flow rate reaches 40 L/min, the output power and the frequency are just reduced by 30 kW and 0.151 GHz, respectively.

Linear and Nonlinear Analyses of a 0.34-THz Confocal Waveguide Gyro-TWT

In this paper, the dispersion relation of the beam wave interaction of the confocal waveguide gyrotron-traveling-wave tube (confocal gyro-TWT) is derived from kinetic theory for the first time; according to this dispersion relation, we can make the linear analysis of confocal gyro-TWT as well as the cylindrical waveguide gyro-TWT. At the same time, a numerical code based on the self-consistent nonlinear theory is written to simulate the behavior of electron beam and electromagnetic wave during beam wave interaction. When neglecting the spread of velocity and guiding center, the gain and growth rate calculated by the nonlinear theory code makes great agreement with that of linear theory in the small-signal region.

Analysis, Design, and 3-D Simulation of a High-Efficiency Overmoded Nonuniform Relativistic Backward-Wave Oscillator

A high-efficiency X-band overmoded relativistic backward-wave oscillator (RBWO) using a nonuniform slow-wave structure (SWS) and cavity resonant reflector (RR) is designed in order to increase the beam–wave interaction efficiency. The electrodynamic SWS is a sinusoidally corrugated and moderately overmoded (D/ $\lambda$ > 1) structure that decreases the strength of electric field per unit area at its surface and RR. This reduces the probability of occurrence of RF breakdown, hence the pulse shortening. The nonuniform SWS enhances the beam–wave interaction efficiency by providing variable coupling impedance between −1st harmonic of backward fundamental mode and slow space-charge wave associated with the electron beam. The 3-D particle-in-cell simulation of the designed RBWO generated an RF output power of ~700 MW at 9.24 GHz, while driving by a trapezoidal voltage pulse of 600 kV. The axial guiding magnetic field is 2.5 T that restricts the velocity of electron beam in the axial direction only. The output signal has a high mode purity because the higher order modes are cutoff by the structure. The frequency tuning is obtained by varying the distance between RR and SWS.