Beam-wave Interaction Research Articles

Start current and growth rate in Smith\u2013Purcell free-electron laser with dielectric-loaded cylindrical grating

We present an analytic theory for Smith–Purcell device in which a cylindrical metal–dielectric grating was derived by an annular electron beam propagating along the grating axis. A dispersion relation is obtained for azimuthally symmetric modes. Also, the first-order and second-order growth rates of the modes which are in phase with the beam are compared. It is shown that the second-order growth rate gives a more accurate description of beam–wave interaction for beams with larger thicknesses, as well as grating slots, with smaller depths and greater lengths. The start current for BWO operation of the SP-FEL is presented too. The importance of the minimum value of start current is that above it, the SP-FEL will operate as an oscillator, even in the absence of external feedback. In this case, the group velocity of the synchronous evanescent wave is negative, while the electron beam travels in the forward direction. It is shown in this paper that the dielectric and grating parameters affect the value of start current. So, by changing these parameters, the minimum value for the start current can be obtained.

Design Modifications in RF Interaction Cavity of a 140 GHZ Gyrotron to Achieve Wide Tunable Bandwidth for DNP NMR Applications

The tapered RF interaction cavity of 140 GHz tunable continuous wave (CW) gyrotron operating in TE0,3,q mode has been tailored with the aim of providing RF power over a tunable bandwidth for 212 MHz DNP NMR spectroscopy applications. Gyrotron device RF interaction cavity design, its beam absent RF characteristics as well as electron beam and RF wave interaction behavior, both analytical and Particle-in-Cell (PIC) simulation studies have been presented. Using linear analysis, the start oscillation currents and the RF field profiles for the various axial operating modes indices q = 1, 2, 3 have been determined. Suitable modifications in the interaction cavity have been incorporated for the enhancement of device tunable bandwidth by operating the gyrotron in the high order axial indices via magnetic tuning. Gyrotron beam-wave interaction behaviour explored using time dependent non-linear multi-mode analysis for various beam currents and magnetic fields and more than >15W of RF power over a tunable bandwidth of 400MHz has been achieved through magnetic field tuning. This tunable bandwidth gyrotron design will of immense use for enhancement of sensitivity of the DNP NMR spectroscopy.

A high-efficiency dual-band relativistic Cerenkov oscillator based on dual electron beams

High efficiency and high frequency are key research topics for the development of high power microwave devices. There are, however, serious issues with mode competition in relativistic Cerenkov devices based on a single electron beam, which can lead to low efficiency in the beam-wave interaction process. In this paper, a high-efficiency relativistic Cerenkov oscillator based on a dual electron beam is proposed. The hollow slow wave structure is embedded in the inner conductor of the coaxial waveguide to obtain a double coaxial electromagnetic structure, which can suppress mode competition and improve the beam-wave interaction efficiency of the dual-band radiation. Moreover, each band of radiation is independent of the other, such that high frequency output radiation is generated. Using the particle-in-cell method, the physical processes involving the beam-wave interaction in the oscillator are studied with the aim of designing a high-efficiency double-electromagnetic structure. Simulation results indicated that the output power levels for the X-band and Ka-band were 1.50 GW and 710 MW, respectively, and the efficiencies were 34.7% and 30.7%, respectively, for a diode voltage of 550 kV and a guiding magnetic field of 0.85 T.

Effect of Operating Region on the Performance of a Spatial Harmonic Magnetron

This article presents the effect of choosing a different operating region on the output performance of a spatial harmonic magnetron (SHM). A 28-vane SHM with a backward spatial harmonic of (π /2)-1 operating mode at 136 GHz has been modeled and analyzed for performance study using CST-particle studio. The steady-state output power of 4.83 kW at 11.10 kV applied voltage with an efficiency of 5.61% has been obtained. An increment in the output power is observed on the application of higher anode voltage, but the efficiency saturates as the applied voltage reaches 0.4 times the threshold voltage. A close observation of the electron cloud or spokes reveals a greater expansion of the electron cloud toward anode as compared to the conventional magnetron. This expansion of the space charge cloud closer to the anode surface results in better beam wave interaction. It is this expansion factor, which is the part of the threshold voltage that perturbs the electron spokes of the fundamental mode but has little effect on the overall steady-state electron cloud.

G-band Rectangular Beam Extended Interaction Klystron Based on Bi-Periodic Structure

A rectangular beam G-band extended interaction klystron (EIK) based on planar bi-periodic slow wave structure (SWS) is proposed. Such structure has the advantages of uniform and strong electric field, as well as the large frequency spacing, which implies that EIK adopting such structure will have strong beam–wave interaction and will be easy to avoid the mode competition. Furthermore, the planar structure is compatible to the microfabrication technology, thus reducing the fabrication difficulty of THz vacuum electron devices with small sizes. Compared with the sheet beam and large beam current, the rectangular beam with small aspect ratio and the decreased current is easy to realize the beam focusing and high power in engineering. Under the voltage of 16.5 kV, current of 0.3 A, and beam size of 0.30 mm × 0.13 mm, particle in cell simulations show a considerable output power of 390 W, with gain of 38.9 dB, efficiency of 7.9%, and relatively wide bandwidth of 800 MHz. The high-frequency structure has been fabricated by computer numerical control method, and the measurement results are close to the simulations. The proposed planar bi-periodic SWS shows certain superiorities in the performance improvement of millimeter-wave and terahertz EIK.

One-dimensional nonlinear analysis of sine waveguide traveling-wave tubes

A 1D frequency-domain nonlinear model for illustrating the beam-wave interactions of sine waveguide (SWG) traveling-wave tubes (TWTs) was studied. Our model considered space-charge fields and Ohmic losses to make the model closer to practical situations. The sheet beam was split into a series of rectangular electron plates in the axial direction, and the space-charge field was calculated by solving Green's function. The dynamic equations and relativistic equations of motion were solved self-consistently to obtain the nonlinear characteristics of the power saturation, as well as the electron velocity, phase space distributions, etc. A 0.22 THz SWG TWT was used to illustrate and verify the validity of the theoretical model. The output power and gain results were in good agreement with those from the Computer Simulation Technology (CST) 3D particle-in-cell simulation. In addition, the code developed based upon the theoretical model produced faster results than the CST simulation.

Over-Sized Mode-Selective Relativistic Backward Wave Oscillator

An oversized mode-selective relativistic backward wave oscillator is proposed. This device operates using the pure TM02 mode in the beam-wave interaction area and transmits a pure TM01 mode in the output waveguide. In the beam-wave interaction area, mode selection is well realized through oversized slow-wave structures with a coaxial inner conductor that provides perfect boundary conditions for the TM02 mode and simultaneously eliminates other modes. A large proportion of the TM02 mode field is eventually exported into the output waveguide in the form of a pure TM01 mode. With the large diameter and high mode purity, the device can be expected to have high power capacity. With a 770 kV, 11.0 kA beam guided by a 3.5 T magnetic field, a 3.2 GW microwave at 9.42 GHz has been obtained in our simulation. The device efficiency is 38%.

Simulation Investigations and Optimization of a Millimeter-Wave Gyrotron for Its Tunability Using Magnetic and Thermal Tuning Schemes

The present gyrotron is designed to operate in $\text{TE}_{\text {7,2}}$ mode at 260 GHz for studying its beam–wave interaction behavior and its tunability for dynamic nuclear polarization/nuclear magnetic resonance (DNP/NMR) application. The operating frequency of the gyrotron is very sensitive to the physical dimension of the RF interaction circuit and its shape can be deformed due to the ohmic loss led temperature. Therefore, the combined magnetic and thermal tuning schemes are used to control the deformation and enhance the tunability of millimeter-wave gyrotron. The 3-D particle-in-cell simulation technique is used to study the beam–wave interaction behavior of gyrotron and validated with a multimode nonlinear code. Further, the structural deformation and thermal studies are made in a finite-element method based ANSYS. The use of combined magnetic tuning and water coolant based thermal tuning schemes have improved the tunable bandwidth of the present gyrotron to ∼1.88 GHz, which is ∼44.60% higher than the one obtained by varying the magnetic field only.

Triode Type Coaxial Inverse Magnetron Injection Gun for 2-MW, 240-GHz Gyrotron

A triode type coaxial inverse magnetron injection gun (CIMIG) is designed using the 2-D and 3-D beam trajectory simulation codes for 240-GHz, 2-MW coaxial gyrotron. In IMIG, the modulating anode is adjusted at the center of the emitter ring and it provides compact size and better control on the beam instability and beam halo. As per the beam-wave interaction simulations, the CIMIG is designed to deliver the 6.5-MW (100 kV, 65 A) helical electron beam of 8.72-mm guiding center radius at the cavity center. First, the synthesis of CIMIG is performed to estimate a range of electrical and geometrical parameters based on the tradeoff equations. The Gaussian type of magnetic field profile is optimized with the peak magnetic field value of 10 T at cavity center and the beam compression ratio of 35.11. The pitch factor of 1.306 and the transverse velocity spread of 2.74% are realized in 2-D trajectory code electron GUN. The design results obtained in 2-D simulations are validated in 3-D particle trajectory simulator CST-Particle Studio. In 3-D optimization, the gun geometry and the electrical parameters are kept similar to 2-D design. The pitch factor of 1.285 and transverse velocity spread of 3.01% are obtained in 3-D design which shows good agreement with the 2-D design.

Effect of cyclotron resonance on ‘hot’ dispersion in a staggered double metallic grating sheet beam travelling wave tube

Based on the beam wave synchronous interaction in transverse and longitudinal directions at the same time and starting from Maxwell’s equation and linear Vlasov equation, the beam–wave interaction ‘hot’ dispersion equation considering both cyclotron resonance and Cherenkov resonance in a staggered double metallic grating traveling wave tube is deduced. Through the reasonable selection for geometric and electrical parameters, the numerical calculation and analysis of the ‘hot’ dispersion equation shows that the beam–wave interaction gain and frequency band with the cyclotron resonance enhancement effect are higher than those with only Cherenkov resonance radiation.

Power enhancement for millimeter-wave extended interaction radiation sources by using the TM31-mode scheme

The application of a TM31 mode scheme in extended interaction radiation sources permits the use of higher beam power and larger power capacity for power enhancement as compared with that of the conventional fundamental mode in the millimeter-wave band. To support this point, the effect of coupling cavities on the electromagnetic characteristics of the TM31 and fundamental modes is studied. This study shows that the TM31 mode can build up (1) a weaker TM11-like field in the gaps which has the same typical distribution pattern as that of a conventional fundamental mode at the same frequency and (2) two extra parts of field energy to support larger coupling cavities. To demonstrate this feature, we observe the field distribution and strength by injecting a certain wave power in two cavities, which are predicted to resonate in the TM31 and fundamental modes at the same frequency. The mode analysis and the beam-wave interaction are discussed to analyze the feasibility of the TM31 mode scheme. Through particle-in-cell simulations, the maximum output power over 26.3 kW is obtained at the desired frequency when the beam voltage and current are 61 kV and 3 A, respectively. The TM31 mode scheme could be a promising candidate for achieving high power in millimeter-wave extended interaction radiation sources.

Input and Output Couplers for an Oversized Coaxial Relativistic Klystron Amplifier atKa-Band

We propose a novel system of input and output couplers, excited in azimuthal symmetric and stable mode of operation, for an oversized coaxial relativistic klystron amplifier (OCRKA) at Ka -band. A mode converter is introduced in the output coaxial waveguide to provide a tunnel for the input waveguide and fix the inner and outer conductors of the OCRKA. After characterizing the proposed input and output couplers, the high-frequency structure of the OCRKA is designed and then optimized by Computer Simulation Technology. The simulated frequency and loaded quality factor of the input, output, and idler cavities are validated against measurement. Also, the beam–wave interaction of the OCRKA using the proposed input and output couplers is simulated by particle-in-cell software, the average saturated output power of 880 MW of the OCRKA at Ka -band, with 29.3% electronic efficiency and 58-dB saturated gain are obtained. Moreover, no pulse shortening of the output power waveform is observed during the simulation time of 100 ns, which indicates that the proposed input and output couplers can suppress the higher order mode self-oscillation in the Ka -band OCRKA studied here.

Design of a High-Gain $X$ -Band Megawatt Gyrotron Traveling-Wave Tube

In this paper, a lossy dielectric-loaded high-gain $X$ -band gyrotron traveling-wave tube (gyro-TWT) which operates at the fundamental circular TE11 mode is designed and analyzed. The designed gyro-TWT has the features of high-gain and megawatt level output power. Lossy dielectric is applied to suppress spurious oscillations and to improve the stability of the gyro-TWT. In addition, the interaction behavior of the electron beam is investigated. In the condition of 4.5 W input power, a peak RF output power of 2.14 MW with a gain of 56.7 dB at 8.4 GHz is predicted, corresponding to the electron beam-wave interaction efficiency of 35.6% at 150 kV, 40 A. The research also obtains stable output power over 1.5 MW in the range of 8–8.4 GHz with 2-W input power and output power over 1.2 MW with 150-W input power in the range of 8.6–9 GHz.

High power folded waveguide traveling wave tube based on variable-width technology

Variable-width technology applied to the folded waveguide traveling wave tube (FW-TWT) is proposed in this paper to suppress the lower band-edge oscillation and to expand the operating bandwidth when the operating frequency shifts toward the lower band for obtaining larger output power. Changes in the width of the slow wave structure (SWS) determine the variation of the lower-cutoff-frequency (LCF), which makes the LCF's distribution a frequency range rather than a specific frequency-point. The lower band-edge oscillation will not be focused on a special position but distributed in a frequency-band range in which multiple oscillation modes compete with each other near the LCF. The lower band-edge oscillation can be suppressed by mode competition to some extent. In addition, the width variation of SWS also results in the phase-velocity variation, and thus, the operating bandwidth of FW-TWT can be further improved by the optimized design of variable-width-SWS parameters. Beam-wave interaction simulations predicted that power and bandwidth improvements have been achieved without the lower band-edge oscillation. Meanwhile, four solutions are given for further certifying the effectiveness of the variable-width method in lower band-edge oscillation suppression and bandwidth widening. An output power level of over 350 W in a frequency range of 85–90 GHz (5 GHz) is obtained, with a maximum power of ∼648 W and an electron efficiency of ∼12.1% at 88 GHz with a beam current of 260 mA and a beam voltage of 20.5 kV.

Calculation and Application of Impedance Matrices for Vacuum Electronic Devices

We present a computationally efficient method for the calculation of impedance (Z-) matrices for a large class of standing- and traveling-wave structures used in klystrons, traveling-wave tubes, and other RF vacuum electronic devices. We apply joining formulas by which the Z-matrix of a structure can be constructed from the Z-matrices of its component parts without a full-scale finite-element (FE) electromagnetic (EM) simulation of the whole structure. For the inverse operation, we apply subtraction formulas that define the Z-matrix of a structure from which a selected section has been removed. New Z-matrix modification equations are derived which determine the Z-matrix of a modified structure, without recomputing the entire structure Z-matrix. The approach and examples are extended to multibeam RF structures. The obtained Z-matrices are suitable for the large-signal 1-D and 2-D beam-wave interaction codes CHRISTINE-CC and TESLA-Z. Application of the techniques described here greatly facilitates the accurate calculation of Z-matrices and optimization of large, complex circuits that are difficult to model whole in a single FE simulation.

Harmonic terahertz gyrotron with a double confocal quasi-optical cavity

To reduce mode competition in a high-harmonic terahertz gyrotron, the gyrotron with a quasi-optical confocal cavity is proposed. Theoretical and experimental investigations demonstrate that the confocal cavity has good-mode selection and is suitable for high-harmonic operation. However, due to the transverse nonuniformity of the radio frequency field, the beam–wave interaction efficiency is low in the confocal cavity. To mitigate this drawback, the double confocal cavity is investigated in this study. Through three-dimensional particle-in-cell simulation on a designed 330-GHz gyrotron with a double confocal cavity, the physical mechanism of beam–wave interactions in a double confocal cavity is analyzed and presented.

Oversized coaxial relativistic extended interaction oscillator with gigawatt-level output at Ka-band

In this paper, an oversized coaxial relativistic extended interaction oscillator (OCREIO) with gigawatt-level output at the Ka-band is proposed. We adopt a four-gap buncher cavity and a three-gap output cavity to increase the power capability and improve the electronic efficiency of the OCREIO. The beam-loading conductance for each mode existing in the buncher cavity is derived based on a small-signal theory. The beam-wave interaction and power capability for the 2π/3 and π modes exciting in the buncher cavity are analyzed. The operation mode 2π/3 is chosen by considering the beam-loading conductance and power capability. In addition, an improved method is proposed to mitigate the electric field intensity of the buncher cavity so as to moderate velocity modulation. The weak velocity modulation offers enough distance to make density modulation, thereby obtaining a relatively high fundamental harmonic current amplitude. Our study on the device performance of the proposed OCREIO, using the particle-in-cell simulation code CHIPIC, predicts an output power of 922.7 MW and a high electronic efficiency of 32.9% at 30.5 GHz, as well as the relatively less time of frequency-lock of self-oscillation <20 ns. The simulated results of the proposed OCREIO motivate us to practically develop the device in the near future.

Broadband and high-power terahertz radiation source based on extended interaction klystron

Terahertz applications require high performance and high reliability terahertz radiation sources, especially the urgent demands of high output power and broad bandwidth. The extended interaction klystron (EIK) has the great potential to generate hundreds of watt output power in terahertz band. The terahertz EIK adopts multiple gap cavities and unequal-width slots structure is proposed with methodological improvement of bandwidth and output power. The unequal-width slots are the key design of the multiple gap cavity, and the influences of unequal-width slots on the electromagnetic field distribution and beam-wave interaction are analyzed in detail. With multiple gap cavities and unequal-width slots structure, EIK has advantages of wider frequency separation and larger effective characteristic impedance. Particle in cell (PIC) simulation indicates that the bandwidth of unequal-width slots structure can reach to 550 MHz in our initial G-band EIK design. Then, we utilize two kinds of resonance cavities with different width ratios to build a six-cavity beam-wave interaction system and make it operate at the state of stagger-tuning, the bandwidth can be extended to 1–1.5 GHz. Our research shows that the unequal-width slots structure has wider tuning frequency range. Furthermore, the bandwidth can be further broadened to over 2 GHz when dynamic-tuning is adopted, while maintains a high output power of 560 W with efficiency of 11.3% and gain of 47.5 dB. Thus, the methods of multiple gap cavities with unequal-width slots structure, stagger-tuning and dynamic-tuning are much important for the bandwidth improvement of EIK in terahertz band.

3-D Fast Nonlinear Simulation for Beam–Wave Interaction of Sheet Beam Traveling-Wave Tube

In this paper, a 3-D fast time-domain nonlinear algorithm (FTDNA-3-D) based on particle-in-cell method for the beam–wave interaction of the sheet beam slow wave structure (SWS) is presented. Calculation equations of the circuit electric field and the space charge electric field are given. Calculation approaches of the energy exchange and the particle mover are displayed. A simplified coupling impedance simulation approach for sheet beam SWS is indicated. The FTDNA-3-D takes the transverse electric field and the focusing magnetic field into consideration. The FTDNA-3-D could reach a high simulation speed. This novel algorithm gives a faster accurate choice for the design of sheet beam traveling-wave tube (TWT). It could be used to enhance the design efficiency of sheet beam TWT. A Ka-band staggered double vane TWT is used to verify the FTDNA-3-D. Simulation results of output power and gain versus frequency from FTDNA-3-D are compared with results from CST particle studio. The results of FTDNA-3-D are in accord with CST particle studio well.

Starting Currents for Eigenmodes of a Gyrotron Cavity With Mode Conversion

In the fixed-field (cold) approximation, a generalized formula is derived for the starting currents of eigenmodes excited by an electron beam in a gyrotron cavity with the mode conversion. Tapered gyrotron cavities with gradual and abrupt transitions are considered as examples. It is shown that the effect of the mode conversion on the starting current consists mainly in the change of the diffractive quality factor and, therefore, is small for cavities with low diffractive losses. For such cavities, our formula is in good agreement with single-mode, self-consistent (hot) calculations of the electron beam–wave interaction. The agreement degrades for high-order axial modes having clear-cut distinctions of cold and hot fields. The derived formula is used to test the validity of the single-mode approximation for a complex gyrotron cavity with the abrupt change in radius.