Beam-wave Interaction Research Articles

Design of a high gain and high efficiency W-band folded waveguide TWT using phase-velocity taper

The folded-waveguide (FW) slow-wave structure (SWS) is a very promising beam-wave interaction circuit for high-frequency traveling wave tubes (TWTs). This paper presents the design methodology for enhancing the gain and efficiency of a practical W-band FWTWT using phase-velocity taper. Initially, phase-velocity, interaction impedance, and gain-growth of a single-section FWTWT are predicted theoretically. Further, these parameters are optimized using the eigenmode solver and transient solver of 3-D CST Studio. The simulated results agreed with theoretically predicted results within ~1% discrepancy. Then the single-section SWS along with the input and output couplers consisting of quarter-wave impedance transformers and pillbox windows are simulated using transient solver and a return-loss of around −20 dB is obtained over the desired band. Finally, the output power, gain and electronic efficiency for a two-section TWT with the phase-velocity taper are obtained using particle-in-cell simulation of CST Studio. At an applied beam voltage of 20 kV and a current of 0.1 A, an output power of 130 W, corresponding to a saturated gain of 39.4 dB, an instantaneous 3-dB bandwidth of around 5.3%, and electronic efficiency of around 6.5% at 94 GHz has been obtained. It was found that at 94 GHz the ‘positively and negatively phase-velocity tapered’ sections enhanced the gain by almost 3 dB and doubles the electronic efficiency of the two-section FWTWT design as compared to the two-section FWSWS with the same interaction circuit length with no phase-velocity taper.

Controllable Thermal-Frequency Tuning of a Terahertz Gyrotron

Gyrotron performance is sensitive to cavity structure parameters, and the cavity shape is temperature dependent due to thermal deformation induced by temperature rise from ohmic loss power on finite-conductivity cavity wall. Accordingly, this paper studies a frequency-tuning scheme for terahertz gyrotron by properly controlling the cavity thermal deformation. By combining gyrotron nonlinear theory and finite-element method software, controllable thermal-frequency-tuning capability of a continuous-wave 263-GHz gyrotron is systematically investigated, toward maintaining gyrotron operating under gyromonotron condition in frequency-tuning band, and achieving high efficiency in broadband frequency-tuning range. After studying cavity thermal distribution, structure deformation, and electron beam–wave interaction, an optimized cavity structure with transition sections on both ends is proposed. Simulation predicts that with the two-transition-section cavity, via additional thermal tuning, the continuous-frequency-tuning band is capable of reaching 1.75 GHz, which is 5 times of the initial bandwidth. Furthermore, using the thermal-frequency-tuning technology, impressive high efficiency above 17% is obtainable in the whole frequency-tuning range.

Theoretical analysis and Vsim simulation of a low-voltage high-efficiency 250 GHz gyrotron

Low-voltage, high-frequency gyrotrons with hundreds of watts of power are useful in radar, magnetic resonance spectroscopy and plasma diagnostic applications. In this paper, a 10 kV, 478 W, 250 GHz gyrotron with an efficiency of nearly 40% and a pitch ratio of 1.5 was designed through linear and nonlinear numerical analyses and Vsim particle-in-cell (PIC) simulation. Vsim is a highly efficient parallel PIC code, but it has seldom been used to carry out electron beam wave interaction simulations of gyro-devices. The setting up of the parameters required for the Vsim simulations of the gyrotron is presented. The results of Vsim simulations agree well with that of nonlinear numerical calculation. The commercial software Vsim7.2 completed the 3D gyrotron simulation in 80 h using a 20 core, 2.2 GHz personal computer with 256 GBytes of memory.

Thermoanalysis and Its Effect on the Multimode Beam-Wave Interaction for a 0.24-THz, Megawatt-Class Gyrotron

The detailed analyses of heat transfer and its effect on the cold cavity, effective conductivity, and beam-wave interaction for a 0.24-THz megawatt-class gyrotron is presented in this paper. In the heat transfer analysis, the commercial finite-element method software ANSYS was used, in which Fluent was selected to simulate the thermal analysis, and Static Structural was selected to simulate cavity mechanics. For the cavity cooling system, 50 uniform axial wedge grooves in the outside surface of the cavity were considered, in which the total external loaded coolant flow rate is 40 L/min. The thermal analysis result shows that the maximum temperature is about 260 °C in the center section of the cavity. The deformed cavity was obtained by the structural analysis. After ANSYS simulation, the cold and the hot cavities with deformation were simulated by the in-house developed time-dependent, self-consistent multimode interaction code, in which the distributed conductivity caused by the distributed temperature was used. For the cold cavity, the electric field profile is not changed significantly, but the diffraction quality factor and resonant frequency are reduced by 60 and 0.191 GHz, respectively. The output power is not changed seriously, but the oscillation frequency is decreased by 0.18 GHz.

High power long pulse microwave generation from a metamaterial structure with reverse symmetry

Experimental operation of a high power microwave source with a metamaterial (MTM) structure is reported at power levels to 2.9 MW at 2.4 GHz in full 1 μs pulses. The MTM structure is formed by a waveguide that is below cutoff for TM modes. The waveguide is loaded by two axial copper plates machined with complementary split ring resonators, allowing two backward wave modes to propagate in the S-Band. A pulsed electron beam of up to 490 kV, 84 A travels down the center of the waveguide, midway between the plates. The electron beam is generated by a Pierce gun and is focused by a lens into a solenoidal magnetic field. The MTM plates are mechanically identical but are placed in the waveguide with reverse symmetry. Theory indicates that both Cherenkov and Cherenkov-cyclotron beam-wave interactions can occur. High power microwave generation was studied by varying the operating parameters over a wide range, including the electron beam voltage, the lens magnetic field, and the solenoidal field. Frequency tuning with a magnetic field and beam voltage was studied to discriminate between operation in the Cherenkov mode and the Cherenkov-cyclotron mode. Both modes were observed, but pulses above 1 MW of output power were only seen in the Cherenkov-cyclotron mode. A pair of steering coils was installed prior to the interaction space to initiate the cyclotron motion of the electron beam and thus encourage the Cherenkov-cyclotron high power mode. This successfully increased the output power from 2.5 MW to 2.9 MW (450 kV, 74 A, 9% efficiency).

Design of W‐band sheet beam travelling wave tubes based on staggered double vane slow wave structure

In this study, a complete and viable plan about a W-band sheet beam travelling wave tube based on a staggered double vane slow wave structure is drawn up. The dispersion characteristics, transposition characteristics of high-frequency system, sheet electron beam gun, vacuum window, periodically cusped magnetic focusing system and beam–wave interaction are analysed by CST Microwave Studio, CST Particle Studio and HFSS. An attenuator is used in this device to suppress oscillation. A phase velocity taper is used to increase output power. The operation voltage is 20.6 kV and the current is 80 mA. With a 10 W input power, the output power is 1100 W versus the gain is 20.41 dB at 95 GHz. The peak amplitude approaches 1200 W versus the gain approaches 20.79 dB at 99 GHz.

0.85 THz truncated sine waveguide traveling‐wave tube with sheet beam tunnel

A sine waveguide (SWG) traveling-wave tube with sheet electron beam tunnel is proposed to amplify the high-frequency terahertz wave. In this study, the slow wave characteristics including the dispersion properties and interaction impedances have been investigated by using the eigenmode solver in the 3D electromagnetic simulation software Ansoft HFSS. The truncated SWG slow wave structure possesses the relatively large average coupling impedance. The beam–wave interaction characteristics of truncated SWG with sheet electron beam tunnel are calculated by high-frequency simulation software CST. From the particle-in-cell simulation results, this beam–wave interaction circuit can produce >490 mW ranging from 0.845 to 0.855 THz with a corresponding gain over 22 dB.

Comparative demonstration of multimode steady-state theory for the gyrotron traveling-wave tube based on a distributed loss-loaded metal cylindrical waveguide

Gyrotron traveling-wave tube (gyro-TWT) is capable of generating high-power microwave radiation in a millimeter wave range. It is one of the most promising candidates for the applications in the millimeter wave radar, communication systems, and environmental monitoring. The gyro-TWT can work at high frequency and produce high power output with high order modes. Although the high mode gyro-TWT can work at high frequency and produce high power output, the instability problem is a main factor to prevent the gyro-TWT performance from further improving and hinder this device from being put into the practical application. The earlier research of the instability primarily concentrated on the single-mode situation, which cannot be used to analyze the mutual effects between the other oscillation modes and the operating mode. Hence, it is important for academic study and engineering application to solve the mode competition problem. In this paper, based on lossy uniform/periodic dielectric-loaded metal cylindrical waveguide usually used in the international academic analysis and engineering research, a multimode steady-state beam wave interaction theory for gyro-TWT is established, which can consider the mutual effects between the other oscillation modes and the operating mode. As application examples, under the same condition of geometrical and electrical parameters, the theoretical results of the beam wave interaction for the TE01 fundamental mode gyro-TWTs are compared with the experimental results reported by NRL and IECAS for Ka band and those simulated with Magic code for W band in order to demonstrate the rationality of the theory. The results show that the theoretical results are in good agreement with the experimental and simulated ones. For the NRL design, when the velocity spread is 9.6%, the maximum output power from the theory is 127 kW at 34.09 GHz with a gain of 47.4 dB, an efficiency of 17.6%, and a -3 dB bandwidth of 1.01 GHz, and an NRL measured maximum output power is 130 kW at 34 GHz with a gain of 47.5 dB, an efficiency of 18% and a -3 dB bandwidth of 1.0 GHz. The maximum difference between the theory and the experiments occurs near the frequency of 34 GHz, the measured power by NRL is 127 kW and the calculated power is 118 kW, the relative error between the theory and the experiment is 8.5%. For the IECAS design, the simulated maximum output power from the theory is 113.73 kW at 33.85 GHz with a -3 dB bandwidth of 1.72 GHz when the velocity spread is 7%. The measured peak output power by IECAS is 110 kW at 33.88 GHz with a -3 dB bandwidth of 1.75 GHz. For a W band TE01 fundamental mode gyro-TWT design, the saturated output power is 112 kW at a frequency of 94.5 GHz with a gain of 34.28 dB and -3 dB bandwidth of about 4.1 GHz, and the saturated output power calculated with Magic code is 106.7 kW with a gain of 34.11 dB and 3 dB bandwidth of 3.9 GHz, the maximum relative errors between the theory and experiment are both about 5% for the output power and the bandwidth.

Design and simulation of output mode conversion structure of relativistic magnetron with all cavity output

A relativistic magnetron using all cavity extraction and semi-transparent cathode has the virtues of compactness, high output power and high efficiency. The three-dimensional particle-in-cell simulations show that 1.15 GW output microwave with an efficiency about 50% can be obtained at S-band with pure TE11 mode of the fan waveguide. However, due to the fact that the output structure is composed of three detached fan waveguides, mode conversion structure in the output region is required for the convenience of practical applications. Therefore, two mode conversion structures are studied for the output mode conversion. The first structure is to widen gradually or abruptly the fan waveguide in the azimuthal direction from a given position (starting point) along the microwave transport direction. And then the three fan waveguides are connected into one coaxial waveguide. The effects of the position of the starting point on the beam-wave interaction and microwave extraction are numerically studied. For the convenience of description, we define L as the axial distance between the center of the output coupling hole and starting point. Simulation results show that for the abrupt and gradual variation case, when the length of L changes in a relatively wide region, the output power is larger than 1.0 GW in TEM mode at S-band. It is about 90% of the conventional fan waveguide with 1.15 GW. For the gradual variation case, the optimal value of L equals 10.0 cm, and the corresponding output power is beyond 1.0 GW. For the abrupt variation case, the optimal value of L equals 13.75 cm, the corresponding output power is about 1.15 GW. But in the abrupt variation case, the output power is a little more sensitive to the value of L. The second structure is to convert the fan waveguide into a rectangular waveguide. Ａcompound waveguide composed of a section of fan waveguide and a section of rectangular waveguide is designed for studying its feasibility. In the compound waveguide, the wide edges of the cross section of the rectangular waveguide are tangent to the inner and outer arc of the fan cross section respectively. And the narrow edges cross the end points of the outer arc. Simulation results show that in the compound waveguide the microwave with TE11 mode of the fan waveguide input at the inlet can be changed into the TE10 mode of the rectangular waveguide at the outlet with almost no power loss. In all, the output microwave power larger than 1.0 GW could be obtained after using the two proposed mode conversion structures. In practical applications, one could choose the relevant mode conversion structure according to the requirement.

Microstrip angular log‐periodic slow wave structure on quartz substrate with coaxial input/output coupler

The microstrip angular log-periodic meander line slow wave structure (SWS) on quartz substrate with coaxial input/output coupler is studied. The effects of different structure parameters on transmission characteristics of the 25 periods SWS during Ka band are discussed in detail. The SWS with the total length of ∼6.5 mm, add coaxial input/output coupler and tapered impedance microstrip line to form an entire assembly. The testing result is accordant with that of simulation. The dispersion characteristics of the SWS were obtained to determine the work voltage. The beam-wave interaction results show that the output power is 11.4 W at the frequency of 32 GHz, with the electron efficiency of 3.3%.

A High-Gain ${X}$ -Band Overmoded Relativistic Klystron

A high-gain ${X}$ -band overmoded relativistic klystron is presented in this paper. The device mainly consists of an input cavity, two buncher cavities, and an output cavity. Moreover, two reflectors are added before and after the input cavity, therefore a standing wave is formed between the two reflectors, improving the initial modulation of the electron beam. With two sectional RF lossy materials inserted, the input cavity and the two buncher cavities are effectively isolated with each other. An additional reflector located just before the output cavity further reflects the backward-flowing power. Particle-in-cell simulations show that for a 10-kW injected microwave with a frequency of 9.37 GHz, the generated microwave power is 1.2 GW, corresponding to a beam-wave interaction efficiency of 30% and a gain of 50.8 dB. As the injected power increases from 10 to 100 kW, the frequency control range extends from 30 to 130 MHz.

Nonlinear theory considering harmonic interaction using Eulerian hydrodynamic analysis

Traveling wave tube amplifiers are one of the most widely used vacuum electronic devices which are employed in various applications, in the areas of such as radar, wireless communication and electronic countermeasures system. Among traveling wave tubes, space-borne helix traveling wave tubes which are of high power, high efficiency, high reliability, long life and radiation hardened, are extensively used in satellite transmitter, data communication system and global positioning system. With the rapid development of the multiphase digital modulation schemes, communication systems are placing greater demands on the output power, electronic efficiency and nonlinear distortion characteristics of space-borne helix traveling wave tubes. However, the nonlinear beam-wave interaction will lead to the generation of harmonics, and thus reduces the output power and electronic efficiency. The harmonics can also act to create beats with the fundamental wave, and thus generate these beat frequencies which are commonly known as intermodulation products. As a result, the bit-error-rate will be increased and the system performance will be compromised. Therefore, the generation of harmonics is of significant current interest in space-borne helix traveling wave tubes. Understanding this effect provides a strong motivation for nonlinear analysis of a helix traveling wave tube. In this paper, a continuous electron phase distribution is obtained by treating the discrete electron beam as a charge fluid based on the Lagrangian theory. Then, to obtain a nonlinear Eulerian theory considering harmonic interaction, the electron phases in Lagrangian theory have been expanded into a series of harmonic components. Considering the 0th component and 1st component of the electron phases only and integrating over the initial phase distribution with the help of the relation of Bessel function, the nonlinear Eulerian theory considering harmonic interaction is established. The nonlinear Eulerian theory considering harmonic interaction is compared to a Lagrangian theory on a set of traveling wave tube parameters which are based on a single section of L-and C-bands traveling wave tubes. It is found that the nonlinear Eulerian theory considering harmonic interaction agrees accords well with the Lagrangian theory before the saturation effect occurs. But, it begins to make a difference near saturation point where the electron overtaking happens. The maximum error in gain between the nonlinear Eulerian theory considering harmonic interaction and the Lagrangian theory is less than 4% at 1 dB gain compression point. So the present nonlinear Eulerian theory considering harmonic interaction can effectively describe harmonic generation at 1 dB gain compression point. The simulation results validate the correctness and effectiveness of our nonlinear Eulerian theory considering harmonic interaction. In futuristic future efforts, it is hoped that the present nonlinear Eulerian theory considering harmonic interaction may provide insights into the behavioral mechanisms of nonlinear effects in space-borne helix traveling wave tubes.

The modified scheme of optimized in simulations Cherenkov type high-power microwave oscillator without guiding magnetic field

The compactness and miniaturization of high-power-microwave (HPM) systems are drawing more and more attention. Based on this demand, HPM generators without a guiding magnetic field are being developed. This paper presents an X-band Cherenkov type HPM oscillator without the guiding magnetic field. By particle-in-cell codes, this oscillator achieves an efficiency of 40% in simulation. When the diode voltage and current are 620 kV and 9.0 kA, respectively, a TEM mode microwave is generated with a power of 2.2 GW and a frequency of 9.1 GHz. In this oscillator, electrons are modulated in both longitudinal and radial directions, and the radial modulation has a significant effect on the energy conversion efficiency. As analyzed in this paper, the different radial modulation effects depend on the phase matching differences of the microwave and electrons. The modified scheme of simulations achieves a structure with an efficient longitudinal beam-wave interaction and optimized radial modulation.

Analysis for beam positioning in a disc-loaded gyro-TWT amplifier

A novel expression for the form factor of a disc-loaded circular cylindrical interaction structure has been derived, which is helpful in finding optimum beam position, so that maximum beam–wave interaction can be achieved in a disc-loaded gyro-TWT amplifier. The penetration of the propagating waves in different regions of the structure was observed using CST Microwave Studio, and it has been found that RF fields are mostly concentrated in the disc-free free-space region. Only a small percentage ( $$\sim $$ 5%) of the travelling wave enters in disc-occupied free-space region. The dependence of the form factor variation on the disc parameters, namely disc-hole radius, disc repetition, and disc thickness of the structure excited in azimuthally symmetric $$\text {TE}_{01}$$ mode, was observed. Maximum coupling of the beam and RF wave was found to be at the ratio of hollow electron beam radius to structure wall radius $$\left( = 0.44 \right) $$ for $$\text {TE}_{01},\left( = 0.39 \right) $$ for $$\text {TE}_{02}$$ , and $$\left( = 0.35 \right) $$ for $$\text {TE}_{03}$$ mode.

Stability of Excitation of Traveling Waves in Gyrotrons With Low-Relativistic Electron Beams

A number of application require compact low-power gyrotrons with relatively low operating currents. In order to provide the start of such gyrotrons, one should use long-length operating cavities with high diffraction Q-factors, and, therefore, with significant losses of the radiated wave power due to Ohmic heating of the cavity wall. In this paper, we demonstrate that in low-voltage gyrotrons there is a possibility for stable operation at higher order axial modes possessing relatively low diffraction Q-factors. An enhanced efficiency of the beam-wave interaction is provided due to the excitation of such modes in the traveling-wave-tube regime.

Large-signal field analysis of a linear beam travelling wave tube amplifier for the anisotropically conducting tape helix slow-wave structure supported by dielectric rods

The large-signal behavior of traveling wave tube amplifier for a linear beam dielectric loaded anisotropically conducting tape helix slow wave structure (SWS) is realized through a swift and reliable field analysis. Using Green’s function sequence, the field components in the SWS are designated as nonlinear functionals of electron arrival time. The electron arrival time in the beam region is formulated into a nonlinear operator in the Banach space mapping form by substituting the axial electric field component into the electron ballistic equation. The nonlinear beam–wave interaction is then obtained by determining the electron arrival time through extensive successive approximations, and thus exact electric and magnetic field components in the tape helix SWS are attained. The numerical computation of the proposed model yields definitive analytical results for the electron exit velocity, induced surface current density, power gain, conversion efficiency, and optimum interaction length.

Nonlinear Investigation of Beam-wave Interaction in E Band Folded Waveguide TWT

A E-band folded waveguide traveling-wave tube (FWTWT) is modelled, and the nonlinear interaction between the electron beam and electromagnetic field is investigated by utilizing a 3-D particle-in-cell (PIC) code, MAGIC3D. The process of the interaction for millimeter wave TWT are presented, including the longitudinal momentum of the electron, the averaged radiation power, and the influence of input power on output power. The radiation power and gain of the FWTWT at 85GHz are 88.5W and 27.5dB.The output power of the FWTWT changes only 1 dB across the 6-GHz bandwidth ranging from 82GHz to 88GHz, which is attractive for many applications, e.g. 5G communication networks , satellite communication, electronic counter measures.

Beam–Wave Interaction From FEL to CARM and Associated Scaling Laws

The development of a microwave tube providing high output power (~1 MW) at a high frequency (~250 GHz) with high efficiency of the beam–wave power conversion is a challenging task. A great deal of theoretical and experimental efforts is directed toward such a goal. A promising powerful source of microwave radiation is the cyclotron autoresonance maser (CARM) oscillator. In this paper, we revisit the well-known physical models in a way, which is suitable for their implementation in the numerical tools for computer-aided design and optimization of a CARM operating at high frequency. The analysis developed by us is an attempt directed toward the realization of an adequate design tool for the development of CARM devices.

Design and Large-Signal Modeling of a $W$ -Band Dielectric TWT

The performance capabilities of a dielectric traveling-wave tube (TWT), designed for operation near 94 GHz near the 100-W power level, are investigated using large-signal simulations. Key design elements include a dielectric liner with a moderately high dielectric constant of 13.5, consistent with magnesium orthotitanate ceramic, and the use of a solid round electron beam with properties (26-kV, 100-mA, and 0.185-mm beam radius) that are comparable to those employed in W -band coupled-cavity TWTs. The optimal simulated performance, computed assuming a 5-cm beam-wave interaction length, is 115 W of output power at 94 GHz, with 6-GHz half-power bandwidth, 10.3-dB large-signal gain, and 4.4% electronic efficiency. Technical issues, including the existence of a higher linearity Crestatron regime, the mitigation of beam charging, and thermal management, are discussed.

Triplet and beam interaction in a plasma

The interaction of three waves requires wavelength and frequency matching conditions. Without the presence of a particle beam, if the conditions are satisfied and if the frequency of the envelope is lower than the lowest frequency of the waves, they exchange energy and the evolution of the envelope of each wave is given by a constant plus a sinusoidal function. On the other hand, if a particle beam propagates within electrostatic and electromagnetic fields with no wavelength and frequency match, the energy exchange between the modes is done due to the particles. One of the modes could be amplified in this scheme. In the present work, we propose a model where a non-relativistic particle beam propagates in a plasma within two electromagnetic modes and one electrostatic mode with wavelength and frequency matching conditions. Then, the waves are allowed to exchange energy between themselves and with the particle beam as well. We present new features in comparison to the isolated triplet interaction and to the beam-wave interaction. These features are relevant for a more realistic triplet interaction model.