Nonlinear Beam-wave Interaction Research Articles

Design and verification of a backward wave oscillation suppression circuit for the Ka-band gyrotron travelling-wave tube.

Backward wave oscillation seriously degrades the stability of gyrotron travelling-wave tubes (gyro-TWTs), especially during high average/continuous wave operation. To solve this problem, a selective mode suppression structure (SMSS) based on the mode coupling principle is proposed and applied in the nonlinear beam-wave interaction region to suppress the parasitic TE11 mode. It is capable of obtaining a high power and improving the tube stability. Simulation results demonstrate that the SMSS can raise the starting current from 10 to 18A and the starting pitch factor from 1.2 to 1.6. Based on this proposed circuit, a Ka-band TE01 mode gyro-TWT was designed, and the particle-in-cell simulation shows that it can achieve a saturated output power of over 150 kW from 29.7 to 31.7GHz with a velocity spread of 2.2%. For verification, a SMSS is manufactured and cold tested. The measurement of S-parameters reveals that it can effectively suppress the parasitic TE11 mode.

Coherent Combining of Phase-Steerable High Power Microwaves Generated by Two X-Band Triaxial Klystron Amplifiers with Pulsed Magnetic Fields

We report the first experimental demonstration of coherent combining of phase-steerable high power microwaves (HPMs) generated by X-band relativistic triaxial klystron amplifier modules under the guidance of pulsed magnetic fields. Electronically agile manipulation of the HPM phase is achieved with a mean discrepancy of 4° at the gain level of 110dB, and the coherent combining efficiency has reached as high as 98.4%, leading to combined radiations with equivalent peak power of 4.3GW and average pulse duration of 112ns. The underlying phase-steering mechanism during the nonlinear beam-wave interaction process is furthermore explored by particle-in-cell simulation and theoretical analysis. This Letter paves the way for high power phase array in large scale and may stimulate new interest in research of phase-steerable high power masers.

A Simulation Method Based on Nonlinear Theory for Noise Analysis in Traveling-Wave Tube

In this article, we propose a simulation method to investigate the noise mechanism of traveling-wave tube (TWT). Based on the nonlinear theory of Lagrangian description, 1-D noise model is established to analyze the shot noise and the velocity noise of the electron beam in the drift space, which clearly shows that the beam noise propagates along the electron beam with standing wave shape. The shot noise and the velocity noise can be periodically converted into each other along electron beam transmission, which is consistent with the prediction of the classical noise theory developed by Pierce and Danielson (1954). Using the nonlinear beam–wave interaction theory, the evolution process of the shot noise and the velocity noise of the electron beam transforming to the electromagnetic wave in TWT is illustrated. The calculated results show that the input position of the slow wave circuit may affect the noise power spectral density (NPSD) of the device. The proposed method can provide more intuitive and simple images to explain the noise mechanism of TWT.

Design of high-power wide-band G-band third harmonic amplifier

To meet the demand of high-power and wide-band signal sources for G-band vacuum electronic devices, the research on G-band third harmonic amplifier is carried out. The amplifier utilizes the third harmonic current in the nonlinear beam-wave interaction of E-band TWT, and realizes G-band electromagnetic wave amplification by cascading harmonic interaction section. The design scheme of high performance and practical G-band wide-band high-power source adopts folded waveguide slow wave structure with modified circular bends, and the G-band third harmonic amplifier is simulated and optimized by using the microwave tube simulator package (MTSS) software. The result shows that the device can obtain harmonic output power greater than 3.6 W in the range of 15 GHz, with conversion gain＞33.3 dB and electronic efficiency＞0.36%. Compared with other miniaturized terahertz radiation sources in this band, it has superior performance in terms of output power and bandwidth, and thus provides a design basis for the subsequent research of G-band third harmonic amplifier.

Effects of the Magnetic Field Taper on a Continuously Frequency-Tunable Gyrotron

Generally, the magnetic field profile in the gyrotron beam-wave interaction section is usually considered to be constant in the theoretical investigation, but actually it is approximately linearly tilted slightly due to the limitation of the superconducting magnet coils. The effects of the weak operating magnetic field taper on the operating frequency, the beam-wave interaction efficiency, and the frequency-tuning range for a continuously frequency-tunable gyrotron are investigated with a self-consistent nonlinear beam-wave interaction theory. It is found that the tapered operating magnetic field has a significant effect on the operating frequency, the frequency tuning bandwidth, and the beam-wave interaction efficiency. In addition, the effect of the weak operating magnetic field taper on the starting current is studied based on the linear theory. It is found that the values of not only the starting current but also the operating magnetic field are obviously different from those when the tapered operating magnetic field is taken into account. With the increase in the slope of the tapered operating magnetic field, the operating frequency and the frequency-tuning range are decreased, but the beam-wave interaction efficiency is increased. When the slope of the tapered operating magnetic field is negative, the variations in the operating frequency, the frequency-tuning range, and the beam-wave interaction efficiency are more obvious. The effects of the tapered magnetic field on different order axial modes are different, and the effect on a higher order axial mode is more notable.

A 3-D Frequency-Domain Nonlinear Theory of the BWO With an Inclined Rectangular Electron Beam

A 3-D frequency-domain nonlinear theory of the backward wave oscillator (BWO) with an inclined rectangular electron beam (IRB) is presented in this article. The ohmic losses, space-charge effects, and full 3-D motion of electrons are considered in the nonlinear theory. A set of self-consistent differential equations that describe the nonlinear beam–wave interaction in the BWO with an IRB (IRB BWO) is given, and a calculation code called IRB BWO-3-D is written. Particle-in-cell (PIC) simulations verify the nonlinear theory of the IRB BWO. The effects of the width of the electron beam, the thickness of the electron beam, and the inclination angle on the output power and efficiency of the IRB BWO are also discussed.

Investigations on the Effect of the Electron Beam Misalignments on a Continuously Frequency-Tunable Gyrotron

The effect of the electron beam misalignments, including the parallel shifted electron beam and the tilted electron beam on the operating frequency, the beam-wave interaction efficiency, and the frequency-tunable range for a continuously frequency-tunable gyrotron has been studied based on a self-consistent nonlinear beam–wave interaction theory. And the effect of the parallel shifted electron beam on the starting current has also been investigated based on linear theory. It is found that the misaligned electron beam has a little effect on the operating frequency and the frequency-tunable range but a significant effect on the beam-wave interaction efficiency. The misaligned electron beam has a different effect on different axial modes, the influences on the operating frequency, the frequency-tunable range, and the beam-wave interaction efficiency of a higher order axial mode are more obvious. Meanwhile, the influence of the parallel shifted electron beam on the starting current is significant; not only the order of magnitude of starting current increases, but the operating magnetic field is also changed. These results present that the effect of the misaligned electron beam is significant; the electron beam misalignments should be taken into account and avoided in the design and fabrication of a continuously frequency-tunable gyrotron.

Nonlinear Analytic Solution of Eulerian Beam-Wave Interaction Theory Considering Harmonic Interaction of Traveling-Wave Tube Amplifiers

In this paper, a novel Eulerian nonlinear beam-wave interaction (BWI) theory considering harmonic interaction of a helix traveling-wave tube (TWT) is developed. Derived from this Eulerian model, the novel Eulerian nonlinear analytic solutions (the fourth-order analytic solution of fundamental and the second-order analytic solution of harmonic) are first obtained by the method of successive approximation. The analytic relationships between electric fields of fundamental/harmonic frequencies and electron phases are also found. Then, the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory are compared to a Lagrangian theory. C-band and Ku-band helix TWTs based on a single pitch section are included in the simulation. It is found that the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory agree well with the Lagrangian theory at 1-dB gain compression point. Interestingly, the saturation effects caused by electron overtaking cannot be found by the traditional Eulerian analysis but can be described by the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory. Moreover, Eulerian nonlinear analytic solutions are simpler and more accurately than existing approaches and, thus, allow analytical progress. This paper confirms that the Eulerian nonlinear analytic solutions can outperform the previous proposals.

Study the Mechanism and Suppression of AM/PM Conversion of Traveling-Wave Tubes Using Eulerian Hydrodynamic Analysis

In this paper, the fourth-order analytic solution of amplitude modulation to phase modulation (AM/PM) conversion is first derived from an Eulerian nonlinear analytic model. The analytic relationships between electron phases, detuning parameter b, and AM/PM conversion are also found. Then, the mechanism of AM/PM conversion is studied. It is found that the generation of the harmonics in the dc component of the electron phase in the nonlinear beam–wave interaction region is the main mechanism of AM/PM conversion. Next, a series of AM/PM conversion suppression schemes is discussed by using the mechanism. The Eulerian formations are validated by an in-house code based on the Lagrangian theory. Results show that the fourth-order analytic solution of normalized axial electric field and AM/PM conversion agree well with the Lagrangian theory in the nonlinear region. In addition, the suppression schemes are applied to a high-efficiency Ku-band space traveling-wave tube (TWT). The AM/PM conversion distortion is greatly reduced by approximately 50% with a slight drop of output power. We hope that our efforts will help the nonlinear design of TWT in the future.

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.

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.

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.

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

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

A three-dimensional nonlinear beam–wave interaction theory for common traveling wave tubes

A three-dimensional (3-D) nonlinear theory model of beam–wave interaction for common traveling wave tubes (TWTs) is described. The equation governing the amplitude of electromagnetic wave is derived analogously to Poynting’s theorem. The electron dynamics are treated using the 3-D Lorentz force equations. RF space charge fields are obtained from solutions of the Helmholtz equations. In the model, the RF field profiles for cold structure are represented by the digitized RF field calculated by a finite-element software, HFSS. Because the digitized RF field can be obtained in the same way, the 3-D simulation code can be used to simulate common TWTs, such as helix TWTs, coupled-cavity TWTs, and even the folded waveguide TWTs. Results from the 3-D code are compared with those from 1-D code, experiment and the existing analytical theories for three types of slow wave structures.

Theoretical analysis and simulation study on a coaxial vircator with enhanced modulation

Based on large-signal theory, a one-dimensional theoretical model of a coaxial vircator is developed to give the microwave gain of the nonlinear beam–wave interaction, and the effect of injected current premodulation on the microwave gain is analysed theoretically. In addition, a coaxial vircator with improved dual-cavity modulation structure, which has the advantage of enhancing the effect of the modulation cavity on the injected electron beam by way of feedback microwaves, is presented. The simulation results are presented to test the validity of the proposed theory, and it can be seen that the system power efficiency can become further strengthened by adjusting the parameters of the microwave feedback channel until the feedback electric field is at the proper phase. Finally, through optimization, a structure capable of generating 7.05 GW average output power and 19.5 % power conversion efficiency at 2.95 GHz operating frequency is obtained.

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

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

Development and Application of a Nonlinear Beam-Wave Interaction Code SBK2D for Sheet Beam Klystrons

To study the nonlinear beam-wave interaction for sheet beam klystron (SBK), a 2-D simulation code of SBK2D, based on the 2-D rod macroparticle model, has been designed and realized thoroughly in this paper. In our physical model, the sheet beam is simulated by a series of rods with nonzero thickness and length in \(y\) and \(z\) directions, respectively ( \(y\) is the direction of sheet beam’s narrow dimension, and \(z\) is the direction of beam motion). Then, the space-charge forces between the rod macroparticles are calculated by Green’s functions approach, and the port-approximation methods are employed to simulate high-frequency fields for each cavity. Furthermore, the relativistic Lorentz motion equation is solved to obtain the parameters for further macroparticle motion, and the specific criterions are introduced to deal with the sheet beam interception problem by the tunnel and cavities. To verify our simulation code, an eight-cavity W-band SBK has been designed, calculated, and analyzed by SBK2D in detail. The good consistency between SBK2D and 3-dimensional Particle in Cell (3-D PIC) program indicates the reliability of the physical model and simulation code for our program. In addition, the calculation time of SBK2D is only about 1% of that of the 3-D PIC, which makes it more feasible and efficient to calculate and optimize the initial physical parameters for the design of complicated SBK.

Research on the beam-wave interaction theory of folded waveguide traveling wave tubes based on three-port network model

A general equivalent model for slow-wave structure is established in this paper, if the unit cell of the periodic slow-wave structures is represented by a three-port network and the parameters of the equivalent model are determined by a high frequency structural simulator. In this method, there is no need to find a complicated equivalent circuit, and the fields in the tunnels can be calculated by the high frequency software directly. Therefore, the three-port network model is simpler than the analytic method and no more complex than the common equivalent circuit model. A one-dimensional nonlinear beam-wave interaction theory suitable for the folded-waveguide traveling wave tubes (TWTs) is accomplished based on the three-port network model. And a one-dimensional nonlinear beam-wave interaction code, which complies with the MATLAB language, is used to simulate a folded-waveguide TWT. The difference between the results obtained from the code and the experimental data is less than 10%. This theory can be used in the design of novel folded-waveguide TWTs and research on nonlinear simulations.

Research on non-linear beam-wave interaction of W-band Gyro-TWT with helical waveguide

Gyro-TWT is one of the most promising candidates for the transmitter microwave source of the next generation imaging radar; meanwhile, it plays an important role in national security. Gyro-TWT with helical waveguide is capable of generating broad-bandwidth radiation and highly stable. In this paper, we derive the dispersion equation of helical waveguide and the non-linear theory for calculating the beam-wave interaction. Numerical stimulations basically accord with the experimental results. We design a W-band Gyro-TWT operating with a 80 keV, 5 A electron beam, producing an output power of 142 kW with 3 dB bandwidth 4.5%, central frequency 95 GHz, and saturation gain 52 dB. In the end, we calculate the effects of the changes of voltage, current and input power on the output performance of Gyro-TWT.