High-power harmonic gyro-TWT's. II. Nonlinear theory and design

For pt.I, see ibid., vol.20, no.3, p.155-162 (1992). Based on an analytical study of the stability problems of gyrotron traveling wave amplifiers (gyro-TWTs), an extremely high power second-harmonic gyro-TWT has been designed, evaluated and optimized with a self-consistent nonlinear numerical simulation code. The design, which is based on the magnetron-injection-gun (MIG)-type beam, is presented. Using a 100 kV, 25 A MIG beam with α=1 and an axial velocity spread of 5%, nonlinear self-consistent analysis of a three-stage second-harmonic gyro-TWT amplifier predicts a peak output power of 533 kW, peak efficiency of 21.3% and a 7.4% saturated bandwidth, which verifies the theoretical predictions that a stable harmonic gyro-TWT can generate power levels an order of magnitude higher than those possible from a fundamental gyro-TWT. It is shown that the positioning of the electron beam is very important. A multistage structure is used to recover the loss in gain resulting from shortening the interaction sections to ensure stability     

High-power harmonic gyro-TWT's. I. Linear theory and oscillationstudy

A linear theory using Laplace transforms which is applicable to both gyrotron traveling wave amplifiers (gyro-TWTs) and gyrotron backward-wave oscillators (gyro-BWOs) is presented. The validity of the linear theory is verified by comparing it with an existing nonlinear self-consistent theory based on a different approach. In conjunction with a time-dependent multimode particle simulation code, the linear theory is applied to study the stability of harmonic gyro-TWTs. It is shown that a harmonic gyro-TWT can be made stable to all forms of spontaneous oscillations by employing a multistage interaction structure and that it can generate power levels far in excess of those possible for a fundamental gyro-TWT. The linear bandwidth of a second-harmonic gyro-TWT amplifier is also calculated     

Stability of a 95-GHz slotted third-harmonic gyro-TWT amplifier

A low-magnetic-field moderate-voltage gyrotron amplifier has been designed for stable high-performance operation at 95 GHz. A slotted interaction circuit is utilized to achieve strong amplification near the third cyclotron harmonic frequency. The start-oscillation conditions were determined by an analytical theory and confirmed by a multimode particle-in cell simulation code. The dominant threat to the amplifier's stability is from a third-harmonic peniotron backward-wave interaction. A slow-timescale particle-tracing simulation code predicts the three-section slotted third-harmonic gyro-TWT, which utilizes an 11.6-kG magnet and a 50-kV 3-A υ_⊥/υ_z=1.4 axis-encircling electron beam with an axial velocity spread of 6% will yield an output power of 30 kW with an efficiency of 20%, a saturated gain of 40 dB, and a constant-drive bandwidth of 2%     

Broadband operation of a Ka-band tapered gyro-traveling waveamplifier

A wideband low-voltage millimeter-wave gyro-traveling wave tube (gyro-TWT) amplifier operating in the TE₁₀ rectangular waveguide mode at the fundamental cyclotron frequency is under investigation, The device incorporates precise axial tapering of both the magnetic field and the interaction circuit for broadband operation. Experimental results of a wide (33%) instantaneous bandwidth with a small signal gain in excess of 20 dB and saturated efficiency of ~10% were achieved and shown to be in good agreement with the theory. Reflective instability due to multi-pass effects by mismatches was observed and characterized. Gain and efficiency have been limited by this reflective instability rather than by absolute instabilities which limit the performance of gyro-TWT's with uniform cross-section. The start-oscillation current in terms of the relevant experimental parameters such as the beam velocity ratio (α), magnetic field detuning and reflection coefficient has been measured and compared with theory. Measurements of the phase variation in terms of the RF frequency have shown that the phase varies ±30° from fitted linear phase line     

分布损耗加载回旋行波管多模稳态注波互作用理论与比较证实

基于目前国际上实验研究的均匀介质加载和周期介质加载结构,建立了一种分布式损耗加载回旋行波管(gyro-TWT)多模稳态注波互作用理论.利用这一理论,以TE01模式基波gyro-TWT注波互作用为例,将Ka和W波段的理论结果与实验和软件仿真进行比较,以证实理论的合理性.     

Nonlinear analysis of high-harmonic slotted gyro-TWT amplifier

A nonlinear self-consistent simulation code is employed to investigate the behavior of the slotted gyrotron traveling-wave amplifier (gyro-TWT), in which an axis-encircling electron beam synchronously interacts with a high-order azimuthal mode in a magnetron-type waveguide. The efficiency of a fourth-harmonic device with an ideal 60 kV, 5 A beam is shown to reach 30% for α≡ν_⊥/ν_z=2. The growth rate for the π mode is roughly 25% larger than for the 2π mode. The efficiency increases for lower voltage and the device is found to be moderately sensitive to the radial spread of the beam's guiding center position and extremely sensitive to the axial velocity spread. For an ideal 60 kV, 5 A beam with α=1.5, the efficiency of a second-harmonic gyro-TWT is 42% and falls to 10% for an eighth-harmonic device. The design of a 35 GHz, 60 kV, 5A, α=1.5, eight-vane, fourth-harmonic gyro-TWT with 7% axial velocity spread is presented. It is predicted that this design will yield a peak output power of 90 kW, a peak efficiency of 30%, and 6.3% saturated bandwidth     

W-Band Second-Harmonic Gyrotron Traveling Wave Amplifier with Distributed-Loss and Severed Structures

The second harmonic TE₀₂ gyrotron traveling wave amplifier (gyro-TWT) is a high-power, broadband, millimeter-wave amplifier with a low applied magnetic field. Mode-selective interaction circuits were applied to suppressing spurious oscillations. However, the mode-selective interaction circuit may perturb the operating mode in the gyro-TWT. A multi-stage gyro-TWT design with distributed-loss and severed structures is proposed to stabilize the amplification. This study presents a nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation (gyro-BWO) and reflective oscillation. The lossy and severed sections of the multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of the absolute instability, gyro-BWO, and reflection oscillation. The multi-stage gyro-TWT is predicted to yield a peak output power of 215 kW at 89.9 GHz with an efficiency of 14.3 %, a saturated gain of 60 dB and a bandwidth of 1.7 GHz for a 100 kV, 15 A electron beam with an axial velocity spread _z/ _z = 5%.     

Nonlinear Analysis of Coaxial Gyro-Travelling-Wave-Tube Amplifier

A set of nonlinear self-consistent equations in the electron guiding center coordinates is derived for the study of the behavior of the coaxial gyro-travelling-wave-tube (gyro-TWT) amplifier. It is found that the input signal grows faster and gets saturated earlier with the increasing of b/a (ratio of the inner to outer radius). Using an electron beam of 90kV, 10A and velocity ratio of 1.0 with 3% axial velocity spread, 275kW peak output power is obtained by calculation over the frequency range of 31.22–33.52GHz, the gain, efficiency and bandwidth are 47.4dB, 30.5% and 7.5%, respectively.     

Ka波段二次谐波损耗波导回旋行波管非线性分析

 建立了由损耗段和铜段组成的波导结构的Ka波段二次谐波回旋行波放大器理论模型,并进行了非线性理论研究。基于稳定性分析,确定35 GHz TE₀₂模二次谐波回旋行波放大器的基本工作参数:波导半径为1.02 cm,电子注工作电压为90 kV,工作电流为25 A,工作磁场为0.642 6 T,横纵速度比为1.2;然后通过模拟详细分析了工作电流、波导损耗和速度零散等因素对该放大器性能的影响。研究表明：在该结构中损耗段可以有效地抑制模式竞争从而提高输出功率和带宽;工作电流对输出功率的影响存在最大值;速度零散对输出功率有很大的影响。     

ELECTROSTATIC WAVE EXCITATION BY LITHIUM ION BEAM IN UPSTREAM RECION OF AMPTE LITHIUM RELEASES

It is shown that the electron cyclotron harmonic waves and the ion acoustic broad band obsefved in the transition region and the upstream region of the two AMPTE lithium releases can be explained ,by the interaction of the lithium ion beams and the solar wind plasmas.The cycloidal motion of the freshly produced lithium ion in the solaz wind magnetic and electric fields is essential for these wave excitations.Two simplified models in ion velocity distribution are used in the dispersion relation analysis,one is an orientating ion beam, the other is an ion beam ring (the hollow beam).It is shown that the electron cyclotron. harmonics can be effectively excited by both of these beams if they are very cold. Satisfactory consistence of the theory with the observed results is obtained for the harmonic excitations.The strong Iow frequency (much less than the electron cyclotron frequency) noices might be multioriginal.It is also proposed that the interaction of the lithium ion beam and the solar wind protons provides a suitable mechanism for exciting these broad bands.     

The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency.     

Design of a 50 kW, wideband Ka-band slow wave cyclotron amplifier

A two-stage slow wave cyclotron amplifier is investigated to demonstrate a high power, stable, and broad Ka-band radiation source, operating at a low beam power (~60 kV, ~5 amps) and a low magnetic field (~7 kG). A linear theory predicts that the second harmonic gyro-BWO is competing in the amplifier and can be stabilized by inserting a sever in the interaction circuit. A slow-time-scale non-linear code, with a sever included, predicts a saturated gain of 24-28 dB, an efficiency of 15-17%, and an instantaneous bandwidth of 15-20% at a beam axial velocity spread of 2%. A broadband RF coupler, a mode converter, and a RF vacuum window are designed by the use of a 3D electromagnetic, finite element code. Measured RF characteristics are in good agreement with predictions     

Gyrotron travelling wave amplifier: II. Effects of velocity spread and wall resistivity

The small signal gain and bandwidth of the gyrotron travelling-wave amplifier (gyro-TWA) operating at the fundamental cyclotron harmonic are examined. The analytical and numerical studies focus on the effects of velocity spread in the electron beam and of a distributed wall resistivity in the waveguide. It is found that wall resistivity reduces the forward gain of the amplifier only by an amount approximately equal to 1/3 of the corresponding cold tube loss. Significant increase in bandwidth may result, under certain conditions, from the presence of wall resistivity. A moderate amount (5–10%) of velocity spread does not reduce the peak gain significantly in general, but may reduce the bandwidth by an amount depending on the applied magnetic field. Based on considerations of such factors as power, stability, gain, bandwidth, and efficiency, operating parameters for the gyro-TWA are suggested.     

Stable high-power TE01 gyro-TWT amplifiers

The stability of high power gyro-TWT amplifiers operating in the low-loss TE₀₁ mode of cylindrical waveguide has been studied, Linear theory has been used to determine the threshold start-oscillation beam current for absolute instability in the operating mode and the critical section lengths for the dominant gyro-BWO interactions occurring at various cyclotron harmonics in other waveguide modes. The performance of the amplifier was evaluated with a nonlinear, self-consistent slow-timescale simulation code. Utilizing interaction sections whose lengths are less than the threshold start-oscillation length and are separated by attenuating severs for isolation, two stable three-section devices have been designed which are predicted to yield: (1) a peak output power of 230 kW at 35 GHz with an efficiency of 23%, a saturated gain of 46 dB and a constant-drive bandwidth of 6% for a 100 kV, 10 A electron beam with an α=ν_⊥ /ν_z =1.0 and an axial velocity spread Δν_z/ν_z=5% and (2) 105 kW at 94 GHz with 21% efficiency, 45 dB saturated gain and 5% constant-drive bandwidth for a similar 5 A electron beam. In addition, the design of the 0 dB input/output couplers and the MIG electron gun are given. Due to the low loss of the TE₀₁ mode, both of these amplifiers can be operated continuously     

W波段连续波30 kW回旋振荡管高频系统和收集极的设计

 根据回旋管的电子回旋脉塞理论,借助于编写的回旋振荡管自洽非线性注-波互作用计算程序,设计出了工作频率94 GHz、工作电压30 kV、工作电流3 A的基次谐波连续波单腔回旋振荡管,工作模式为TE02模。设计的回旋振荡管在电压30.0 kV、电流3.0 A、速度横纵比1.5的条件下,获得了31.8 kW的输出功率,电子效率约35％。利用粒子模拟仿真软件对设计的回旋管收集极辅助线包散焦系统进行了粒子模拟仿真分析,模拟结果表明：借助于辅助线包散焦系统可以有效缩短回旋振荡管的轴向尺寸,并使回旋管收集极上的电子束功率密度低于500 W/cm2; W波段回旋振荡管收集极的热测试验结果表明：利用粒子模拟仿真获得的收集极上的电子束功率密度分布与其试验测量结果比较吻合。     

Dielectric-loaded wideband gyro-TWT

The bandwidth of a gyro-TWT (traveling-wave tube) can be widened by employing a dielectric-loaded waveguide to reduce the circuit's dispersion. Fast wave interaction allows the requirements on the beam's quality to be relaxed compared with slow wave interaction. A low-α (≡ν_⊥/ν_z) electron beam is chosen to avoid the absolute instability and minimize the possibility of dielectric charging. This device is investigated using a self-consistent single-mode, large-signal simulation based on a slow time scale formulation. Simulation results show that a constant drive bandwidth of 20% can be achieved for a 100 kV, 5 A electron beam with a velocity ratio of α=0.59 and an axial velocity spread of 2.0%. The growth rate is relatively low because of the low α of the electron beam. The design of a proof-of-principle experiment is described. The tube is expected to deliver a power of 80 kW from 9 to 11 GHz with 15% efficiency and a saturated gain of 30 dB. The performance of a single-anode magnetron injection gun designed to produce the required high-quality electron beam has been studied through simulation     

Prebunched high-harmonic gyrotron

A scheme for harmonic wave generation using a prebunched electron beam has been demonstrated. The prebunched electron beam has been used to further increase the efficiency of the authors' axis-encircling high-harmonic gyrotron. The proof-of-principle experiment was performed at the third harmonic with a TE₃₁₂ mode at 27.7 GHz. The conversion power of 6.7 kW was significantly greater than that used in the nonprebunched experiment. Also, mode competition was effectively suppressed. As expected, the unsaturated output power is proportional to the square of the electron beam current and the start of oscillation current is essentially zero. A linear theory, derived by taking into account the spread of the guiding center and the spread of the axial velocity, gives good agreement with the experimental results     

A scheme to enhance the conversion efficiency of slow‐wave electron cyclotron masers in the large signal approximation

Based on the anomalous Doppler effect, we propose a scheme to improve the practicability of slow‐wave electron cyclotron masers in the large signal approximation. This scheme simultaneously contains the tapered guiding magnetic field and tapered refractive index. Numerical calculations show that this scheme enables the conversion efficiency to reach a higher value within a shorter time than previous schemes. Besides, this scheme also works well in the cases of THz wave band and beam axial‐velocity spread.     

Electrostatic Waves in the Warm Magnetoplasma at the Cyclotron Harmonic Frequencies

Mode conversion and collisionless absorption of electromagnetic wave at the cyclotron harmonic frequencies in an inhomogeneous non-Maxwellian magnetoplasma have been studied. Under suitable energy transfer condition the converted electrostatic wave (plasma wave) either grows or damps. The expressions for the growth/damping rates of this wave have been derived and studied at the cyclotron harmonic frequencies. The effect of the temperature anisotropy on the growth/damping rate of the electrostatic wave at the second cyclotron harmonic frequency has been shown. Growth of such electrostatic waves at ionospheric heights may explain the observed upper hybrid resonance (UHR) echoes and noise bands at the second cyclotron harmonic frequency.