Multimode Time Dependent Analysis and Simulation Studies of the Gyro-TWT Amplifier

Abstract

The horizon of microwave continues to expand not only in the millimetre waves but also in the sub-millimetre-wave frequency range encompassing various applications such as high resolution radar and high information density communication, deep space and specialized satellite communication, advanced high gradient RF linear accelerators, plasma diagnostics and chemistry, material processing, waste remediation, ceramic sintering, laser pumping, power beaming and electron cyclotron resonance (ECR) heating of fusion plasmas, radar and imaging in atmospheric and planetary science, nonlinear spectroscopy and so on. However, there is a lack of high-power wideband millimetre and sub-millimetre waves devices to meet the systems requirement for these applications. There exists a technology gap due to (i) the limitation of conventional microwave tubes caused by the reduction of their sizes, and (ii) the limitation of optical devices, like, laser caused by the reduction of quantum energy as well as by the difficulty of retaining the population inversion. The advents of fast-wave gyro-devices like the gyrotron and the gyro-amplifiers like the gyro-klystron or the gyro-TWT have filled-up this gap to a large extent. The gyro-TWT amplifier incorporates a non-resonant RF interaction circuit, supporting propagating waves, enjoys a wider bandwidth potential than its other counterpart devices like the gyro-klystron, using a system of resonant cavities. So, gyro-TWT exhibit potential to work as the high power amplifier with considerable bandwidth for communication applications in the millimetre and sub-millimeter wave frequency regime. This has aroused considerable research interest for the design and development of gyro-TWT. At the high frequency operations, requirement of DC magnetic field in the gyrotron devices can be reduced by its harmonic operation (cyclotron harmonic frequency close to but slightly less than signal frequency). The RF interaction structure cross section also gets increased, thereby lower RF power loss density and enhanced power handling capacity of the structure. However, with the increase in the waveguide size, the structure becomes over-moded. So, the study of mode competition problem in the device becomes essential that would provide information about the selection of the desired mode amongst the competing modes vis-à-vis their RF power growth and corresponding start-oscillation currents. Consequently, this has motivated the author, in the present thesis, to explore the study of multi-mode electron beam and RF wave interaction of the gyro-TWT. The author has extended the single mode nonlinear analysis of the gyro-TWT for the time-dependent multi-mode regime. The author has also PIC simulated the device for the multi mode beam wave interaction case to validate the developed analysis. The work has further extended to develop the methodology for the design of high harmonic gyro-TWT amplifier and study the stability of its operation. The design methodology and stability analysis is also validated with the help of PIC simulation and nonlinear analysis developed. The PIC and analytical results were also validated by comparing them with the previously reported experimental values. Accordingly, the present thesis has been divided in seven chapters. The chapter 1 outlines the background of the problem undertaken, discussing the various issues such as the applications of millimetre waves at high power levels; the limitations of both the conventional microwave tubes and solid-state devices as well as those of quantum-optical devices in the high power regime, millimetre-wave frequency regime; the role of bunching (Bremstrahlung) gyro-devices in filling up the technology gap in the high power, millimetre-wave frequency regime; significance of the present work; significant contributions; objective and scope of the present work, adopted methodology to solve the giving problem; and the advantage of a gyro-TWT, with respect to its wide bandwidth potential, over its other gyro-device counterparts. In chapter 2, basics of the microwave electron beam devices and their applications have been described. The classification of microwave tubes, various instabilities in electron beam devices, CRM interaction and phase bunching mechanism in a gyro-device have been elaborated. Operating principle of gyro-devices including gyrotron has been described and the concepts relevant to the gyro-TWT problem undertaken. Present scenario of the gyro-TWT has been reviewed with their scope and limitations. In chapter 3, a generalized the time-independent single-mode non-linear analysis of the gyro-TWT amplifier operating at arbitrary cyclotron harmonics of the interaction structure under single mode consideration has been presented. The electron motion has been represented by equations for its phase and energy which results in simplified and reduced number of equations. In order to get optimum beam-wave interaction, the electron beam is positioned at the radius where the RF electric field inside the cylindrical waveguide is maximum. Accordingly, the electron beam guiding centre radius selection for a particular mode of operation has been presented with the help of form factor variations for the RF structure parameter which decides the beam wave coupling. An optimum value of the beam guiding centre radius is chosen for the set of parameters. The RF power flowing through the structure cross-section is described by the norm factor. This nonlinear analysis results have also been compared with the linear analysis results. The beam wave interaction mechanism has been explained with the help of bunching of electrons along the axial position and also in Larmor radii. The RF output power and efficiency reduces as the bunch quality degrades. So, the selection of appropriate value of axial magnetic field is very important for the proper beam-wave interaction in order to get optimum RF saturated power. For the numerical appreciation of the device performance, the electron beam formulations have been presented by considering the electron beam to be composed of a large number of macro particles (an ensemble of electrons). The set of coupled differential equations describing the electron energy, phase and RF amplitude have been solved by using Runge-Kutta-Verner fifth order method an efficient and fast method to solve ordinary differential equation with very small local and global errors. Finally, the calculations for gain, efficiency and output power has been performed using a self consistent loop. The results obtained through the non-linear analysis has been benchmarked against the reported experimental W-band gyro-TWT values. In Chapter 4, the PIC simulation of a fundamental harmonic Ka band and W-band gyro-TWT amplifiers have been presented which helped to validate the analyses developed in Chapter 3. In the PIC simulation, beam absent and beam present EM behavior of a metal cylindrical waveguide interaction circuit has been demonstrated using ‘CST microwave studio’ in order to confirm the desired mode and frequency of operation of the interaction circuit. The beam-wave interaction behavior has been studied through the beam present simulation using the commercial tool ‘CST Particle Studio’. The PIC simulation results have been compared with the results obtained from the time-independent nonlinear single mode analysis. In Chapter 5, a second harmonic gyro-TWT using the wedge shaped lossy ceramic rods loaded RF interaction circuit operating in an azimuthally symmetric TE02 mode has been investigated. Such lossy dielectric loading leads to the mode selective behavior and proper choice of wedge dimensions is found to controls the stability condition of the device. A self-consistent nonlinear analysis has been used to investigate the beam-wave interaction behavior of the amplifier. The stability of the amplifier is investigated by placing six wedge shaped lossy ceramics symmetrically at 60o spacing along the azimuth of the RF circuit. By controlling the lossy ceramic rods parameters, the condition for maintaining the stability against the absolute instability and self-start oscillations has been studied. The nonlinear analysis predicted ~450kW at 91.4GHz for the operating beam characteristics of 100kV, 25A with 5% velocity spread. A saturated gain of ~30dB and an efficiency of ~18% has been obtained for the azimuthally symmetric mode with instantaneous 3dB bandwidth of ~3%. In the Chapter 6, nonlinear time dependent multimode analysis has been presented to investigate the temporal RF interaction behavior of the operating as well as all other competiting modes in the gyro-TWT amplifier. In a highly overmoded gyro-TWT waveguide RF interaction structure, the mode spectrum becomes very dense and electron beam is probable to interact several nearby modes simultaneously. In this approach, the transverse and longitudinal modal electric and magnetic field components are substituted in the Maxwell’s equations. The differential equations thus obtained as a function of complex field amplitudes and induced AC current densities are time as well as position dependent. Then, the electron beam dynamics expressed in terms of Lorentz force with transformed coordinates from the waveguide center to the electron guiding center. Further, to transform the expressions into the slow time-scale domain, Graff’s addition theorem for Bessel functions has been used. This provided us information about the electron momentum, phase angle and electron center motion equations. Hence, combining these obtained differential equations with the Lorentz force equation for electron momentum, phase angle, and electron guiding center motion equations gave a self-consistent equations which demonstrate the overall interaction process yielding information in time space taking all the modes into the simultaneous consideration. Using this time dependent multi-mode analytical expressions, a W-band, second harmonic wedge shaped lossy ceramic gyro-TWT amplifier has been anlyzed and a saturated RF output power of ~438kW with conversion efficiency ~17% for the gyrating beam of 100kV, 25A with a pitch of 1.2 and an axial spread of 5% has been obtained. Further, the saturated gain of the amplifier has been calculated as ~30dB with an instantaneous bandwidth ~3%. The PIC simulation values have also been validated with the multi-mode nonlinear analytical results and found in agreement within 3%. In Chapter 7, finally, the summary of the work and the conclusions drawn from the major findings of the work have been presented, pointing out the limitations of the work as well as the scope for the furtherance of the present study, such as those with respect to the gyro-TWT amplifier RF interaction structure has been characterized analytically and through PIC simulations in the present thesis and needs to be characterized experimentally. Moreover, in the present study, important aspects of thermal and structural analyses have not been considered. For the practical implementation of a gyro-TWT amplifier, these studies are very much important.