Quadrupole Strong Focusing for Space-Charge Dominated Electron Beams in Traveling-Wave Tubes

Analysis of quadrupole focusing lattices for high-frequency TWTs is presented. This work is motivated by recent work performed at the Naval Research Laboratory (NRL) which demonstrated an advantageous case for strong focusing employing a Halbach quadrupole lattice. Using realistic Permanent Magnet Quadruple (PMQ) field cancellation, the advantage of using PMQ to transport higher current densities than Permanent Periodic Magnet (PPM) lattices disappears, while other advantages for employing quadrupole focusing remain. This dissertation gives a comprehensive analysis of the applicability of PMQ focusing in vacuum electronic devices.\u2

A Contemporary Study in the Theory of Traveling-Wave Tubes

The traveling-wave tube (TWT) is a widely used amplifier in satellite communications and radar. An electromagnetic signal is fed into one end of the device and is amplified over a distance until it is extracted downstream at the output. The physics behind this spatial amplification of an electromagnetic wave is predicated on the interaction of a linear DC electron beam with the surrounding circuit structure. J. R. Pierce, known as the “father of communications satellites,” was the first to formulate the theory for this beam-circuit interaction, which was since used in other electronic devices such as free-electron lasers, gyrotrons, and Smith-Purcell radiators. In this thesis, we extend the classic Pierce theory in two directions: harmonic generation and the effect of high beam current on both the beam mode and circuit mode. The classical Pierce theory was formulated for a single (fundamental) frequency, same as the input signal. However, in a TWT with an octave bandwidth or greater, in particular the widely used helix TWT, the second harmonic of the input signal may also be within the amplification band and thus may also be generated and amplified. There is no input at this second harmonic frequency. An extension to the Pierce formulation that incorporates the generation of harmonics, including non-uniform taper, will be presented. We show that the second harmonic arises mostly from a newly discovered dynamic synchronous interaction instead of by the kinematic orbital crowding mechanism that is the most dominant harmonic generation mechanism in a klystron. The methodology provided may be applicable to the bi-frequency recirculating planar magnetron and other high-power microwave sources. In beam-circuit interactions, the space-charge effect of the beam is important at high beam currents. In Pierce's TWT theory, this space-charge effect is modeled by the parameter which he called Q in the beam mode. A reliable determination of Q remains elusive for a realistic TWT. In this thesis, the author constructed the first exact small-signal theory of the beam-circuit interaction for the tape helix TWT, from which Q may be unambiguously determined. In the process of doing so, it was discovered that the circuit mode in Pierce's theory must also be modified at high beam current, an aspect overlooked in Pierce’s original analysis. We quantify this circuit mode modification by an entirely new parameter that we call q, introduced here for the first time in TWT theory. For the example using a realistic tape helix TWT, we find that the effect of q is equivalent to a modification of the circuit phase velocity by as much as two percent, which is a significant effect equivalent to a detune of two percent. Lastly, we apply the theory developed for Q and q to a high-power TWT amplifier of current interest, the disk-on-rod TWT. For this configuration, the exact analytical forms of these parameters are extracted from the exact dispersion relation, which the author has also constructed. Comparisons of the numerical solutions to the analytic results to simulations done in ANSYS HFSS, ICEPIC, and MAGIC are made.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145994/1/pywong_1.pd

HIGH EFFICIENCY AXIAL DIFFRACTION OUTPUT SCHEMES FOR THE A6 RELATIVISTIC MAGNETRON

High-power microwave research strives for compact and highly efficient vacuum diode-driven sources. MAGIC particle-in-cell (PIC) computer simulations have shown that the performance of the well-known A6 relativistic magnetron with radial power extraction through one or more of its cavities can be improved by instead using axial power extraction through a mode-converting horn antenna, resulting in improved efficiency (30% improved to 70%) and greater output power handling capability (sub-gigawatt improved to multi-gigawatt) without breakdown. In addition, axial extraction results in a more compact profile that is compatible with mounting permanent magnets, which eliminate the need for bulky pulsed electromagnets or cryo-magnets and greatly enhance system efficiency. To this end, a variety of technologies were simulated and tested in experiment, the latter which required the design, construction, testing, and calibration of new diagnostics, pulsed power systems, and hardware, such as the complex A6 magnetron with diffraction output horn antenna (MDO). The primary goal of the experiments was to verify simulated 70% efficiency and greater than 1 GW of output power from the MDO. A less expensive vii compact MDO\u27 variant, essentially an A6 magnetron with a flat-plate mode converter and \u03c0-mode strap was also simulated. Although both the MDO and the compact MDO are compatible with permanent magnets fitted around their exteriors, an effective configuration was simulated for the compact MDO, promising reduced size and increased efficiency of the total microwave system. In addition, both versions of the MDO were susceptible to bombardment of leakage electrons on their output windows; cathode endcaps were developed and tested to mitigate this issue. Finally, to further improve output power, a rodded metamaterial-like cathode that showed improved power in other relativistic magnetrons was also considered by simulation in an A6 magnetron with radial extraction.\u2

Investigation of Radio Frequency Discharges and Langmuir Probe Diagnostic Methods in a Fast Flowing Electronegative Background Gas

Discharges in a flowing background gas are used to produce charged and excited species for numerous applications including etching semiconductors and pumping gas discharge lasers (Pinhero and others, 1998). The effect of a flowing background gas on the charged and excited neutral species generation by an RF discharge in a flow tube and the diagnostics of the resulting plasma with a Langmuir probe have been investigated for pressures between 0.001 to 1 Torr and flow velocities up to 1000 m/s. This investigation was performed using a fluid method coupled to a chemical kinetic model and a hybrid Particle-In-Cell/Monte Carlo Collision modeling method based on the approaches of Boeuf, 1987 and Cartwright and others, 2000. A factor of two reduction in the sheath length was realized for an increase in flow velocity from 25 m/s to 500 m/s. This resulted in an increased average ionization rate and factor of ten increases in positive and negative ion densities, while the electron densities remained approximately constant. At pressures less than 0.01 Torr, existing probe theory was adequate for performing diagnostics, however, at pressures of 1 Torr convection limited probe theory underestimated the positive ion density of the flowing electronegative plasma by up to 50%

Innovative Crossed-Field Devices for the Generation of High Power Microwaves

Modern High Power Microwave (HPM) initiatives pursue challenges in fundamental science, such as fusion research and particle accelerators, as well as industrial applications and homeland security. RADAR, telecommunications, and counter-IED (improvised explosive device) measures also rely on HPM. Crossed-field devices, like the magnetron and magnetically insulated line oscillator (MILO), are a subclass of microwave sources capable of delivering HPM. This dissertation describes the theory, simulation, and design processes applied to produce novel contributions in two separate projects, one a relativistic magnetron and the other a MILO. The magnetron is an inherently narrowband source, which is undesirable for applications such as counter-IED technologies. Past Recirculating Planar Magnetron (RPM) concepts have proven multispectral microwave generation in magnetrons, and the Harmonic-RPM was designed to expand and further understand these capabilities. In the innovative configuration of this dissertation, the HRPM implements a 1 GHz, L-Band Oscillator (LBO) and a 2 GHz, S-Band Oscillator (SBO) on the same side of the planar cathode, both that are made frequency-agile by leveraging the novel phenomenon of harmonic frequency locking. An experimental investigation of harmonic frequency locking between the LBO and SBO demonstrated the LBO can be used to control the SBO frequency and phase through harmonic beam content, and the SBO responds to this excitation at varying degrees depending on its quality factor. In the low quality factor experiment, the HRPM was driven at 255 ± 19 kV, 1.23 ± 0.32 kA, producing microwave bursts up to 40 MW with shot-averaged pulse duration of 77 ± 17 ns at 7.3 ± 2.4% total efficiency. When the HRPM was properly tuned to excite the SBO on resonance in the low quality factor experiment, the shot-averaged SBO power was 28 ± 9 MW at 2.102 GHz ± 1.5 MHz. Harmonic frequency locking enabled tuning of the SBO over a range of 33 MHz in this experiment, corresponding to 1.6% tunability. By reversing electron rotation direction by the magnetic field, it was shown that the SBO was no longer influenced by the harmonic content of the LBO-modulated beam. The MILO is a variant of the magnetron, differentiating itself in its method of producing the magnetic field for synchronous interaction. The magnetron uses permanent magnets or pulsed solenoidal coils, whereas the MILO magnetic field is established by large, pulsed currents along the central axis of the device. The vast majority of MILO devices in the literature operate at a low impedance (V/I) of roughly 10 Ω and typically 50-60 kA, resulting in efficiencies commonly in the single digits of percent. The MILO investigated in this dissertation was the first to demonstrate oscillations at less than 10 kA currents, at -240 kV for an impedance of 25-30 Ω. Microwave bursts were observed up to 25 MW at 1.5% efficiency with shot-averaged frequency and pulse duration of 993 ± 7 MHz and 118 ± 43 ns, respectively. The shot-averaged output power was highly irreproducible at 10 ± 7 MW, and is significantly lower than simulation estimates. These experiments were compared with a contemporary theoretical treatment of Brillouin flow in the coaxial MILO geometry, which revealed consistent device operation in a unique condition near the Hull cutoff condition.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169812/1/drupac_1.pd