Constable, David and Ronald, Kevin and He, Wenlong and Phelps, Alan D.R.
(2013)
*The numerical and experimental investigation of gyro-multiplier configurations.*
PhD thesis, University of Strathclyde.

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## Abstract

This thesis examines the feasibility of two different configurations of gyromultiplier, both of which operate at the fourth harmonic of the electron cyclotron frequency. The full numerical modelling and design of components for the testing of a novel, single cavity gyro-multiplier experiment has been documented. In addition, numerical simulations of a configuration featuring three distinct cavity sections have also been conducted. The introduction of an eight-fold azimuthal corrugation into the walls of a cylindrical cavity allows for the realisation of a single cavity gyro-multiplier arrangement, with generation of 2nd harmonic, TE2,2, and 4th harmonic, TE4,3, resonances, at frequencies of 37.5 GHz and 75 GHz, respectively. The interaction region is of mean radius, 8 mm, with a corrugation depth, 0.7 mm, and is 39 mm in length. The idealised electron beam utilised is of voltage, 60 kV, with current between 5 A and 10 A, confined in a magnetic field of ~0.7 T. Separation of the two emission frequencies was intended through the use of a 6 mm length cut-off taper; however, mode conversion to two above cut-off modes has been numerically demonstrated. The power contained in the 4th harmonic has been estimated at ~10-50 W. Extension of the output taper has proven to be sufficient to reduce the mode converted signals by an order of magnitude, while not impinging on the propagation of the 4th harmonic signal. The design and simulation of a knife-edge electron gun and kicker system has also been performed, with the final beam predicted to have a velocity spread of ~19%. In order to demonstrate the “cold” response of the interaction region to the 2nd harmonic signal, the design, construction and testing of several additional components are also documented. Novel slotted wall mode converters, capable of generating TEm,1 modes from a rectangular TE1,0 input signal, have demonstrated high spectral purity and large, ~10% bandwidth. A set of TE2,1 launchers, of 3.98 mm radius, operating between 37-41 GHz have demonstrated ~56% conversion efficiency, while a similar set for the TE4,1 mode, of 3.78 mm radius, demonstrated 20% conversion efficiency, between 70-80 GHz. A set of ripple wall mode converters, of maximum radius, 8.7 mm, featuring a 20 period, axial sinusoidal ripple, of depth 0.30 mm, designed to convert the TE2,1 mode to a TE2,2, have also been demonstrated. These converters display ~20 MHz bandwidth, at ~38 GHz. Using these couplers demonstrated the corrugated interaction region dispersion was insensitive to the polarisation of incident quadrupole modes, in keeping with theory. By examining a gyro-multiplier setup with three distinct cavity sections, it has been demonstrated that by operating the first and third cavities at the fundamental harmonic, effective generation of a 4th harmonic signal can be realised from a second cavity of radius slightly larger than that of the initial cavity. The interaction regions examined were of radius 0.7 mm, 0.783 mm, and 1.5 mm, and of lengths 2.4 mm, 2.4mm and 3.6 mm, respectively. By using an idealised electron beam of voltage, 80 kV, beam current of 0.7 A, and pitch factor of 1.4, generation of the TE1,2 and TE1,3 modes at a fundamental frequency of 342.5 GHz, and 4th harmonic, polarised in the TE4,6 mode at a frequency of 1.37 THz has been predicted, for a modest confining magnetic field of ~14.15 T. Although sensitive to the magnitude of the applied field, the maximum power contained in the 4th harmonic signal has been estimated to be 120 W.