Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 181-186).This thesis reports theoretical and experimental research on a novel accelerator concept using a photonic bandgap (PBG) structure. Major advances in higher order mode (HOM) damping are required for the next generation of TeV linear colliders. In this work, PBG HOMs are studied theoretically and experimentally for the first time. PBG HOMs are shown in simulation to be low Q lattice modes, removed from the cavity defect and beam position. Direct wakefield measurements were made in hot test using the bunch train produced by the MIT HRC 17 GHz linear accelerator. Measurements are compared with beam-loading theory, and wakefield simulations using ANALYST. Excellent agreement is observed between theory predictions and power measured in the 17 GHz fundamental operating mode; reasonable agreement is also seen with the 34 GHz wakefield HOM. In order to understand the performance of PBG structures under realistic high gradient operation, an X-band (11.424 GHz) PBG structure was designed for high power testing in a standing wave breakdown experiment at SLAC. The PBG structure was hot tested to gather breakdown statistics, and achieved an accelerating gradient of 65 MV/m at a breakdown rate of two breakdowns per hour at 60 Hz, and accelerating gradients above 110 MV/m at higher breakdown rates. High pulsed heating occurred in the PBG structure, with many shots above 270 K, and an average of 170 K for 35x10⁶ shots. Damage was observed in both borescope and scanning electron microscope imaging.(cont.) No breakdown damage was observed on the iris surface, the location of peak electric field, but pulsed heating damage was observed on the inner rods, the location of magnetic fields as high as 1 MA/m. Breakdown in accelerator structures is generally understood in terms of electric field effects. PBG structure results highlight the unexpected role of magnetic fields on breakdown. The hypothesis is presented that the low level electric field on the inner rods is enhanced by pulsed heating surface damage, and causes breakdown. A new PBG structure was designed with improved pulsed heating, and will be tested. These results greatly further the understanding of advanced structures with wakefield suppression that are necessary for future colliders.by Roark A. Marsh.Ph.D