High gradient acceleration is a core challenge of accelerator physics. Achieving high gradients is made challenging by issues relating to rf breakdown and pulsed surface heating, which are caused by intense surface fields in the accelerating cavities. The excitation of multiple harmonically related modes within a cavity could reduce the onset of these effects. The temperature rise from pulsed surface heating can be reduced by lowering the average magnetic surface field squared and rf breakdown could be avoided by creating an asymmetry between the anode and cathode surface electric fields. This thesis will present several different cavity designs that show a reduction in the temperature rise on the surface of over 10% for second and third harmonic cavity structures or an asymmetry in the surface electric anode and cathode fields of a factor of 2. The harmonic mode could have undesirable consequences for beam stability. A study of the longitudinal beam dynamics is included that will derive the equations governing the longitudinal motion and show that the harmonic mode will have a minor and predictable effect on the rf bucket. The Compact LInear Collider (CLIC) is a major contender for the next generation of lepton linear colliders and is made challenging by high power requirements and distribution throughout the linac. A high current drive beam is decelerated parallel to the main linac in order to create the required rf power, which can overcome some of these issues. This thesis will describe a novel design for a CLIC-like accelerating structure, using collinear acceleration through fundamental mode detuned cavities. The design will accommodate interleaved drive and test bunches, such that the drive bunches are decelerated and the test bunches are accelerated within the confines of the same cavity which can result in high transformer ratios. The analytical theory based on the circuit model will be verified by time domain simulations. A multi-harmonic detuned accelerating structure is introduced that exhibits the properties of pulsed surface heating reduction and can be used for collinear acceleration. Time domain simulations will verify the transformer ratio to within 3% of theoretical predictions and the average magnetic field squared reduction will be within 20% of the value calculated from eigenmode simulations.

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With the rapid development in today&rsquo / s technology, reliability and performance requirements on components of various mechanical systems, which tend to be much lighter and work under much more severe working conditions, dramatically increased. In general, analysis techniques based on simplified model of structural components with linearity assumption may provide time saving for solutions with reasonable accuracy. However, since most engineering structures are often very complex and intrinsically nonlinear, in some cases they may behave in a different manner which cannot be fully described by linear mathematical models, or linear treatments may not be applicable at all. In fact, some studies revealed that deviations in the modal properties of dynamic structures gathered from measured data are due to nonlinearities in the structure. Hence, in problems where accuracy is the primary concern, taking the nonlinear effects into account becomes inevitable. In this thesis, it is aimed to analyze the harmonic response characteristics of multi degree of freedom nonlinear structures having different type of nonlinearities. The amplitude dependencies of nonlinearities are modelled by using describing function method. To increase the accuracy of the results, effect of the higher order harmonic terms will be considered by using multi harmonic describing function theory. Mathematical formulations are embedded in a computer program developed in MATLAB&reg / with graphical user interface. The program gets the system matricies from the file which is obtained by using substructuring analysis in ANSYS&reg / , and nonlinearities in the system can easily be defined through the graphical user interface of the MATLAB&reg / program.