Investigation of Propagation Characteristics of Twisted Hollow Waveguides for Particle Accelerator Applications

A new class of accelerating structures employing a uniformly twisted waveguide is investigated. Twisted waveguides of various cross-sectional geometries are considered and analyzed. It is shown that such a twisted waveguide can support waves that travel at a speed slower than the speed of light c. The slow-wave properties of twisted structures are of interest because these slow-wave electromagnetic fields can be used in applications such as electron traveling wave tubes and linear particle accelerators. Since there is no exact closed form solution for the electromagnetic fields within a twisted waveguide or cavity, several previously proposed approximate methods are examined, and more effcient approaches are developed. It is found that the existing perturbation theory methods yield adequate results for slowly twisted structures; however, our efforts here are geared toward analyzing rapidly twisted structures using modifed finite difference methods specially suited for twisted structures. Although the method can handle general twisted structures, three particular cross sections are selected as representative cases for careful analysis. First, a slowly twisted rectangular cavity is analyzed as a reference case. This is because its shape is simple and perturbation theory already gives a good approximate solution for such slow twists rates. Secondly, a symmetrically notched circular cross section is investigated, since its longitudinal cross section is comparable to the well known disk-loaded cavity (used in many practical accelerator designs, including SLAC). Finally, a 'dumbbell' shaped cross section is analyzed because of its similarity to the well-known TESLA-type accelerating cavity, which is of great importance because of its wide acceptance as a superconducting cavity. To validate the results of the developed theory and our extensive simulations, the newly developed numerical models are compared to commercial codes. Also, several prototypes are developed employing the three basic shapes discussed previously. Bench measurements are performed on the prototype cavities to evaluate dispersion by measuring the field distribution along these cavities. The measurement results are compared to the simulations and theoretical results, and good agreement is shown. Once validated, the developed models are used to design twisted accelerating structures with specific phase velocities and good accelerating performance.