Structure wakefield accelerators can achieve very high accelerating gradients within a very small device. As such they are an exciting new technology with a wide range of potential applications. But with currently available software, the simulations needed for the design and optimization of these fundamentally new devices require excessive computational resources. GENERAL STATEMENT OF HOW THE PROBLEM IS BEING ADDRESSED We will extend conformal mapping techniqueswidely used in two dimensionsto three dimensions. This work will enable rapid computation of analytic or semi-analytic models of the fields inside structure wakefield accelerators, and this will facilitate very general and rapid design studies and optimization efforts. By the end of Phase II, we will have developed a web-based tool that integrates our conformal mapping analysis with beam dynamics computations to enable sophisticated investigation and optimization of innovative structure wakefield accelerator designs. This tool will make the conformal mapping techniques developed under this project easily accessible to scientists working in the field. WHAT IS TO BE DONE IN PHASE I? During the Phase I project, we will select a couple of simple structure wakefield accelerator designs for testing, and explore the full range of conformal mappingsincluding quaternionic conformal mappingswith the goal of identifying how best to use conformal mapping techniques to model the fields within those test-case devices. We shall compare our work against benchmark solutions or measurements of those designs. In addition, we will investigate how to generalize our efforts to more complex structure wakefield accelerator designs, and how to automate the required computations. COMMERCIAL APPLICATIONS AND OTHER BENEFITS Structure wakefield accelerators have enormous potential for applications across a range of fields, including medicine and manufacturing. This technology is moving towards miniaturization on the scale of Accelerator on a Chip, which will open the door to even more potential applications, particularly in medicine. The development of fast modeling and evaluation techniques for dielectric structures will enable scientists to explore and optimize innovative designs. Moreover, the conformal mapping techniques developed under this project will apply to other diverse applications that make use of dielectric structures to manipulate and use radio-frequency fields.
