Our research generally involves the use of high power computation to explore advanced concepts for future particle accelerators. We develop algorithms to simulate Maxwell's equations for electrodynamics in the presence of dielectric objects and curved metal boundaries. We use these algorithms to investigate potential uses of accelerator devices (and RF sources) based on photonic crystals.
A photonic crystal is a regular array or lattice of electromagentic-wave-scattering objects (for example, an array of glass spheres in air). Some photonic crystals exhibit a photonic band gap, which is a range of frequencies in which there are no (propagating) electromagnetic states within the crystal; this is analogous to the band gap in a semiconductor (that is, a range of energies in which there are no electron states). In practice this means that a photonic crystal acts like a mirror for waves that have frequencies within the band gap; in fact, dielectric mirrors (alternating slabs of contrasting dielectrics) are examples of one-dimensional photonic crystals. Therefore, photonic crystals can replace metal in traditional (microwave) wave-guiding structures. However, where metal reflects a very broad spectrum of waves, a photonic crystal may reflect a very narrow spectrum. The unusual properties of photonic crystals may be exploited to create more flexible and more robust accelerator structures.
G. R. Werner, C. A. Bauer, and J. R. Cary, Wakefields in photonic crystal cavities, Phys. Rev. Spec. Top., Accel. Beams 12, 071301 (2009).
C. Nieter, J. R. Cary, G. R. Werner, D. N. Smithe, and P. H. Stoltz, Application of Dey-Mittra conformal boundary algorithm to 3D electromagnetic modeling, J. Comput. Phys. 228, 7902 (2009).
G. R. Werner, Analytical Wake Potentials in a Closed Pillbox Cavity, arXiv:0906.1007 (2009).
C. A. Bauer, G. R. Werner, and J. R. Cary, Truncated photonic crystal cavities with optimized mode confinement, J. Appl. Phys. 104, 053107 (2008).
G. R. Werner and J. R. Cary, Extracting degenerate modes and frequencies from time-domain simulations with filter-diagonalization, J. Comput. Phys. 227, 5200 (2008).
G. R. Werner and J. R. Cary, A stable FDTD algorithm for non-diagonal anisotropic dielectrics, J. Comput. Phys. 226, 1085 (2007).