• S.J. Cooke, B. Levush
  NRL, Washington, DC

We present results of a new method for fast, accurate calculation, in 3-D, of the electromagnetic mode spectrum of long, tapered accelerator structures. Instead of discretizing the entire structure directly and solving a huge matrix eigenvalue problem, we use a new two-step technique that scales much better to long, multi-cavity structures. In the first step we compute a small number of eigenmodes of individual cavities, achieving 0.05% frequency accuracy using a new second-order finite-element code. In the second step we use these 3-D mode solutions as field basis functions to obtain a reduced matrix representation of Maxwell’s equations for the complete structure. Solving the reduced system takes just a few minutes on a desktop PC even with more than 100 non-identical cavities, and gives the complete mode spectrum in the first few bands of the structure. By judicious choice of the basis modes, we retain 0.05% frequency accuracy for these global solutions, and can reconstruct the complete 3-D field of each mode in order to perform beam-interaction calculations. Solution times are faster by orders of magnitude than comparable calculations using a direct finite-element method.