Numerical calculation of electromagnetic eigenfields and dispersion relation for slow-wave device simulation

Summary form only given. Slow-wave structures support microwave amplification via electromagnetic coupling with an injected electron beam. Critical in the design of such devices is the dependence of the dispersion relation on the geometry of the guiding structure. The dispersion relation provides phase and group velocities, and the fields provide the impedance as seen by the beam. To this end, a computer model is developed which first numerically solves a wave equation in finite difference form subject to boundary conditions periodic in z and conducting elsewhere. The direction of wave propagation is along the z-axis. The solution produces a sequence of eigenfrequencies and eigenfields beginning with cut-off. Fourier decomposition of each eigenfield along selected mesh lines coincident with the location of the electron beam is then performed to establish a correspondence between eigenfrequency and wave number. From this data the dispersion relation for the slow-wave structure can then be formed. An example showing the first two TM passbands and E/sub z/ fields for a slotted waveguide in xz coordinates is demonstrated. We plan to incorporate plasma loading with space-time dependent dielectric constant.