Development of Numerical Simulation Codes and Application to Klystron Efficiency Enhancement

Abstract

This thesis discusses performance characteristics of depressed collectors, and hollow beams aiming at appreciable enhancements of klystron efficiencies. Also presented are developments of a set of 2-dimensional numerical codes to investigate these two approaches. The results are summarized as follows. (i) A new Finite Element eigenmode solver (KUEMS) has been developed in this study, aiming at improved accuracy in calculating cylindrically symmetric modes. Instead of θ H , or θ rH preferentially used so far in the existing codes, the quantity H r θ is newly used in this study to represent the electromagnetic fields. This present Finite Element formulation is found to result in remarkably higher accuracy than the other formulations, particularly, in the eigenfrequency of the fundamental mode. It is also found to result in smoother convergence of the solutions with respect to number of the mesh points, to provide good extrapolation property. (ii) Also developed was a solenoidal field solver (KUSOS) for calculating external focusing fields in klystrons. A new hybrid method is proposed, 112 which can deal with unbounded problems including nonlinear media by combining the Finite Element method and the Moment method. The numerical results show good agreements with the analytical solutions, no difference in the numerical solutions for different choices of the picture frames, and excellent continuity of the calculated magnetic fields on the picture frames. (iii) Two particle-in-cell simulation codes have been developed by modifying the existing codes. One is for simulations of electron trajectories in static fields (KUAD2). It was verified through comparisons of gun perveances with experiments, showing excellent agreements within –2.3% ∼ +2.4% relative errors. The other is for simulations of interactions between electron beams and klystron cavities (KUBLAI). A modified Newmark method is proposed to stabilize the numerical instability in calculating simultaneously both electron motions, and beam-induced fields. Also proposed is a modified method for calculating cavity voltages, which eventually shows faster convergence to the steady-state solutions than the basic method. Comparisons were also made between the KUBLAI simulations and experiments, showing excellent agreements within –4.9% ∼ +6.9% relative errors with respect to the saturated output powers of klystrons. (iv) By use of the verified codes developed in this study, the aforementioned two approaches were investigated for the klystron efficiency enhancements. Theoretical limit of the energy recovery with depressed collectors was evaluated. It is found that a 5-stage collector could, theoretically, enhance the efficiency up to 80.3% from the basic efficiency of 60.5%, and neither additional stages nor optimized potentials would enhance the 113 efficiency appreciably further. A 5-stage depressed collector was, then, designed through the KUAD2 simulations, leading to an enhanced efficiency of 71.3%, which is very encouraging compared with the 60.5% efficiency without depressed collectors. Hollow beams are found also to result in higher efficiencies than the currently used solid beam. It is found that, with an optimized hollow radius, an enhanced efficiency of 67.0% could be achieved without depressed collectors. It is also found that larger hollows than the optimum tend to result in rather lower efficiencies. In summary, the simulation codes newly developed in this study are found to be efficient in high-power klystron designing, and, also, by use of these numerical codes, either the depressed collectors, or the hollow beams are found, numerically, to result in appreciable efficiency enhancements of klystrons.