Collector design with time dependent spent beam using the Michelle code

Summary form only given. The MICHELLE two-dimensional (2D) and three-dimensional (3D) electrostatic steady-state and time-domain particle-in-cell (PIC) code has been employed successfully by industry, national laboratories, and academia and has been used to design and analyze a wide variety of devices, including multistage depressed collectors, gridded guns, multibeam guns, annular-beam guns, sheet-beam guns, beam- transport sections, and ion thrusters. Its ability to manage large mesh sizes and large particle counts in complex geometries requiring the resolution of disparate spatial scales in 2D and 3D on desktop computers has allowed it to be applied to devices that could not have been readily modeled. Time domain effects in collector modeling has shown to be an important effect to model. Spent Beam Collectors, whether they are for energy recovery or just a beam dump, are often large devices with very a large ratio of incoming beam radius to device size. Required mesh resolution with such disparate spatial scales makes time-domain electromagnetic modeling not efficient and not the method of choice in many cases. Because of the demanding meshing requirements, MICHELLE with its finite-element meshing capability has been found to be an effective simulation tool for time-domain collector design. In the case of high-average power compatible collector design, mitigating potential virtual cathode behavior of the time-dependent beam is important. In particular, for high- perveance fundamental-mode MBK collector designs, attention must be paid not only on the energy spectrum of the spent beam but also on the time-dependent nature of the bunched beam upon entering the collector. This time- dependent behavior, if not properly taken into account, can lead to substantial and unexpected particle reflections, since the depth of the depression is a function of the peak RE beam current. We will present as an example the time-dependent spent beam collector modeling of an NRL high average power multiple beam klystron (MBK) collector.