Vacuum tube operation analysis under multi-harmonic driving and heavy beam loading effect in J-PARC RCS

An rf cavity in the J-PARC RCS not only covers the frequency range of a fundamental acceleration pattern but also generates multi-harmonic rf voltage because it has a broadband impedance. However, analyzing the vacuum tube operation in the case of multi-harmonics is very complicated because many variables must be solved in a self-consistent manner. We developed a method to analyze the vacuum tube operation using a well-known formula and which includes the dependence on anode current for some variables. The calculation method is verified with beam tests, and the results indicate that it is efficient under condition of multi-harmonics with a heavy beam loading effect.