Evaluation of Klystron Modulator Performance in Interleaved Pulsing Schemes for the ESS Neutrino Super Beam Project

It has been proposed that the relatively low duty cycle of the European Spallation Source (ESS) linac allows acceleration of additional $\mathbf{H}^{-}$ ion pulses interleaved with the baseline proton pulses, representing a unique opportunity to construct a neutrino super beam (ESSnuSB) facility of unparalleled luminosity. Coupled with a distant Cherenkov detector, it is believed that evidence of CP violations in leptons could be obtained, representing a significant step towards understanding the matter/antimatter asymmetry. In this paper, several such interleaved pulsing schemes are considered from the perspective of the klystron modulators and the RF power system in investigating the possibility to realize the ESSnuSB. Conserving the required output RF energy, these pulsing schemes vary in terms of 1) number of added H- ion pulses per baseline cycle, 2) pulse amplitude and 3) pulse length. Each prospective pulsing scheme offers unique advantages while differently impacting klystron modulator performance. Whereas the ESS linac baseline design requires 33 klystron modulators (rated for pulse amplitude 115kV/4x25A, pulse length 3.5ms and pulse repetition rate 14Hz; each modulator powering 4 parallel klystrons rated 1.6MWpk at 704MHz), the proposed upgrade requires doubling the baseline linac average output power and thus either doubling the capacity of existing modulators or the procurement of additional modulator systems. In order to evaluate and compare the merit of these solutions from a system perspective, a mathematical framework connecting the attributes of the proposed pulsing schemes to the power transfer curves of the klystrons and subsequently to the performance of the klystron modulators is developed. Finally, a preferred solution is selected and the impact on grid-to-RF efficiency, modulator average input power quality, total upgrade cost and required additional system size is assessed.