Comment on “Empirical condition of betatron resonances with space charge”

Abstract

In the article of K. Kojima, H. Okamoto, and Y. Tokashiki [Phys. Rev. Accel. Beams 22, 074201 (2019)PRABCJ2469-988810.1103/PhysRevAccelBeams.22.074201] the authors claim that the optimum working point on the tune diagram of circular accelerators at high intensity should be determined by using a framework of coherent resonances instead of the commonly accepted and widely used “standard” diagrams based on incoherent resonance conditions. However, their proposal is based on a questionable interpretation of Vlasov’s equation as well as an over-interpretation of their multi-particle simulations in the case of Gaussian-like distributions. Furthermore, the suggested coherent diagram is not supported by detailed published data from operating synchrotrons at GSI and CERN, which are in line with the incoherent resonance picture. As far as waterbag (or similar truncated) distributions, the authors model of coherent resonance diagrams is not questioned in this Comment.