“…Further progress in the proton beam power needs improvements in the accelerator technology [4] and addressing problems related to desired beam pulse structure, beam losses, and the lifetimes of beam targets [5][6][7]. Of particular challenge are issues associated with the beam dynamics, such as space-charge effects, instabilities, emittance growth, halo formation and losses, collimation, accumulation of secondary charges, linear and non-linear optics optimizations, etc -see comprehensive analysis in Refs.…”