Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2018 / S19 / 3 / c

For ideal transfer of the proton bunch's kinetic energy to the witness bunch,ThusThis is a minimum driver population for unit efficiency and full depletion under the stated energy budget. If only a fraction $\eta$ is usefully transferred, the required ratio becomes $1.8/\eta$. The equality to the transformer ratio uses the same ideal matching assumption as part b.