 Solution

If the driver can be fully depleted with transformer ratio six, the largest ideal witness gain from a $62.5$ GeV proton is $375$ GeV. Each lepton then hasFor equal opposing electron and Positron beam energies,The associated ideal population ratio would be $N_p/N_e=6$. This energy-budget ceiling ignores wake-generation and transfer losses, staging limits, emittance preservation and the difficulty of accelerating both charge signs with suitable focusing. It is the consequence of the stipulated transformer-ratio bound, not a prediction of an achievable upgrade.