If the driver can be fully depleted with transformer ratio six, the largest ideal witness gain from a GeV proton is GeV. Each lepton then has
For equal opposing electron and Positron beam energies,
The associated ideal population ratio would be . 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.

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