Determine the upper bound of the depressed phase advance for operation with o > 90°

Determine the upper bound on the depressed phase advance per cell o for high-intensity linear accelerators operating with o > 90°, quantifying the maximum practical value of o in this regime.

Background

The authors propose operating linacs with depressed phase advance o greater than 90° to avoid the fourth-order particle resonance and the envelope instability, and present simulations indicating minimal emittance growth in such regimes.

They note that parameter space appears available up to at least o ≈ 125° or higher but explicitly state that the upper limit remains to be explored, identifying an unresolved boundary for practical operation.