A Shear-Capped Acceleration Stage: Gradient Limits for a Compact Linear Accelerator Set by the Aldred Shear Bound

This paper presents a complete design study of the device is a ten-metre copper accelerating stage intended to add a stated energy increment to a charged-particle beam, with its gradient chosen not by optimism but by an explicit shear criterion applied to the electromagnetic stress in the cavity walls, derived from stated assumptions and computed throughout by the accompanying script. At 100 MV/m the field stress in the walls is 0.044 MPa and the ten-metre stage adds 1.0 GeV to a beam; at 50 MV/m it adds 0.5 GeV. Across the full scan the shear criterion is never the binding constraint, because surface breakdown intervenes first. Every figure in the study is a computed result of the stated model and nothing was built or tested: the study is SIMULATED, NOT MEASURED, and its limits are stated as plainly as its performance.