Influence of conducting plate boundary conditions on the RMS envelope equations describing intense ion beam transport

In typical diagnostic applications, intense ion beams are intercepted by a conducting plate with slits to measure beam phase-space projections. This results in the transverse space-charge field near the plate being shorted out, rendering simple envelope models with constant space-charge strength inaccurate. Here we develop a simple corrected envelope model based on analytical calculations to account for this effect on the space-charge term of the envelope equations, enabling more accurate comparisons with experiment. Results are verified with 3D self-consistent PIC simulations.