Transportable Charge in a Periodic Alternating Gradient System

A simple set of formulas is derived which relate emittance, line charge density, matched maximum and average envelope radii, occupancy factors, and the (space charge) depressed and vacuum values of tune. This formulation is an improvement on the smooth limit approximation; deviations from exact (numerically determined) relations are on the order of ±2%, while the smooth limit values are in error by up to ±30%. This transport formalism is used to determine the limits of transportable line charge density in an electrostatic quadrupole array, with specific application to the low energy portion of the High Temperature Experiment of Heavy Ion Fusion Accelerator Research. The line charge density limit is found to be essentially proportional to the voltage on the pole faces and the fraction of occupied aperture area. A finite injection energy (≥2 MeV) is required to realize this limit, independent of particle mass.