RMS emittance measures for solenoid transport and facility for rare isotope beams front-end simulations

Measurement of beam phase-space area via rms emittances in solenoid focusing channels with x-y coupling is complicated relative to transport channels with decoupled plane focusing. This stems from correlated azimuthal flow of the beam induced by the coupled focusing influencing how the thermal component of the flow should be measured. This is exacerbated when the beam has net canonical angular momentum - as is the case for beams born in a magnetic field within ECR-type sources. In this study, a systematic analysis is carried out to derive an multi-species beam envelope equation and motivate measures of rms emittance and phase-space area for use in solenoid transport for beams with canonical angular momentum. These results are applied in Warp PIC simulations of the near-source region of the front-end of the Facility for Rare Isotope Beams (FRIB) linac. In these simulations, a multi-species heavy-ion DC beam emerging from an ECR source are simulated in transverse slice mode using a realistic lattice description. Emittance growth due to nonlinear applied fields and space-charge is analyzed including the influence of net canonical angular momentum. It is found that emittance growth in the near source region of FRIB front-end should in most cases be minimal and that the beam size can be readily controlled over a wide range of parameter uncertainties.