Emittance growth from bend straight transitions for beams approaching thermal equilibrium

In certain applications such as heavy ion fusion, intense beams with large space charge tune depressions will be transferred from linear transport sections into bent, transport, sections. In some. designs, such as recircutating induction accelerators, transport. through bends will occur over thousands of betatron periods and in some driver designs the final transports through a bend will occur over tens of betatron periods. Over such distances, non-linear space charge forces are expected to produce particle phase space distributions which are close to thermal equilibrium, especially with respect to lower order moments. Here we calculate the properties of thermal equilibrium beams in bends assuming uniform focusing, as a function of two dimensionless parameters. We also outline the calculation of the change in emittance for a beam that is initially in thermal equilibrium in a straight transport section. and that finally reaches thermal equilibrium in a bent system, using an energy conservation constrint to connect, the two states