An analytically derived periodic solution of the Kapchinskij-Vladimirskij envelope equation in the emittance-dominated regime

It is shown that the Kapchinskij-Vladimirskij envelope equation in the emittance-dominated regime admits analytical solutions. Its periodic solution in a periodic focusing channel is evaluated, using a power expansion technique. As an example, the periodic solution in a FOFO channel is analytically evaluated to first order and found to be in good agreement with the numerically obtained solution. (author)