NEW DEFINITION OF THE STOP-BAND FOR THE INTENSITY DEPENDENT EMITTANCE TRANSFER BASED ON THE ENVELOPE EQUATIONS

The influence of space charge on the transverse emittances has been discussed in Ref. [1] by solving the Kapchinskij and Vladimirskij envelope equations for small perturbations on top of equilibrium beam sizes. Formulae for the transverse emittances in the presence of space charge were derived that include the uncoupled emittances, the space-charge coupling strength, and the tune distance from the resonance. A stop-band was also defined. The purpose of this note is to discuss this stop-band and give another definition of it, more useful for comparison with machine experiments or simulations.