Beams passing through a solenoid fringe field experience x-y coupling and change of their eigen-emittances. As reported previously (C.~Xiao et al., Phys. Rev. ST Accel. Beams 044201, {bf 16} 2013) constant settings of a subsequent decoupling section
can be found such that variation of the fringe field strength will not change the Twiss parameters $beta$ and $alpha$ in both transverse planes at the exit of the decoupling section. For time being this feature was understood for a generic beam line but not to the generality to which it is observed. This report is on explanation of the convenient decoupling of fringe-coupled beams by any beam line that provides decoupling. For better coherence this report includes recapitulation of previous works.
For injection of beams into circular machines with different horizontal and vertical emittance acceptance, the injection efficiency can be increased if these beams are flat, i.e. if they feature unequal transverse emittances. Generation of flat elect
ron beams is well known and has been demonstrated already in beam experiments. It was proposed also for ion beams that were generated in an Electron Cyclotron-Resonance (ECR) source. We introduce an extension of the method to beams that underwent charge state stripping without requiring their generation inside an ECR source. Results from multi-particle simulations are presented to demonstrate the validity of the method.
