Stability of linear particle motion in arbitrary periodic focusing and accelerating systems

Stability of transverse and longitudinal particle motion in arbitrary periodic system is studied. Actions of the focusing and phasing forces are approximated by linear thin lenses. On the basis of smooth approach to a solution of motion equations general formulas for the Floquet functions in focusing and accelerating systems are derived. The formulas are accurate for a period containing two thin lenses. If a period contains more lenses the formulas remain approximately valid over a wide parameter range. The proposed approach enables to study directly a dependence of specific values of the Floquet functions on a period structure. It significantly simplifies a search of an optimum period configuration satisfying the given requirements. Application of the formulas to calculate the particle motion stability in the RF crossed lens focused linac is considered.