Beam symmetry preservation through a dipole with zero pole face rotations and uniform field

Abstract

It is shown that the cylindrical symmetry of a charged particle beam can be preserved precisely while it is bent through a single dipole with zero pole face rotations and uniform field, although in one plane the beam is freely drifting whereas in the other plane the beam is focused. The beam conditions at the entrance to the dipole are derived and cast into two analytic formulas. It is shown that symmetry preservation calls for matched beam optical functions (β,α), that is, matched orientation and amplitude of the beam phase space ellipses into the dipole. The beam conditioning at the entrance to the dipole is discussed and formulated. Some illustrative cases are calculated, and an example design is presented. Finally, it is proved that such a symmetric matched beam may be defined for any system with equal diagonal R-matrix elements, and the results are applied to another specific case of a parallel sided magnet.