BEAM SYMMETRY PRESERVATION THROUGH A DIPOLE WITH ZERO POLE FACE ROTATIONS AND UNIFORM-FIELD

It is shown that the cylindrical symmetry of a charged particle beam c an be preserved precisely while it is bent through a single dipole wit h zero pole face rotations and uniform field, although in one plane th e beam is freely drifting whereas in the other plane the beam is focus ed. The beam conditions at the entrance to the dipole are derived and cast into two analytic formulas. It is shown that symmetry preservatio n calls for matched beam optical functions (beta,alpha), that is, matc hed orientation and amplitude of the beam phase space ellipses into th e dipole. The beam conditioning at the entrance to the dipole is discu ssed and formulated. Some illustrative cases are calculated, and an ex ample design is presented. Finally, it is proved that such a symmetric matched beam may be defined for any system with equal diagonal R-matr ix elements, and the results are applied to another specific case of a parallel sided magnet.