Generating catalogs of transverse matching solutions

An algorithm is described which rapidly finds a catalog of approximate transverse beam matching solutions. For a given initial beam, the algorithm finds the gradients of four quadrupole magnets so as to get four Twiss parameters (alpha and beta for horizontal and vertical planes) which are close to a set of desired values at the exit of a constant-energy beam line with no horizontal-vertical cross coupling and no space charge. The beam line may contain bending elements with edge corrections and other elements for which the r matrixes are known. The algorithm transforms the entrance and exit beam specifications to waist specifications and uses the properties of waist-to-waist transport to reduce the problem from a four-dimensional search to a two-dimensional search. The procedure described has been added to the TRACE package used by the LAMPF (Los Alamos Meson Physics Facility) accelerator operators. First indications are that use of the procedure results in significant time savings when the operators are determining the best way to match the beam into one of the linacs