Can one hear the shape of an electrode? II. Theoretical study of the Laplacian transfer

For improved measurements of the key astrophysical reaction (12)C(alpha , gamma)(16)O in inverted kinematics, a recoil separator ERNA is being developed at the 4 MV Dynamitron tandem accelerator in Bochum to detect directly the (16)O recoils with about 50% efficiency. Calculations of the ion beam optics including all filtering and focusing elements of ERNA are presented. Since the (12)C projectiles and the (16)O recoils have essentially the same momentum, and since the (12)C ion beam emerging from the accelerator passes through a momentum filter (analysing magnet), the (12)C ion beam must be as free as possible from (16)O contamination for ERNA to succeed. In the present work, the (16)O contamination was reduced from a level of 1 * 10^-11 to a level below 2 * 10^-29 by the installation of Wien filters both before and after the analysing magnet. The measurement of these and other beam specifications involved other parts of the final ERNA layout - sequentially a Wien filter, a 60° dipole magnet, another Wien filter, and a (delta)E-E telescope. The setup led to a measured suppression factor of 5 * 10^-18 for the (12)C ion beam. The experiments also indicate that an almost free choice of the charge state for the (16)O recoils is possible in the separator.