Exploring the null space of the chromaticity response matrix at the Diamond Light Source

Many different techniques have been investigated at Diamond for optimising sextupole strengths*. One method not previously studied is to exploit the null space of the chromaticity response matrix. By performing a singular value decomposition (SVD) of the chromaticity response matrix, combinations of sextupole strengths are identified which alter the nonlinear lattice whilst keeping the chromaticity unchanged. Applying these sextupole strength changes opens an avenue to improve the beam lifetime and the injection efficiency at fixed chromaticity, thereby preserving the instability thresholds from collective effects. The results of applying this technique are presented both for beam tracking simulations for the Diamond-II lattice, including machine errors, and for machine-based measurements on the present Diamond synchrotron.