APPLICATION OF FREQUENCY MAP ANALYSIS TO THE STUDY OF THE SOLEIL AND ESRF BEAM DYNAMICS

The Frequency Map Analysis (FMA) [1] is a refined numerical method based on Fourier techniques which provides a global view of the dynamics of multi-dimensional systems and which was successfully applied to accelerator dynamics starting with the Dumas and Laskar work [2]. Two third generation synchrotron light sources, the SOLEIL Project and the ESRF are studied with this method. A full computation of the dynamic aperture (DA) is performed with a discussion of its inner complex structure (resonances) in correlation with its associated frequency map (FM) through diffusion (long term stability criterion). We also underline that despite the large DAs of both machines, the FM shapes are fully distinct due to the high sensitivity of the dynamics to the sextupole strengths. The lattices of SOLEIL [3] and the ESRF [4] are built up of strong focusing quadrupoles generating large chromatic aberrations. Sextupole magnets enable to compensate the chromaticity but induce geometric and nonlinear chromatic aberrations exciting resonances that may lead to unstable motions. To improve the performance of such light sources, accelerator dynamicists try to reduce the resonance influence but unfortunately the prediction of resonance strengths is a difficult task. Here after a brief description of both light sources, frequency maps and dynamic apertures are computed. The principal resonances are revealed, a one-to-one correspondence between the configuration space and the frequency space is performed. We show that the shape of a FM is highly sensitive to sextupole strengths and very different from one machine to another. Moreover time variations of the betatron tunes give some additional information for the global dynamics of the beam.