Author: Adamy, J.
Paper Title Page
WEPPP061 A Method to Obtain the Frequency of the Longitudinal Dipole Oscillation for Modeling and Control in Synchrotrons with Single or Double Harmonic RF Systems 2846
  • J. Grieser, J. Adamy, D.E.M. Lens
    TU Darmstadt, RTR, Darmstadt, Germany
  • H. Klingbeil
    TEMF, TU Darmstadt, Darmstadt, Germany
  Funding: This work was partly funded by GSI Helmholtzzentrum für Schwerionenforschung GmbH
In a heavy-ion synchrotron the bunched beam can perform longitudinal oscillations around the synchronous particle (single bunch dipole oscillation, SBDO). If disturbances/instabilities exciting the SBDO exceed the rate of Landau damping, the beam can become unstable. Furthermore, Landau damping is accompanied by an increase of the beam emittance which may be undesired. Thus, control efforts are taken to stabilize the beam and to keep the emittance small. It is known that for a single harmonic cavity and a small bunch the SBDO oscillates with the synchrotron frequency* if the oscillation amplitudes are small. For a larger bunch or a double harmonic RF systems that introduces nonlinearities**, this is no longer valid. This work shows how the frequency of the SBDO can be determined in general. As a result, the SBDO can again be modeled as a harmonic oscillator with an additional damping term to account for Landau damping. This model can be used for feedback designs which is shown by means of a simple example. As the frequency of the SBDO and the damping rate depend on the size of the bunch in phase space, it is shown how this information can be obtained from the measured beam current.
* F. Pedersen and F. Sacherer, IEEE Transactions on Nuclear Science, 24:1296–1398, 1977
** A. Hofmann and S. Myers, Proc. of the 11th International Conference on High Energy Acceleration, 1980
THPPC076 Comparison of LLRF Control Approaches for High Intensity Hadron Synchrotrons: Design and Performance 3464
  • K. Gross, J. Adamy
    TU Darmstadt, RTR, Darmstadt, Germany
  Funding: Federal Ministry of Education and Research
A usual and effective way to realize closed-loop controllers is to use cascaded SISO feedback and to rely on some kind of linear PID structure with parameters adjusted manually in simulations or experiments. Such a control may not reach optimal performance if the system is coupled or non-linear. Regarding intense beams, longitudinal beam loading can be compensated by detuning. But the coupling between phase and amplitude (or I and Q component) highly depends on the tuning, that is on the resonant frequency of the cavity. It is derived that cavity and beam dynamics thus show bi-linear nature, i.e. belong to a well investigated class of non-linear systems with appropriate control strategies available*. Different controller designs are compared in terms of performance but also design transparency, the need of previous knowledge like the expected magnitude of beam loading and adaptability to different conditions, e.g. during acceleration or if applied to the full range of ion species as at GSI. The performance evaluation is based on macro-particle tracking simulations. In particular avail and limits of an optimal (quadratic cost) MIMO controller for bi-linear systems are shown**.
* H.K. Khalil: Nonlinear Systems, 3rd Edition, Prentice-Hall, 2002
** Z. Aganović, Z. Gajić: Linear Optimal Control of Bilinear Systems, Springer-Verlag, 1995.