Simulations of longitudinal beam dynamics in storage rings

Longitudinal single and multibunch instabilities in the damping ring have to be avoided to guarantee the high quality bunch trains required for the operation of the linear collider. This thesis studies the longitudinal dynamics in the damping ring by analytical and numerical methods. It demonstrates that the design single bunch current is well below the instability threshold. Furthermore, the growth rate of longitudinal multibunch instabilities resulting from higher-order modes are smaller than the damping rate from synchrotron radiation. The detuning of the cavity resonance frequency for reasons of beam-loading optimization gives, however, rise to an instability of the multibunch mode nearest in frequency. A feedback loop will be necessary to counteract the instability. In Chapter 2, the sub-systems of the damping ring are introduced in detail, especially the parameters which determine the longitudinal dynamics. The theory underlying the longitudinal dynamics in electron storage rings is summarized in Chapter 3. The concept of wake fields and impedances is explained. The analytical methods to treat collective effects are compiled and applied to the dog-bone damping ring. The tracking techniques used for the computer simulations are described in Chapter 4. Single bunch and multibunch tracking are addressed separately due to different simulation methodologies. The former is characterized by using macroparticles and quasi-delta wake functions, the latter by a one-particle model (per bunch), higher-order cavity mode wake functions, and beam loading in the fundamental cavity mode. The higher-order mode studies were carried out as if there were no beam loading. When accounting for this effect (nearby-mode and transient beam-loading studies), the cavity voltage is decomposed into a generator and a beam component. The impedance model of the dog-bone ring used in the simulations is presented in Chapter 5. It is followed by a presentation of simulation results in Chapter 6. The computer code which was developed has also been applied to the SLAC damping ring, where longitudinal instabilities have been observed. The simulations concur with the experimental results. The details are presented in Chapter 7 of this thesis. Furthermore, the dog-bone tracking results are compared to those obtained by K. Yokoya's code. The results and methods are summarized in the final chapter. (orig.)SIGLEAvailable from TIB Hannover: RA 8919(2001-012) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman