Boine-Frankenheim, O.

Paper	Title	Page
WEM1C03	Analysis of Resonances Induced by the SIS-18 Electron Cooler	121
	S. Sorge, O. Boine-Frankenheim, G. Franchetti GSI, Darmstadt
	Due to the requirements concerning the quality of the particle beams in the FAIR project, i.e. a small momentum uncertainty together with high currents and, in the case of the storage rings, particle target interaction, there will be a strong need of electron cooling. On the other hand, an electron cooler acts as a non-linear optical element besides electron cooling. This may lead to the excitation of resonances possibly resulting in an increase of the emittance. The aim of this work is the calculation of resonances driven by the electron cooler in the Schwerionensynchrotron (SIS) 18 being a present device at GSI Darmstadt having an electron cooler. So, we get the opportunity to prove our results experimentally. For our calculations, we used a model system consisting of a rotation matrix representing the lattice and giving the according phase advance, and a non-linear transverse momentum kick representing the electron cooler in thin lens approximation. Proceeding in this way, we got only the resonances driven by the cooler. Furthermore, we used the MAD-X code to perform our calculations.
	Slides
THAP02	Implementation of Synchrotron Motion in Barrier Buckets in the BETACOOL Program	163
	A. V. Smirnov, A. O. Sidorin, G. V. Trubnikov JINR, Dubna, Moscow Region O. Boine-Frankenheim GSI, Darmstadt
	In the case of the internal pellet target the electron cooling and the stochastic cooling systems cannot compensate the mean energy losses of the ion beam. In bunched ion beams the space charge limit is reduced and the influence of intrabeam scattering is enhanced, which causes a decrease of the luminosity in comparison with a coasting beam. To resolve these problems barrier buckets are proposed for experiments with the pellet target. In the barrier bucket the long ion bunch fills nearly the whole circumference of the storage ring and a rf pulse is applied at the head and at the tail of the bunch. The general goal of the BETACOOL program is to simulate long term processes (in comparison with the ion revolution period) leading to the variation of the ion distribution function in six dimensional phase space. The investigation of the beam dynamics for arbitrary distribution functions is performed using multi particle simulation in the frame of the Model Beam algorithm. In this algorithm the ion beam is represented by an array of macro particles. The heating and cooling processes involved in the simulations lead to a change of the particle momentum components and particle number, which are calculated each time step. The barrier bucket model was developed in the Model Beam algorithm of the BETACOOL program. The trajectory of each model particle is solved analytically for a given barrier bucket voltage amplitude. An invariant of motion is calculated from the current position of the model particle and from the barrier bucket voltage amplitude. Then the phase of the invariant is calculated in accordance with the integration step and the particle gets a new coordinates. The heating and cooling effects are applied in usual procedure of the Model Beam algorithm. First simulation results for the FAIR storage rings are presented.