Beam Dynamics

The measurement of the mass of the W boson requires an accurate determination ofthe beam energy and a good understanding of the accelerator to guarantee stable running withhigh luminosities at high beam energies. In this thesis a reliable method was developed tomeasure the horizontal detuning with amplitude which turned out to be an important stabilitycriterion for the high energy optics. The detuning with amplitude was measured for variousoptics using measurements of the center-of-charge position of a bunch oscillating after a sin-gle excitation. In general there is a reasonable agreement of measurements and predictionsof the simulation program.The beam energy of is used as a kinematic constraint in the determination of the mass ofthe W boson. An error on the beam energy therefore translates into an uncertainty on the Wmass. The impact of beam parameters like center-of-mass energy and asymmetries of elec-tron and positron beam energies on the measurement of the mass of the W boson is studiedwith generator level Monte Carlo.The standard procedure of the energy calibration above the WW threshold of 80 GeV isbased on precise energy determinations in the energy range from 40 to 60 GeV with resonantdepolarization measurements and on magnetic extrapolations to the respective physics ener-gies (80 to 102 GeV). Since such extrapolations involve systematic uncertainties, alternativemethods have been developed and studied which are based on measurements of the energyloss due to synchrotron radiation. Since the energy loss increases with the fourth power ofenergy, observable sensitive to the energy loss per turn can be used to determine the beamenergy. Measurements of the radiation damping in transverse coherent oscillations and theanalysis of the sawtooth-like horizontal orbits in the ring were studied as a means to de-rive the beam energy. The uncertainties of these two methods were found to be too large to 4.11. NEW DOCTORAL THESES IN BEAM DYNAMICS51 serve as a cross check for the standard extrapolations. The required relative uncertainty isof the order of 10 4 (or 10 MeV). The beam energy measurement based on the analysis ofsynchrotron oscillations however provides a powerful and reliable high precision cross checkfor high energy calibration. The dependence of the synchrotron tune on various parameterswas studied in detail to control systematic effects on the analysis. The error was found to bein the range from 20 to 30 MeV. Future experiments and studies are expected to reduce thisuncertainty.