Beam-dynamics calculations including magnetic field measurements for the high-energy storage ring (HESR) at FAIR

This thesis deals with beam-dynamics simulations and magnetic measurements for the High-Energy Storage Ring (HESR), a synchrotron designed for antiprotons. The HESR is part of the future Facility for Antiproton and Ion Research (FAIR) near Darmstadt. As the facility is under construction at the moment, the first magnets are built and measured. This work comprises magnetic measurements and beam-dynamics simulations. Different types of magnets are used to guide and focus the beam. The magnetic quadrupole elements are measured at the manufacturer’s site. These measurements are conducted with rotating coils. As part of this thesis these measurements are analysed in order to to describe the elements in the beamdynamics simulations. Therefore the measurements of the magnetic flux density is expressed in harmonic coefficients. In contrast the measurements of the dipole that are performed by the manufacturer are not suited to extract harmonic coefficients. Thus a new measurement device - based on Hall effect probes - is developed to measure the desired quantities. As a proof of concept, measurements with the existing Hall-probe mapper are performed. The measurement results from the proof-of-concept measurements along with the measured harmonic content from the quadrupoles are used as basis for the beam-dynamics simulations. The measured values are randomised within limits as expected from the measurements to characterise the individual magnets. These individual magnets are used to describe the entire accelerator in the simulations. To randomise the measurement and transfer it to the simulation software an own C++ code is written. To estimate the stability of the particle beam in the HESR, tracking simulations are performed. In these single-particle trackings a particle is described by its phase-space coordinate. The track of this particle is then the evolution of its phase-space coordinate. The trackings are performed starting at several points in the phase space transverse to the particle’s motion. For each of this initial points it is estimated if it leads to stable or chaotic motion. To distinguish between both kinds of motion a criterion based on the Lyapunov exponent is used. The border between stable and chaotic motion is called the dynamic aperture. To estimate the stability of the tracking results and thus the estimated dynamic aperture, the trackings are repeated with different sets of randomised harmonic content of the magnets. The reliability of the tracking results is demonstrated by a tune scan. For this the dynamic aperture calculation is performed with different settings of the simulated accelerator. The results show the expected resonance structure in the tune diagram. The tracking is then used to investigate if a stable operation of the HESR with particles at injection energy is possible. Therefore a point in tune space is chosen and influences to the dynamic aperture are studied. Both investigated influences, a possible momentum deviation of the particles, as well as a possible skew quadrupole component in the accelerators dipole magnets, seem to have no critical influence to the stability of the stored antiprotons