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Chechenin, A.N.

Paper Title Page
WEPCH072 The High Order Non-linear Beam Dynamics in High Energy Storage Ring of FAIR 2083
 
  • A.N. Chechenin, R. Maier, Y. Senichev, E. Senicheva
    FZJ, Jülich
  
  The High Energy Storage Ring (HESR) is part of the international project FAIR for antiproton physics with beam in the momentum range from 1.5 to 15 GeV/c to explore the research areas of hadron structure and quark-gluon dynamics. An important feature of the project is the combination of phase space cooled beams with thick internal targets. Therefore there are two obvious reasons of beam heating: the target-beam interaction and the intra-beam scattering. Another source of the beam size growth is the higher order resonances. In the paper we investigate the non-linear beam dynamics together with different correction schemes minimizing this effect and compare with other sources of beam heating. Since the tune working point has a spread dependent on the chromaticity correction scheme and space charge, we include in our consideration both effects as well. All beam dynamics calculations are carried out with the SIMBAD code from the Unified Accelerator Library (UAL). We use 10000 macro particles, grid sizes 64x64 and 1000 turns per run.  
WEPCH087 Normal Form for Beam Physics in Matrix Representation 2122
 
  • S.N. Andrianov
    St. Petersburg State University, Applied Mathematics & Control Processes Faculty, St. Petersburg
  • A.N. Chechenin
    FZJ, Jülich
  
  The modeling of long beam evolution dynamics in nonlinear accelerator structures has raised new interest in the effective methods of nonlinear effects calculation. Moreover, it is preferably to use both analytical tools and numerical methods for evolution modeling. Usually the standard numerical methods and computer codes are based on the concept of symplectic transfer maps, whereas the analytical tool is the theory of normal forms. The method of normal forms can be realized in symbolic and numerical modes easily enough. In this paper, we discuss the normal form theory based on the matrix formalism for Lie algebraic tools. This approach allows using well known methods of matrix algebra. This permits to compute necessary matrices step-by-step up to desired order of approximation. This procedure leads to more simple structure of matrix representation for very complicated structure of this map does not allow using this map for practical computing. Therefore, it is necessary to transform this map in more appropriate form. In another words the new matrix representation for the map is particularly simple and has explicit invariants and symmetries.  
WEPCH088 High Order Aberration Correction 2125
 
  • S.N. Andrianov
    St. Petersburg State University, Applied Mathematics & Control Processes Faculty, St. Petersburg
  • A.N. Chechenin
    FZJ, Jülich
  
  It is known that modern accelerators fall under nonlinear aberrations influence. The most of these aberrations have harmful character, and their effect must be maximally decreased. There are a set of approaches and codes to solving this problem. In this paper, we consider an approach for solving this problem using the matrix formalism for Lie algebraic tools. This formalism allows reducing the starting problem to linear algebraic equations for aberration coefficients, which are elements of corresponding matrices. There are discussed results evaluated using suggested approach and nonlinear programming tools. Some examples of corresponding results are given.  
THPCH008 The Non-linear Space Charge Field Compensation of the Electron Beam in the High Energy Storage Ring of FAIR 2802
 
  • A.N. Chechenin, R. Maier, Y. Senichev
    FZJ, Jülich
  
  In the High Energy Storage Ring, a part of the FAIR project at GSI in Darmstadt, the internal target is used. To compensate the interaction of the beam with the target, the electron beam cooling is needed. However, together with the cooling, the non-linear space charge field of electron beam modifies the dynamic aperture. We investigate the possible schemes of this effect compensation using the multi-pole correctors on the HESR.