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Andrianov, S.N.

Paper Title Page
MPPE006 Particle Distribution Function Forming in Nonlinear Systems 985
 
  • S.N. Andrianov, S. Edamenko
    St. Petersburg State University, Applied Mathematics & Control Processes Faculty, St. Petersburg
 
  Modern ion-optical systems are used in different fields of beam physics both independent facilities as consisting of largemachines. One of these destination is to create beams with a desired distribution of beams particles. Often there is a need to ensure a homogeneous distribution for a terminal beam phase portrait in a transverse configuration space. This is one of problems of nonlinear aberrations management. It is known that nonlinearity properties inhere to any beam lines. Such these nonlinearities have unremovable character, and their influence can be remove using only special nonlinear lattice elements, which are introduced artificially into the beam line. In this paper we suggest a procedure to find necessary nonlinear correcting control elements for purposive forming of beam particle distribution functions.  
MPPE007 Problems of Conservative Integration in Beam Physics 1087
 
  • S.N. Andrianov, S. Abramova
    St. Petersburg State University, Applied Mathematics & Control Processes Faculty, St. Petersburg
 
  In this paper an approach to conservative integration methods development is discussed. This problem is very important for beam physics: from beam line synthesis up to long time evolution simulation. This approach is based on a Lie algebra technique. On the first step we find a special form of decomposition for a Lie map, describing the system under study. On the second step a researcher finds exact solutions for some classes of hamiltonians in symbolic forms. These steps allows forming an integration scheme, which have a desired symplectic property. The additional invariant and symmetry properties can be included using dynamical invariants conception.  
MPPE008 Synthesis of Beam Lines with Necessary Properties 1096
 
  • S.N. Andrianov
    St. Petersburg State University, Applied Mathematics & Control Processes Faculty, St. Petersburg
 
  In this paper a new approach to the problem of synthesis of beam lines is discussed. Usually this problem can be overcome by the use of numerical simulation and optimal control theory methods. But this results in sufficiently great number of variable parameters and functions. Obviously, that this degrades quality of a modeling procedure. The suggested approach is demonstrated on a problem of a microprobe design problem. Essence of the problem is that necessary to design a high precision focusing system which satisfies some additional conditions. For solution of this problem we use an algebraic treatment based on Lie algebraic methods and computer algebra techniques. Using the symmetry ideology this approach allows rewriting beam properties to enough simple conditions for control parameters and functions. This leads a set of desired solutions and show results in some most suitable form. Moreover, this approach decreases the number of variable parameters.