Complex modeling of the behavior of marine objects under the influence of real external excitation is the most important problem At present, the accuracy of direct simulation of phenomena with knovvn physics is compar...
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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 co...
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ISBN:
(纸本)9290832789
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.
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 too...
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ISBN:
(纸本)9290832789
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. Some examples of corresponding results are given.
Some problems of long-time evolution of particle beam are considered. It Is known that most of real physical effects are very sensitive to properties of numerical Integration methods used for beam evolution Investigat...
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Some problems of long-time evolution of particle beam are considered. It Is known that most of real physical effects are very sensitive to properties of numerical Integration methods used for beam evolution Investigation. That Is why a researcher should guarantee not only accuracy of any computing but qualitative properties, which are Inherent In the system under study. In this paper some variant of geometrical Integration methods Is discussed. It allows to apply high performance computing systems more effectively. Some practical problems of particle beam evolution are considered.
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