Symmetric multistep methods for charged-particle dynamics
نویسندگان
چکیده
منابع مشابه
Symmetric multistep methods for charged - particle dynamics
A class of explicit symmetric multistep methods is proposed for integrating the equations of motion of charged particles in an electro-magnetic field. The magnetic forces are built into these methods in a special way that respects the Lagrangian structure of the problem. It is shown that such methods approximately preserve energy and momentum over very long times, proportional to a high power o...
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A method of choice for the long-time integration of constrained Hamiltonians systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitraril...
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The symmetric multistep methods developed by Quinlan and Tremaine (1990) are shown to suffer from resonances and instabilities at special stepsizes when used to integrate nonlinear equations. This property of symmetric multistep methods was missed in previous studies that considered only the linear stability of the methods. The resonances and instabilities are worse for high-order methods than ...
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Invited ta Accelerator Ph 2, 2004. Correspond E-mail addr Work suppo contract numbe Support by gratefully ackno cations of parallel computational methods to charged-particle beam dynamics A. Kabel , Y. Cai, M. Dohlus, T. Sen, R. Uplenchwar Stanford Linear Accelerator Center, 2575 Sand Hill Road, Menlo Park, CA 94025, USA Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22603 Hamburg, Germ...
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The Diierential Algebraic Methods, a natural tool for the description and determination of the solution of diierential equations, have proven useful for the computation of aberrations of any desired order in any particle optical system. Besides conventional symplectic systems based on strongly or weakly focusing elements including fringe elds, they also readily allow the treatment of spin dynam...
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ژورنال
عنوان ژورنال: The SMAI journal of computational mathematics
سال: 2017
ISSN: 2426-8399
DOI: 10.5802/smai-jcm.25