Lie algebraic methods for particle tracking calculations

Technical Report · Mon Aug 01 04:00:00 EDT 1983

DOI:https://doi.org/10.2172/5362638· OSTI ID:5362638

Douglas, D R; Dragt, A J

A study of the nonlinear stability of an accelerator or storage ring lattice typically includes particle tracking simulations. Such simulations trace rays through linear and nonlinear lattice elements by numerically evaluating linear matrix or impulsive nonlinear transformations. Using the mathematical tools of Lie groups and algebras, one may construct a formalism which makes explicit use of Hamilton's equations and which allows the description of groups of linear and nonlinear lattice elements by a single transformation. Such a transformation will be exactly canonical and will describe finite length linear and nonlinear elements through third (octupole) order. It is presently possible to include effects such as fringing fields and potentially possible to extend the formalism to include nonlinearities of higher order, multipole errors, and magnet misalignments. We outline this Lie algebraic formalism and its use in particle tracking calculations. A computer code, MARYLIE, has been constructed on the basis of this formalism. We describe the use of this program for tracking and provide examples of its application. 6 references, 3 figures.

• Research Organization: Lawrence Berkeley Lab., CA (USA); Maryland Univ., College Park (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5362638
• Report Number(s): LBL-16008; CONF-830822-49; ON: DE84004310
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
ALGEBRA
BEAM DYNAMICS
COMPUTERIZED SIMULATION
DATA
HAMILTONIANS
INFORMATION
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
NUMERICAL DATA
ORBITS
QUANTUM OPERATORS
SIMULATION
STORAGE RINGS
SYMMETRY GROUPS
THEORETICAL DATA
TRAJECTORIES