Lie algebraic methods for charged-particle beams and light optics

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5087193

Forest, J C.E.P.E

The motion of a charged particle or the propagation of a ray in an optical system can be described in many cases by a Hamiltonian. One is often interested in deviation from a certain ideal trajectory. For this problem, the Lie algebraic methods are ideal tools. It has been shown that the Lie operators offer a very efficient parameterization of Hamiltonian maps. Along these lines, the parameterization of optical interfaces is examined. It is shown that their Lie algebraic polynomials are made of irreducible representations of the symplectic group. The methods are also ideally suited for tracking particles in small and large rings. A complete theory of the computation of Lie algebraic maps is presented. In particular, the author looks at the general time dependent Hamiltonian. It allows treatment of fringe-field effects exactly and elegantly. As an example, a solenoid system of electron microscopy is studied in great detail. The body of this thesis is therefore devoted to the computation of the Lie operators. However, interest is also shown in extracting some standard information from the map itself.

• Research Organization: Maryland Univ., College Park (USA)
• OSTI ID: 5087193
• Country of Publication: United States
• Language: English

Related Subjects

654001 -- Radiation & Shielding Physics-- Radiation Physics
Shielding Calculations & Experiments
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CALCULATION METHODS
CHARGED-PARTICLE TRANSPORT
GRADED LIE GROUPS
HAMILTONIANS
LIE GROUPS
LIGHT SCATTERING
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
RADIATION TRANSPORT
SCATTERING
SYMMETRY GROUPS
TRAJECTORIES