U.S. Particle Accelerator School

The Use of Hamiltonian and Lie Algebra Methods to Analyze and Design Accelerator Beamlines course

Sponsoring University:

Rice University

Course:

The Use of Hamiltonian and Lie Algebra Methods to Analyze and Design Accelerator Beamlines

Instructors:

Yiton Yan and Andrei Terebilo, SLAC


The use of Hamiltonian and Lie algebra methods to analyze and design accelerator beamlines will be surveyed, ranging from basic theory to numerical algorithms and practical applications. Topics include beamline fundamentals; Hamilton's equations and Lie generators; particle orbit tracking and transfer map concepts; truncated power series algebra and one-turn Taylor map extraction; long-term behavior and dynamic aperture; symplectic map and Lie transformation; map symplectification and generating functions; explicit integrable polynomials and kick factorizations; linear coupling and linear normalization; working tunes and linear trombone; Baker-Campbell-Hausdorff theorem and similarity transformation; sextupoles and chromaticity; invariants and nonlinear normalization; octupoles and tune shift with amplitude; resonance basis map and normalized driving terms; nPB tracking and synchro-betatron resonances; parameterization and dynamical maps. Computer labs will be included in the curriculum with numerical examples. Prerequisites: Intermediate Classical Mechanics, Accelerator Physics.