U.S. Particle Accelerator School

Particle Beam Optics Using Lie Algebra Methods course

Sponsoring University:

Yale University


Particle Beam Optics Using Lie Algebra Methods


John Irwin, SLAC

Lie operator methods have proven to be powerful tools in designing beamlines with strong nonlinearities, and were employed in the design of the PEP-II B-factory and Final Focus Test Beam beamlines at SLAC. The goal of this course will be to build an intuitive understanding of the meaning and use of these tools. The curriculum will begin with a thorough introduction to advanced classical mechanics concepts and Lie operator fundamentals, and continue with a detailed description of their application to the easy and difficult aspects of beamline design. In particular the course will include: truncated power series algebras (TPSA), canonical dynamics and symplecticity, Poisson bracket basics, Lie operator basics, representation of simple and difficult beamline elements, representation of beamline modules, factorization methods, resonance basis and normal forms, and fields (non-Hamiltonian Lie operators) for synchrotron radiation. Prerequisites: a course in Accelerator Physics.