U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

Michigan State University

Classical Mechanics and EM in Accelerator Physics

Gennady Stupakov and Zhirong Huang, SLAC

**Purpose and Audience **

The course will focus on several topics of classical mechanics and electrodynamics of particular importance for accelerator physics.

**Prerequisites
** Undergraduate Classical Mechanics and Electromagnetism course.

**Instructional Method**

The course consists of lectures in both morning (3 hrs. per class day) and afternoon sessions (minimum of 2 hrs. per class day). In addition, afternoon exercise sessions are planned to assign and explain homework each day.

**Course Content**

Linear oscillator and resonance. Stochastic force acting on an oscillator. Nonlinear oscillator, dependence of frequency versus amplitude. Nonlinear resonance, parametric resonance. Lagrangian formulation of equations of motion and Hamilton’s equations. Canonical transformations and action-angle variables. Hamiltonian for a circular accelerator. Hamiltonian theory of perturbations and nonlinear resonances arising in circular accelerators. Adiabatic invariants in classical mechanics. Resonance overlapping and transition to stochastic motion. Maps and symplectic integrators. Phase space and Vlasov equation for the distribution function of a beam.

Self-field of a relativistic beam in vacuum. Electromagnetic interaction of the beam with environment. Skin effect and the Leontovich boundary condition at the metal surface. Longitudinal and transverse wake and impedance. Effect of the wake on the beam – loss factor and the kick factor. Resistive wall wake. EM computer codes for accelerator physics.

Lorentz transformations and the Lienard-Wiechert potentials for radiation processes in electrodynamics. Synchrotron radiation, transition radiation, and Compton scattering. Spatial and temporal coherence and formation length of the radiation. Laser interaction with relativistic beams and the Lawson-Woodward theorem. The relation between radiation and ‘inverse radiation’ acceleration schemes.

**Reading**** Requirements**

(*to be provided by the USPAS*): "Classical Electrodynamics" third edition, by John D. Jackson, (1999) Wiley publishers. Instructors will provide additional lecture notes.