U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

University of New Mexico

Classical Mechanics and Electromagnetism in Particle Accelerators

Gennady Stupakov, SLAC and Daniel Ratner, Stanford University

**Purpose and Audience **

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

**Prerequisites
**Classical Mechanics and Electromagnetism.

**Instructional Method**

The course includes lectures in the morning (3 hrs. per class day), and afternoon exercise sessions (minimum of 2 hrs. per class day). There will be a final exam at the conclusion of the course.

**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 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 radiation. Laser interaction with relativistic beams and the Lawson-Woodward theorem. The relation between radiation and ‘inverse radiation’ acceleration schemes.

**Reading Requirements **

Instructors will provide lecture notes.

**Credit Requirements **

Students will be evaluated based on the following performances: Final exam (40%), Homework assignments (60%).