U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

Colorado State University

Classical Mechanics and Electromagnetism in Accelerator Physics

Gregg Penn and Gabe Marcus, Lawrence Berkeley National Laboratory

**Purpose and Audience**

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

Prerequisites

Physics: Upper level undergraduate Classical Mechanics and Electromagnetism.

Mathematics: Multivariate calculus

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

**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 the 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 on the metal surface. Wakefield 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**

*(to be provided by the USPAS)* "Classical Dynamics: A Contemporary Approach" by Jorge V. Jose and Eugene J. Saletan, Cambridge University Press, 1998.

**Credit Requirements**

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

**IU/USPAS course: Physics 570**