U.S. Particle Accelerator School

U.S. Particle Accelerator School

Education in Beam Physics and Accelerator Technology

University of Texas, Austin

Classical Mechanics and Electromagnetism in Accelerator Physics

Gregg Penn, 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 two-week course includes lectures in the morning (3 hrs. per class day), and afternoon review and 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, adiabatic invariants. Lagrangian formulation of equations of motion and Hamilton’s equations. Canonical transformations, Liouville’s theorem, and action-angle variables. Extended canonical transformations, Hamiltonian for a circular accelerator, Hill’s equation and betatron functions. Hamiltonian theory of perturbations and nonlinear resonances arising in circular accelerators. Resonance overlapping and transition to stochastic motion. Maps and symplectic integrators. Phase space and the Vlasov equation for the distribution function of a beam, and fluid equations.

Special relativity, Lorentz transformations and Maxwell equations. Self-field of a relativistic beam in vacuum. Electromagnetic interaction of the beam with environment. Examples of numerical computations. Skin effect and the Leontovich boundary condition on the metal surface. Gaussian radiation modes and waveguide fields. Retarded time and the Lienard-Wiechert potentials for radiation processes in electrodynamics. Synchrotron radiation, transition radiation, and diagnostics. Formation length and coherence of radiation. Wake fields, impedances and the Panofsky-Wenzel theorem.

**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%).

**UT Austin course number & course title on transcript: **PHY 396T (69874): CLASSCL MECH/ELEC IN ACCEL PHY**
Indiana University course number: **Physics 570, Introduction to Accelerator Physics