U.S. Particle Accelerator School

Fundamentals of Wakefields and Impedance course

Sponsoring University:

University of California, Santa Barbara


Fundamentals of Wakefields and Impedance: from Physical-Mathematical Analysis to Practical Applications


Roger Jones, SLAC

The progress of multiple bunches of electrons through a linear or circular accelerator gives rise to a trailing electromagnetic field. This wakefield can have catastrophic consequences if its progress is left unchecked as the beam can become unstable and develop a BBU (Beam Break Up) instability. This course discusses the beam dynamics issues associated with wakefields and means of damping the fields to acceptable levels. Examples are taken from recent international next generation linear colliders damping schemes. Wakefield issues in storage rings will also be discussed. 

This course will address the fundamentals of wakefields and their relation to the beam impedance. The features of both long-range and short-range wakefields will be discussed. Circuit models of relativistic electron beams coupled to multiple accelerator cavities will be developed to calculate the coupled modal frequencies and wakefields. In addition to the general theoretical formalism of wakefields, practical methods to damp and measure the wakefields will be described with techniques taken from ongoing research on high-energy linacs. Throughout the course, basic physical principles such as superposition, energy conservation and causality will be emphasized. Prerequisites: a course on electromagnetism and a minimum mathematical background of at least first-year undergraduate calculus.