The Cockcroft Institute

Post-graduate Lecture Courses: Academic Year 2005-6

Energy and momentum gains from electric fields; the different methods of acceleration;
The synchronous acceleration from radio frequency electric fields;
The phase stability and its consequences; the production of RF fields: single cell and multi-cells cavities;
RF characteristics of accelerating cavities;
The acceleration of ultra-relativistic particles;
The capture and the bunching phenomena;
Various types of  RF accelerators.

Longitudinal dynamics in a synchronous linear accelerator;
Longitudinal dynamics in non-synchronous accelerators: the cyclotron, the RF gun, the beam capture at the front end of an electron linac.
Dispersion effects in the synchrotron;
Transition energy;
Phase-energy equations;
Small amplitude oscillations;
The case of electron synchrotron.

Hamiltonian of the longitudinal motion;
Large amplitude oscillations;
Bohm and Foldy diagram;
Separatrix and energy acceptance;
Adiabatic damping of synchrotron oscillations;
Additional damping in electron synchrotron;
Longitudinal dynamics near transition;
Stationary bucket;
Non-linear dynamics and dilution phenomena;
Beam matching.

Introduction to beam loading;
Longitudinal dynamics in the presence of space charge forces at high beam density (front end, linac, synchrotron);
High intensity accelerators: RF gun, RF quadrupole, induction linac.