Collective Beam Instabilities
Bill K.Y. Ng, Fermilab
This course offers a brief introduction to wake functions and coupling impedances in accelerator rings. We will also study the theory of collective instabilities in coasting and bunched beams, their observations and methods of cure. Basic equations of motion and Vlasov equation will be covered. Longitudinal phase space: potential-well distortion, microwave instability, mode-mixing instability, coupled-bunch instability will be addressed. Transverse phase space: tune shifts, strong head-tail instability, head-tail instability, coupled-bunch instability, beam breakup. Special emphasis will be made separately on proton and electron machines. Other special topics: Landau damping, Sacherer integral equations, Landau cavity, saw-tooth instability, Robinson stability criteria, beamloading, impedance compensation, transition crossing, two-stream instabilities, collective instability issues near transition. Prerequisites: Accelerator Physics and Classical Electrodynamics.