U.S. Particle Accelerator School

Nonlinear Dynamics and Collective Processes in High-Intensity Beams course

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Nonlinear Dynamics and Collective Processes in High-Intensity Beams


Ronald Davidson and Hong Qin, Princeton University

This course makes use of the Vlasov-Maxwell equations to investigate the nonlinear dynamics and collective processes in intense nonneutral beams propagating in periodic focusing accelerators and transport systems. Particular emphasis is placed on determining the effects of the beam space-charge and current on the detailed equilibrium, stability and transport properties. Specific topics to be covered include: range of validity of the Vlasov-Maxwell formalism; derivation of local and global conservation constraints; influence of intense self fields on beam equilibrium and stability properties; development and application of nonlinear kinetic stability theorem for quiescent beam propagation over large distances; effects of space charge on the equilibrium and stability properties of the Kapchinskij-Vladimirskij distribution function; canonical transformation and Hamiltonian averaging techniques for intense beam propagation in periodic focusing field configurations; kinetic derivation of envelope equation for the rms beam radius including space-charge effects; determination of the effects of beam intensity on halo particle production induced by envelope mismatch and/or moderate-amplitude collective mode excitations; properties of the two-stream instability and collective interactions induced by a second charge component interacting with the beam particles; and application of nonlinear perturbative simulation techniques to matched-beam propagation in periodic focusing field configurations, quiescent beam propagation over large distances in the smooth-focusing approximation, and properties of the electron-proton instability in proton linacs and storage rings. Finally, a reduced macroscopic description (neglecting heat flow) is developed and applied to pressure-driven instabilities in intense particle beams. Prerequisites: Accelerator Physics, Electromagnetism, and Classical Mechanics.