Title :
Unified treatment of collective instabilities and nonlinear beam dynamics
Author :
Ng, K.Y. ; Lee, S.Y.
Author_Institution :
FNAL, Batavia, IL, USA
Abstract :
Nonlinear dynamics deals with parametric resonances and diffusion, which are usually beam-intensity independent and rely on a particle Hamiltonian. Collective instabilities deal with beam coherent motion, where the Vlasov equation is frequently used in conjunction with a beam-intensity dependent Hamiltonian. We address the questions: Are the two descriptions the same? Are collective instabilities the results of encountering parametric resonances whose driving force is intensity dependent? The space-charge dominated beam governed by the Kapchinskij-Vladimirskij (KV) envelope equation is used as an example
Keywords :
Vlasov equation; nonlinear dynamical systems; particle beam dynamics; particle beam stability; space charge; Kapchinskij-Vladimirskij envelope equation; Vlasov equation; beam coherent motion; beam-intensity dependent Hamiltonian; collective instabilities; diffusion; nonlinear beam dynamics; parametric resonances; particle Hamiltonian; space-charge dominated beam; unified treatment; Apertures; Distributed computing; Eigenvalues and eigenfunctions; Frequency; Hysteresis; Nonlinear equations; Nonlinear magnetics; Particle beams; Resonance; Synchrotrons;
Conference_Titel :
Particle Accelerator Conference, 1999. Proceedings of the 1999
Conference_Location :
New York, NY
Print_ISBN :
0-7803-5573-3
DOI :
10.1109/PAC.1999.794282
