Particle-beam approach to collective instabilities -- application to space-charge dominated beams
Nonlinear dynamics deals with parametric resonances and di usion. The phenomena 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 ad- dress the questions: Are the two descriptions the same? Are collective instabilities the results of encountering parametric resonances whose driving force is intensity depen- dent? We study here the example of a space-charge dominated beam governed by the Kapchinskij-Vladimirskij (K-V) envelope equation [1]. The stability and instability regions as functions of tune depression and envelope mismatch are compared in the two approaches. The study has been restricted to the simple example of a uniformly focusing channel.
- Research Organization:
- Fermi National Accelerator Laboratory, Batavia, IL
- Sponsoring Organization:
- USDOE Office of Energy Research (ER)
- OSTI ID:
- 2061
- Report Number(s):
- FERMILAB-Conf-98/344; ON: DE00002061
- Country of Publication:
- United States
- Language:
- English
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