Critical nonlinear phenomena for kinetic instabilities near threshold
- Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
- Dipartimento di Energetica, Politecnico di Torino, Torino 10129 (Italy)
- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
- Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
A universal integral equation has been derived and solved for the nonlinear evolution of collective modes driven by kinetic wave particle resonances just above the threshold for instability. The dominant nonlinearity stems from the dynamics of resonant particles that can be treated perturbatively near the marginal state of the system. With a resonant particle source and classical relaxation processes included, the new equation allows the determination of conditions for a soft nonlinear regime, where the saturation level is proportional to the increment above threshold, or a hard nonlinear regime, characterized by explosive behavior, where the saturation level is independent of the closeness to threshold. In the hard regime, rapid oscillations typically arise that lead to large frequency shifts in a fully developed nonlinear stage. The universality of the approach suggests that the theory applies to many types of resonant particle driven instabilities, and several specific cases, viz. energetic particle driven Alfv{acute e}n wave excitation, the fishbone oscillation, and a collective mode in particle accelerators, are discussed. {copyright} {ital 1997 American Institute of Physics.}
- Research Organization:
- Univesity of Texas
- DOE Contract Number:
- FG03-96ER54346
- OSTI ID:
- 548803
- Report Number(s):
- CONF-961102--
- Journal Information:
- Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 5 Vol. 4; ISSN 1070-664X; ISSN PHPAEN
- Country of Publication:
- United States
- Language:
- English
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