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Resonance and Chaotic Trajectories in Magnetic Field Reversed Configurations.

DE2005839123

Publication Date	2005
Personal Author	Landsman, A. S.; Cohen, S. A.; Edelman, M.; Zaslavsky, G. M.
Page Count	50
Abstract	The nonlinear dynamics of a single ion in a field-reversed configuration (FRC) were investigated. FRC is a toroidal fusion device which uses a specific type of magnetic field to confine ions. As a result of angular invariance, the full three-dimensional Hamiltonian system can be expressed as two coupled, highly nonlinear oscillators. Due to the high nonlinearity in the equations of motion, the behavior of the system is extremely complex, showing different regimes, depending on the values of the conserved canonical angular momentum and the geometry of the fusion vessel. Perturbation theory and averaging were used to derive the unperturbed Hamiltonian and frequencies of the two degrees of freedom. The derived equations were then used to find resonances and compare to Poincar(copyright) surface-of-section plots. A regime was found where the nonlinear resonances were clearly separated by KAM (Kolmogorov-Arnold-Mosher) curves. The structure of the observed island chains was explained. The condition for the destruction of KAM curves and the onset of strong chaos was derived, using Chirikov island overlap criterion, and shown qualitatively to depend both on the canonical angular momentum and geometry of the device. After a brief discussion of the adiabatic regime the paper goes on to explore the degenerate regime that sets in at higher values of angular momenta. In this regime, the unperturbed Hamiltonian can be approximated as two uncoupled linear oscillators. In this case, the system is near-integrable, except in cases of a universal resonance, which results in large island structures, due to the smallness of nonlinear terms, which bound the resonance. The linear force constants, dominant in this regime, were derived and the geometry for a large one-to-one resonance identified. The above analysis showed good agreement with numerical simulations and was able to explain characteristic features of the dynamics.
Keywords	Toroidal fusion device Magnetic field Ions Hamiltonian systems Nonlinear oscillators Equations of motion KAM curves Princeton Plasma Physics Laboratory Field-reversed configuration (ERC)
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Princeton Univ., NJ. Plasma Physics Lab.; Department of Energy, Washington, DC.
Supplemental Notes	Sponsored by Department of Energy, Washington, DC.
Document Type	Technical Report
NTIS Issue Number	200603

Resonance and Chaotic Trajectories in Magnetic Field Reversed Configurations.

Resonance and Chaotic Trajectories in Magnetic Field Reversed Configurations.
DE2005839123

Publication Date	2005
Personal Author	Landsman, A. S.; Cohen, S. A.; Edelman, M.; Zaslavsky, G. M.
Page Count	50
Abstract	The nonlinear dynamics of a single ion in a field-reversed configuration (FRC) were investigated. FRC is a toroidal fusion device which uses a specific type of magnetic field to confine ions. As a result of angular invariance, the full three-dimensional Hamiltonian system can be expressed as two coupled, highly nonlinear oscillators. Due to the high nonlinearity in the equations of motion, the behavior of the system is extremely complex, showing different regimes, depending on the values of the conserved canonical angular momentum and the geometry of the fusion vessel. Perturbation theory and averaging were used to derive the unperturbed Hamiltonian and frequencies of the two degrees of freedom. The derived equations were then used to find resonances and compare to Poincar(copyright) surface-of-section plots. A regime was found where the nonlinear resonances were clearly separated by KAM (Kolmogorov-Arnold-Mosher) curves. The structure of the observed island chains was explained. The condition for the destruction of KAM curves and the onset of strong chaos was derived, using Chirikov island overlap criterion, and shown qualitatively to depend both on the canonical angular momentum and geometry of the device. After a brief discussion of the adiabatic regime the paper goes on to explore the degenerate regime that sets in at higher values of angular momenta. In this regime, the unperturbed Hamiltonian can be approximated as two uncoupled linear oscillators. In this case, the system is near-integrable, except in cases of a universal resonance, which results in large island structures, due to the smallness of nonlinear terms, which bound the resonance. The linear force constants, dominant in this regime, were derived and the geometry for a large one-to-one resonance identified. The above analysis showed good agreement with numerical simulations and was able to explain characteristic features of the dynamics.
Keywords	Toroidal fusion device Magnetic field Ions Hamiltonian systems Nonlinear oscillators Equations of motion KAM curves Princeton Plasma Physics Laboratory Field-reversed configuration (ERC)
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Princeton Univ., NJ. Plasma Physics Lab.; Department of Energy, Washington, DC.
Supplemental Notes	Sponsored by Department of Energy, Washington, DC.
Document Type	Technical Report
NTIS Issue Number	200603