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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear instability and chaos in plasma wave–wave interactions. II. Numerical methods and results (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 4149-4160 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In Part I of this work [Phys. Plasmas 2, 1926 (1995)], the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. Explosive instability arose from nonlinear coupling between positive and negative energy modes, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. The time evolution is modeled with an explicit symplectic integrator derived using Lie algebraic methods. For amplitudes large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region in phase space. Diffusive growth then leads to explosive instability, effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, slow growth via Arnold diffusion might still lead to instability; however, this was not observed in numerical experiments. The diffusion rate is probably underestimated in this simple model. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871039
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  • 2
    Electronic Resource
    Electronic Resource
    Response to "Comment on ‘Dielectric energy versus plasma energy, and Hamiltonian action-angle variables for the Vlasov equation' '' [Phys. Fluids B 4, 3038 (1992)] (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 1371-1372 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The energy density expression Best presents is not (when integrated) equal to the energy of a linear perturbation in Vlasov theory. The exact expression is given by either Eq.(42) or Eq.(48) of Ref.2. The authors comment on this and other discrepancies. (AIP)
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870687
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  • 3
    Electronic Resource
    Electronic Resource
    Magnetic field lines, Hamiltonian dynamics, and nontwist systems (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 2279-2289 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Magnetic field lines typically do not behave as described in the symmetrical situations treated in conventional physics textbooks. Instead, they behave in a chaotic manner; in fact, magnetic field lines are trajectories of Hamiltonian systems. Consequently the quest for fusion energy has interwoven, for 50 years, the study of magnetic field configurations and Hamiltonian systems theory. The manner in which invariant tori breakup in symplectic twist maps, maps that embody one and a half degree-of-freedom Hamiltonian systems in general and describe magnetic field lines in tokamaks in particular, will be reviewed, including symmetry methods for finding periodic orbits and Greene's residue criterion. In nontwist maps, which describe, e.g., reverse shear tokamaks and zonal flows in geophysical fluid dynamics, a new theory is required for describing tori breakup. The new theory is discussed and comments about renormalization are made. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.874062
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear instability and chaos in plasma wave–wave interactions. I. Introduction (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 1926-1940 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Conventional linear stability analyses may fail for fluid systems with an indefinite free-energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave–wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper (submitted to Phys. Plasmas), this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various integrable systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871280
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  • 5
    Electronic Resource
    Electronic Resource
    The energy of perturbations for Vlasov plasmas*,a) (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 1447-1451 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called, the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that solves the linear Vlasov–Poisson equation. This solution, together with the Kruskal–Oberman energy [Phys. Fluids 1, 275 (1958)], is used to obtain an energy expression in terms of the electric field [Phys. Fluids B 4, 3038 (1992)]. It is described how the integral transform amounts to a change to normal coordinates in an infinite-dimensional Hamiltonian system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870694
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  • 6
    Electronic Resource
    Electronic Resource
    Cycloseychellene: a structural revision (1981)
    s.l. : American Chemical Society
    The @journal of organic chemistry 46 (1981), S. 4819-4820 
    Details
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/jo00336a052
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  • 7
    Electronic Resource
    Electronic Resource
    Extrasolar X-Ray Sources (1967)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Astronomy and Astrophysics 5 (1967), S. 325-350 
    Details
    ISSN: 0066-4146
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.aa.05.090167.001545
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  • 8
    Electronic Resource
    Electronic Resource
    Drift wave vortices in nonuniform plasmas with sheared magnetic fields (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1238-1246 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Nonlinear coherent structures governed by the coupled drift wave–ion-acoustic mode equations in nonuniform plasmas with sheared magnetic fields are studied analytically and numerically. A solitary vortex equation that includes the effects of density and temperature gradients and magnetic shear is derived and analyzed. The analytic and numerical studies show that for a plasma in a sheared magnetic field, even without the temperature and drift velocity gradients, solitary vortex solutions are possible; however, these solutions are not exponentially localized due to the presence of a nonstructurally stable perturbative tail that connects to the core of the vortex. The new coherent vortex structures are dipolelike in their symmetry, but are not the modons of Larichev and Reznik. In the presence of a small temperature or drift velocity gradient, the new shear-induced dipole cannot survive and will separate into monopoles, like the case of the modon in a sheared drift velocity as studied in Su et al. [Phys. Fluids B 3, 921 (1991)]. The solitary solutions are found from the nonlinear eigenvalue problem for the effective potential in a quasi-one-dimensional approximation. The numerical simulations are performed in two dimensions with the coupled vorticity and parallel mass flow equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860131
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  • 9
    Electronic Resource
    Electronic Resource
    Nonlinear interactions of tearing modes in the presence of shear flow (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 845-854 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The interaction of two near-marginal tearing modes in the presence of shear flow is studied. To find the time asymptotic states, the resistive magnetohydrodynamic (MHD) equations are reduced to four amplitude equations, using center manifold reduction. These amplitude equations are subject to the constraints due to the symmetries of the physical problem. For the case without flow, the model that is adopted has translation and reflection symmetries. Presence of flow breaks the reflection symmetry, while the translation symmetry is preserved, and hence flow allows the coefficients of the amplitude equations to be complex. Bifurcation analysis is employed to find various possible time asymptotic states. In particular, the oscillating magnetic island states discovered numerically by Persson and Bondeson [Phys. Fluids 29, 2997 (1986)] are discussed. It is found that the flow-introduced parameters (imaginary part of the coefficients) play an important role in driving these oscillating islands.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860238
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  • 10
    Electronic Resource
    Electronic Resource
    The free energy of Maxwell–Vlasov equilibria (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1105-1113 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A previously derived expression [Phys. Rev. A 40, 3898 (1989)] for the energy of arbitrary perturbations about arbitrary Vlasov–Maxwell equilibria is transformed into a very compact form. The new form is also obtained by a canonical transformation method for solving Vlasov's equation, which is based on Lie group theory. This method is simpler than the one used before and provides better physical insight. Finally, a procedure is presented for determining the existence of negative-energy modes. In this context the question of why there is an accessibility constraint for the particles, but not for the fields, is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859246
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