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  • 1
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    Stuttgart : Bundesanstalt für Geowissenschaften und Rohstoffe
    Associated volumes
    Call number: K 94.0045 ; K 93.0010/CC6318
    In: Geologische Übersichtskarte
    Branch Library: GFZ Library
    Branch Library: GFZ Library
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1486-1497 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Corrections and clarifications are made of some past treatments of the variational nature of the eigenfrequency calculation for dispersion equations and new results are presented. The main conclusions are the following: (1) Any relation between a normal mode and its dual must be consistent with the fact that the boundary conditions satisfied by the normal mode may differ from the adjoint boundary conditions satisfied by the dual. This will affect whether or not a given bilinear form will yield a variational result for the eigenfrequency. (2) If a dispersion matrix is constructed from the dispersion operator by using left and right basis functions that satisfy homogeneous boundary conditions on the dual eigenfunction and the eigenfunction, respectively, then generally a second-order accurate eigenfrequency is obtained by solving the matrix form of the dispersion equation. (3) When solving for the normal modes in terms of perturbation potentials, the adjoint boundary conditions are gauge dependent. For cases where the adjoint boundary conditions allow only the trivial solution for the dual eigenfunction, it may be possible to obtain variational results for the eigenfrequency by requiring that the trial functions for the normal mode and its dual satisfy variational boundary conditions.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1026-1040 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A two-dimensional kinetic description of field-reversed equilibria has been developed. Three equilibrium models are presented: a kinetic model, a rigidly rotating model, and a magnetohydrodynamics (MHD) model. The kinetic model of equilibrium provides spatial distributions of the macroscopic moments, including velocity shear, that are in good agreement with experimental observations. The rigidly rotating and MHD models allow more general pressure profiles than previous studies. These models, which allow the computation of a wide range of equilibria, suggest that for parameters typical of the current experiments kinetic modifications of the equilibrium are small; however, they may be important if the field-reversed configuration is interacting strongly with a magnetic mirror. Also, the ability to compute kinetic equilibria makes possible a self-consistent examination of the stability of field-reversed configurations, which is believed to be strongly influenced by kinetic effects.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2414-2428 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Symmetry properties are presented for a multidimensional dispersion functional. If the system of linearized Vlasov-field equations is "completely Hamiltonian,'' the dispersion operator satisfies a certain formal self-adjointness property as a function of omega. For appropriate boundary conditions this implies a relation between an eigenfunction and its dual. If the equilibrium admits "conjugate orbits'' for a completely Hamiltonian system and if the "conjugate-orbit parity condition'' is satisfied, then the kinetic part of the dispersion matrix is symmetric. For this case and for appropriate boundary conditions the entire dispersion matrix for the multispecies Vlasov or Vlasov-fluid models is symmetric. It then follows that the complex conjugate of the dual eigenfunction is proportional to the eigenfunction itself. The analytic continuation of the dispersion functional of the linearized Vlasov-field equations into the lower half of the frequency plane is derived.
    Type of Medium: Electronic Resource
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