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  • 1
    Electronic Resource
    Electronic Resource
    The pseudospectrum of the resistive magnetohydrodynamics operator: Resolving the resistive Alfvén paradox (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 3151-3160 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The "Alfvén paradox'' is that as resistivity decreases, the discrete eigenmodes do not converge to the generalized eigenmodes of the ideal Alfvén continuum. To resolve the paradox, the ε-pseudospectrum of the resistive magnetohydrodynamic (RMHD) operator is considered. It is proven that for any ε, the ε-pseudospectrum contains the Alfvén continuum for sufficiently small resistivity. Formal ε-pseudoeigenmodes are constructed using the formal Wentzel–Kramers–Brillouin–Jeffreys solutions, and it is shown that the entire stable half-annulus of complex frequencies with ρ||ω||2=||k⋅B(x)||2 is resonant to order ε, i.e., belongs to the ε-pseudospectrum. The resistive eigenmodes are exponentially ill-conditioned as a basis and the condition number is proportional to exp(R1/2M), where RM is the magnetic Reynolds number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870468
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  • 2
    Electronic Resource
    Electronic Resource
    Averaged cold plasma equations for ion cyclotron waves in stellarators (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 366-371 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: When the toroidally varying component of a stellarator equilibrium is much smaller (larger) than the helically varying component, the cold plasma equations can be averaged over the helical (toroidal) angle to yield a two-dimensional description of ion cyclotron wave propagation. Higher order corrections may be computed iteratively; at each step only a two-dimensional operator need be inverted. Since the cold plasma equations have a singularity at the cyclotron resonance, a special coordinate system is introduced that exactly represents the resonance surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866869
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Quasilinear driven transport in a sheared flow field (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 299-312 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The evolution of a passive scalar field is considered for a slowly varying stratified medium, which is convected in an incompressible sheared flow with many overlapping static flux islands. Within the quasilinear/random phase approximation, a multiple scale expansion is made. Because of the rapid spatial variation of the temperature, the "ensemble'' averaged slowly varying part of the solution is not described by the arithmetic average of the oscillatory evolution equation. The standard Markovian and continuum approximations are shown to be invalid. For times of order N, where there are O(N2) excited modes, most of the time-dependent perturbation phase mixes away and the fluid reaches a new saturated state with small time oscillations about the temperature. This saturated state has smaller resonance layers (corresponding to magnetic islands), than those that occur in the isolated resonant perturbation case. Thus the quasilinear response to the resonant interactions reduces the effective size of the perturbations. The temperature gradient of the saturated state vanishes at all the excited resonance surfaces but has a nonzero average. Thus either the quasilinear approximation ceases to be valid on long time scales or the fluid remains essentially in this modified equilibrium and does not evolve diffusively. Thus collisionless, driftless fast particles will not be lost rapidly in equilibria with many small islands.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860278
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  • 4
    Electronic Resource
    Electronic Resource
    Multiple helicity quasilinear ballooning modes (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 2522-2524 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The validity of the ballooning mode transformation in quasilinear calculations is examined. If the range of interacting helicities is too large, the equivalence of harmonics is destroyed. The criterion for the validity of the ballooning mode transformation is Lm δn δm(very-much-less-than)n, where δm and δn are the spreads of excited poloidal and toroidal harmonics, respectively, and Lm is the number of harmonics necessary to represent the quasilinear pressure profile flattening. The quasilinear formalism of Riedel [Phys. Fluids B 1, 1780 (1989)] is generalized to the multiple toroidal helicity case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859373
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Flux coordinates, self-consistent equilibria, and variational principle (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 890-893 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The magnetohydrodynamic (MHD) equations are presented in an invariant form in flux variables and variational principles are formulated for these variables. These equations are then solved in Boozer coordinates in the small curvature expansion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866771
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  • 6
    Electronic Resource
    Electronic Resource
    Geometric optics at lower hybrid frequencies (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 3643-3647 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Geometric optics is analyzed at lower hybrid frequencies using a realistic scaling of the cold plasma conductivity tensor. An explicit example displays the inadequacy of standard geometric optics in treating spatially varying plasmas. A new term is added to the ray Hamiltonian to remove this inconsistency. An adiabatic invariant, corresponding to the poloidal rotation of the ray, is introduced. The cold plasma waves can develop a singularity only at those points where the flux surface is tangent to upper and lower hybrid resonance surfaces, thus supporting the conjecture that heating occurs only at these points. The only other spatial points where singularities may develop in the geometric optics ray equations are the cyclotron resonances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865795
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Quasilinear ballooning mode saturation (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1780-1787 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: At small amplitudes, resistive ballooning modes form a quasilinear sheet current, which opposes the magnetic flux reconnection. In the ensuing Rutherford regime [Phys. Fluids 16, 1903 (1973)] the sheet current at each resonance surface decays. To remain in a quasistatic equilibrium, magnetic islands form and thereby flatten the pressure at each resonance surface. For local instabilities, a spectrum of modes are excited, each flattening the pressure gradient at its resonance surface. The resulting averaged quasilinear pressure profile has a Cantor setlike structure. Using the equivalence of harmonics, the calculation of the saturated amplitudes is reformulated as a nonlinear eigenvalue problem of an integral differential equation with the quasimode formalism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858908
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  • 8
    Electronic Resource
    Electronic Resource
    The spectrum of resistive viscous magnetohydrodynamics (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 1093-1104 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The spectrum of scalar resistivity εη˜, scalar viscosity εμ˜, incompressible magnetohydrodynamics (MHD) is calculated in a slab geometry. The equilibrium may have a mode rational surface. The Alfvén continuum of ideal MHD is replaced by point eigenvalues on specific curves in the stable ω half-plane. As the dissipation parameter ε decreases, the curves containing these eigenvalues remain fixed and do not approach the ideal MHD continuum. The spatial resonances of these eigenfunctions are calculated. Viscosity removes the accumulation of eigenvalues at ω=0. The position of the curves depends on the ratio of resistivity to viscosity, but the topology of the curves is independent of this ratio.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865907
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