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  • 1
    Electronic Resource
    Electronic Resource
    A new formulation of the resistive magnetohydrodynamics stability problem for finite β toroidal plasmas (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 4070-4083 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A new approach to the study of linear resistive magnetohydrodynamics stability is described. The approach is based on the traditional toroidal plasma model where the plasma resistivity and mass effects are essential only in thin layers around resonance surfaces, whereas the outer plasma is ideal and inertia free. This leads to differential equations with singular points. A new technique to solve these equations is proposed and it is shown that it has superior numerical convergence and accuracy properties to previous methods. The new technique is generally applicable to other problems in which differential equations with singular points arise. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1289688
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  • 2
    Electronic Resource
    Electronic Resource
    Thiazine Derivatives. III. The Synthesis of Some 2-Substituted 5,6-Dihydro-1,3(4H)-thiazines and Tetrahydro-1,3-thiazines Related to Cephams1 (1966)
    s.l. : American Chemical Society
    The @journal of organic chemistry 31 (1966), S. 556-558 
    Details
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/jo01340a049
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  • 3
    Electronic Resource
    Electronic Resource
    Stability of tearing modes in finite-beta plasmas (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 2645-2652 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of classical tearing modes in a finite-beta, cylindrical plasma is reconsidered. The different regimes of tearing mode instability are delineated by means of critical Lundquist numbers. The well-known criterion Δ'(approximately-greater-than)Δc due to Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)] defines a critical Lundquist number above which the plasma is stable. However, the physical importance of this Lundquist number is diminished by the fact that there is another critical Lundquist number, which is typically an order of magnitude smaller, above which the mode changes qualitatively in that the growth rate scales linearly with resistivity, and eventually becomes indistinguishable from resistive diffusion. The effect of parallel viscosity, which reduces the stabilizing coupling to the sound wave, is also considered. For large parallel viscosity, it is shown that Δc tends to zero. Thus, the stability criterion Δ'(approximately-greater-than)Δc for a finite-beta plasma is simply replaced by the criterion Δ'(approximately-greater-than)0. These analytical results are shown to be in good agreement with numerical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870592
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  • 4
    Electronic Resource
    Electronic Resource
    Inertial corrections to the matching condition for tearing modes (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 1236-1241 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In the usual matching condition for resistive tearing modes between an inner resistive layer and an outer ideal region, the inertia of the outer region is ignored; that is, the growth rate Q is set equal to zero in the outer region. However, in the large growth rate limit of these modes, the inertia plays a significant role throughout the inner layer, and up to and through the transition between the inner and outer layers, so that the matching between the inner layer and outer region becomes more subtle. Either inertial effects must be retained in the outer region or they must be modified in the inner layer. Here, the latter course is taken by modifying the density in the inner layer so that it vanishes outside some region confined within the inner layer. This can result in a large difference for the inner region matching data Δ(Q), where Q is the normalized growth rate and Δ(Q)=Δ' is the dispersion relation. Even the sign of Δ(Q) can be affected. The large growth rate limit is only one regime where inertial corrections are important. Regions of large pressure gradient and/or low magnetic shear are also shown to require inertial corrections. A final conclusion is that the above modifications extend the parameter range in which it is possible to treat finite-n ideal and resistive stability within a single formalism. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871400
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  • 5
    Electronic Resource
    Electronic Resource
    Noncircular, finite aspect ratio, local equilibrium model (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 973-978 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A tokamak equilibrium model, local to a flux surface, is introduced which is completely described in terms of nine parameters including aspect ratio, elongation, triangularity, and safety factor. By allowing controlled variation of each of these nine parameters, the model is particularly suitable for localized stability studies such as those carried out using the ballooning mode representation of the gyrokinetic equations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872666
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  • 6
    Electronic Resource
    Electronic Resource
    Effect of toroidal plasma flow and flow shear on global magnetohydrodynamic MHD modes (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 2236-2241 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effect of a subsonic toroidal flow on the linear magnetohydrodynamic stability of a tokamak plasma surrounded by an external resistive wall is studied. A complex non-self-adjoint eigenvalue problem for the stability of general kink and tearing modes is formulated, solved numerically, and applied to high β tokamaks. Results indicate that toroidal plasma flow, in conjunction with dissipation in the plasma, can open a window of stability for the position of the external wall. In this window, stable plasma beta values can significantly exceed those predicted by the Troyon scaling law with no wall. Computations utilizing experimental data indicate good agreement with observations. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871247
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  • 7
    Electronic Resource
    Electronic Resource
    A numerical study of the Alfvén continuum damping of toroidal Alfvén eigenmodes (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 1214-1225 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Alfvén continuum damping of the toroidal Alfvén eigenmodes is explicitly formulated for a large aspect ratio force-free tokamak using analytic continuation. A set of jump conditions across the Alfvén singularities are derived which have to be satisfied by the mode amplitudes. The method is then applied to a simple model equilibrium. The characteristics of the modes and their damping are investigated. The method is expected to be generalizable to models with more complete plasma dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870718
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  • 8
    Electronic Resource
    Electronic Resource
    A new formulation of the resistive tearing mode stability criterion (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1593-1604 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A new formulation of the toroidal, finite beta, resistive tearing stability problem is presented. As in standard tearing mode theory, the mode structure throughout most of the configuration is determined by an ideal, inertia-free model. Thus, it is very closely related to that obtained from standard ideal magnetohydrodynamic (MHD) numerical stability programs that depend on an energy principle. The effects of inertia, resistivity, and any other plasma properties are important only in thin layers enclosing resonant surfaces. These surfaces are distinguished by the fact that they are composed of closed field lines. Instability growth rates are obtained from the condition of matching between the inner and outer regions. The data needed from the outer region for matching are conventionally reduced to a quantity Δ', but in toroidally coupled axisymmetric systems the relevant quantity is a matrix. A previous paper [Pletzer and Dewar, J. Plasma Phys. 45, 427 (1991)] presented a relation between an extension of the ideal energy and the information from the outer region that is needed in matching to the inner layers. Here, this is used to construct a relation for the tearing mode growth rates directly in terms of an extension of the ideal energy matrix. This demonstrates a convenient way to extend the numerical programs for ideal stability to include stability against tearing modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860899
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  • 9
    Electronic Resource
    Electronic Resource
    A tearing mode energy principle for an axisymmetric finite beta plasma (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 97-105 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A self-adjoint, gauge invariant stability functional δWTG for determination of a sufficient condition of tearing mode stability is obtained for a plasma with arbitrary current and pressure profiles. The plasma is stable if there is no free energy available to support energy flux into the singular layer. The pressure gradient near the singular layer is found to be stabilizing. The tearing mode energy drive is extracted by casting the problem into its nonlinear context, demanding that both large and small solutions be continuous across the singular layer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859492
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  • 10
    Electronic Resource
    Electronic Resource
    A numerical study of the high-n shear Alfvén spectrum gap and the high-n gap mode (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 3713-3721 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The toroidicity-induced gaps of the shear Alfvén wave spectrum in tokamaks are shown to satisfy an envelope equation. The structure of these gaps, and the location of the high-n gap modes, which are localized modes with frequency in the gap, are studied for general numerically generated equilibria. The dependence of the frequencies of the gaps and the gap modes on the equilibrium properties, such as elongation, triangularity, and β of the plasma are explored.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860327
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