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Proceedings of the workshop on nonlinear MHD and extended MHD

Description: Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
Date: December 1, 1998
Partner: UNT Libraries Government Documents Department

Magnetohydrodynamic calculations with a nonmonotonic q profile and equilibrium, sheared toroidal flow

Description: The linear and nonlinear stability of a nonmonotonic q profile is examined using a reduced set of magnetohydrodynamic (MHD) equations with an equilibrium, sheared toroidal flow. The reversed shear profile is shown to be unstable to a rich variety of resistive MHD modes including pressure-driven instabilities and tearing instabilities possessing a tearing/interchange character at low Lundquist number, S, and taking on a double/triple tearing structure at high S. Linear calculations show that the destabilizing effect of toroidal velocity shear on tearing modes is enhanced at finite pressure seen previously for tearing modes at high S. Nonlinear calculations show the generation of a large, m = 1, n = 0, Reynolds-stress-driven poloidal flow in the absence of significant flow damping. Calculations in which the poloidal flow was heavily damped show that sub-Alfvenic, sheared toroidal flows have a minimal effect on weakly-coupled, localized instabilities.
Date: July 1, 1998
Creator: Held, E.D.; Leboeuf, J.N. & Carreras, B.A.
Partner: UNT Libraries Government Documents Department

Tearing mode analysis in tokamaks, revisited

Description: A new {Delta}{prime} shooting code has been developed to investigate tokamak plasma tearing mode stability in a cylinder and large aspect ratio ({epsilon} {le} 0.25) toroidal geometries, neglecting toroidal mode coupling. A different computational algorithm is used (shooting out from the singular surface instead of into it) to resolve the strong singularities at the mode rational surface, particularly in the presence of finite pressure term. Numerical results compare favorably with Furth et al. results. The effects of finite pressure, which are shown to decrease {Delta}{prime}, are discussed. It is shown that the distortion of the flux surfaces by the Shafranov shift, which modifies the geometry metric element stabilizes the tearing mode significantly, even in a low {beta} regime before the toroidal magnetic curvature effects come into play. Double tearing modes in toroidal geometries are examined as well. Furthermore, m {ge} 2 tearing mode stability criteria are compared with three dimensional initial value MHD simulation by the FAR code.
Date: December 1, 1997
Creator: Nishimura, Y.; Callen, J.D. & Hegna, C.C.
Partner: UNT Libraries Government Documents Department

Generalized reduced MHD equations

Description: A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson.
Date: July 1, 1998
Creator: Kruger, S.E.; Hegna, C.C. & Callen, J.D.
Partner: UNT Libraries Government Documents Department

Dynamics of seed magnetic island formation due to geometrically coupled perturbations

Description: Seed magnetic island formation due to a dynamically growing external source in toroidal confinement devices is modeled as an initial value forced reconnection problem. For an external source whose amplitude grows on a time scale quickly compared to the Sweet-Parker time of resistive magnetohydrodynamics, the induced reconnection is characterized by a current sheet and a reconnected flux amplitude which lags in time the source amplitude. This suggests that neoclassical tearing modes, whose excitation requires a seed magnetic island, are more difficult to cause in high Lundquist number plasmas.
Date: June 1, 1998
Creator: Hegna, C.C.; Callen, J.D. & LaHaye, R.J.
Partner: UNT Libraries Government Documents Department