ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The equations of resistive magnetohydrodynamics (MHD) are recast in a form that is useful for studying the evolution of those toroidal systems where the fast magnetosonic wave plays no important role. The equations are exact and have ∇ ⋅ B=0 satisfied explicitly. From this set of equations it is a simple matter to derive the equations of reduced MHD to any order in the inverse aspect ratio ε of the torus and for β∼ε or smaller. This is demonstrated by deriving a reduced set of MHD equations that are correct to fifth order in ε. These equations contain the exact equilibrium relation and, as such, can be used to find three-dimensional stellarator equilibria. In addition, if a subsidiary ordering in η, the resistivity, is made, the equations of Glasser, Greene, and Johnson [Phys. Fluids 8, 875 (1967); 19, 567 (1967)] are recovered. This set of reduced equations has been coded by extending the initial value code hilo [Phys. Fluids 26, 3066 (1983)]. Results obtained for both ideal and resistive linear stability from the reduced equations are compared with those obtained by solving the full set of MHD equations in a cylinder. Good agreement is shown for both zero and finite-beta calculations. Comparisons are also made with analytic theory illuminating the present limitations of the latter.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.865061
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