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3
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18544385331
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a recent discussion of the existence and uniqueness of magnetic-field-line velocities, including a model time-dependent axisymmetric toroidal example, can be found in A. L. Wilmot-Smith, E. R. Priest, and G. Hornig, Geophys. Astrophys. Fluid Dyn. 99, 177 (2005);
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a recent discussion of the existence and uniqueness of magnetic-field-line velocities, including a model time-dependent axisymmetric toroidal example, can be found in A. L. Wilmot-Smith, E. R. Priest, and G. Hornig, Geophys. Astrophys. Fluid Dyn. 99, 177 (2005);
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4
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33646585173
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a brief review including select-but-key references is given in D. H. Nickeler and H.-J. Fahr, Sol. Phys. 235, 191 (2006).
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a brief review including select-but-key references is given in D. H. Nickeler and H.-J. Fahr, Sol. Phys. 235, 191 (2006).
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6
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36048942312
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x goes to zero?
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x goes to zero?
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7
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36048956864
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This assumes that the magnetic differential equation B·E, B·▽s can be solved for a single-valued ▽s (Ref. 3)-always the case for an electrostatic E
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This assumes that the magnetic differential equation B·E=- B·▽s can be solved for a single-valued ▽s (Ref. 3)-always the case for an electrostatic E.
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8
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36048995608
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Often, before transforming from x to a flux-surface coordinate, one first takes the derivative with respect to Ψt of the flux-diffusion equation (A2) or (A3, arriving at a diffusion-equation for q, To the author's knowledge, S. Jardin was the first to point out that solving the transport equation for q rather than for a magnetic flux eases the numerics in coupling to a Grad-Shafranov solver. It eliminates having to take a numerical derivative, One then transforms the independent variable of this diffusion-equation from x to a flux-surface-labelling coordinate other than q, of course, typically chosen as some function of normalized poloidal or toroidal flux for convenience, e.g, to reduce the numerical error in. computational applications, or, in the case of RFP's, to avoid a double-valued problem were Ψt to be used as the independent variable. Note that the choice of Ψt for the independe
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x, which does not vanish in tokamaks (except in resistive steady state), fully into account.
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