By Gastón Andrés García

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**Extra resources for Quantum Groups and Hopf Algebras**

**Example text**

For 6 mn ^ 0 , a finite pressure gradient drives an infinite parallel current at the rational surface. Elimination of this singularity requires the vanishing of the pressure gradient at rational surfaces. Originally this was discarded as unphysical, but in fact the magnetic perturbations will not be ideal in form, and will produce small magnetic islands and stochastic layers at rational surfaces, decreasing in size as m, n increase. Thus one should expect a local flattening of the pressure profile in the vicinity of such surfaces as the correct physical solution.

Take the major radius as the unit of distance, and normalize the magnetic field to unity on the major axis. , X = 1 is the magnetic axis location with magnetic surfaces as shown in Fig. 2. We choose this description for the convenience of defining X=1 to be the magnetic axis location, with the location of the outermost flux surface given by A. Physically, note that if the outermost flux surface is fixed by a conducting metal wall it is the magnetic axis which shifts its position in space according to the ~ value of p A, which as we will see depends on the plasma pressure.

This equation determines A, and thus the physical location of the flux surfaces in terms of the two functions defining the equilibrium. Eliminate g' in this equation and p multiply by rf , then note ( 2ri f,l . }[ i r f l f ^ j ' . R 2 W, F 2 I M L _ L + [ W] . 78 . Note that normally p' < 0 so A' > 0. The constant of integration is zero, otherwise A' = « at r = 0. These terms have a simple interpretation. 79 Q 2 2 where I = 2/(r BQ) J*£ B 2 rdr = 2 W length, I the current, and 6 average pressure.