Fixed boundary tokamak equilibrium problem

15 Fixed boundary tokamak equilibrium problem

The ﬁxed boundary equilibrium problem (also called the “inverse equilibrium problem” by some authors) refers to the case where the shape of a boundary magnetic surface is given and one is asked to solve the equilibrium within this magnetic surface. To make it convenient to deal with the shape of the boundary, one usually uses a general coordinates system which has one coordinate surface coinciding with the given magnetic surface. This makes it trivial to deal with the irregular boundary. To obtain the equilibrium, one needs to solve the GS equation in the general coordinate system.

  15.1 Toroidal elliptic operator in general coordinates
  15.2 Finite diﬀerence form of toroidal elliptic operator in general coordinate system
  15.3 Special treatment at coordinate origin, wrong! to be deleted
  15.4 Pressure and toroidal ﬁeld function proﬁle
  15.5 Boundary magnetic surface and initial coordinates
  15.6 Fixed boundary equilibrium numerical code
  15.7 Benchmark of the code
  15.8 Low-beta equilibrium vs. high-beta equilibrium
  15.9 Analytical form of Jacobian (need cleaning up)
  15.10 Grad-Shafranov equation with prescribed safety factor proﬁle (to be ﬁnished)

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