The free boundary equilibrium problem for helically symmetric plasmas

An iterative technique is described for solving the helically symmetric plasma equilibrium equations with a free boundary. The method involves an application of Green’s theorem , and has been formulated for the geometry of a heliac. Provision is made to incorporate the field of the external solenoid into the model, and the limits of applicability of the conventional Fourier-Bessel series representation of th a t field are investigated. The free boundary model is implemented as p art of an inverse equilibrium version of the PEST code and is applied to the SHEILA heliac. Mercier and ballooning stability are examined for fixed and free boundary equilibria as a function of pressure and a deformation parameter which is taken to be the current in an extra helical winding near the centre of the configuration. The free boundary stability properties depend almost entirely on the existence of a vacuum magnetic well