Analytical models of axisymmetric toroidal magnetic fields with non-circular flux surfaces

Axisymmetric toroidal magnetic configurations relevant to current and future tokamak experiments are analytically modelled taking into account an arbitrary aspect ratio, noncircularity and up-down asymmetry of flux surface shapes. It is shown that equilibrium tokamak magnetic fields can be satisfactorily described using only four geometric parameters, which determine the shape and position of the flux surfaces. These are the Shafranov shift, the elongation, and the parameters of triangularity and of up-down asymmetry. To cover the variety of observed flux surface shapes, three different analytical expansions are provided. Comparison of the modelled with the equilibrium flux surfaces in NSTX (Princeton), JET (Abingdon) and TCV (Lausanne) demonstrates good coincidence.