Abstract
Solov'ev profiles, which are the simplest that allow analytic solutions for the Grad–Shafranov (G–Sh) equation, can reproduce some features of experimental equilibria when the free parameters are appropriately chosen. The purpose of this paper is to study how the freedom in the choice of the parameters and the number of terms in a series solution to the homogeneous equation affect the equilibria obtained. Keeping equatorial symmetry for simplicity, the limits of this approach are tested. The behavior of the solutions for devices with different sizes and aspect ratios, such as ITER, ST40, and MAST-U, is studied, and also examples in which physically relevant figures of merit are found. While the toroidal current density profile is necessarily limited, and cannot be realistic, some of the main features of the magnetic field flux surfaces can be obtained. Three sets of parameters are distinguished, so their roles can be better understood: (1) The geometrical parameters of the boundary conditions, which determine the last closed magnetic field flux surface, (2) The general parameters of an experiment, such as the plasma current, the major radius, and the toroidal magnetic field at the major radius, and (3) the Solov'ev parameters. The regions of acceptable values for the Solov'ev parameters, are identified, depending on the topology of the solutions.
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