Study of Shafranov Shift by the Simplest Grad Shafranov Equation Solution for Various Tokamaks

Abstract

Plasma internal energy is not conserved on a magnetic surface if nonlinear flows are considered. The Magnetohydrodynamic equilibrium in an axisymmetric plasma is described by the Grad Shafranov equation in terms of the magnetic flux. A generalized Grad Shafranov type equation has been used. Specific functional forms of plasma internal energy and current are used. A simplest analytic solution of the Grad Shafranov equation is used. This solution is over constrained both in shape and in plasma current. We demonstrate that the Shafranov shift for this solution is independent of plasma current for various tokamaks. We studied the dependence of Shafranov shift on various plasma parameters and found that Shafranov shift depends on parameters such as major radius, minor radius, aspect ratio and inverse aspect ratio. The Shafranov shift shows a direct relation with major radius „ ‟. The value of Shafranov shift increases with the increase in value of major radius. Similarly for minor radius „a‟ there exist a direct relation between Shafranov shift and minor radius. And inverse aspect ratio „a/ ‟ is also varies directly with Shafranov shift. For the case of aspect ratio Shafranov shift is inversely related to the aspect ratio „ ‟.