Investigating different methods for calculating the lambda equilibrium parameter for the plasma column in the Damavand tokamak

•Two general methods have been compared for calculating lambda parameter.•The first method is based on the solving the Grad-Shafranov equation in two different coordinates.•The second method is based on Shafranov Integrals and expansion of the poloidal field until the order of 6.•It was shown that the accuracy of the second method is more than others and it is more reliable. In this paper, various methods of measurement and calculation of the lambda equilibrium parameter (Λ=βp+li2) have been studied and applied. The main purpose is comparing different methods to increase the accuracy of the lambda parameter calculation in the Damavand tokamak. Two general methods have been used to calculate the lambda parameter. The first method is based on the calculation of the external and internal fluxes of the plasma using the Grad-Shafranov equation. Because Damavand is a tokamak with an elongated cross-section and its profile is approximated to the ellipse, the solution of the first order flux due to Grad-Shafranov equation is used in the elliptic cylindrical coordinate system. Also the first order tangential and radial fields are calculated and then the lambda parameter is determined by comparing the values obtained from the analytic relations and the measurement data in cylindrical coordinate. In the second method, the lambda parameter has been calculated using Shafranov integrals and poloidal magnetic field’s expansions. Finally, by using the calculated lambdas for estimating the vertical position of the Damavand plasma, it was observed that the accuracy of the second method is highest.