Semi-analytic approach for determination of poloidal beta limits using plasma internal inductance in Damavand tokamak

Abstract

The Grad-Shafranov equation plays a very important role in analysis of the plasma equilibrium in magnetic confinement configurations such as the tokamak. In tokamaks which are operating in Ohmic heating regime, the Grad-Shafranov equation can be expanded through the inverse aspect ratio parameter. Consequently, the first order of poloidal flux function and the poloidal/radial components of the magnetic field are obtained. In this study, by considering the effect of tokamak non-circularity, a semi-analytic model which is based on magnetic measurements was developed and highest and lowest values of plasma internal inductance and poloidal beta were estimated by means of the poloidal and radial magnetic field experimental data acquired from Damavand tokamak magnetic probes.

Magnetic measurement based methods in determination of plasma equilibrium parameters in Damavand tokamak

“…As a benchmark, the first order (with respect to inverse aspect ratio parameter ε) of radial and poloidal components of the magnetic field are considered which are derived from analytic solution of the GSE for approximated plasma surface [20].…”

“…Figure 8(a) shows the time evolution of Shafranov parameter for the fixed plasma minor radius a = 7 cm and elongation factor κ = 1.41 in a typical shot of Damavand tokamak. Figure 8(b) represents the evolution of the q eff and comparison with semi-empirical description of edge safety factor [20,28,29] where the plasma elongation factor is treated as a constant parameter and the minor radius is obtained from (2.18). It is found that during the large majority of the plasma discharge (after ramp-up and before ramp-down), the difference of the introduced models in assessment of Shafranov parameter is less than 0.03 which indicates that the two introduced methods are in good agreement during the ramp domain of the plasma current evolution (from 1.5 ms until 19.5 ms) but there are significant differences out of the ramp domains.…”

“…The evolution of q eff is also well matched to the empirical evaluation of the q edge when the plasma current is in its steady state, flat-top regime. In order to explain the agreements and differences of Shafranov parameter measurement, error analysis of the first order solution of the GSE [20] is made. The measured error of kth harmonic of the poloidal and radial components of the magnetic field from magnetic probe number m is defined as [19]:…”

“…This approximate approach is mainly appropriate for circular or near circular geometries of the plasma surface and has been used to provide trace of the parameters in tokamaks such as HT-7, JT6 and IR-T1 [16][17][18]. However, the non-circularity of the plasma surface can be considered as a correction factor in order to make a qualitative estimations about the equilibrium parameters [19,20]. Therefore, the GSE model becomes inaccurate when the non-circularity of the plasma surface increases.…”

Application of poloidal beta and plasma internal inductance in determination of input power time of Damavand tokamak

“…It is also possible to extract many other plasma parameter such as displacement of plasma column, prediction of vertical displacement event (VDE) and energy confinement time of tokamak using equilibrium parameters [4][5][6][7]. In tokamaks with circular cross section, it is possible to find evolution of the Shafranov parameter using model which is based on expansion (with respect to the inverse aspect ratio parameter of the tokamak) of polidal flux function w and the first order solution of the well known Grad-Shafranov equation (GSE) in toroidal coordinate system [8][9][10]. This approach (the first order solution of the poloidal flux function and finding the first order poloidal and radial components of the magnetic field), however, is an approximate method which provide reliable information about Shafranov parameter and horizontal displacement of the plasma column (Shafranov shift) in tokamaks with circular cross section or when the non-circularity of the plasma surface is considered as a correction factor.…”