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

Abstract

In this study, magnetic measurement of poloidal fields were used to determine poloidal beta and plasma internal inductance of Damavand tokamak combination of poloidal beta and plasma internal inductance (b p þ l i 2 ), known as Shafranov parameter, was obtained experimentally in terms of normal and tangential components of the magnetic field. Plasma internal inductance and poloidal beta were obtained using parametrization method based on analytical solution of Grad-Shafranov equation (GSE) and compared with parabolic-like profile of toroidal current density approach for determination of the plasma internal inductance. Finding evolution of b p þ l i 2 and plasma internal inductance. Finding poloidal beta (Shafranov parameter and internal inductance) and using energy balance equation, thermal energy and energy confinement were determined qualitatively in terms of poloidal beta during a regular discharge of Damavand tokamak.

Modeling and robust decentralized control system design for plasma current and position in Damavand tokamak

“…M ps and L p can be determined using equations (A1) and (A2), the estimated current and position of plasma, location of active coils, and current of active coils. Also, the relationship between β p , and plasma current, I p , is shown in figure 2 [27]. Therefore, β p is approximated using equation (4) [28], where δ denotes the uncertainty in linear approximation of β p .…”

“…Using equation ( 17) and triangle inequality, the regions of the k p − k i plane in which the desired bandwidth is at an appropriate level can be obtained as equation (27).…”

“…By choosing a point in the overlapping region at the k p − k i plane, obtained by equations ( 22), (25), and (27), the values of k p and k i can guarantee the robust stability and performance of the closed-loop system.…”

“…Based on the desired performance and using equations ( 22), (25), and (27), and the Kharitonov transfer functions in equation ( 28), the extracted regions for robust stability and performance of the plasma current are shown in figure 10…”