Feedback controller input design for ignition of deuterium–tritium in NSTX tokamak

• Specific solution for equilibrium problem in NSTX tokamak was presented.
• Poloidal magnetic flux, toroidal current density and normalized pressure profiles were calculated.
• Toroidal and poloidal flows effects on the equilibrium are numerically investigated using the FLOW code.
• Our analytical solution can be served as good benchmark against the equilibrium FLOW code.

Nuclear fusion is a nuclear reaction in which two or more atomic nuclei (such as a deuterium–tritium) come very close and then collide at a very high speed and join to form a new high energy nucleus (Helium). Determination of accurate plasma horizontal position during plasma discharge is essential to transport it to a control system based on feedback. The solutions of Grad-Shafranov equation (GSE) analytically can be used for theoretical studies of plasma equilibrium, transport and magneto hydrodynamic stability. Here we have presented specific choices for source functions, kinetic pressure and poloidal plasma current, to be quadratic in poloidal magnetic flux and derive an analytical solution for Grad-Shafranov equation. With applying this solution to NSTX tokamak, we calculated poloidal magnetic flux, toroidal current density and normalized pressure profiles for this tokamak. Toroidal and poloidal flows can considerably change the equilibrium parameters of tokamak. These effects on the equilibrium of tokamak plasmas are numerically investigated using the code FLOW. As a comparative approach to equilibrium problem, the code is used to model equilibrium of NSTX tokamak for case pure toroidal flow. Comparison of the results of these two methods for NSTX tokamak shows good agreement between two and that our analytical solution can be served as good benchmark against the equilibrium code FLOW.