Application of modified ASTRA-SPIDER code to simulation of free boundary equilibrium evolution

摘要

In our studies a coupling of the equilibrium solver with a transport code is considered. In such 1.5D codes the evolution of poloidal magnetic flux, density and temperatures of plasma species are simulated in 1D approximation on the flux grid and with metric coefficients calculated consistently by 2D equilibrium solver. Our simulations are based on the Automated System for Transport Analysis (ASTRA) [1] and equilibrium solver SPIDER [2]. In the original coupling of the SPIDER to ASTRA7.0 [3] the evolution of the poloidal magnetic flux is computed outside the equilibrium solver. We modified the iteration loop to include the poloidal flux evolution into the internal iteration loop of the equilibrium solver and circuit equations using the grid adapted to magnetic fluxes. So the 2D Grad-Shafranov (GSE) equation in a fixed or free boundary configuration is solved by iterations together with the set of two one-dimensional equations relative to poloidal Ψ and toroidal Φ fluxes on the common grid inside the fixed plasma boundary by means of the SPIDER code [4]: {formula} where the first equation of (1) is the poloidal magnetic field diffusion equation derived from the Ohm's law {formula}, and the second equation is the flux averaged Grad-Shafranov Equation (GSE). Here metric coefficients a22, a33 and the plasma boundary are taken from the solution of 2D GSE, plasma conductivity, σ, plasma pressure, P, and external current, jB, are taken from the transport block, {formula}-volume averaging between two magnetic surfaces, V-volume inside the magnetic surface, {formula} designations of derivatives by the flux variable a(R,Z) and by time. Additionally the iteration loop includes the circuit equations for each current filament in control and passive coils, which determine the control coil voltages and passive coil currents.