Simulations of tokamak disruptions including self-consistent temperature evolution

Abstract

Three-dimensional simulations of tokamaks have been carried out, including self-consistent temperature evolution with a highly anisotropic thermal conductivity. The simulations extend over the transport time-scale and address the question of how disruptive current profiles arise at low-q or high-density operation. Sharply defined disruptive events are triggered by the m/n = 2/1 resistive tearing mode, which is mainly affected by local current gradients near the q = 2 surface. If the global current gradient between q = 2 and q = 1 is sufficiently steep, the m = 2 mode starts a shock which accelerates towards the q= 1 surface, leaving stochastic fields, a flattened temperature profile and turbulent plasma behind it. For slightly weaker global current gradients, a shock may form, but it will dissipate before reaching q= 1 and may lead to repetitive minidisruptions which flatten the temperature profile in a region inside the q= 2 surface.

Hybrid magnetohydrodynamic-gyrokinetic simulation of toroidal Alfvén modes

“…Without finite drift-orbit size effects (PkH= a= 0), Eqs. (38) and (40) would have predicted the TAE mode to be more unstable than the upper KTAE branch, showing the essential role played by these effects in bringing the TAE mode so close to the lower shear Alfven continuous spectrum that complete mode stabilization occurs due to the coupling to the lower KTAE branch. The nonperturbative hybrid simulations are performed by retaining the toroidal corrections to the equilibrium magnetic field [i.e., including the (1,0) Fourier component in the equilibrium poloidal flux t{leq] and evolving the electromagnetic field self-consistently along with the energetic-particle response.…”

“…38 Making reference to a toroidal coordinate system (r, (), 'P), with () the poloidal angle, the code uses finite difference in the radial direction and Fourier expansion in the poloidal and toroidal directions. The system of coupled equations for the Fourier components of the magnetic and velocity stream functions i fF and U is advanced in time using a semi-implicit algorithm, where all the linear terms that couple with the cylindrical part of the equilibrium (that is, with poloidal and toroidal mode numbers m = O,n = 0) are treated implicitly.…”

“…III, which correspond to a predominantly TAE-like mode, the mode transition from a stable (or very weakly unstable) TAE to an unstable KTAE branch expected from the theoretical predictions of Eqs. (38) and (40) will be explicitly shown. Without finite drift-orbit size effects (PkH= a= 0), Eqs.…”

“…6, where the analytical estimates for the growth rate y of the TAE, Eq. (38). and that of the KTAE,Eq.…”

Hybrid magnetohydrodynamic-particle simulation of linear and nonlinear evolution of Alfvén modes in tokamaks

“…The field solver for the O(⑀ 3 ) reduced MHD equations 29,27 is based on a previous O(⑀ 2 ) version. 45 The code uses finite difference in the minor radius direction and Fourier expansion in the poloidal and toroidal directions. The equilibrium is calculated, to the desired order in ⑀, from the Grad-Shafranov equation, by assigning a q-profile, which determines the symmetric (mϭ0,nϭ0) zeroth-order Fourier component of the magnetic-flux function , and integrating the equation for the first-order correction (mϭ1,nϭ0).…”