Development of numerical techniques toward extreme scale fusion plasma turbulence simulations

The magnetic confinement fusion is one of the most promising approaches to a fusion reactor, and in the next generation experiment, the International Thermonuclear Experimental Reactor (ITER), the scientific and technological feasibility of a magnetic fusion reactor will be demonstrated. Fusion plasmas are extremely complex physical system consisting of multiple fluids (electrons and multiple species ions) coupled through electromagnetic fields and weak Coulomb collisions. Because of this complexity, computer simulations have been established as essential tools in wide spectrum of fusion science. Among several critical issues, the turbulent transport is the most demanding issue, because five dimensional (5D) gyrokinetic simulations [1, 2] are needed for studying turbulent fusion plasmas. So far, we have been developing a global Gyrokinetic Toroidal 5D Eulerian code (GT5D) [3]. GT5D is based on the so-called global full-f approach, in which the equilibrium part f0 and turbulent perturbation δf of particle distribution are solved simultaneously using the same first principles in a full torus computational domain. In contrast to conventional δf simulations, which solve only δf with fixed f0 by assuming complete spatiotemporal scale separation between f0 and δf , full-f simulations can simulate relevant multi-scale phenomena such as interactions between macro-scale mean flows and microscale turbulence and evolutions of temperature profiles affected by turbulent energy transport in a self-consistent manner. The full-f approach requires robust and accurate numerical treatments, which can resolve small amplitude perturbations (δf/f0 ∼ 1%) for time scales much longer than a turbulent correlation time. Such numerical requirements were satisfied by developing a Non-Dissipative Conservative Finite Difference (NDCFD) scheme [4]. The accuracy of GT5D was demonstrated through quantitative verification studies [3]. In addition, validation studies [5, 6] captured qualitative transport properties in the experiment, such as the stiffness of temperature profiles, intermittency of avalanche-like heat transport, spontaneous plasma rotation, and the plasma size scaling of the heat diffusivity. Although the rapid progress of computing power enhanced capabilities of GT5D, we need to establish the path towards next generation Peta-scale and Exascale computing for simulating the ITER, which is several times larger than existing fusion devices. In such extreme scale computing, severe requirements on the memory usage and the parallel efficiency are expected. In this work, we present numerical techniques required for extreme scale fusion plasma turbulence simulations. 2 Calculation models