No abstract

We describe properties of the reduced quintic triangular finite element. The expansion used in the element will represent a complete quartic polynomial in two dimensions, and thus the error will be of order h 5 if the solution is sufficiently smooth. The quintic terms are constrained to enforce C 1 continuity across element boundaries, allowing their use with partial differential equations involving derivatives up to fourth order. There are only three unknowns per node in the global problem, which leads to lower rank matrices when compared with other high-order methods with similar accuracy but lower order continuity. The integrations to form the matrix elements are all done in closed form, even for the nonlinear terms. The element is shown to be well suited for elliptic problems, anisotropic diffusion, the Grad-Shafranov-Schlüter equation, and the timedependent MHD or extended MHD equations. The element is also well suited for 3D calculations when the third (angular) dimension is represented as a Fourier series.

Abstract. Recent experiments in the Current Drive eXperiment -Upgrade provide a first-ever test of large area liquid lithium surfaces as a tokamak first wall, to gain engineering experience with a liquid metal first wall, and to investigate whether very low recycling plasma regimes can be accessed with lithium walls. The CDX-U is a compact (R=34 cm, a=22 cm, B toroidal = 2 kG, I P =100 kA, T e (0)~100 eV, n e (0)~ 5 × 10 19 m -3 ) spherical torus at the Princeton Plasma Physics Laboratory. A toroidal liquid lithium tray limiter with an area of 2000 cm 2 (half the total plasma limiting surface) has been installed in CDX-U. Tokamak discharges which used the liquid lithium limiter required a fourfold lower loop voltage to sustain the plasma current, and a factor of 5-8 increase in gas fueling to achieve a comparable density, indicating that recycling is strongly reduced. Modeling of the discharges demonstrated that the lithium limited discharges are consistent with Z effective <1.2 (compared to 2.4 for the pre-lithium discharges), a broadened current channel, and a 25% increase in the core electron temperature. Spectroscopic measurements indicate that edge oxygen and carbon radiation are strongly reduced.

DIII-D physics research addresses critical challenges for the operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by integrating high performance core and boundary plasmas. Substantial increases in off-axis current drive efficiency from an innovative top launch system for EC power, and in pressure broadening for Alfven eigenmode control from a co-/counter-I p steerable off-axis neutral beam, all improve the prospects for optimization of future long pulse/steady state high performance tokamak operation. Fundamental studies into the modes that drive the evolution of the pedestal pressure profile and electron vs ion heat flux validate predictive models of pedestal recovery after ELMs. Understanding the physics mechanisms of ELM control and density pumpout by 3D magnetic perturbation fields leads to confident predictions for ITER and future devices. Validated modeling of high-Z shattered pellet injection for disruption mitigation, runaway electron dissipation, and techniques for disruption prediction and avoidance including machine learning, give confidence in handling disruptivity for future devices. For the non-nuclear phase of ITER, two actuators are identified to lower the L–H threshold power in hydrogen plasmas. With this physics understanding and suite of capabilities, a high poloidal beta optimized-core scenario with an internal transport barrier that projects nearly to Q = 10 in ITER at ∼8 MA was coupled to a detached divertor, and a near super H-mode optimized-pedestal scenario with co-I p beam injection was coupled to a radiative divertor. The hybrid core scenario was achieved directly, without the need for anomalous current diffusion, using off-axis current drive actuators. Also, a controller to assess proximity to stability limits and regulate β N in the ITER baseline scenario, based on plasma response to probing 3D fields, was demonstrated. Finally, innovative tokamak operation using a negative triangularity shape showed many attractive features for future pilot plant operation.