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Non-local closures allow kinetic effects on parallel transport to be included in fluid simulations. This is especially important in the scrape-off layer, but to be useful there the non-local model requires consistent kinetic boundary conditions at the sheath. A non-local closure scheme based on solution of a kinetic equation using a diagonalized moment expansion has been previously reported. We derive a method for imposing kinetic boundary conditions in this scheme and discuss their implementation in BOUT++. To make it feasible to implement the boundary conditions in the code, we are lead to transform the non-local model to a different moment basis, better adapted to describe parallel dynamics. The new basis has the additional benefit of enabling substantial optimization of the closure calculation, resulting in an O(10) speedup of the non-local code.
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A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak X-point geometry, the code is able to simulate a wide range of fluid models (magnetised and unmagnetised) involving an arbitrary number of scalar and vector fields, in a wide range of geometries. Time evolution is fully implicit, and 3rd-order WENO schemes are implemented. Benchmarks are presented for linear and non-linear problems (the Orszag-Tang vortex) showing good agreement. Performance of the code is tested by scaling with problem size and processor number, showing efficient scaling to thousands of processors. Linear initial-value simulations of ELMs using reduced ideal MHD are presented, and the results compared to the ELITE linear MHD eigenvalue code. The resulting mode-structures and growth-rate are found to be in good agreement (BOUT++ = 0.245, ELITE = 0.239). To our knowledge, this is the first time dissipationless, initial-value simulations of ELMs have been successfully demonstrated.
By using a non-local model, fluid simulations can capture kinetic effects in the parallel electron heat-flux better than is possible using flux limiters in the usual diffusive models. Non-local and diffusive models are compared using a test case representative of an ELM crash in the JET SOL, simulated in one dimension. The non-local model shows substantially enhanced electron temperature gradients, which cannot be achieved using a flux limiter. The performance of the implementation, in the BOUT++ framework, is also analysed to demonstrate its suitability for application in three-dimensional simulations of turbulent transport in the SOL.
In the cold pulse experiments in J-TEXT, not only are the rapid electron temperature increases in core observed, but also the steep rises of inner density are found. Moreover, the core toroidal rotation is also accelerated during the non-local transport process of electron temperature. These new findings of cold pulse experiments in J-TEXT reveal that turbulence spreading is the possible mechanism for the non-local transport dynamics.
In cold pulse experiments in J-TEXT, the ion transport shows similar non-local response as the electron transport channel. Very fast ion temperatures decreases are observed in the edge, while the ion temperature in core promptly begin to rise after the injection of cold pulse. Moreover, the cutoff density is also found for the ion non-local effect. The experimental observed density fluctuation in a high frequency ranging from 500 kHz to 2 MHz is obviously reduced in the whole plasma region during non-local transport (NLT) phase.
Experiments of electron cyclotron resonance heating (ECH) power scan in KSTAR tokamak clearly demonstrate that both the cut-off density for non-local heat transport (NLT) and the threshold density for intrinsic rotation reversal can be determined by the collisionality. We demonstrate that NLT can be affected by ECH, and the intrinsic rotation direction follows the changes of NLT. The cut-off density of NLT and threshold density for rotation reversal can be significantly extended by ECH. The poloidal flow of turbulence in core plasma is in the electron and the ion diamagnetic direction in ECH plasmas and high density OH plasma, respectively. The auto-power spectra of density fluctuation are almost the same in the outer region for both ECH and OH plasmas. On the other hand, in the core region of ECH plasmas, the power spectra of the density fluctuations are broader than those of OH plasma. All these observations in macroscopic parameters and micro fluctuations suggest a possible link between the macro phenomena and the structural changes in micro-fluctuations.
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