B2.5-Eunomia simulations of Pilot-PSI

Nuclear fusion, the merging of light nuclei into a heavier one, is an attractive future energy source. It is safe, produces no carbon-dioxide and its resources are practically unlimited. Currently, the most promising concept of nuclear fusion as a commercial energy source is the tokamak. In a tokamak, the hot plasma is confined by a torus shaped magnetic field. However, the plasma gradually diffuses outwards to the so-called scrapeoff layer and is guided to the divertor, the exhaust of a fusion device. In the divertor of ITER, a tokamak experiment under construction that has to demonstrate that fusion is a feasible energy source, an enormous heat flux density of around 10 MW m-2 and particle flux density of around 1024 m-2s-1 are expected. Pilot-PSI and Magnum-PSI, two linear plasma devices at DIFFER, are unique in producing the plasma conditions as expected in the ITER divertor in a well controlled and diagnosed set-up. Therefore, Pilot-PSI and Magnum-PSI are crucial for a successful divertor design for next generation tokamaks. Via computer simulations results of Pilot-PSI and Magnum-PSI can be translated to ITER. The wide ranges of time and length scales of the processes in the divertor make simulations very challenging. For simulation of neutral particles under ITER divertor conditions, a non-linear, kinetic Monte Carlo code is required. Hereto, Eunomia has been developed and coupled to the multi-fluid plasma code B2.5. Eunomia is a welldocumented, modular code with a modern fortran programming style, using objects and dynamic memory allocation. The challenging part of B2.5 simulations of Pilot-PSI and Magnum-PSI is to describe the low temperature, high density plasma beam in suitable boundary conditions. For Monte Carlo simulations of neutral species in a linear device the statistically most challenging region is the plasma region, in particular in front of the target. The aim for B2.5-Eunomia is to simulate both the geometries of linear devices and the scrape-off layer and divertor region of a tokamak and to improve understanding of the important physics in the ITER divertor conditions. Since for a new code validation is essential, Eunomia has been subjected to several test problems, such as Couette flow, to ensure correctness of neutral flow calculations. In addition, performance of several features of Eunomia has been tested, such as the parallel speedup and the algorithms reducing statistical noise. The importance of various collision processes has been studied. As expected, for Pilot-PSI conditions the neutral-neutral collisions and charge exchange collisions with a proton are of great importance. Although typically neglected, because of the small scattering angle, the elastic collisions between a proton and atomic and molecular hydrogen should be included at the relatively high pressure of several Pascals, created by the recycling plasma. The density distributions of excited hydrogen atoms and line-of-sight integrated Balmer emission profiles were calculated with a collisional-radiative model, using Eunomia results as input. Simulation of the vibrational states of the hydrogen molecule as separate species in Eunomia is crucial. The distribution of the molecules over the vibrational states strongly deviates from local thermal equilibrium, due to transport and dissociative processes. This has an impact on the shapes and intensities of the emission profiles. Comparison to spectroscopic measurements in Pilot-PSI showed reasonably good agreement in both the widths and amplitudes of the line integrated emission profiles of Balmer-a. However, the results are sensitive to uncertainties in the association probability of atoms at the vessel wall and the distribution of molecules, produced by this association process, over the vibrational states. B2.5-Eunomia has successfully been coupled and applied to the cylindrically symmetric geometry of Pilot-PSI. The vibrationally excited molecules efficiently recombine the plasma at the edge of the plasma beam, whereas atoms efficiently cool the plasma. Comparison of B2.5-Eunomia simulations to Thomson scattering measurements near the target of Pilot-PSI showed good agreement. B2.5-Eunomia could not reproduce the floating potential and the saturation current to the target quantitatively, however, the amount of biasing required to reach saturation of the total current to the target is reproduced. When the target in Pilot-PSI is floating, so when the total net current is zero, locally strong plasma currents run into and out of the target. B2.5-Eunomia results show current paths from the anode to the target, returning via the center of the plasma to the source. Furthermore, B2.5-Eunomia simulations show that saturation of the total current, as measured experimentally in Pilot-PSI for a biased target, is not a good indicator for obtaining the ion saturation current density over the whole target surface. Locally, at the center of the target, the ion saturation current is only reached when biasing the target 20 V more negative. Only when locally the ion saturation current density has been reached, the sheath potential will increase linearly with the bias potential. Further development of Eunomia, to improve the B2.5-Eunomia code package in the future, and additional benchmarking of B2.5-Eunomia have been discussed. The incorporation of the collisional-radiative model has been initiated. There remain no technical limitations to simulate other linear devices, as well as tokamak divertors, with B2.5-Eunomia

Numerical modelling for Pilot-PSI and Magnum-PSI, the num'' of Magnum

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