Knudsen number

The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is named after Danish physicist Martin Knudsen (1871–1949). The Knudsen number helps determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation. If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of the problem, and the continuum assumption of fluid mechanics is no longer a good approximation. In such cases, statistical methods should be used. Definition The Knudsen number is a dimensionless number defined as :\mathrm{Kn}\ = \frac {\lambda}{L}, where : \lambda = mean free path [L1], : L = representative physical length scale [L1]. The representative length scale

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Plasma rotation and momentum transport studies at JET

An experimental study in plasma rotation and momentum transport was carried out at JET. The toroidal rotation profile was found to scale approximately with that of the ion temperature. However, significant deviations from this were found in high density ELMy H-mode discharges, which had broader rotation profiles. A rotation database analysis showed the variation of the dimensionless Mach number with respect to the plasma scenario. For predominantly NBI heated discharges the Mach number was found to be in the range of 0.3-0.45. Larger Mach numbers were observed in type I ELMy H-modes, while scenarios exhibiting type III ELMs or L-mode had lower Mach numbers. Advanced scenarios often showed a significant increase in the central Mach number when an internal transport barrier formed. A detailed study was done to investigate the Prandtl number, P-r, defined as the ratio between momentum and ion heat diffusivity. Generally the Prandtl number was found to be significantly below unity, e. g. 0.18 < P-r < 0.35. Although it is often predicted that momentum and heat diffusivity are equal in ITG dominated plasma, also for high density ELMy H-mode discharges with temperature profiles close and above the ITG threshold, the Prandtl number was P-r similar to 0.3.

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The ion temperature is not frequently measured in the boundary of magnetic fusion devices. Comparisons among different ion temperature techniques and simulations are even rarer. Here we present a comparison of ion temperature measurements in the boundary of the Alcator C-Mod tokamak from three different diagnostics: charge exchange recombination spectroscopy (CXRS), an ion sensitive probe (ISP), and a retarding field analyzer (RFA). Comparison between CXRS and the ISP along with close examination of the ISP measurements reveals that the ISP is space charge limited. It is thus unable to measure ion temperature in the high density (>10^19 m−3) boundary plasma of C-Mod with its present geometry. Comparison of ion temperatures measured by CXRS and the RFA shows fair agreement. Ion and electron parallel heat flow is analyzed with a simple 1D fluid code. The code takes divertor measurements as input and results are compared to the measured ratios of upstream ion to electron temperature, as inferred respectively by CXRS and a Langmuir probe. The analysis reveals the limits of the fluid model at high Knudsen number. The upstream temperature ratio is under predicted by a factor of 2. Heat flux limiters (kinetic corrections) to the fluid model are necessary to match experimental data. The values required are found to be close to those reported in kinetic simulations. The 1D code is benchmarked against the 2D plasma fluid code UEDGE with good agreement.

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