Abstract
The Stellarator is a magnetic configuration considered a realistic candidate for a future thermonuclear fusion commercial reactor. The most widely accepted scaling law of the energy confinement time for the Stellarator is the ISS04, which employs a renormalisation factor, fren, specific to each device and each level of optimisation for individual machines. The fren coefficient is believed to account for higher order effects not ascribable to variations in the 0D quantities, the only ones included in the database used to derive ISS04, the International Stellarator Confinement database. This hypothesis is put to the test with symbolic regression, which allows relaxing the assumption that the scaling laws must be in power monomial form. Specific and more general scaling laws for the different magnetic configurations have been identified and perform better than ISS04, even without relying on any renormalisation factor. The proposed new scalings typically present a coefficient of determination R2 around 0.9, which indicates that they basically exploit all the information included in the database. More importantly, the different optimisation levels are correctly reproduced and can be traced back to variations in the 0D quantities. These results indicate that fren is not indispensable to interpret the data because the different levels of optimisation leave clear signatures in the 0D quantities. Moreover, the main mechanism dominating transport, in reasonably optimised configurations, is expected to be turbulence, confirmed by a comparative analysis of the Tokamak in L mode, which shows very similar values of the energy confinement time. Not resorting to any renormalisation factor, the new scaling laws can also be extrapolated to the parameter regions of the most important reactor designs available.
Highlights
On the other hand, in the first generations of Stellarator devices, the energy confinement was severely affected by neoclassical losses, related to the asymmetries inherent in the 3D topology of the fields [4]
The Need to Move beyond fren: Concluding Remarks. It has been investigated whether good quality scaling laws, for the energy confinement time in Stellarators, can be obtained without having recourse to any renormalization factor
The main tool deployed has been symbolic regression via genetic programming. It has been shown how relaxing the constraint that the scaling laws have to be in power law form allows particularising the models for the main configurations, with and without shear
Summary
Optimisation and the Scaling of the Confinement Time The Stellarator is a toroidal magnetic confinement device for the achievement of thermonuclear fusion, with potentially sufficient efficiency to become a realistic candidate for the final commercial reactor [1]. Modern Stellarator machines are conceived with a completely different approach, in which a plasma equilibrium with good neoclassical confinement properties is analysed first, and the external coils are configured to approximate the required magnetic fields as much as possible. (0D quantities are global values, characterising the whole plasma) It has been the basis for the identification of the most widely accepted scaling law for the Stellarator confinement time τE, the so called ISS04. This scaling is in power law monomial form and, in order to fit the experimental data acceptably, it employs a dimensionless renormalisation factor, called fren, for each device and for each sufficiently different optimisation level. In the case of the shearless devices, due to the quite heterogeneous character of the entries, a form of constrained minimisation has been implemented, and the confidence intervals have been obtained with the method of the bootstrap
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