PhD and MPhil Thesis Classes - Université Libre de Bruxelles

1.9 Global Energy Confinement Scaling1.9 Global Energy Confinement ScalingBecause of the complexity of the processes determining heat and particle transportin fusion plasmas, it is not yet possible to provide a first principle derivation of thedependence of energy confinement properties on plasma parameters. The descriptionof the global energy confinement time by empirical scaling that are based on relevantdatabases within specific operating regimes such as L-mode or H-mode has, therefore,become the key tool in extrapolating plasma performances to a next step device, suchas ITER as well as an approximate constraint on the form of theoretical models. Thesescalings connect empirical confinement times with machine and plasma parameters likemajor radius, R, minor radius, a, toroidal magnetic field strength, B T , plasma current,I, electron line average density, n e and plasma temperature, T , along with other geometricalparameters and profile functions, the ion mass and charge numbers m i andZ i . This approach is of course already well established in other areas of science andengineering - the performance of airplanes and ships can be reliably predicted usingsimilar scalings without a detailed understanding of turbulent hydrodynamics flow.The ELMy H-mode standard database provides the basis for a robust confinementpredictions for ITER. The power law scaling expression for thermal energy confinementtime can be expressed as (3):IT ERHτth,E = 0.0562I 0.93 B 0.15 P −0.69 ne 0.41 m 0.19 R 1.97 ɛ 0.58 κ 0.78a (1.17)(in s, MA, T , MW , 10 19 m −3 , AMU, m) where m = average ion mass, P = loss power,κ a = elongation and ɛ = a/R inverse aspect ratio.The study of the scaling relations promoted dimensionless scaling or similarity rules(wind tunnel experiments). Similarity rules compare plasma behavior in geometricallysimilar devices. There are dimensional constraints that follow the similarity rules andone needs to identify the relevant dimensionless parameters. However, the number ofdimensionless parameters for confined plasma is large, up to 19 have been identified(17). They include plasma physics parameters, such as β the ratio of the plasma kineticpressure to the magnetic pressure, the collisionallity ν ∗ ≡ ν eff /ω b (see sec. 1.8.3) andthe normalized Larmor radius ρ ∗ ≡ ρ i /a. There are also parameters describing the21