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1. INTRODUCTIONFigure 1.10: Schematic representation of the diffusion coefficient in a tokamak as afunction of the collisionallity. Here, the following notation has been used A = ɛ −1 where ɛis the inverse aspect ration.1.8.3 Neo-classical TransportAn effect which has to be taken into account in fusion plasmas is the effect of the magneticfield on the free motion of the particles. The magnetic fields produced in fusiondevices are spatially inhomogeneous and have a globally toroidal topology. The particleorbits in such magnetic fields are either helices encircling (but also drifting away from)the field lines, or else depending on their velocity, they may be trapped in low-fieldregions because of the inhomogeneousity (magnetic mirror effect, see chapter 3). Whenthe classical theory (based on collisions) is combined with these effects on the geometry,one finds transport coefficients that are enhanced as compared to the classical ones.This theory is called the neoclassical transport theory of plasmas (14; 15; 16). Theneoclassical transport levels exceed the classical ones by geometrical factors: q 2 ɛ −3/2 inthe low collision frequency ”banana” regimes (ν ∗ < 1.0) and q 2 in the collisional limit,as a result of toroidal geometry. Here, ɛ = r/R is the inverse aspect ratio, with r andR being the minor and major radii of the magnetic surface. The collisionallity parameteris ν ∗ ≡ ν eff /ω b , where ν eff ≡ ν ei /ɛ is the effective collision frequency for particledetrapping, and ω b ≈ ɛ 1/2 V th /(Rq) is the trapped particle average bounce frequency.18
1.8 Mechanisms of Transport in TokamaksAlthough neoclassical transport theory is a significant step forward towards describingtransport in magnetically confined plasmas, in general the neoclassical predictionsare still far from explaining the full picture (D neo for electrons is of the order10 −3 [m 2 s −1 ] and for ions of the order 10 −1 [m 2 s −1 ]).1.8.4 Anomalous TransportThe transport theory based on particle collisions can incorporate the geometry of theTokamak magnetic system, but neoclassical theory still assumes that the plasma is inequilibrium and axisymmetric. Real Tokamak plasmas always show the presence of abroad spectrum of fluctuations, e.g. in plasma density, temperature and electromagneticfields (3); thus real Tokamak plasma are turbulent. The turbulent fluctuationsgive rise to transport across the equilibrium magnetic surfaces and it is necessary toincorporate their effect in a comprehensive transport theory. From the theoretical pointof view, most of the instabilities that we think are responsible for the observed plasmaturbulence have a very small component of wave number vector parallel to the magneticfield, compared to the perpendicular component. That is, most of the turbulent eddiesare quasi-perpendicular to the toroidal magnetic field. Therefore, we can expect thatturbulence dominates perpendicular transport, in this case we are in the presence ofanomalous transport. The influence of the plasma turbulence on the parallel transportis rather small, as experiments confirms.The anomalous transport is the least understood transport process in plasma physics.In recent years tremendous progress has been made to describe the anomalous transporttheoretically, in particular with the help of complex computer codes which calculate thegrowth rates of the underlying instabilities and allow to deduce the resulting transportcoefficients. These instabilities are driven essentially by the gradient of density andtemperature.The fluctuations of the magnetic and electric fields (δE, δB) can provide the sourcesto the anomalous transport across the magnetic field lines. If the fluctuations are purelyelectrostatic in nature (δB = 0) they would lead to enhanced cross field transport byE × B drift:19
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9. DISCUSSIONthat the impurity dens
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REFERENCES[21] Weiland J. Collectiv
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REFERENCES[73] Neuhauser J. et al.
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PhD and MPhil Thesis Classes - UniversitÃ© Libre de Bruxelles

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