PhD and MPhil Thesis Classes - Université Libre de Bruxelles

1.8 Mechanisms of Transport in Tokamaksclouds of negative and positive charge will surround the positive and negative ballsrespectively, with their density decreasing with distance from the charged balls. Thisis due to the mobility of the electrons and ions in plasma. For cold plasma with nothermal motions, as many charges will be observed in the surrounding clouds as arerequired to neutralize the inserted charges. However, plasma temperature is finite andthe plasma particles possess a substantial kinetic energy of thermal motion so some -particularly those at the edge of the cloud - will escape from the shielding cloud and theshielding is not complete. The edge of the cloud then occurs at the radius where thepotential energy is approximatively equal to the thermal energy k B T of the particles.This characteristic shielding range, is the Debye length which in non-magnetized plasmais defined (for further details see Ref. (1; 13))λ D = ( ɛ 0k B T en e e 2 )1/2 (1.10)where ɛ 0 is the primitivity of the free space, e is the electron charge and n e is taken asthe electron density far away from the shielding cloud.Transport in plasmas is dominated by the long-range collective electric field E k,ω ,part of the Coulomb interactions between the charged particles. Here the subscriptdenote the wave-number k and frequency ω of the electric field fluctuation E k,ω . For aplasma of density n and temperature T the single particle Coulomb electric field fallsoff exponentially beyond the Debye length λ D . Therefore, for kλ D ≪ 1 the electric fieldfluctuations are collective self consistent interactions while for kλ D 1 the interactionsare binary collisional. For a plasma with a large number of particles inside the Debyesphere N D = (4π/3)nλ 3 D≫ 1, the collective electric fields dominate the plasma dynamicsthrough collective modes. In magnetized plasmas the modes with low frequency,ω ≪ Ω c , dominate the transport.The effects related to the collective interactions which exist in a plasma as a resultof the long range Coulomb forces, fall outside the scope of the classical theory and arethe object of anomalous transport theory which will be discussed later in this chapter.17