Self-consistent ECCD calculations with bootstrap current J. Decker, Y.Peysson † , A. Bers and A. K. Ram Plasma Science and Fusion Center, MIT, Cambridge, MA 02139, USA † Association Euratom-CEA, CEA/DSM/DRFC, CEA Cadarache, F-13108, St Paul lez Durance, France Introduction To achieve high performance, steady-state operation in tokamaks, it is increasingly important to find the appropriate means for modifying and sustaining the pressure and magnetic shear profiles in the plasma. In such advanced scenarios, especially in the vicinity of internal transport barrier, RF induced currents have to be calculated self-consistently with the bootstrap current, thus taking into account possible synergistic effects resulting from the momentum space distortion of the electron distribution function f e . Since RF waves can cause the distribution of electrons to become non-Maxwellian, the associated changes in parallel diffusion of momentum between trapped and passing particles can be expected to modify the bootstrap current fraction; conversely, the bootstrap current distribution function can enhance the current driven by RF waves [1]. For this purpose, a new, fast and fully implicit solver has been recently developed to carry out computations beyond those in [1], including new and detailed evaluations of the interactions between bootstrap current (BC) and Electron Cyclotron current drive (ECCD). Moreover, Ohkawa current drive (OKCD) appears to be an efficient method for driving current when the fraction of trapped particles is large. OKCD in the presence of BC is also investigated. Here, results are illustrated around projected tokamak parameters in high performance scenarios of Alcator C-MOD [4]. The Drift Kinetic Equation The self-consistent calculation of the bootstrap current in presence of RF waves is carried out by solving the steady-state drift kinetic equation satisfied by the electron distribution function f averaged over the gyromotion v // r B θ B ∂f ∂θ + V Dr ∂f ∂r = Cf ( 29 + Qf ( 29 for an axisymmetric tokamak in the low inverse aspect ratio limit ε << 1 and with a circular poloidal cross- section, where C and Q are respectively the relativistic collision and RF quasilinear operators, θ the poloidal angle, B θ the poloidal magnetic field, B the total magnetic field, and v // the parallel velocity along the field line. The drift velocity across the field lines is given by the relation (29 μ ω ∂θ ∂ , // // E ce Dr v r v V = where ce ω is the gyrofrequency for electrons of kinetic energy E and magnetic moment μ. As in [1], an approximate formulation, based on a Taylor expansion f = f 0 + δf 1 +… ,is used to determine the electron distribution function in the small parameter δ = τ t,b /τ dr , where τ t,b is the electron's transit or bounce time, and τ dr is a typical time for the electron radial drift due to magnetic field gradient and curvature. The expansion is carried out in the banana regime τ t,b /τ dt << 1, where τ dt is the detrapping time due to collisions. The number of dimensions of the problem is reduced by appropriately averaging over the fast poloidal motion τ t,b for trapped or passing particles, according to the definition {} ∫ - ± =       ∑ = c b b t c A B B v r d A θ θ θ σ θ τ // 1 , 2 1 1 , where ∫ - = c c b t B B v r d θ θ θ θ τ // , is the normalized transit or bounce time. Here σ = sgn( // v ) and θ c = π for passing particles, while the bounce averaging