HYDRODYNAMIC MODELING OF PARTICLE AND ANGULAR-MOMENTUM TRANSPORT IN ROTATING TOKAMAK PLASMAS WITH IMPURITIES

We have developed a 1 + 1 D time dependent code for the description of ion-impurity transport in a rotating tokamak plasma, using a pseudo-spectral discretization in the poloidal angle θ and a staggered finite difference mesh in the minor radius r. The plasma is assumed to have a constant uniform temperature T, to be in the high collisionality (Pfirsch-Schlüter) regime, and to contain electrons "e," fuel ions "i," and a single impurity species "Z" of charge eZ, where e is the proton charge. We are particularly interested in the case when: (1) flow velocities in the toroidal (symmetry) direction φ are in the range typical of neutral beam injection experiments, i.e., vthZ < Vφi,Z {less-than or approximate} vthi, (vthj √2T/mj is the thermal speed, mj is the mass); (2) the relative concentration of impurities in the plasma, n ̇z n ̇i, is significant and comparable to that observed in present tokamaks, i.e., √me/mi ≪ n ̇zZ2/ n ̇i ≈ 1 in order of magnitude. The model fluid equations are obtained via a moment approach, and an expansion in powers of the small ordering parameter δpi = (mivthi/eBθ)((1/ n ̇ | ∂ n ̇i/∂r| ≪ 1 (B is the magnetic field) is then employed. The equations at each order in δpi up to the second are solved, and the characteristic features of the results presented: to lowest order, outboard impurity peaking on each magnetic surface appears due to centrifugal forces; to first order, radial gradients driven ion-impurity friction gives rise to up-down asymmetries in the poloidal profiles; to second order, the radial profiles of density and rotation frequency evolve to steady state under the action of particle and angular momentum sources. The evolution of the poloidal profiles is decoupled from the evolution of the radial ones, thanks to the fact that the corresponding time scales belong to different orders in δpi: an algorithm is proposed to treat the 2D problem, alternating the solution of 1D problems. © 1992.