Parametric dependences of impurity transport in neoclassical, reactive drift wave and gyrokinetic descriptions
msra(2007)
摘要
Impurity transport in tokamaks is studied using an electrostatic fluid model for main ion and impurity temperature gradient (ITG) mode and trapped electron (TE) mode driven turbulence and the results are compared with nonlinear gyrokinetic simulations using GYRO and neoclas- sical theory. Transport scalings with magnetic shear and impurity fraction are investigated, and the validity of the trace impurity approximation is studied . Comparisons between anomalous and neoclassical transport predictions are performed for I TER-like profiles based on ASTRA modelling. Reactive drift wave model The reactive drift wave model is based on the solution of a set of fluid equations for the pertur- bations in density, parallel velocity and pressure for ions, impurities and trapped electrons (1) in the collisionless, electrostatic limit. The closure of the equations is obtained by assuming that the heat flux is equal to the diamagnetic heat flux for all parti cle species. For the trapped electron model, the electron magnetic drift is, after the bounce aver aging, replaced by the precession fre- quency of trapped electrons as h ωDei = ωDeλt with λt = 1= 4+ 2s= 3 (2), where s = (r= q)dq= dr and q is the safety factor. We assume adiabatic free electrons and the quasi-linear particle fluxes are computed from Γn j = δ n jvE j ® , which is summed over all unstable modes for a fixed space scale of the turbulence, with (krρs)2 = (kθ ρs)2 = 0:1, where r and θ are radial and poloidal co- ordinates, ρs = cs= Ωci, cs = p Te= mi is the sound speed and Ωci is the cyclotron frequency. The eigenvalue equation is reduced to a set of algebraic equations using the semilocal analysis of (3) where the norms h k2 k i ;h k 2 ⊥i ;h ωDi;zi , with h¢ ¢ ¢ i = R π −π φ(¢ ¢ ¢ )φ dθ , are calculated using a strongly ballooning eigenfunction. The solution of the eigenvalue problem gives the eigenvalues and the perturbations in density, temperature and parallel veloci ty in terms of the perturbed electrostatic potential. The saturation level of the electrostatic poten tial is estimated by balancing the lin- ear growth with the dominant convective nonlinearity in the energy and continuity equations. The strong ballooning approximation has recently been shown to give results in good agree- ment with the results of calculations based on a shear-dependent eigenfunction with general
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