Verlag des Forschungszentrums Jülich

JUEL-3958
Nicolai, Albert
Numerical and analytical interpretation of rotation and radial electric fields in collision dominated edge plasmas
86 S., 2002



The ambipolarity constraint and the parallel momentum balance equation of neoclassical theory, accounting for finite Larmor radius effects and inertia, allow to describe the radial electric field and the related spin up in collision dominated edge - plamas with steep gradients. Thus they may contribute significantly to the understanding of the L-H transition.
The variation of the toroidal velocity from the last closed magnetic surface up to a position r within the plasma is predicted to be proportional to the integral of the product u_ΘαlnT⁄αr i.e., to ∑d[T_i´²⁄T_i]L_d, if the interaction with the neutral gas can be neglected. The summation is over different radial domains, such as the edge pedestal. L_d is the radial extension of the respective domain. The dimensionless parameter Λ = viq²R²⁄ΩirLTi = viaip⁄L_Ti [where vi = qRvi⁄ci > 0.22 is the relevant collision parameter and aip the poloidal ion Larmor radius] characterizes the ratio of the diamagnetic rotation frequency to the heat diffusion rate along magnetic field lines. Conventional neoclassical theory assumes Λ → 0. However, e. g. in ALCATOR C-MOD ohmic H-mode pedestals, Λ is sufficiently large that conventional neoclassical results are invalid: it follows from the neoclassical theory that the poloidal velocity decreases below the standard prediction V_neo = -1.83Ti⁄eB as Λ² increases and changes sign for Λ² = Λ²0 (typically ≈ 1-2).
The equations are treated analytically using a linear interpolation for the poloidal velocity, vΘ(Λ²), based on vΘ(Λ²0) = 0 and on the neoclassical value Vneo for small Λ. This allows to account for finite Λ effects in the just mentioned integration.
The equations are also solved numerically (1) to benchmark with a simplified analytical theory with Λ=O and vanishing neutral gas density; (2) to compare with the analytical theory accounting for finite A effects and (3) to explore the parameter space in regions where the analytical theory is not valid, in particular in the cases where the neutral gas density is larger than 10¹⁴m^-3.
The method resorts to an ODE - solver for the classical momentum balance which is combined with a solver for transcendental equations yielding VΘ.
The results concern the comparison with the analytical solution and the experimental results ofthe ohmically heated ALCATOR plasma. For Λ = 0 the numerical solution and the analytical one agree exactly. For finite Λ ≈ 1 the deviations are surprisingly small. The toroidal spin up of the ALCATOR plasma, characterized by a very short decay length Lv = 0.76 cm, is ≈ 40 km⁄sec. This compares well the measured value of 35 km⁄sec .The radial electric field profile assumes the characteristic shape and absolute values reported by the DIII-D Group.

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