Neoclassical Transportation in the ELMO Bumpy Torus

Abstract

In the ELMO bumpy torus, neoclassical transport coefficients depend critically on the ambipolar electric field. These coefficients, calculated for arbitrary radial electric fields, are applied in a one-dimensional radial-transport calculation which, for the first time, treats the electric field self-consistently. This purely classical model predicts many features of experimental operation including a steady-state solutions with radially inward-pointing ambipolar fields.There have been many investigations 1 * 2 of radial transport in axially symmetric toroidal magnetic traps such as tokamaks where lowest-order neoclassical transport is independent of radial electric fields. For axially asymmetric systems such as the bumpy torus, neoclassical transport depends sensitively on the ambipolar field, and radially resolved calculations including self-consistent ambipolar electric fields have not previously been attempted. Here we calculate neoclassical transport coefficients for the ELMO bumpy torus 3 (EBT) for arbitrary radial electric fields, and we apply these coefficients in a one-dimensional radial-transport model which includes the ambipolar field self-consistently. Previous neoclassical calculations for bumpy tori have treated only the large-electricfield limit 4 and transport in zero dimensions. 5 Self-consistent, one-dimensional calculations are necessary to predict transport scaling and stability limitations for large fusion-grade systems.To model EBT realistically, we calculate transport coefficients without using Kovrizhnykh's 4 simplifying assumption that poloidal drifts due to electric fields dominate those due to magnetic field gradients. We use the drift kinetic equation 6 in bounce-averaged form, where (> denotes a bounce average, / is the distribution of guiding centers, v d is the guiding center velocity, C f is the collision operator, m is the mass, e is the charge, E is the electric field, and v ± and v n are velocity components perpendicular and parallel to the magnetic field B, respectively. Assuming a purely radial electric field with no poloidal component, we separate/ into an equilibrium Maxwellian part and a firstorder perturbation f x which is Fourier analyzed in the poloidal angle 9 a,sf 1 = Re(f 1 e ie ).A vari-ety of collision operators has been used in Eq.(1) including the complete Fokker-Planck operator 7 and the simpler Krook models. 8 Here, we use the particle-and energy-conserving Krook model. In this case moments of Eq. (1) reduce to algebraic equations for integrals required in computing the neoclassical fluxes. This simple solution provides good agreement with results of Spong etal. 9 where the detailed kinetic theory is displayed for the complete Fokker-Planck operator. Our treatment of particle orbits and the 9 dependence of f x implicitly assumes sufficiently collisional behavior that banana-shaped orbits (occurring in regions where Ex B and gradjB drifts cancel) do not dominate diffusion. Such an approximation is appropriate to the collisionality of the present experiment 3 [v/S...

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