Discrete shear Alfvén modes such as the TAE (toroidal Alfvén eigenmode) are susceptible to destabilization by energetic alpha populations and neutral beams; this can lead to enhanced fast ion losses and degraded heating efficiencies. A gyrofluid model with Landau closure has been developed for understanding both the linear and nonlinear phases of these instabilities. The linear wave–particle resonances necessary to excite Alfvén instabilities are included in a coupled set of fluid equations. This model is used to analyze several nonlinear saturation mechanisms that arise from mode coupling effects. The effects of shear flow velocity generation (through the Reynolds stress) and localized current generation (leading to modifications in the q profile) are specifically examined.

The toroidicity-induced shear Alfvén eigenmode (TAE) can be destabilized by energetic particle populations through inverse Landau damping. It may also be significantly damped by coupling with adjacent shear Alfvén continua. A gyrofluid model with Landau closure that includes both of these effects is developed and applied to this instability. The model consists of the usual reduced magnetohydrodynamic (MHD) equations for the evolution of the poloidal flux and toroidal component of vorticity, coupled with equations for the density and parallel velocity moments of the energetic species. The latter two equations include Landau damping/growth effects through use of a consistent closure relation, which is equivalent to a two-pole approximation to the plasma dispersion function. These equations are solved numerically using a three-dimensional initial value code (tae/fl) in toroidal geometry. The unstable TAE growth rate and continuum damping rates are compared with recent analytical estimates, and reasonable agreement is obtained.

A simple neoclassical point model is presented for the ELMO Bump¥ Torus experiment. Solutions for steady state are derived. Comparison with experimental observations is made and reasonable agreement is obtained. * Work supported by Energy Research and Development Administration under Contract W-7405-eng-26 with Union Carbide Corporation, Contract EY-76-C-03-0167, Project 38 with General Atomic Company, and Contr~ct AT-04-3-1018 with Science Applications, Incorporat~d.

Closure relations are developed to allow approximate treatment of Landau damping and growth using fluid equations for both electrostatic and electromagnetic modes. The coefficients in these closure relations are related to approximations of the plasma dispersion function by ratios of polynomials. Thirteen different numerical sets of coefficients are given and explicitly related to previous fits to the plasma dispersion function. The application of the techniques presented in this paper is illustrated with the specific example of resistive g modes. Comparisons of full kinetic and approximate results are made for the solutions to the dispersion relation, radially resolved modes in sheared magnetic geometry, and the plasma dispersion function itself.

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...