J. S. Tolliver

Bootstrap current control in stellarators

The poloidal coil system of a stellarator can be used to modify the ‖B‖ spectrum and, as a consequence, change the magnitude of the bootstrap current. The addition of a small l=1 field component to a stellarator field can cancel or reverse the direction of the bootstrap current. It is shown that currentless operation in the collisionless regime is not impaired by bootstrap current, because the effects of bootstrap current can be eliminated by an appropriate external coil system. The advanced toroidal facility (ATF) [Fusion Technol. 10, 179 (1986)] can be used to test some of these results.

Orbits in asymmetric toroidal magnetic fields

Orbits in an asymmetric toroidal magnetic field are studied for the case in which the local variation of the field strength due to ripple is rapid compared with that due to toroidicity. In this case, to lowest order the poloidal variables are constant and particles move primarily in the toroidal direction. Invariants and averaged equations of motion for the locally passing and locally trapped particles are derived based on this approximation. The equations imply that transitions between the locally trapped and locally passing states occur. The probabilities for these transitions are calculated.

Bootstrap current and parallel viscosity in the low collisionality regime in toroidal plasmas

Bootstrap currents in the low collisionality regime in nonaxisymmetric toroidal plasmas are calculated analytically using a model drift kinetic equation. The results obtained using the analytic expression are compared with those calculated from the numerical solutions of the drift kinetic equation. Qualitatively and quantitively, the results are in reasonable agreement.

Parallel viscosity‐driven neoclassical fluxes in the banana regime in nonsymmetric toroidal plasmas

Analytic expressions for the parallel viscosity‐driven neoclassical fluxes in the banana regime in arbitrary nonsymmetric toroidal plasmas are derived without considering boundary layer effects. They can be evaluated numerically if the Fourier decomposition of the strength of the magnetic field ‖B‖ is known. Since no averaging over the high‐frequency component of the Fourier decomposition of ‖B‖ has been employed, these expressions can reproduce all the known results in symmetric systems and predict the possibility of reversing the direction of the bootstrap current and Ware pinch flux in a stellarator.

Recent results from the ATF torsatron

Recent experiments in the Advanced Toroidal Facility (ATF) torsatron [Plasma Physics and Controlled Nuclear Fusion Research 1990 (IAEA, Vienna, in press)] have emphasized the role of magnetic configuration control in transport studies. Long‐pulse plasma operation up to 20 sec has been achieved with electron cyclotron heating (ECH). With neutral beam injection (NBI) power of ≥1 MW, global energy confinement times of 30 msec have been obtained with line‐average densities up to 1.3×1020 m−3. The energy confinement and the operational space in ATF are roughly the same as those in tokamaks of similar size and field. The empirical scaling observed is similar to gyro‐reduced Bohm scaling with favorable dependences on density and field offsetting an unfavorable power dependence. The toroidal current measured during ECH is identified as the bootstrap current. The observed currents agree well with predictions of neoclassical theory in magnitude and in parametric dependence. Variations of the magnetic configuration ...

Bounce‐averaged Monte Carlo energy and pitch angle scattering operators

Beginning with a linearized Coulomb collision operator, the derivations of bounce‐averaged energy and pitch angle scattering terms that have been suitably discretized for Monte Carlo use are described. The derivation assumes that the electrostatic potential is constant along a magnetic field line. The collision operators are applied to electron transport in ELMO Bumpy Torus.

Resonant ion transport in the ELMO Bumpy Torus

Modeling the ELMO Bumpy Torus as a bumpy cylinder with toroidally induced vertical drift, neoclassical transport coefficients are obtained for resonant ions as integrals over the energy‐dependent flux. A continuous approximation to this energy‐dependent flux reduces to the correct results in the banana and plateau regimes and yields simple analytic formulas for the diffusion coefficients which agree well with numerical results.

Monte Carlo estimates of particle and energy confinement times in a bumpy torus and a bumpy square with poloidal electric fields

Since significant poloidal structure in the electrostatic potential in Elmo Bumpy Torus (EBT) has been observed experimentally [Phys. Fluids 2 8, 2848 (1985)] and predicted theoretically (C. L. Hedrick, submitted to Phys. Fluids), a Monte Carlo calculation has been used to make estimates of the particle and energy confinement times in EBT with varying degrees of asymmetry in the electric field. The code is applicable to the bulk ion population and the ‘‘cool’’ electron population in EBT, but not to the intermediate‐energy electrons believed to be responsible for the formation of the potential. A similar calculation is possible for an alternate magnetic field configuration known as a bumpy square, which is expected to have more symmetric potential profiles because of much better centering of the particle orbits. The calculations indicate that the confinement time in a bumpy square would be two to three orders of magnitude better than in EBT.

The poloidal potential in the low-collisionality regime in a nonaxisymmetric torus

The poloidal potential is calculated numerically in the low‐collisionality regime for nonaxisymmetric tori such as stellarators and bumpy tori. It is found that even fairly deep into the superbanana regime, the poloidal potential retains the simple azimuthal dependence of the plateau regime.

Nonresonant ELMO Bumpy Torus transport coefficients in the small electric field regime

A conservative BGK collision operator is used to obtain nonresonant neoclassical transport coefficients for a bumpy torus when the ∇B drift dominates over the E×B drift. Previous nonresonant coefficients have considered the opposite limit. For large collisionalities, the diffusion coefficients are only weakly dependent on the E×B drift, while for small collisionalities, plateau diffusion coefficients are obtained which have an exponential dependence on the E×B drift.