D. E. Hastings

THE AMBIPOLAR ELECTRIC FIELD IN STELLARATORS

In a three-dimensional device like a stellarator, the ambipolar electric field must be determined self-consistently from the ambipolarity constraint and can have a significant effect on transport through the diffusion coefficients. A differential formulation and an algebraic formulation for the electric field are solved, together with the density and temperature equations. The results are compared, and in both cases multiple electric field solutions can exist, with bifurcations occurring between different solutions. It is shown that heating of the electrons encourages bifurcation to the more favourable positive electric field root.

A differential equation for the ambipolar electric field in a multiple‐helicity torsatron

In a torsatron, the ambipolar electric field is obtained by equating the ion and electron fluxes. This formulation, when solved simultaneously with the density and temperature rate equations, gives continuous electric fields but may lead to the radial derivative of the electric field being discontinuous. This unphysical situation arises from the neglect of the finite orbit deviation from the flux surfaces. If the fluxes are calculated to higher order in inverse aspect ratio to include the finite orbit deviation, then a second‐order differential equation is obtained that will give a continuous first derivative for the electric field.

Effects of trapped alpha particles on ballooning modes in tokamaks

The effects of a trapped, precessing alpha particle population on ballooning modes are examined for a large aspect ratio, shifted circular flux surface tokamak equilibrium. The alphas are modeled in the deeply trapped limit and with a Maxwellian distribution in energy. The resulting kinetic ballooning equation is solved numerically, and the dependence of the eigenvalues and stability boundaries on shear, background pressure gradient, and ratio of hot‐to‐background tempera‐ tures (and densities) is investigated. In the low‐frequency regime (ω ≪ ωdH =alpha precessional drift frequency), the alpha component has a stabilizing influence, while in the intermediate frequency range (ω≲ωdH) the alphas destabilize ballooning modes through interaction with the trapped particle precessional drift resonance. Parameter ranges which should be typical of alpha production in near term tokamak devices such as the Tokamak Fusion Test Reactor (TFTR) [Phys. Rev. Lett. 52, 1492 (1984)] are considered.

Superbanana plateau regime transport in a multiple-helicity torsatron and a bumpy torus

An analytic expression for the neoclassical flux valid in both a multiple‐helicity torsatron and a bumpy torus in the superbanana plateau regime is obtained. The expression is valid for arbitrary values of Φ’, the radial electric field, ∂eH/∂r with eH the effective helical modulation or bumpiness, and ∂eT/∂r with eT the effective toroidal modulation. When small mirror force terms are included in the flux, a nonlinear first‐order ordinary differential equation in Φ’ is obtained from the ambipolarity relationship.

Neoclassical transport associated with collisionless detrapping in a bumpy torus

In the low‐collisionality nonresonant regime in a bumpy torus the transitional particles can make a large contribution to neoclassical transport. This contribution can be moderated by the toroidally induced radial drift which causes transitional particles to detrap and retrap in the mirror sectors. This effect leads to diffusion coefficients which are linear in the collision frequency and scale with the inverse aspect ratio instead of the more usual square of the inverse aspect ratio.

Ambipolarons: solitary wave solutions for the radial electric field in a plasma

The ambipolar radial electric field in a nonaxisymmetric plasma can be described by a nonlinear diffusion equation. This equation is shown to possess solitary wave solutions. A model nonlinear diffusion equation with a cubic nonlinearity is studied. An explicit analytic step‐like form for the solitary wave is found. It is shown that the solitary wave solutions are linearly stable against all but translational perturbations. Collisions of these solitary waves are studied and three possible final states are found: two diverging solitary waves, two stationary solitary waves, or two converging solitary waves leading to annihilation.

Electron transport in the ELMO bumpy torus in the low collision frequency limit

The electron neoclassical transport coefficients are calculated in a bumpy torus for the low collisionality regime. The electron radial drift is calculated as a function of the plasma position, as well as the poloidal electric field, which is determined self‐consistently. A bounce‐averaged differential collisional operator is used and the results are compared to previous treatments using a BGK operator.

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.

Bifurcation phenomena and the radial electric field in a nonaxisymmetric plasma

The radial electric field in a nonaxisymmetric plasma is known to be a multivalued function of the plasma state. It is shown that the theorem of minimum entropy production rate cannot be used to distinguish between different electric field solutions. The possibility of bifurcation phenomena in the coupled electric field, density, and temperature equations are examined. It is shown that the functional dependence of the plasma source can strongly influence the type of bifurcation that can occur.

Transport studies of ECH-heated bumpy torus plasmas in the Elmo Bumpy Torus (EBT) and in the Nagoya Bumpy Torus (NBT)

A model of the measured potential profile for ECH-heated plasmas in EBT/NBT is used in the radial-transport equations for bumpy tori. The particle and energy confinement times are predicted along with the ECH power, the ion temperature and the neutral density necessary for a steady state to be maintained in these machines.