J.A. Rome

The Topology of Tokamak Orbits

Guiding-centre orbits in non-circular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, ζ, ψm. Here, v is the particle speed, ζ is the pitch angle with respect to the parallel equilibrium current, J||, at the point in the orbit where ψ = ψm, and ψm is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding-centre orbit. Two D-shaped equilibria in a flux-conserving tokamak having values of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point, and different types of orbit (e.g. circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher- (7.7%) equilibrium results in an orbit topology dramatically different from that of the lower- case. The differences indicate the confinement of additional high-energy (v → c, within the guiding-centre approximation), trapped, co- and counter-circulating particles, with an orbit ψm falling within the absolute B-well.

Monte Carlo studies of transport in stellarators

Transport is studied in toroidal geometry by integrating the guiding‐center equations in magnetic coordinates and simulating collisions with a Monte Carlo collision operator. The effects of the ambipolar electric field on diffusion losses are determined for model magnetic fields and the correct magnetic field of the Advanced Toroidal Facility (ATF‐1) stellarator. Comparisons are made of the computed diffusion coefficients and the theoretically predicted values.

Progress in stellarator/heliotron research: 1981?1986

Substantial progress was made during the period 1981-1986 in plasma parameters, physics understanding, and improvement of the stellarator/heliotron concept. Recent advances include (1) substantial achievements in higher plasma parameters and currentless plasma operation, (2) new theoretical results with respect to higher beta limits, second stability region, effect of a helical axis, effect of electric fields on transport, and reduction of secondary currents; and (3) improvements to the reactor concept. The key issues have been further refined, and the short-term direction of the program is clear; a number of new facilities that were designed to resolve these issues are about to come into operation or are in the final design stages. This report summarizes these advances.

Neutral-beam injection into a tokamak. Part I. Fast-ion spatial distribution for tangential injection

The production processes and spatial distribution of fast ions resulting from tangential injection of a diffuse neutral beam into a tokamak are discussed. The spatial distribution of fast ions for various injection trajectories and absorption mean free paths are calculated and discussed in detail. Maximum beam absorption for a parabolic density profile is shown to occur for injection roughly halfway between the inner wall of the torus and the magnetic axis; however, since this maximum is near unity and only weakly dependent on the injection trajectory, this is not the most important possible optimization. Since the drift orbit surface area over which the fast ions are distributed is roughly proportional to the distance from the magnetic axis, the fast ion density is found to be strongly peaked at the magnetic axis for present experiments where the absorption mean free path λ is comparable to the plasma radius a. This geometric peaking effect is strong enough to overcome the exponential beam attenuation and cause the fast-ion density and consequent beam energy deposition to be peaked at the plasma centre as long as λ0 a/4. Charge exchange of the fast ions with neutrals in the plasma can deplete the fast-ion population, particularly near the plasma edge. When charge exchange is an important loss mechanism, beam injection nearly tangent to the magnetic axis is found to maximize the beam effectiveness in heating.

Numerical evaluation of magnetic coordinates for particle transport studies in asymmetric plasmas

A numerical procedure is described for the evaluation of magnetic coordinates given a toroidal, scalar pressure plasma with an arbitrary magnetic field. The accurate representation of magnetic field strength in this way is invaluable for the calculation of drift orbits and transport in asymmetric plasmas.

Results of hydrogen pellet injection into ISX-B

High speed pellet fueling experiments have been performed on the ISX-B device in a new regime characterized by large global density rise in both ohmic and neutral beam heated discharges. Hydrogen pellets of 1 mm in diameter were injected in the plasma midplane at velocities exceeding 1 km/s. In low temperature ohmic discharges, pellets penetrate beyond the magnetic axis, and in such cases a sharp decrease in ablation is observed as the pellet passes the plasma center. Density increases of approx. 300% have been observed without degrading plasma stability or confinement. Energy confinement time increases in agreement with the empirical scaling tau/sub E/ approx. n/sub e/ and central ion temperature increases as a result of improved ion-electron coupling. Laser-Thomson scattering and radiometer measurements indicate that the pellet interaction with the plasma is adiabatic. Penetration to r/a approx. 0.15 is optimal, in which case large amplitude sawtooth oscillations are observed and the density remains elevated. Gross plasma stability is dependent roughly on the amount of pellet penetration and can be correlated with the expected temporal evolution of the current density profile.

Neutral beam injection benchmark studies for stellarators/heliotrons

Neutral beam injection in stellarators/heliotrons is studied with Monte Carlo codes that treat the initial beam deposition and the fast-ion thermalization process. The birth deposition model carefully treats the geometry of the vacuum vessel and includes beam divergence, focusing, and aperture losses. The thermalization process is determined by integrating the guiding centre equations of the fast ions and simulating collisions with the plasma by Monte Carlo collision operators. This process may include charge exchange and neutral reabsorption. For the purposes of this benchmark, we review the different formulations of the guiding centre equations and the Monte Carlo collision operators. We studied perpendicular injection into Heliotron-E, which is located at the Plasma Physics Laboratory at Kyoto University. The magnetic fields of Heliotron-E are computed using the Biot-Savart law with realistic filament models. The sensitivity of the computed heating efficiency to the modelling of the particle loss boundary and to the numerical procedures is examined. The results of three different codes were compared. When the codes solve the same problem, the answers agree quite well. However, changing some of the modelling assumptions (such as the loss boundary location) can create significant differences in the results.

The calculation of stellarator equilibria in vacuum flux surface coordinates

Abstract Details are given of a three-dimensional stellarator equilibrium code NEAR. This code uses a set of vacuum flux coordinates as a Eulerian grid for the equilibrium calculations. This coordinate system provides an economic representation of the complex geometry associated with stellarators. The equilibrium equations are solved by an energy minimization technique employing a conjugate gradient iteration scheme. The results of extensive numerical convergence studies are presented. Also comparisons with existing codes are made to benchmark the NEAR code.

Orbit topology in conventional stellarators in the presence of electric fields

Orbits are considered in conventional stellarators (i.e. with helical coils) using Boozer co-ordinates. The Advanced Toroidal Facility (ATF) in Oak Ridge, Tennessee, will be used as an example to study the effects of its configurational flexibility on orbit topology. It is shown that the symplectic integration technique yields superior results for single particle orbits. These orbits will be compared with predictions using the J* invariant. J* conservation allows examination and understanding of the global stellarator topology, both with and without radial electric fields

Realization of the Advanced Toroidal Facility Torsatron Magnetic Field

AbstractThe Advanced Toroidal Facility is a large torsatron device with a major radius R0 = 2.1 m, an average plasma minor radius a ≈ 0.3 m, and a magnetic field B0 ≤ 2T. The sheared magnetic configuration [τ(0) ≈ 0.3, τ(a) ≈ 1] is produced by an l = 2, M = 12 field period helical winding set and associated circular vertical field coils. The segmented helical windings were constructed with a tolerance of ±1-mm deviation from the ideal winding law using computer-aided manufacturing and assembly techniques. Nevertheless, in the initial operating period, it was found that field errors produced significant magnetic islands (island width ≈6 cm at τ = ½), which reduced the effective plasma radius by ∼30%. The main cause of these islands was the toroidally asymmetric field perturbation produced by the geometry of the electrical coil feeds. After “symmetrization” of the buswork, the dominant magnetic islands were reduced in size to ≤1 cm at the operating field of 1 T.