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An overview of recent AFT (Advanced Toroidal Facility) experimental results and program plans is presented, with emphasis on the role of magnetic configuration controls in transport studies. The ATF operating space is bounded by a density limit that effectively sets a limit on the energy confinement time tau /sub E/. Although this limit is not solely due to impurities, it has recently been raised by improved cleanliness following titanium gettering. This has led to collapse-free neutral beam injection discharges with global tau /sub E/ approximately=16 ms. Preliminary experiments show that stored energy and bootstrap current are sensitive to details of the magnetic configuration. >

Plasmas in the Advanced Toroidal Facility (ATF), an l = 2 torsatron with 12 field periods, are produced by 200–400 kW of electron cyclotron heating (ECH) and up to 1.5 MW of neutral-beam injection (NBI). The characteristics of the plasmas are sensitive to the type of wall conditioning employed. A progression of techniques, beginning with glow discharge cleaning and baking and evolving to gettering with chromium and titanium, has significantly reduced the low-Z impurity content, lowered the fraction of radiated power, and permitted improved control over the electron density. As a result, plasma-parameters and machine performance have been enhanced significantly. The maximum values achieved for stored energy, line-averaged density, and confinement times are 28 kJ, 1.2 × 1020m−3, and 25 ms. These parameters are comparable to those obtained in the ISX-B tokamak. In addition, with titanium gettering, quasisteady operation for 200 ms of neutral beam injection has been obtained without the collapses that characterized earlier periods of operation.

Experiments involving plasma improvement, confinement scaling, bootstrap currents, and edge fluctuations have been carried out in the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)]. Average densities ne≤9×1019 m−3 have been obtained, with global energy confinement times τ*E≤20 msec. Confinement times generally follow the stellarator/torsatron empirical scaling law, τSL =0.17×P−0.58n0.69eB0.84a2R0.75 (with τSL in seconds, power P in megawatts, density ne in 1020 m−3, and plasma radius a and major radius R in meters). Gas injection during neutral beam injection (NBI) causes increases in ne, so that τ*E does not decrease during NBI. Edge plasma fluctuations are found to exhibit a mode change near the peak of the energy confinement time. Plasma currents observed during electron cyclotron heating have been identified as bootstrap currents.

Measurements of the effective charge Z{sub eff} in plasmas with electron cyclotron heating (ECH) and neutral beam injection (NBI) in the Advanced Toroidal Facility (ATF) have been carried out using visible bremsstrahlung. The electron temperature needed for the analysis is calculated from the measured stored energy and electron density. The value of Z{sub eff} varies widely depending on experimental conditions. In ECH plasmas it is between 2 and 8. In NBI plasmas, which are subject to radiation collapse, Z{sub eff} is between 3 and 5 at the time the stored energy reaches a maximum. However, Z{sub eff} is less than 2.5 in quasi-steady medium-density plasmas and is close to 1.2 in the highest-density plasmas, where the average electron density {bar n}{sub e} is of the order of 10{sup 14} cm{sup {minus}3}. 12 refs., 29 figs., 1 tab.

An overview of recent experimental results from the Advanced Toroidal Facility (ATF) is presented. Beam-heated plasmas with {bar n}{sub e} of 10{sup 20} m{sup {minus}3} and {tau}{sub E}{asterisk} of {approx}20 ms have been achieved. Thermal collapse of the plasmas is mitigated by wall conditioning and particle fueling. Confinement time scales positively with density and magnetic field, offsetting deterioration with power. Results fit the LHD scaling and the drift wave turbulence scaling. Bootstrap currents observed during ECH agree with neoclassical theory in magnitude and parameter dependences. Fast reciprocating Langmuir probe measurements show that edge fluctuations in ATF have many similarities to those in the TEXT tokamak. The location of {tilde B} instabilities has shifted outward in radius, consistent with the broader pressure profiles. 14 refs., 6 figs.

A variational principle is developed for computing accurate values of local plasma transport coefficients in nonsymmetric toroidal confinement configurations. Numerical solutions of the linearized drift Fokker–Planck equation are used to obtain the thermodynamic fluxes as functions of collision frequency and the radial electric field. Effects resulting from the variation of the longitudinal adiabatic invariant J along an orbit (resulting from particle transitions from helically trapped to toroidally trapped orbits) are treated. The velocity‐space distribution resulting from trapped, circulating, and transition particle orbits is well represented by a Legendre polynomial expansion in the pitch angle coordinate. The computational effort is significantly reduced from that required with Monte Carlo methods through use of an efficient treatment of the disparity between the time scales of collisionless and collisional particle dynamics. Numerical computations for a stellarator configuration are presented.

Stellarator transport scalings with electric field, geometry, and collision frequency in the reactor‐relevant collisionless‐detrapping regime are determined from numerical solutions of the drift kinetic equation. A new geometrical scaling, proportional to e3/2t rather than ete1/2h, is found, where et is the inverse aspect ratio and eh is the helical ripple. With the new scaling, no reduction in energy confinement time is associated with large helical ripple, which provides design flexibility. Integral expressions for the particle and heat fluxes that are useful for transport simulations are given.

Stimulated by the necessity of numerically integrating the one-dimensional, first-order, magnetic-flux-surface-averaged particle continuity equation to study impurity transport in tokamaks, we have investigated how to obtain estimates of functions and their first derivatives correct to second order in the grid spacing for arbitrary grids. Using integral-averaged values with arbitrary weight functions, we readily find two-term linear approximations to the functions that satisfy the accuracy criterion. However, in the case of two-term linear approximations to the first derivative, we find that the grid partition must satisfy a nodal equation to obtain the desired accuracy. When the entire grid cannot be set up to satisfy the nodal equation, transitions involving three-term linear approximations to the derivative are required. We also determine the point between two grid points at which the integral-averaged function value can be identified with the function evaluated at that point. Finally, we give examples of grid selection for two different weight functions: w = 1 and w = r.

A recent review article by Hirshman and Sigmar includes expressions needed to calculate the parallel friction coefficients, the essential ingredients of the plateau-Pfirsch-Schluter transport coefficients, using the method of reduced charge states. These expressions have been collected and an expanded notation introduced in some cases to facilitate differentiation between reduced charge state and full charge state quantities. A form of the Coulomb logarithm relevant to the method of reduced charge states is introduced. This method of calculating the f/sub ij//sup ab/ has been implemented in the impurity transport simulation code IMPTAR and has resulted in an overall reduction in computation time of approximately 25% for a typical simulation of impurity transport in the Impurity Study Experiment (ISX-B). Results obtained using this treatment are almost identical to those obtained using an earlier approximate theory of Hirshman.

To simulate multispecies impurity transport in tokamaks, a set of coupled continuity equations including source and sink terms from atomic processes (rate terms) were solved numerically. The diffusion and rate terms are integrated separately in time using a fractional step-splitting technique which is accurate to second order in the time step. Calculations were performed treating individually all the ionization stages of oxygen and iron impurities in a hydrogen plasma. Calculated O VI and O VII relative density profiles agree qualitatively with profiles measured in the Adiabatic Toroidal Compressor (ATC) tokamak when purely neoclassical diffusion coefficients are used.