We present a new algorithm for interpolation of static current-free magnetic fields based on the use of specialized fourth-degree vector polynomial functions (Maxwell elements) which solve the static current-free Maxwell equations. This method provides sufficient accuracy for the demands of stellarator applications and retains a great speed advantage over direct Biot-Savart calculation of the fields.

Recent results are summarized for the Helically Symmetric Experiment (HSX), which has the capability of running as a quasi-helically symmetric stellarator or as a more conventional, nonsymmetric stellarator. From X-ray measurements, we have demonstrated improved confinement of energetic particles. With central electron cyclotron heating, the density profiles in the quasi-symmetric configuration are peaked, in contrast to the hollow or flat profiles when the symmetry is broken. The difference in profiles is attributed to the lowering of the neoclassical thermodiffusive flux when the symmetry is present. The central electron temperature is similar to 200 eV higher for the quasi-symmetric configuration over the nonsymmetric case. The power deposition profiles are similar for the two cases, implying that the neoclassical electron thermal conductivity is reduced with quasi-symmetry. Related to the good confinement characteristics in the quasi-symmetric mode of operation, fluctuations in the density and magnetic field, consistent with that of a global Alfven eigenmode (GAE), are observed. While the neoclassical characteristics of the quasi-symmetric and nonsymmetric configurations are very different, we have yet to find, under present operating conditions, any significant difference (other than the possible GAE mode) in turbulence characteristics or blob formation at the plasma edge.

Following experimental demonstration of Alfvén Wave Current Drive (AWCD) on the Phaedrus‐T tokamak a redesigned high power antenna has been installed that couples 0.5 MW to the plasma. Evidence is shown for core electron heating coexisting with AWCD. There was no observable increase in the AWCD efficiency during these heating experiments, although the spread in kz launch made it difficult to determine if the ratio of wave phase speed to electron thermal speed was actually reduced and whether any decrease in efficiency due to changes in the electron trapping fraction occurred. Scans of toroidal magnetic field show systematic changes in the time dependence of the drop in loop voltage during the RF pulse. Reflectometer data indicates two radial locations for RF fluctuations.

The first experimental evidence of Alfvén Wave Current Drive (AWCD) in a tokamak is shown. In a low-density experiment, an estimated 20–35 kA out of 65 kA total current, or 30%–55% of the total current has been driven. The estimated efficiency for current driven per unit RF input power is approximately ICD/PRF≊0.2 A/W, which is near the predicted efficiency, and corresponds to the commonly used figure of merit, neR0ICD/PRF≊0.4×1018 A m−2 W−1, where ne is plasma density and R0 is the major radius. The significant 30%–40% drop in loop voltage observed cannot be explained by any plausible increase in electron temperature Te, or decrease in inductive plasma energy, or changes in plasma resistivity. Independently measured loop voltage, Te, effective ionic charge Zeff, and plasma inductance and resistance are all consistent with this conclusion.

Summary form only given. The first experimental evidence of low frequency current drive in a tokamak has been observed on the Phaedrus-T tokamak (R/sub major/=0.92 m, r/sub minor/=0.255 m, B/sub T//spl ap/0.6-1 T, I/sub p/<100 kA, n/sub e0/=0.2-1.5/spl times/10/sup 19/ m/sup -3/). Low frequency current drive utilizes waves with frequencies below the ion cyclotron frequency to inject momentum to electrons to drive a toroidal current, and is often referred to as Alfven wave current drive (AWCD). Like other noninductive current drive techniques, AWCD would allow fusion tokamak reactors to operate as steady state devices. AWCD would also allow tailoring of the energy and current density profiles. Properly modified profiles would make the plasma less susceptible to instabilities. The presence of noninductive current is inferred from the behavior of the plasma loop voltage measured at the edge of the plasma The loop voltage can be roughly related to the sum of the ohmic dissipation, product of plasma current and resistance, and the time rate of change in the stored magnetic energy of the plasma during a plasma discharge, the plasma current is kept constant through automatic feedback control and is produced by pulsed magnetic induction. Therefore, the loop voltage can decrease if there is a decrease in plasma resistance, a change in stored magnetic energy, or a noninductive current source is present.

In the course of our Alfven wave heating and current drive experiments several different two and four strap antennas have been installed in Phaedrus‐T. The motivation focusing the redesign of the antenna into a four strap design was to enable traveling wave phasing, and to reduce the k∥≊0 component of the wavenumber spectrum, and consequent edge power deposition. The latest modifications to the 4 strap antenna have dramatically improved its behavior, and enabled us to suppress its RF power induced impurity generation. The remaining gas reflux fueling is significant and is not local to the antenna.

Summary form only given. Measurements of the Phaedrus-T edge plasma parameters have been made with triple probe, swept Langmuir probes, swept emissive probes, self-emissive probes, reciprocating probes, capacitive probes, and shadowed probes of various sizes and materials. ICRF current drive studies are the focus of the Phaedrus-T program; and, consequently, most Phaedrus-T probe measurements have been of ICRF/edge plasma interactions. Data have been obtained that show strong ICRF modifications of edge plasmas when an antenna with a conventional, stainless steel Faraday shield was used; greatly reduced ICRF/edge coupling when boron nitride side limiters were placed on the Faraday shield; and no significant change in the ICRF/edge coupling when the Faraday shield was later removed (even though there was a significant reduction in plasma impurities).

Heating in the Alfvén resonant regime has been demonstrated in the Phaedrus-T tokamak [Fusion Technol. 19, 1327 (1991)]. Electron heating during injection of radio-frequency (rf) power is indicated by a 30%–40% drop in loop voltage and modifications in sawtooth activity. Heating was observed at a frequency ωrf≊0.7Ωi on axis, using a two-strap fast wave antenna operated at 7 and 9.2 MHz with 180° phasing (N∥∼100). Numerical modeling with the fast wave code fastwa [Plasma Phys. Controlled Fusion 33, 417 (1991)] indicates that for Phaedrus-T parameters the kinetic Alfvén wave is excited via mode conversion from a surface fast wave at the Alfvén resonance and is subsequently damped on electrons.

Evidence is given that the presence of an open ion cyclotron resonance layer in a tandem mirror can result in enhanced radial ion transport.

Inductively generated rf sheaths and self‐bias effects at antenna Faraday screens are at least partly responsible for the impurity influx and edge modifications often seen in rf heating experiments1,2. Analysis of JET results has shown that the effectiveness of solutions utilized in that experiment to reduce rf impurity influxes can be explained in terms of rf sheath effects.1 On both JET and TFTR magnetic field‐aligned Faraday shield elements, low‐Z coatings, and 180° phasing of adjacent antenna straps have been effective at reducing impurities. However, alignment of Faraday shield elements is difficult, low‐Z coatings do not remove the underlying causes of sputtering, and 180° phasing reduces loading resistance and is incompatible with certain rf goals, such as fast wave current drive. Here we show that rf generated impurity influxes in the Phaedrus‐T tokamak are due to self‐bias effects in the edge plasma generated by rf sheaths at the Faraday shield, and that these effects can be largely eliminated for any antenna phasing by the use of insulating limiters on the Faraday shield.

Experiments in progress on the Phaedrus‐T tokamak focus on effects associated with fast wave current drive at low harmonics of the cyclotron frequency, typically either 3ΩCD or 1.5ΩCH on axis. Areas of investigation include edge effects, directionality of wave launch, and comparison of wave absorption to numerical predictions. More general aspects of current drive, such as wave helicity effects which can be viewed as part of a complete picture of the nonlinear contributions to current drive,1 will be extensively studied. Early Thomson scattering data appears to indicate that rf power coupling to electrons is affected by antenna phasing. However, current drive has not yet been observed. Several innovations have also been implemented on the experiment, including insulating limiters on the Faraday shield to reduce rf ‐ edge plasma interactions, an antenna design which reduces inductive coupling between the straps for operation at arbitrary phase, modelling of the coupled straps to allow predictive retuning on phase changes, and a two‐channel transformer coupled transmitter.

Phaedrus-T is a moderate sized tokamak with low toroidal field and substantial radio frequency power capabilities. This machine has only recently become operational and full RF power is expected in the next year. The initial studies include edge modifications due to variable phased antenna structures and RF helicity current drive experiments. Spheromak particle refueling tests will be started in the Fall of 1991. The tokamak is also being used as a test site for diagnostic development.

High bandwidth capacitive probes are useful tools for potentials measurements in the tokamak scrape off layer. An improved capacitive divider probe design with very high frequency bandwidth is shown. The gain of this system is between 0 and -8 dB for frequencies from 0.1 Hz to more than 100 MHz, with the -3 dB point at approximately 40 MHz. The probe structure, circuits, performance, and experimental results from the Phaedrus-T tokamak are given.