K. Uo

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.

Studies of currentless, high-beta plasma in the Heliotron E device

A currentless plasma with a volume-averaged beta value of 2% has been produced with neutral beam heating. Target plasmas were created by second harmonic resonance heating with electron cyclotron waves (150–350 kW and 53.2 GHz) at a magnetic field strength of 0.94 T. Neutral beam injection (23–30 keV and 1.3−2.6 MW) was used to heat the plasma further. MHD stable and unstable high-beta plasmas were observed. The Q-mode plasmas were produced with the help of intense neutral gas puffing. Properties of the MHD activity and confinement of high-beta plasmas are discussed and compared with theoretical studies.

Analysis of the plasma-wall interaction in the Heliotron E device

The plasma-wall interaction (PWI) of the currentless plasmas with temperature To, Tio ≤ 1.1 keV, density Ne = (2–10)× 1013/cm3, and volume-averaged beta value of β

The Helical Heliotron field for plasma confinement

≤ 2% was investigated. We have observed that PWI took place mainly where the divertor field line intersected the chamber wall (called divertor traces). Boundary plasmas were measured with electrostatic probes, which showed the presence of the divertor region with the parameters in the range of Ned = 1010–1011/cm3 and Ted = 10–50 eV. Surface analysis techniques (ESCA, AES, and RBS) were applied to analyze the surface probes (Si, graphite and stainless steel) and the test pieces (SiC, TiC, and stainless steel), which were irradiated by plasmas for short and long times respectively.

ICRF heating of currentless plasma in Heliotron E

The Helical Heliotron field of the first kind is composed of a helical field, vertical field and toroidal solenoid field. The helical field is produced by a current carrying single helical conductor which is wound around the minor axis and closes on itself after making l-circuits around the major axis. By using a computer, the authors have traced the helical lines of force and computed the rotational transform, the shear and the well depth. The complex behaviour of the separatrix is also clarified. In the l=2 case, the Helical Heliotron field of the first kind has large rotational transform and strong shear simultaneously, and also has a magnetic well.

Heating and confinement studies of electron cyclotron resonance heated plasmas in Heliotron E

In the Heliotron E device, a non-axisymmetric helical system, ICRF heating experiments were carried out for the first time, using fast-mode and slow-mode waves. In the fast-wave heating experiment, ICRF power of up to 550 kW was emitted during 15 ms by four antenna loops. Effective heating of a current-less ECRH-produced target plasma was observed over a wide density range. The plasma loading resistance of an antenna loop reached about 5 ?. This is a value comparable with that of tokamak experiments. The increments of ion and electron temperatures by fast-wave heating were about 200?230 eV at an electron density of about 3 ? 1019m?3. Minority heating and pure second-harmonic heating have almost the same efficiency ((1?2) ? 1019eV?m?3?kW?1) during the short RF pulse used (t ? 15 ms). The energy transfer rate from the waves to ions and electrons could be explained by mode conversion. The signals of toroidal eigen-modes were experimentally observed and radial mode numbers could be determined using a simple model. In the slow-wave heating experiment, the upper density limit of effective heating appeared to be in qualitative agreement with wave theory.

Visible and VUV spectroscopic diagnostics on Heliotron E

Radiofrequency (RF) heating of currentless plasmas is performed at the fundamental electron cyclotron frequency. The absorbed power profile is determined from the decay of the electron internal energy profile immediately after the RF pulse is turned off. Measurements of the absorbed power profile at various positions of the cyclotron resonance layer are compared with single-pass absorption profiles predicted by a ray tracing code. The profiles of electron temperature, density and ion temperature are studied as a function of the absorbed power, its radial profile and the electron line averaged density. Finally, a scaling of the energy confinement time obtained by regression analysis is compared with a scaling for neutral beam heated plasmas.

Monte-Carlo calculation of perpendicular neutral-beam injection in helical systems

Diagnostic applications of visible and VUV spectroscopic techniques, as applied to the currentless Heliotron E plasma device, are described. Visible spectroscopy has been used to measure (i) ion temperature, (ii) proton‐to‐electron density ratio, (iii) Zeff by charge exchange recombination from an intense neutral beam, (iv) radial electric field by poloidal rotation velocity measurement, and (v) electron density around an ablating pellet by a Stark profile. VUV spectroscopy has been used to investigate emission spectra due to multiply ionized impurity species. This information is used to measure the densities of these species, and to learn about the transport of these particles. Recently, a flat‐field survey spectrometer has been constructed and used to study the emission spectra due to metallic impurities in ICRF‐heated plasmas.

The straight helical heliotron field

The effect of a helical field ripple on the slowing-down process of the fast ions created by neutral injection is investigated numerically. For this purpose, the guiding-centre orbits are followed in a model magnetic field without plasma current, on the assumption that the slowing-down process is to be classical. Optimum injection angles in two types of helical magnetic traps are compared. One is the Heliotron-E configuration with a large rotational transform and deep helical ripple; the other one is the conventional stellarator field with a small rotational transform and shallow helical ripple. In contrast to the stellarator, the heating efficiency as calculated for Heliotron-E does not decrease monotonically when the injection angle is perpendicular to the toroidal direction; a heating efficiency of above 70% was obtained for perpendicular injection into a high-density plasma with negligible charge-exchange loss. The difference in heating efficiency versus injection angle between heliotron and conventional stellarator fields is explained by a difference in drift motion of the helically trapped fast ions.

Transport analysis of injected impurities in currentless Heliotron E plasmas

The general expression of the l = 2 straight helical heliotron field is obtained by integrating Biot-Savarts formula after expanding the integrand. Solving the differential equation of the line of force, a general expression for the magnetic surfaces, which is in good agreement with the results of a computer calculation up to the separatrix, is obtained. The rotational transform and the shear of this field are calculated as functions of the average radius of the magnetic surface. For a certain range of α*, the ratio of the longitudinal field produced by the Bz–coil to the longitudinal component of the field produced by the helical coil, the field cannot form a closed magnetic surface. The width of this range, the forbidden zone, is a function of γ = 2πa/p, where a is the radius of the helical winding and p is the pitch. For small γ, the zone is wide and the closed magnetic surface has very small shear. For large γ, the zone is narrow and the magnetic surface has very small rotational transform and shear. Only for intermediate γ, the zone is narrow and rotational transform and shear are both large. These values of γ could be considered to be optimum values for plasma confinement.