I. Katanuma

Observation of scaling laws of ion confining potential versus thermal barrier depth and of axial particle confinement time in the tandem mirror GAMMA 10

In the thermal barrier tandem mirror GAMMA 10, the scaling law governing the enhancement of the ion confining potential, c, resulting from thermal barrier formation, is obtained experimentally, and is consistently interpreted in terms of the weak and strong ECH theories set up by Cohen and co-workers. The scaling law on the axial particle confinement time, τp||, related to this c formation, is also demonstrated in detail; it is in good agreement with the Pastukhov theory as modified by Cohen and co-workers. This scaling is verified at any radial position in the core plasma region and at any time through the various stages of a discharge; this indicates a scaling with drastic improvement of τp||, due to the potential formation in the tandem mirror plasma.

Plasma confinement in the GAMMA 10 tandem mirror

The central cell density and the diamagnetic signal were doubled as a result of plug potential formation by ECRH in hot ion mode experiments on the GAMMA 10 tandem mirror. In order to obtain these remarkable results, the axisymmetrized heating patterns of ECRH and ICRF heating were optimized. Furthermore, conducting plates were installed adjacent to the surface of the plasma along the flat shaped magnetic flux tube located in the anchor transition regions; the plates may contribute to the reduction of some irregular electric fields produced possibly with ECRH in these thin flux tube regions. The conducting plates contributed to reducing the radial loss rate to less than 3% of the total particle losses, along with improvements in the reproducibility of the experiments and the controllability of the potential confinement. The increases in central cell density and diamagnetism in association with the increase in plug potentials scaled well with increasing ECRH power. A plug potential of 0.6 kV and a density increase of 100% were achieved using an ECRH power of 140 kW injected into both plug regions. The plasma confinement was improved by an order of magnitude over a simple mirror confinement owing to the tandem mirror potential formation.

Anchor plasma buildup by using central cell ICRF antennas in the tandem mirror GAMMA 10

The paper presents a study of anchor cell plasma buildup in the tandem mirror GAMMA 10 with the use of central cell ICRF antennas. For plasma buildup, it is demonstrated that an ion cyclotron resonance layer exists within the closed mod-B surface in the minimum-B anchor cell. The experimental plasma buildup rate in the anchor cell is compared with a one-dimensional Fokker-Planck simulation. A rapid increase in the anchor plasma density is observed and an associated reduction of the end-loss current when radiofrequency is applied.

Thermal barrier potential and two‐dimensional space‐potential measurements with gold neutral‐beam probes in GAMMA 10

Gold neutral‐beam probes are used for the space‐potential measurements in the barrier and in the central cells of the GAMMA 10 tandem mirror. The thermal barrier potential depth is directly observed by simultaneous measurements of the on‐axis space potentials at both locations. Two‐dimensional space potentials in the barrier region are measured by sweeping the probing beams with different beam energies.

Neoclassical resonant plateau transport calculation in an effectively axisymmetrized tandem mirror with finite endplate resistance

Calculations are made for neoclassical resonant plateau transport in the geometry of the effectively axisymmetrized tandem mirror GAMMA 10 magnetic field, which has minimum B inboard anchors inside the axisymmetric plug/barrier mirror cells. Azimuthal drifts in the local, non-axisymmetric regions are included. The radial potential profile is determined by solving the charge neutrality equation self-consistently. A finite resistance connecting the end plate to the machine ground provides appropriate boundary conditions on the radial electrostatic potential distribution so that it can be determined uniquely. The calculation is consistent with experimental results of GAMMA 10.

Progress in potential formation and findings in the associated radially sheared electric-field effects on suppressing intermittent turbulent vortex-like fluctuations and reducing transverse losses

Following the 19th IAEA Fusion Energy Conference (Lyon, 2002), (1) three-time progress in the formation of ion-confining potential heights c including a record of 2.1 kV in comparison to those attained 1992–2002 is achieved for tandem-mirror plasmas in the hot-ion mode with ion temperatures of several kiloelectronvolts. (2) The advance in the potential formation gives the bases for finding the remarkable effects of radially produced shear of electric fields Er, or non-uniform sheared plasma rotation on the suppression of intermittent vortex-like turbulent fluctuations. (i) Such a shear effect is visually highlighted by x-ray tomography diagnostics; that is, spatially and temporally intermittent vortex-like fluctuated structures are clearly observed as two-dimensionally reconstructed visual structures for the first time in kiloelectronvolt order ion-cyclotron heated plasmas having a weak shear in GAMMA 10. (ii) However, during the application of plug electron-cyclotron heatings (ECH), the associated potential rise produces a stronger shear (dEr/dr = several 10 kV m−2) resulting in the disappearance of such intermittent turbulent vortices with plasma confinement improvement. X-ray observations also show elongation of a vortex structure from a circular into an ellipsoidal shape, as depicted in H-mode theories, with an outward shift. (3) For the physics interpretations and control of such potential and the associated shear formation, the validity of our proposed theory of the potential formation is extensionally tested under the conditions with auxiliary heating. The data described above fit well to the extended surfaces calculated from our proposed consolidated theory of the strong ECH theory (plateau formation) with Pastukhovs theory on energy confinement.

High-density plasma production with potential confinement in the GAMMA 10 tandem mirror

The improvement of potential confinement was attained in the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985); Proceedings of the 13th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Washington, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 539] by axisymmetrization of heating systems for the plasma production, heating, and potential formation. A significant increase of the density and diamagnetism by the potential confinement was observed. In the previous experiment, it was difficult to increase the central cell density higher than 2.7×1018 m−3. One of the possible mechanisms is the density clamping due to the eigenmode formation of the ion–cyclotron-range of frequency (ICRF) waves in the axial direction. With high harmonic ICRF waves (RF3), the experiments to overcome this problem have been performed. In preliminary experiments with RF3 and NBI the maximum density of 4×1018 m−3 was attained.

Production of hot electrons for axisymmetric thermal barrier formation in a tandem mirror

Hot electrons have been produced by second harmonic electron‐cyclotron resonance heating in axisymmetric end mirrors of the tandem mirror GAMMA10 [Phys. Rev. Lett. 55, 939 (1985)] with an on‐axis density fraction reaching 80% and temperature of 25–50 keV, satisfying theoretically required conditions for the formation of thermal barriers. The successful control of the electron temperature may be attributed to the relativistic detuning of the second harmonic resonance for localized microwave power absorption. The time evolutions of relevant parameters are studied with extensive diagnostics.

Extended consolidation of scaling laws of potential formation and effects covering the representative Tandem mirror operations in GAMMA 10

Scaling laws of potential formation and associated effects along with their physical interpretations are consolidated on the basis of experimental verification using the GAMMA 10 tandem mirror. A proposal of extended consolidation and generalization of the two major theories—(i) Cohens strong electron cyclotron heating (ECH) theory for the formation physics of plasma confining potentials and (ii) the generalized Pastukhov theory for the effectiveness of the produced potentials on plasma confinement is made through the use of the energy balance equation. This proposal is then followed by verification using experimental data from two representative operational modes of GAMMA 10, characterized in terms of (i) a high-potential mode having plasma confining potentials of the order of kilovolts and (ii) a hot ion mode yielding fusion neutrons with bulk ion temperatures of 10–20 keV. The importance of the validity of the proposed physics-based scaling is highlighted by the possibility of extended capability inherent in Pastukhovs prediction of requiring an ion confining potential of ~30 kV for a fusion Q value of unity on the basis of an application of Cohens potential formation method. In addition to the above potential physics scaling, an externally controllable parameter scaling of the potential formation increasing with either plug or barrier ECH powers is summarized. The combination of (i) the physics-based scaling of the proposed consolidation of potential formation and effects with (ii) the externally controllable practical ECH power scaling provides a new direction for future tandem mirror studies.

Temperature Anisotropy Measurement Using Diamagnetic Loop Array

The anisotropy of the ion distribution function in the velocity space is observed in the ion cyclotron range of frequency heating experiments on the tandem mirror GAMMA 10. The anisotropy, defined as T⊥/T// (ratio of ion temperatures perpendicular and parallel to the magnetic field line), is evaluated quantitatively using three diamagnetic loops aligned in the direction of the magnetic field line. Depending on the anisotropy and the plasma pressure, fluctuations below the ion cyclotron frequency are excited. In terms of the quantitative estimation of the anisotropy, it is established clear that the parameter region in which the fluctuations are observed agrees well with a theoretically predicted region of the convectively unstable Alfven ion cyclotron mode.