Y. Kiwamoto

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.

Observation of hot electrons produced by second harmonic electron cyclotron heating in the axisymmetric tandem mirror GAMMA 10

Microwave power, PECH ≤ 140 kW, has been injected at 28 GHz into the axisymmetric plug/barrier cell in the axisymmetrized tandem mirror GAMMA 10. As observed by soft X-ray measurements, the microwaves generate a hot (50-60 keV) electron population, radially peaked on the magnetic axis, which results in the formation of a thermal barrier. The production mechanism of these hot electrons is found to be second harmonic electron cyclotron heating (ECH), corrected for the effects of the relativistic mass variation and the Doppler shift. This mechanism also explains the first experimental observation of a saturation of the single-component hot electron temperature Teh as being caused by the finite width of the incident microwave lobe. The dependence of the plasma parameters on the filling gas pressure, the plasma density and the ECH power is studied. It is found that the heating process can be interpreted as a competition between electron acceleration by the incident wave, electron deceleration by collisions, and the mirror trapping efficiency of the source electrons for hot electrons. The axial profile of the soft X-rays is investigated in relation to the mechanism of the second harmonic ECH. The heating process is discussed in terms of the electron pitch angle and the magnetic field intensity.

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.

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.

Temporal behaviour of the potential confined electrons in the central cell and in the plug region during a period with thermal barriers

An increase with time of the central-cell electron temperature during a period with thermal barrier potentials has been observed. The increase is explained by an improvement of the electron energy confinement due to the presence of thermal barriers. Different evolutions of the electron energy in the plug region have been observed; these are closely related with the variation in time of the confining potential of the plug electrons. The observed behaviour of the potential confined electrons provides the first data set for the evolution of the effect of thermal isolation caused by the formation of a thermal barrier in the kilovolt range.

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.

Microwave absorption at the fundamental electron cyclotron resonance and potential formation in a tandem mirror

Strong one‐pass absorption of high‐power microwaves is observed at the fundamental electron cyclotron resonance in an axisymmetric end mirror of the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985); Phys. Fluids 29, 2781 (1986)]. The radial profile of microwave power deposition is directly measured without the influence of wall reflection. It coincides with that of the axial flow of warm electrons driven by the fundamental heating as well as with that of the plasma potential at the resonance. This indicates that strong electron cyclotron heating largely affects the potential formation through driving an axial flow of warm electrons.

Thermal barrier potential of a tandem mirror

The relation between the electrostatic potential and the low energy electron density under electron cyclotron resonance heating (ECRH) in the thermal barrier of a tandem mirror is investigated analytically and numerically. The distribution function of mirror trapped electrons at low energy is found to stretch out in the perpendicular direction to the magnetic field and to be well approximated by a bi‐Maxwellian (T⊥≥T∥) rather than by a Maxwellian. Under this approximation it is found analytically that the conventionally used Boltzmann formula derived from the full Maxwellian plasma for the barrier depth is modified to another expression including the ratio between T⊥ and Te (central cell electron temperature). The bounce‐averaged Fokker–Planck simulations show that T⊥/Te itself is a function of the potential depth and that the conventional formula is modified to q(φb−φe)=Te ln(αnc/nb) with α=1.5–1.8 depending on ECRH power. This expression agrees well with experimental results on GAMMA 10 [Phys. Rev. Lett...

Neoclassical resonant‐plateau transport in the noncircular equipotential surface of a tandem mirror

Neoclassical resonant‐plateau transport in a minimum‐B anchored tandem mirror is calculated in an experimentally observed case where a flux tube of equipotential contours is not circular at the central cell.

Fokker–Planck calculation of hot electron buildup in the thermal barrier region of a tandem mirror

The hot electron buildup by second harmonic electron cyclotron resonance heating in the thermal barrier region of a tandem mirror has been studied by using a Fokker–Planck code with a self‐consistent potential profile taken into account. It has been found that the evolution of the hot electron population and the potential profile consists of two phases. In the first phase the rf diffusion is dominant and a quick increase in both the hot electron density and the mean energy is observed. No further increase in the mean energy is observed thereafter. The potential is deepest during the first phase. The second phase starts in the mean free time of the pitch angle scattering of hot electrons on cold electrons and ions. In this phase the hot electron population increases at the rate of the pitch angle scattering. The potential dip becomes shallow because of the accumulation of pitch‐angle‐scattered passing ions.