H. Zushi

Scalings of energy confinement and density limit in stellarator/heliotron devices

The paper presents a study of empirical scaling of energy confinement observed experimentally in stellarator/heliotron devices (Heliotron E, Wendelstein VII-A, L2, Heliotron DR) for plasmas heated by electron cyclotron heating and/or neutral beam injection. The proposed scaling of the gross energy confinement time is: , where P is the absorbed power (MW), n is the line average electron density (1020 m?3), B is the magnetic field strength on the plasma axis (T), a is the average minor radius (m) and R is the major radius (m). The empirical scaling of the density limit obtainable under the optimum condition is proposed to be: . These scalings for helical systems are compared with those in tokamaks. The energy confinement scaling has a similar power dependence as the L-mode scaling of tokamaks. The density limit scaling for helical systems seems to indicate an upper limit of the achievable density similar to that in many tokamaks. From the energy confinement time and the density limit , a beta limit can be derived: , which can be lower than the stability/equilibrium beta limit. Thus, from the viewpoint of designing a machine, the values of B, a and R should be selected with care because the dependence of the confinement time (or n?ET) and of the above beta limit on these values is different.

Physics of collapse events in toroidal plasmas

A review is made of the crash phenomena in toroidal plasmas. The emphasis is placed on the physics that causes the crash of global plasma parameters. Recent progress in the measurement has provided a unified view of various crash phenomena, i.e. the sudden occurrence of the crash, the sensitivity (or probabilistic dependence) of the occurrence of the crash on the global parameters, and the abrupt excitation of a symmetry-breaking perturbation (magnetic trigger). Essential observations that describe the physics of collapse are surveyed. The theoretical study of the nonlinear plasma dynamics is overviewed. Theories of the onset and explosive growth, which are based on magnetic braiding, are discussed. As an example, a picture based on a turbulence-turbulence transition is explained. A picture based on hysteresis and bifurcation, not on the linear instability criterion, emerging from advanced measurements and recent progress, describes the basic physics of the collapse.

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.

ICRF heating of currentless plasma 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.

Heating and confinement studies of electron cyclotron resonance heated plasmas in 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.

Visible and VUV spectroscopic diagnostics on Heliotron E

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.

Detection of the free boundary plasma shift in a toroidal helical plasma on Heliotron-E

This paper describes the first successful realization of the magnetic detection of the free boundary plasma shift for helical plasmas. A procedure for determining the equilibrium plasma displacement in a stellarator by means of external magnetic field measurements (psi loops and modulated Rogowski coils) is discussed. Recent experimental results, the normalized displacement Δb/ap as a function of volume averaged beta β, are discussed and compared with analytical and published numerical MHD computational results. The typical measured plasma boundary shift, Δb/ap, in the standard Heliotron-E configuration (Rp = 2.20 m, ap = 0.21 m, ι(0)/2π ~ 0.53, ι(ap)/2π ~ 2.8) is (8-10) × 10-3, when the volume averaged beta is 0.50%. The measured normalized plasma boundary shift is nearly proportional to the diamagnetic volume averaged beta, for values of beta up to 0.95%. The magnetically determined plasma boundary shift Δb is less than 3 mm. The experimental observations on shift (Δb/ap versus βdia) are compared with the analytically expected plasma boundary shift. The measured shift lies in the range between the expected upper limit (Δb/ap = β(0)/2βeq) and the lower limit (Δb/ap= β/2βeq), where βeq=[ι(ap)/2π]2(ap/Rp) ~ 0.77 for the standard configuration of Heliotron-E. It is found that the measured plasma boundary shift depends strongly on the initial vacuum magnetic configuration parameters such as the horizontal position of the magnetic axis and the rotational transform. When the vacuum magnetic axis is shifted inward towards the major axis, significant decreases of the normalized plasma shift (Δb/ap) and of the plasma induced vertical field are observed, which are interpreted as being due to a reduction of the Pfirsch-Schluter current

Transport analysis of injected impurities in currentless Heliotron E plasmas

Impurity transport in currentless Heliotron E plasmas is examined. The main aim of the experiment is to clarify the density dependence of impurity transport both in electron cyclotron heated (ECH) and neutral beam injected (NBI) plasmas. In experiments with a stationary electron density, the confinement time of impurities is determined as a function of the line averaged electron density. The inherent difference between ECH and NBI plasmas, observed in an earlier measurement, seems to have been masked by the operating conditions. From a direct comparison between NBI plasmas and simultaneous ECH and NBI heated plasmas of the same density, a pumping-out effect of impurities by the ECH pulse is established. From numerical analyses, the unexpected discrepancy between observed and calculated VUV spectral data can be explained by a charge exchange process. The observed impurity transport is found to be well described by a model which incorporates the effects of radial diffusion and inward convection. The inward flow does not seem to be due to the plasma potential because the flow is also observed in ECH plasmas where the heating power is expected to contribute to a reversed potential. The flow velocity is of the order of the classical friction between background ions and seems to play only a minor role in various aspects of impurity transport in NBI plasmas, such as impurity accumulation. The variety in impurity transport in Heliotron E plasmas is best understood by changes in the diffusion coefficient.

Effects of magnetic shear on electron cyclotron resonance heating in heliotron/torsatron configurations

Effects of magnetic shear on electron cyclotron resonance heating (ECRH) are studied in heliotron/torsatron configurations. In such configurations, the poloidal magnetic field is comparable to the toroidalmagnetic field, and varies spatially along the minor radius, making a strong magnetic shear. When high power millimeter waves are launched into a plasma, it is coupled to propagating modes at the plasma peripheral region. The existence of a transition layer between the core plasma region and the vacuum region, where the magnetic field direction is largely changed, requires accurate polarization control for good single pass absorption. The mode conversion between the propagation modes due to the magnetic shear also affects the launching conditions. The polarization control experiment by using second harmonic ECRH in Heliotron E [T. Obiki, Fusion Technol. 17, 101 (1990)] are compared with the numerical calculation in which one dimensional second order coupled equations are solved. The polarization dependence experimentally measured is in good agreement with the numerical results including the magnetic shear terms.

DENSITY FLUCTUATIONS IN CURRENTLESS HIGH BETA PLASMAS IN HELIOTRON E

The stability properties of currentless high beta plasmas have been investigated over a wide range of density profiles ne(r), by varying the gas puffing conditions and by pellet injection. Line density fluctuations correlated with a pressure driven MHD instability were measured by a multi-channel far-infrared laser interferometer. When an increase in the plasma beta was accompanied by a peaking of ne(r), line density fluctuations with a frequency of 2–5 kHz periodically appeared. The repetition time of the fluctuations was typically 2–5 ms. The poloidal and toroidal mode numbers of the fluctuations were identified as m=l and n=l. For plasmas with an extremely peaked profile, density fluctuations corresponding to the m=3/n=2 mode were observed. With the growth of this mode, internal disruptions occurred. Because of these disruptions, the profile of ne(r) rapidly changed from a peaked one to a broader one. The normalized average radius, r/a, of the phase reversal in the density profile variation caused by the disruption is about 0.5, which roughly corresponds to the ι =2/3 surface, ι being the rationalized rotational transform. It is most likely that the large amplitude mode with m=3/n=2 triggers the internal disruptions. The onset regions for MHD instability have also been investigated for various density profiles and beta values.