Table of contents

The active beam scattering method was applied to ion temperature measurements in JT-60 plasmas. The ion temperature found was in reasonable agreement with that obtained from Doppler broadening of the Ti XXI and Ti XXII resonance lines in the temperature range of 1.5 to 10 keV. With the help of the scattering system, the central ion temperature of JT-60 plasmas during 40 keV and 70-75 keV NBI heating was measured. Higher ion temperature was obtained during 70 to 75 keV than during 40 keV NBI heating. These data and a possible explanation are presented. A numerical simulation of this diagnostic indicates that the ion temperature as deduced from the diagnostic is almost equal to the bulk temperature when the ratio of high energy ion component to the total ion stored energy is less than 0.3.

A method based on the utilization of magnetic field and field gradient distributions for calculating the gradient of the magnetic surface function, ∇ψ, in stellarator systems is treated. The distributions of ∇ψ and associated quantities over the magnetic surfaces of torsatrons obtained by this method are discussed. The method can also be applied to other toroidal systems which confine plasma in an asymmetrical magnetic field.

In the ohmically heated W VII-A stellarator, the behaviour of which is similar to that of a medium sized tokamak, the additional shearless external rotational transform t₀ (Δι₀/ι₀ < 1%, ι = 1/q) improves the stability properties and allows stationary and reproducible helium discharges with large amplitude tearing modes to be produced for 0.10 ≤ ι₀ ≤ 0.15. Discharges of this type are used to study, by means of Thomson scattering, the modification of electron temperature and density profiles by large amplitude tearing modes. The two-dimensional shapes of the profiles found experimentally can be attributed to the magnetic islands predicted by tearing mode theory. These shapes are further used to define an effective, locally enhanced radial transport coefficient κ_⊥,e in a one-dimensional heat transport code. In this way, the measured temperature profiles can be reproduced quite well and the energy confinement time of discharges with tearing mode activity can be predicted quantitatively. The transport model is used to investigate the explicit dependence of κ_⊥,e on the plasma current and to study the importance of plasma current driven instabilities for the energy confinement in the W VII-A stellarator as well as in tokamaks.

The maximum attainable beta values which can be expected in tokamaks with crescent (BEAN 1) and rounded (BEAN 2) bean shaped cross-sections are obtained numerically by using the linear ideal MHD stability analysis code ERATO. The current profiles are optimized with a fixed pressure profile for high values of beta, keeping Mercier, high-n ballooning and n = 1 kink modes stable. The poloidal plasma cross-sections are inscribed in a rectangle with an aspect ratio of three and an ellipticity of two. A confocal wall, the distance of which from the plasma surface is equal to the horizontal minor plasma radius, is present to stabilize against the kink mode. Depending on the shape and triangularity (indentation), a beta value of 10 to 17% is obtained. It is also shown that the coefficient of the Troyon-type beta scaling increases for an indented plasma. In the case of small indentation, the BEAN 1 type tokamaks show higher beta values than the BEAN 2 type. For strong indentation, the BEAN 2 type gives the highest beta value.

A rotating field antenna set — a pair of two closely spaced dual half-turn antennas — is used to tailor the azimuthal spectrum of the antenna field. It is demonstrated that the azimuthal mode of ICRF waves can be controlled by proper phasing of the antenna set. Ion heating is shown to be strongly dependent on the azimuthal mode number. When the antenna set is operated in the m = −1 (left rotating) mode, the m = −1 modified ion cyclotron wave is selectively excited, resulting in efficient ion heating.

The paper reports observations of a sub-millimetre diameter Z-pinch discharge initiated in hydrogen gas at high pressure (0.33-2 bar) and powered by a fast rising current (dI/dt ≈ 1 kA·ns−1). The conditions for heating the pinch ohmically under pressure balance are established by using a small preheat current of short duration (5 kA, 70 ns). Measurements of the radial density profiles of the electrons in the pinch and the surrounding neutral gas are presented. The peak electron temperature in the pinch is estimated from the soft X-ray emission. The observations show that during the preheat phase, when there is no equilibrium, the plasma column expands radially and drives a shock into the neutral gas. This results in an increase of the neutral gas density in a thin layer surrounding the pinch. When the main current is applied, a pinch in radial equilibrium, with a radius of about 400 μm and peak electron density on axis (2.5 × 10²⁴ m−3 at 0.33 bar), is observed. The estimated peak electron temperature on axis (69 eV at 0.33 bar) is about twice the Bennett temperature. An increase of the line density is observed during the equilibrium. This is ascribed to a flow of neutral particles from the high density layer surrounding the pinch column. The equilibrium is destroyed by an m = 1 instability which grows from a helical perturbation on axis. The experimental results are compared with calculations based on ideal MHD stability theory, and it is shown that the existence of a centrally peaked current density profile can be inferred from the nature of the observed instabilities. An explanation is offered for the absence of the m = 0 mode, on the basis of cooling of the outer region of the plasma.

Ion temperatures around 10 keV were obtained in JT-60 limiter plasmas by high power neutral beam heating (H⁰ → H⁺), which is much higher than the maximum value of 6.6 keV obtained in JT-60 diverted plasmas. The experiment was performed in the parameter region of I_p = 1−2 MA, _e (before heating) = (0.7−1.5)×10¹⁹ m⁻³, _e (end of heating) = (2.5−4.1)×10¹⁹ m⁻³ and = 19−21.8 MW. The Z_eff values of the limiter plasmas were high (i.e. 4 to 7) compared with those of the diverted plasmas (i.e. 1 to 2). Transport analysis indicates that, since the deposition power to electrons, P_be, increases with Z_eff, high Z_eff is effective in raising the electron temperature. Furthermore, it is shown that since the equipartition loss is reduced by both the increase in electron temperature and the decrease in the effective ion density, n_p + n_zZ²m_p/m_z, with increasing Z_eff, high ion temperatures are obtained in limiter plasmas with high Z_eff.

A theoretical investigation of the thermal equilibria of detached plasmas has been performed. The transport model used is that for the η_e modes. The model explains the scaling of the plasma radius, central electron temperature, impurity radiation, electron energy confinement time with plasma current and central density as observed on TFTR. Furthermore, assuming that the plasma disrupts when the safety factor reaches two at the edge of the detached plasma, a density limit n_cr is obtained. For the impurity density n_I independent of the plasma density, whereas for n_I = fn(0), where f is the fraction of impurities, n_cr ∝ B_T/R.

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.

The authors have written a code for the solution of the integro-differential equations describing coupling, propagation and absorption of high frequency waves in the ion cyclotron frequency range in tokamak plasmas, taking into account finite Larmor radius effects and parallel dispersion. The wave equations are discretized by a semi-spectral approach, using cubic Hermite finite elements in the radial direction and an expansion in Fourier modes in the poloidal direction. The latter permits analytic evaluation of the orbit integrals along magnetic field lines in the presence of a poloidal component of the static magnetic field. Thus, the code describes mode conversion to ion Bernstein waves, ion cyclotron damping at the fundamental and at the first harmonic, and electron transit time and Landau damping in full toroidal geometry. A few simulations of ion cyclotron heating of the ASDEX tokamak are presented. They show generally good agreement with the predictions of simpler models, namely plane layered models and ray tracing. Furthermore, the simulations can be used to identify a few interesting toroidal effects, particularly regarding the efficiency of mode conversion and the propagation of ion Bernstein waves.

The impurity transport characteristics of ohmically and neutral beam heated diverted plasmas in JT-60 have been studied. In sawtoothfree, ohmically heated plasmas with I_p = 1.5 MA, _e = (2−3) × 10¹⁹ m⁻³, q(a) = 3.2, no radiation buildup is observed. The temporal evolution of injected titanium has been measured by VUV and X-ray crystal spectrometers and PIN diodes. The spectral lines of Ti XX (259.3 Å) and Ti XXI (2.6097 Å) are compared with one-dimensional diffusive/convective impurity transport calculations. The transport calculations for Ohmic discharges with I_p = 1.5−2 MA, _e = (1–3) × 10¹⁹ m^–3, q(a) = 3−3.7, show that D_A =(1−2) m²⋅s⁻¹ and that the inward convective velocity is small. In neutral beam heated plasmas with I_p = 1.5 MA, _e = 4 × 10¹⁹ m^–3, q(a)= 3.6, P_b = 8 MW, no difference is observed in the global time evolution of the Ti XXI line emissions between co- and counter-injected discharges. The experimental observations are well represented by choosing D_A = (1–2) m²⋅s⁻¹ and a small inward velocity.

The paper discusses the feasibility of a current drive technique based on the collinear excitation of plasma waves by two high frequency electromagnetic pump waves. Particle trapping into the intense plasma wave creates hot electrons which sustain a slowly decaying current. Momentum and energy transfer to electrons can be enhanced by pump wave cascading. The method offers possibilities to localize the generation region and to control the current profile. With a CO₂ laser, the maximum current density rises to approximately 50 kA·cm⁻² at 10¹² W·cm⁻² in a 10¹⁵ cm⁻³ plasma. A current density of 1.0 kA·cm⁻² in a 10¹⁴ cm^–3 plasma is predicted for a 100 μm free electron laser operating at 4 × 10¹⁰ W·cm⁻2. The total induced current is about J_tot (MA) R(m)n_e(10¹⁴cm⁻³)/P_avg(MW)≅0.5 (R is the major radius, n_e is the plasma density and P_avg is. the average laser power) for the 10-200 μm cases considered; the actual value depends on the hot electron collision rate and the amount of cascading taking place. The main problems and the basic parameter scalings are discussed. Also, a novel method for amplifying the induced current by the bootstrap effect is suggested. A seed current of 0.2-0.4 MA in a spot of 30-50 cm diameter would be sufficient for a tokamak reactor; this appears achievable as far as laser requirements are concerned.

Stability against axisymmetric modes and free boundary n = 1 kink modes in a nearly circular tokamak with a poloidal divertor is investigated by using the linear ideal MHD code ERATO-J. Perturbations localized near the plasma surface (divertor) are shown to reduce the growth rate of MHD modes. Although the local variation of the n-index is large because of the presence of an X-point, a wide stability window for axisymmetric modes similar to limiter configurations is obtained. The detailed characteristics of the axisymmetric stability depend on the position of the X-point in the poloidal plane and on the structure of the divertor coil system. The large shear near the plasma surface is effective in stabilizing free boundary n = 1 kink modes. This shear stabilization is sensitive to the details of the divertor geometry, such as the location and number of X-points, and to the plasma pressure. The dependence of the critical beta on the current profile is also discussed.

A new equilibrium reconstruction procedure using magnetic, line integrated electron density and Faraday rotation measurements has been developed. The method has been applied to a number of elongated tokamak equilibria which were computed by using a free-boundary MHD equilibrium code. Typical errors in four global plasma parameters (β_p, ℓ_i, μ and q₀) are evaluated as functions of the measurement errors and the number of source function parameters. Assuming realistic random perturbations in the measurements, the method allows source functions with up to six independent parameters to be reconstructed. It is shown that, when electron density and Faraday rotation measurements are included, the accuracy in the determination of q₀ is increased by at least a factor of two, compared with cases without Faraday rotation data. The effects of adding a diamagnetic probe and of varying the plasma elongation are also investigated.

The breakdown of a hydrogen plasma using RF heating has been studied in a modular stellarator. The time delay between the beginning of an RF pulse and the production of a measurable density is examined as a function of puff pressure, RF power and magnetic field strength. The confinement time of the ionizing electrons is found to be independent of the collision frequency and their scaling is inversely proportional to the square root of the applied power. The ionization coefficient peaks when the electron cyclotron resonant layer coincides with a saddle point in the magnetic field on the outside of the torus, in agreement with a simple model for the heating rate. Under this condition, the electron cyclotron emission during the discharge is greater by an order of magnitude than when the resonant layer coincides with the magnetic axis. Application of approximately 100 W of power in the ion cyclotron range of frequencies in conjunction with electron cyclotron heating is shown to improve the confinement of the ionizing electrons by about 70%.

Stabilization of the m = 2/n = 1 tearing mode by resistive walls is effective in tokamaks at low-q operation, 2 < q ⪅ 2.6, when the mode rotates quickly compared with the time constant of the wall and with resistive growth times. A sharp stability limit at q_a ≈ 2 results from the loss of wall stabilization when the q = 2 surface moves out of the conducting plasma. This stability limit correlates well with the experimentally observed disruptive limit in plasma current. Simulations of wall locking initiating a disruption at the q_a = 2 limit show very short precursors in comparison with density limit disruptions at high q_a.

A new mode of improved energy confinement, for which the confinement time is not worse or is sometimes even better than that for the well known H-mode and the density of which is in a quasi-stationary state, has been obtained in neutral beam heating experiments on JFT-2M. The new mode is different from the H-mode in many respects. The central electron temperature is higher in the new mode than in the H-mode. Radiation loss and density are reduced in the peripheral region but not in the central region. Therefore, the density and radiation profiles are highly peaked in the new mode, in contrast to the broad profiles in the H-mode. Particle confinement in the peripheral region seems to be worse in the new mode than in the H-mode. The new mode can be obtained in both divertor configurations and limiter discharges in JFT-2M.

Short deuterium beam pulses are injected into the D III–D tokamak to study the variation of beam slowingdown time with temperature and density. The slowing-down time is inferred from the rate of decay of the d(d,n)³He neutron emission. To within ∼30%, the results are consistent with Sivukhin's classical theory. The short beam pulses,are also useful for measurements of the central deuterium density.

The magnetic divertor structure in a modular stellarator has been predicted to change with the addition of an external vertical magnetic field. The diverted flux is expected to emerge predominantly on the inside of the torus when a vertical magnetic field which shifts the magnetic surfaces towards the inside is applied, and vice versa. The prediction has been verified using probe arrays located in the divertor regions. In addition to the redistribution of diverted particle flux, the distance a field line travels from the separatrix until it reaches the wall has been predicted to increase for each of the magnetically altered cases. The formation of magnetic island chains beyond the separatrix has been found to be responsible for the increase.