Table of contents

The authors present an analytical calculation of the neutral particle distribution and its effects on ion heat and momentum transport in three-dimensional plasmas with arbitrary temperature and density profiles. A general variational principle, taking advantage of the simplicity of the charge exchange (CX) operator, is derived to solve self-consistently the problem of neutral-plasma interaction. To facilitate an extremal solution, the short CX mean-free-path (λ_x) ordering is used. Furthermore, a non-variational, analytical solution providing a full set of transport coefficients is derived by making the realistic assumption that the product of the CX cross-section with relative velocity is constant. The effects of neutrals on plasma energy loss and rotation appear in simple, sensible forms. It is found that neutral viscosity dominates ion viscosity everywhere, and in the edge region by a large factor

The authors consider the mechanism of the contraction of the thermal contact area between the plasma and the wall in a tokamak. This mechanism is attributed to the strong dependence of the thermionic emission of electrons on the temperature of the wall surface. A simple, largely analytical model for the description of the heat balances of the plasma and the wall is developed. An instability of small perturbations of homogeneous stationary states is investigated. The possibility of the existence of 'autosolitons', i.e. long living solitary hot spots with a surface temperature of 3000 degrees C, being an intensive source of impurities in a discharge, is shown. The theoretical results are compared with experimental data from TFTR and JET

The MHD equilibrium properties of neutral beam heated plasmas have been experimentally investigated in the Compact Helical System (CHS)-a low aspect ratio (A_p ~ 5) heliotron/torsatron. This configuration is characterized by a strong breaking of helical symmetry. The radial profiles measured by various diagnostics have shown a significant Shafranov shift due to the plasma pressure. The deviation of the magnetic axis from is vacuum position has become as large as 50% of the minor radius. When the three-dimensional equilibrium code VMEC is used to reconstruct the equilibrium from the experimental data, the result is in good agreement with the experimentally observed Shafranov shift as well as with the diamagnetic pressure in plasmas with ⟨β⟩ ⩽ 1.2% and β₀ ⩽ 3.3%. This beta values corresponds to half of the conventional equilibrium β limit defined by the Shafranov shift reaching a value of half of the minor radius. Although tangential neutral beam injection causes pressure anisotropies, p_||/p_⊥ ⩽ 3, the description of the equilibrium assuming isotropic pressure is consistent with the experiment

Analysis of MHD activity in pellet enhanced performance (PEP) pulses is used to determine the position of rational surfaces associated with the safety factor q. This gives evidence for negative shear in the central region of the plasma. The plasma equilibrium calculated from the measured q values yields a Shafranov shift in reasonable agreement with the experimental value of about 0.2 m. The corresponding current profile has two large off-axis maxima in agreement with the bootstrap current calculated from the electron temperature and density measurements. A transport simulation shows that the bootstrap current is driven by the steep density gradient, which results from improved confinement in the plasma core where the shear is negative. During the PEP phase (m,n)=(1,1) fast MHD events are correlated with collapses in the neutron rate. The dominant mode preceding these events usually is n=3, whereas the mode following them is dominantly n=2. Toroidal linear MHD stability calculations assuming a non-monotonic q-profile with an off-axis minimum decreasing from above 1 to below 1 describe this sequence of modes (n=3,1,2), but always give a larger growth rate for the n=1 mode than for the n=2 mode. This large growth rate is due to the high central poloidal beta of 1.5 observed in the PEP pulses. Finally, a rotating (m,n)=(1,1) mode is observed as a hot spot with a ballooning character on the low field side. The hot spot has some of the properties of a 'hot' island consistent with the presence of a region of negative shear

A 1-D relativistic Eulerian Vlasov code, with a fluid description of the plasma motion in the direction normal to the external magnetic field, is used to study the laser-plasma beat wave or backward Raman scattering current drive and heating. The code is validated by comparison with a fully kinetic 1-D 2/2 Vlasov code. Emphasis is placed on the dynamics of electrons in the low density region of phase space which generally is badly represented in the usual particle-in-cell methods. The low noise level of the Vlasov code allows precise measurements to be made of action transfer between photons, plasmons and electrons in Raman scattering processes. Results relevant to MTX- and ITER=like parameters are presented

Simple semi-analytical models are presented to calculate the temporal evolution of the plasma temperature and length or thickness in the Coaxial Slow Source (Nucl. Fusion 27 (1987) 1478) for both tearing formation and programmed formation. It is assumed that energy is delivered to the plasma via Ohmic heating and compressional work and is lost through impurity line radiation. The plasma is considered to be always fully ionized and in pressure balance; the external magnetic field is taken to be a known function of time, and particle losses are neglected. In tearing formation, a long and thin plasma sheet is initially formed. This can be studied using a 1-D model; it is shown that the higher the external field and the smaller the line integrated density, the faster the temperature increases. In programmed formation, an axial equilibrium is quickly established and a 2-D model is required. It is shown that when the external magnetic field exceeds a critical value, which depends on the temperature, the impurity fraction and the effective plasma thickness, the radiated power overcomes Ohmic heating and a radiative collapse occurs. Various time histories of the external magnetic field are analysed in order to determine the conditions that result in the fastest increase in plasma temperature

The shapes of the electron temperature and electron density profiles in the OH, L- and H-mode confinement regimes of ASDEX are explored by statistical analysis. It is shown that the shape of T_e(r) is conserved in the outer half of the plasma in these regimes and that it is invariant with respect to heating power, heating profile, density, density scale length, q value and ion mass. These results suggest that microturbulence constrains the shape of the temperature profile by adjusting the electron heat diffusivity χ_e(r). No such invariance is found for the temperature profile in the inner half of the plasma and for the density profile over the whole cross-section. Properties of the empirical electron heat diffusivity and the diffusion coefficient in different regimes can be described by T_e profile invariance. The improved confinement with peaked density profiles, the reduction of χ_e in the bulk of H-mode plasmas and the power dependence of χ_e in the L-regime are discussed

Local heat transport in auxiliary heated JT-60 plasmas has been analysed, with emphasis on the understanding of the deteriorated confinement observed in the L-mode. The dependence of the local thermal transport on plasma current, density and heating power have been studied in both divertor (single null, lower X-point) discharges and limiter discharges with hydrogen beam injection into hydrogen plasmas. The deterioration of the energy confinement time with increasing auxiliary heating power-the so-called power scaling-is mainly due to the stronger impact of the ion heat transport. It is found that the ion thermal diffusivity has a favourable density dependence. Experimentally obtained profiles of the ion temperature have been compared with the predictions of the theoretical model, especially with regard to the transport coefficients derived from the theory of the ion temperature gradient instability. For L-mode plasmas in JT-60, the theory has been found to be in good quantitative agreement with measurements over a wide range of plasma parameters, with the exception of limiter discharges with a plasma current of 1 MA

The effect on H-mode energy confinement of operating at low values of the plasma safety factor q has been investigated experimentally on the DIII-D tokamak (see Plasma Physics and Controlled Nuclear Fusion Research 1986 (Poroc. 11th Int. Conf. Kyoto, 1986), Vol.1, IAEA, Vienna (1987) 159). Operationally, the linear increase of H-mode energy confinement with plasma current ceases when the ratio of the plasma current to the toroidal magnetic field is high than approximately=1 MA/T. Experimentally, it has been determined that this saturation of confinement is not the result of a ceiling imposed by saturated Ohmic confinement, by the plasma reaching a toroidal beta limit, by enhanced plasma radiation or by edge localized modes. The observed saturation of confinement is found to be quantitatively consistent with a model of global energy confinement degradation resulting primarily from the macroscopic phenomena of sawteeth. The experimental data are also qualitatively consistent with an alternative explanation for the confinement saturation which involves enhanced transport brought about by ion temperature gradient driven turbulence

Neoclassical transport in the banana regime has been analysed with the DKES (Drift Kinetic Equation Solver) code for the Large Helical Device (LHD). It is found that in the 1/ν regime the diffusion coefficients change by one order of magnitude for various LHD configurations, depending on the structure of the helical magnetic ripple. The neoclassical transport calculated with the DKES code is quantitatively in good agreement with a multi-helicity theory formulated by Shaing and Hokin (1983). Incorporating the multi-helicity effect into the diffusion coefficient, the authors propose an interpolation formula for the diffusion coefficient in the 1/ν and ν regimes. When the ion temperature is increased at a fixed density of n = 10²⁰ m^-3, the ions undergo a transition from 1/ nu neoclassical transport to the nu regime when T_i > 3 keV, with a radial electric potential eϕ comparable to the ion temperature (eϕ/T_i ≈ 1). For the optimized configuration, the ion thermal diffusivity has a maximum value of ≈ 3.5 m²/s at a minor radius r/a ≈ 0.5. The bootstrap current has also been studied and the results have been compared with the theory. At the collisionless limit with a moderate radial electric potential of eϕ/T_i ≈ 1, the DKES calculations evaluated for various LHD configurations support the theoretical formula given by Shaing and Callen (1983). For collision frequencies between the plateau regime and the banana regime, where the analytical theory is not applicable, the bootstrap current might become larger (by a factor of about two) than in the collisionless limit, depending on the radial electric field

The details of the bulk transport in DIII-D across the L-H transition have been studied with a time dependent transport analysis of a series of repeat discharges. Time dependent profiles of n_e, T_e, T_i, Z_eff, V_ϕ and P_rad were obtained for these discharges. The confinement properties were observed to improve in the plasma bulk after the transition. The dominant improvement is in the electron channel. The electron diffusivity profile flattens and drops to values comparable to those of the ion diffusivity. The changes in the ion diffusivity are within the error bars, thus preventing any definite conclusions, but after the transition the data show a consistent drop in the values. The drop in the electron diffusivity does not occur abruptly at the time of the transition; rather, the improvement starts within 30 ms after the transition and the improvement continues until at least 80 ms after the transition. The nature of changes in the electron density is similar to that of changes in the diffusivities, suggesting that the density gradient length is a critical quantity in the L-H transition. Experimental data are compared with a model for the ion temperature gradient (ITG) mode. Stabilization of the ITG mode does not seem to take place in the L-H transition, but the plasma might be marginally stable against the ITG mode in both the L-mode and the H-mode

An approximate expression for the beam driven current in which the trapping effects of fast ions and electrons are included is derived by means of a variational principle. The beam driven current due to arbitrary fast ions can be calculated easily from this expression in an axisymmetric magnetic field with finite aspect ratio. It is shown that in a tokamak with circular cross-section this expression gives a good approximation to the results obtained by numerically solving the Fokker-Planck equation. The beam driven current due to energy diffusion, which is neglected in the approximate expression, is also estimated

Effects of finite beta , ion kinetic damping and trapped electrons on the toroidal ion temperature gradient (ITG) mode have been investigated by two methods-a fully toroidal fluid analysis corrected for ion Landau damping, and an electromagnetic local kinetic dispersion relation. When trapped electrons are ignored, the ITG mode is stabilized at a beta value well below the critical beta for the ideal MHD ballooning mode (β_MHD). Trapped electrons are destabilizing and increase the upper limit of beta to a level comparable with β_MHD. Ion Landau damping increases the critical temperature gradient typically by a factor of two (L_T/L_B ≲ 0.18), and the growth rate remains smaller than the ion transit frequency, ω_Ti = k_||v_Ti

Report on the 8th International Workshop, IAEA Technical Committee Meeting held at Khar'kov, Union of Soviet Socialist Republics, 27-31 May 1991.

Report on the Course and Workshop held at the International School of Plasma Physics `Piero Caldirola', Villa Monastero, Varenna, Italy, 27 August to 6 September 1991.