Table of contents

In this review, a systematic overview of dynamical processes in complex (dusty) plasmas is given. Complex plasmas consist of electrons, ions, neutrals, and microparticles of nanometre to micrometre size, which are responsible for the unusual properties of this kind of plasmas, such as the formation of liquid or solid phases at strong electrostatic coupling. The examples represent the progress in this field within the last five years and mostly such cases were chosen, in which experimental results could be compared with theory or where the phenomenon has a diagnostic application. The presentation begins with single particle effects, where levitation, confinement in plasma traps, charging, and oscillations are involved. It is shown that vertical oscillations can be used for particle charge measurements. Nonlinear and parametric effects as well as self-excited oscillations are discussed. Then the interaction force between the particulates is explored in few-particle systems. Scattering experiments show that the interaction in the levitation plane can be described by shielded Yukawa-type potentials, while the vertical interaction is governed by additional attractive wake fields. The latter are shown to be asymmetric and lead to the formation of vertical strings. The normal modes of one-dimensional or two-dimensional particle arrangements are useful tools for diagnostics. Many-particle effects are discussed in terms of low-frequency electrostatic waves. The dust-acoustic wave, the dust ion-acoustic wave, and two types of dust lattice waves (shear and compressional) are discussed with respect to diagnostic applications, among them Mach cones in plasma crystals. Laser methods are now established for the excitation of such modes. Two novel types of instabilities, the wake-field instability and the void-forming instability, as well as first results on dust ion-acoustic shocks are presented.

Localized driven current profile by electron cyclotron (EC) waves is measured on the JT-60U tokamak, considering transient inductive current. The inductive current is derived from temporal evolution of internal magnetic field, which is evaluated by reconstructions of MHD equilibria with a spline function of total current and with motional Stark effect polarimetry. The analysis clearly shows that the EC-driven current is in a thin layer of about 10% of the minor radius of the plasma. The determined EC-driven current agrees with the one calculated by ray tracing and Fokker-Planck codes. The analysis shows the change in driven current profile when the deposition location of EC waves is changed. The current drive efficiency is about 5×10¹⁸ A W^-1 m^-2 at an electron temperature of 7 keV.

High-triangularity ELMy H-mode experiments (δ_x~0.45) have been carried out in JT-60U. In the low-density regime (_e/n^GW<0.5), the discharges are characterized by type-I ELMs and high-triangularity plasmas produced higher H-mode pedestal pressure than low-triangularity plasmas (δ_x~0.20). In the high-density regime (_e/n^GW>0.5), at fixed neutral beam heating power type-III ELMs are generated and the pedestal pressure reduces gradually with density whereas the ELM frequency at low triangularity is much lower at a given density. Compared to low-triangularity plasmas at low densities, higher pedestal temperature was obtained at high triangularity and the core temperature was also improved by almost the same factor. The profiles of temperature are stiff in the sense that there seems to exist a minimum scale length of temperature gradient. Since plasma shaping affects strongly the peripheral region of toroidal magnetic flux surfaces, the improvement of the edge stability by triangularity leads to higher pedestal temperature, which in turn raises the core temperature.

Interaction of high-frequency electrostatic waves and a static electron density perturbation is considered in a dusty plasma including the effect of dusty charging. The static electron density perturbation is created by the low-frequency ponderomotive force in the parameter regime of a dusty plasma where the electron Debye length and temperature are much greater than the ion Debye length and temperature, respectively. The electron momentum damping rate (ν_e) due to the high-frequency charging process of the dust grains can be much greater or much smaller than the electron plasma frequency or wave frequency (ω) under consideration, depending upon the parameters of the dusty plasma.

When ω>>ν_e, the nonlinear high-frequency wave coupled with the electron density perturbation is described by a nonlinear Schrödinger equation, which bears a modulationally unstable envelope. When ω<<ν_e, the high-frequency electrostatic wave reduces to a dust charge relaxation mode and the coupled nonlinear wave equation yields a solution of envelope shocks.

Experimental VUV spectra from the JET tokamak and from the reversed field pinch RFX have been simulated. For the former device both n = 2 to n = 2 L-shell Ar and Ne spectra (respectively, in the 14.5-43.0 and in the 35.0-80.0 nm ranges) were considered, whereas for RFX only the Ne spectrum was available. The spectra have been observed with the SPRED spectrometer. From the simulation of the spectra, relative sensitivity curves have been obtained for each instrument in the ranges of the simulation. For RFX only, it has been possible to extend this curve from ~13.0 to ~105 nm, by simulating intrinsic C and O emissions. The photon emission coefficients of the lines with wavelengths in the ranges of the experimental spectra were obtained from collisional-radiative models. For Ar and Ne these coefficients have been calculated by the Hebrew University Lawrence Livermore Atomic Codes atomic physics codes, whereas for C and O the corresponding coefficients have been taken from the `Atomic Data and Analysis Structure' database. Impurity modelling is performed using a one-dimensional impurity transport code, calculating for each atomic species the radial distribution of the impurity ions. The line brightnesses are evaluated in a post-processing subroutine and the simulations of the spectra are obtained. The spectral simulations (including impurity ion transport) give confidence in the atomic physics calculations, and allow the determination of the transport coefficients in the plasma regions from which the considered ionization states emit. Finally, the obtained relative sensitivity curves of the two SPRED spectrometers have been compared with the calibrations performed by means of the branching ratio technique.

We investigate nonlinear stationary structures in a system of coupled equations describing drift wave turbulence and associated self-consistent zonal flows. The short-scale drift wave turbulence is described by a kinetic wave equation for the action density of drift waves, whereas the longer-scale zonal flows are described by a dynamic equation for the m = n = 0 (toroidally and poloidally symmetric) component of the potential. Nonlinear stationary structures in a moving frame can be obtained by retaining novel effects associated with `trapped' and `untrapped' drift wave trajectories. We show that drift wave turbulence can self-consistently sustain coherent, radially propagating modulation envelope structures such as solitons, shocks, nonlinear wave trains, etc.

We present a self-consistent method to include in edge plasma simulations the mutual interactions of the secondary electrons emitted by a solid divertor target and the near-target plasma properties. Based on a semi-analytical model, our procedure accounts for the re-absorption of the secondary electrons hitting the wall during their first gyro-period. Theoretical considerations and numerical simulations performed with the B2Solps-5.0 code show that, for parameters in the operational range of present-day tokamaks, the effective electron-induced secondary-electron emission coefficient can be quite small. However, it increases sharply where the electron temperature has a maximum, i.e. near the separatrix. We compare the results of the self-consistent determination of secondary-electron emission with the commonly adopted constant-value assumption. The exact profile of the secondary-electron emission turns out not to have a dominant influence, at least for cases of low temperature at the plates, which have the biggest experimental relevance. The main limitations of our model, in particular the exclusion of roughness effects, are also briefly discussed.

The excited state fractions of hydrogen isotopes in neutral beams are calculated from compact expressions for the rate coefficients and rate equations. The results are presented in a form suitable for beam emission plasma diagnostic interpretation. Comparisons with results in the published literature reveal discrepancies there up to a factor of two in some cases in the H_α emission rate or its density derivative.

This paper discusses some problems of the island divertor in the Wendelstein \mbox{7-X} configuration. These islands exist on the ι = 1 surface at the plasma boundary and will be utilized for impurity control in the Wendelstein \mbox{7-X} experiment. The structure of this island region depends on the plasma pressure and the tendency is to become more and more ergodic with rising plasma pressure. Thermal transport in the divertor region is described by the transport equation, which is inherently three-dimensional. By averaging along the helical geometry of the island, this equation can be reduced to a two-dimensional one describing the temperature distribution in the poloidal plane. In this approximation a strong similarity to tokamak geometry exists. Since the plasma currents modify the islands, a finite-β equilibrium is computed as the basis of a geometric analysis of divertor action. Anomalous transport strongly affects the width of the scrape-off layer and the width of the wetted area on the divertor target plates; therefore it is investigated how anomalous transport modifies the transport equation. The non-linearity of the radiation losses in the divertor region and the non-linearity of the boundary conditions can lead to a bifurcation of the temperature distribution and to multiple solutions. Some numerical examples of one-dimensional temperature profiles and bifurcated solutions are given.

This paper reports on the behaviour of high-energy ions created by ion cyclotron range of frequency (ICRF) heating on the Large Helical Device (LHD). In the third experimental campaign conducted in 1999, it was found that minority heating has good heating performance, and high-energy particles were observed. In the fourth campaign in 2000, the temporal behaviour of high-energy ions was investigated in the minority heating regime using turnoff or modulation of ICRF power. The time evolution of the high-energy particle distribution was measured using a natural diamond detector (NDD) and a time-of-flight neutral particle analyser (TOF-NPA). It was found that the count number of higher-energy particles declines faster than that of lower-energy particles after ICRF turnoff. In the modulation experiments, the phase difference of the flux of high-energy particles with respect to the ICRF power modulation increased with energy. These results were explained qualitatively by the Fokker-Planck equation with a simple model. The pitch-angle dependence of the distribution function was also measured in the experiment by changing the line of sight of the TOF-NPA, and an anisotropy of the high-energy tail was found. This anisotropy was reproduced by solving the bounce-averaged Fokker-Planck equation. The second harmonic heating was conducted successfully for the first time in the LHD in high-β plasma, and high-energy particles were also detected in this heating regime.

A model for an ultimate density limit in tokamaks is presented. The model is based on considerations of radiative power balance and ideal ballooning stability limits at the plasma edge. Predictions for MAST are made and a comparison with experimental data on MAST is presented and discussed.

A method using a tracer-encapsulated solid pellet (TESPEL) has been developed to diagnose particle transport. TESPEL consists of polystyrene as the outer part and another material as the inner core. At first, it was confirmed at the compact helical system (CHS) that the tracer of lithium was deposited locally in the plasma. Moreover, the behaviour of the tracer particles was observed by charge exchange recombination spectroscopy. TESPEL was also injected into the large helical device (LHD). In this case, the Kα line of titanium was observed without the necessity of a neutral beam, and it was shown that this method is promising.

The electron part of the heat flux calculated in section 8 was not calculated correctly, and this section should be replaced by the following.

8. Additional heating associated with divertor biasing

The heat flux to the divertor plate surface is equal to [17]

in the case of nearly normal incidence characteristic of the present MAST design. Here W_i is defined so as to make nu W_i equal to the ion energy flux on the plasma side of the sheath. In the unbiased case these fluxes have a common value

Assuming that the density and the temperatures do not change after the biasing (they are determined by the conditions in the upper part of the SOL, which is not affected by the biasing), and using equation (A2.4), one finds that

Even for e varphi_b/T_e=10, corresponding to 100 V biasing voltage, the relative (with respect to q^*) increase of the heat load is modest, about 50%.