Table of contents

The results leading to the identification of coherent structures emerging from the background turbulence in the edge region of the reversed field pinch experiments EXTRAP-T2R and RFX are reviewed. These structures have traits of vortices in velocity field and blobs in density, and the reconstruction of their spatial structure and of their time evolution is discussed focusing on the analysis tools applied. The role of these structures in the particle anomalous transport is addressed, showing that their collisions can contribute up to 50% the total particle losses.This process is shown to be responsible for bursts in particle flux and it is found to set a characteristic collision time, which is in agreement with the statistical properties of laminar times for particle flux bursts.

Laser-induced fluorescence (LIF) has become a standard diagnostic for ion temperature and ion drift measurements in plasmas. LIF is non-invasive and provides a high-spatial and a high-energy resolution. With the recent development of advanced laser systems LIF is more and more used to also detect perturbations of the ion-velocity distribution function (IVDF) and to get detailed information about the ion dynamics. This paper reports on a method to perform phase-resolved measurements of the IVDF in periodically perturbed plasmas. As an example LIF measurements during magnetic reconnection are discussed. The parallel component of the IVDF is measured with and without reconnection. If reconnection is driven, the ion temperature is found to be twice as high as without reconnection. The evolution of the IVDF during a reconnection cycle reveals strong variations of the ion temperature correlated with the reconnection drive.

We report results from experiments performed to study how a change in boundary conditions affects the plasma state in the toroidal geometry of the Blaamann device in Tromso. The boundary condition was changed by applying a dc bias on a limiter extended around the entire poloidal circumference of the plasma column. Two distinctly different plasma potential states were found. One state was associated with a bias at or negative with respect to the floating potential of the limiter, and a small ion-saturation current. The other state was associated with a positive bias with respect to the floating potential, near or in the electron saturation regime of the limiter. In the latter case the potential minimum in the middle of the cross-section was significantly less negative than in the case of ion-saturation current to the limiter. On the other hand, the grounded limiter provided the best confinement properties, for which the density maximum was significantly higher than for both more positive and more negative biases. This state also had the lowest fluctuation levels, and near zero poloidal velocities close to the boundaries, as well as the smallest radial, anomalous particle transport.

The formation and propagation of spatiotemporal fluctuation structures in drift-wave turbulence in a linearly magnetized helicon device is investigated. Structures are extracted by correlation analysis. Their typical lifetime exceeds the eddy turnover time by one order of magnitude. The radial correlation analysis yields radial propagation of turbulent fluctuations with velocities up to 50% of the ion sound speed. The two-dimensional analysis of the entire azimuthal cross-sections reveals that the propagation is purely azimuthal and that the radial speeds are an artefact of the one-dimensional measurement of a multi-dimensional propagation.

The boundary conditions in an electron cyclotron resonance (ECR) source have been modified to mimic the operating conditions where current-free double-layers (DLs) have been recently measured in rf helicon plasmas. The plasma is heated or generated by the ECR at 875 G inside a dielectric source tube, and expands into a grounded diffusion chamber (terminated by a glass plate) by a rapidly decreasing magnetic field. Preliminary studies of the plasma expansion have been performed. For the present conditions (1 mTorr, 500 G and 500 W), no DL is observed near the source exit and the plasma diffusion is well described by a Bolzmann expansion.

The detection of large-scale structures in broadband turbulence is a recent task in neutral fluids and plasma physics. Conditional averaging is one of the most commonly used methods for this purpose. In this paper, the prospects and limitations of conditional averaging are systematically investigated. By means of an analytic model, synthetic and experimental data, the reliability of the conditional averaging method to resolve amplitudes and phase shifts of density and potential structures embedded in a noisy background are discussed.

The temporal evolution and other characteristics of intense quasi-static electric fields in the return current region are discussed using Cluster observations. A narrow-scale, divergent electric field, the high-altitude signature of a positive U-shaped potential structure, was observed at the poleward edge of the central plasma sheet, close to magnetic midnight at a geocentric distance of about 4.2 Earth radii. Its acceleration potential increased from less than 1 to 3 kV on a 100 s timescale, similar to the formation time for ionospheric plasma density holes, and consistent with previous results for this kind of structure. In the adjacent upward current region, an energy decrease in inverted-V ions was observed some minutes prior to this. The inverted-V potential decrease was roughly equal to the subsequent perpendicular potential increase in the return current region, suggesting that a potential redistribution took place between the two adjacent current branches. Other characteristics of this and three other return current structures are summarized, to illustrate both common and different features of these. The structures are characterized by (all values have been mapped to the ionospheric level) peak electric-field magnitudes of ≈1 V m⁻¹, bipolar or unipolar profiles, occurrence at plasma boundaries associated with plasma density gradients, perpendicular scale sizes of ≈10 km, downward field-aligned currents of ≈10 μA m⁻², and upward electron beams with characteristic energies of a few hundred to a few thousand eV. The bipolar and unipolar electric-field profiles are proposed to reflect whether plasma populations, dense enough to support upward field-aligned currents (by which the return current can close) exist on both sides, or on one side only of the boundary.

The spontaneous generation of large-scale flows by the rectification of small-scale turbulent fluctuations is of great importance both in geophysical flows and in magnetically confined plasmas. These flows regulate the turbulence and may set up effective transport barriers. In the present contribution the generation of zonal flows will be illustrated in a simple fluid experiment performed in a rotating container with radial symmetric bottom topography. An effective mixing that homogenizes the potential vorticity in the fluid layer will lead to the replacement of the high-potential vorticity near the centre with low potential vorticity from the outside, which will imply the formation of a large-scale flow. The experimental results are supported by direct numerical solutions of the quasi-geostrophic vorticity equation in the β-plane approximation modelling the experimental situation. The analogy to large-scale flow generation in drift-wave turbulence dynamics in magnetized plasma is briefly discussed.

Two-dimensional (2D) plasma profiles, gradient-driven low frequency electrostatic waves and anomalous particle transport are studied experimentally in a purely toroidal plasma configuration. The plasma is produced by a negatively biased, emissive cathode in conjunction with a variably biased anode plate localized on the same field line. Nearly circularly symmetric potential profiles, positive or negative, can be obtained by varying the anode plate bias. Confinement loss in the form of plasma ejection in the major radius direction is only observed when the anode is biased close to ground potential. For the cases of circularly symmetric plasma flow electrostatic flute modes with poloidal mode number m = 1 and m = 2 are identified as unstable on the low-field side of the density maximum, but indications are also given that they coexist with spatially quasi-uniform oscillations and, for low frequencies, with an ion acoustic mode with toroidal mode number n = 1 propagating parallel to the magnetic field. The anomalous particle flux density is found to be non-uniformly distributed on a toroidal surface, and the main flux is passed through two lobes directed almost vertically upwards and downwards, while almost no flux takes place along the major radius direction.

We apply a newly developed set of gyrotropic fluid transport equations to the solar wind. The transport equations are based on a perturbed bi-Maxwellian velocity distribution function and describe number density, flow speed, temperature along andacross the magnetic field and heat flow. The equations are designed to provide an improved description of collisions in fully ionized plasmas, leading to a better description of heat conduction and thermal forces than previously developed gyrotropicequations, while retaining the description of collisionless plasma flow provided by gyrotropic equations. The equations are implemented in a solar wind model extending from the chromosphere to 1 AU and are solved for ahydrogen-proton-electron plasma. The new model solutions are compared with other solar wind models. We find that in a rapidly expanding coronal-flow geometry, the new equations lead to a solar wind solution very different from previous gyrotropic models, with a solar wind mass flux seven times larger, and the asymptotic-flow speed reduced by a factor 4. Thisdifference is caused by the different description of heat flow in the two models, which affects the energy transport between the corona and lower layers of the solar atmosphere. In a radially expanding geometry, the differences between new and oldsolutions are much smaller. The proton temperature anisotropy in the collisionless outer solar wind behaves very similarly with the new and old gyrotropic equations, with both providing a good description of the effect of the Lorentz force.

We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect of turbulence on the microscopic particle dynamics. Our main goal is to analyse the dispersion of ideal test particles faced to diverse conditions in the turbulent domain. Depending on the amplitude of the background field and the input test particle velocity, we observe distinct transport regimes ranging from subdiffusion of guiding centres in the limit of Hamiltonian dynamics to random walks on a percolating fractal array and, further, to nearly diffusive behaviour of the mean-square particle displacement versus time. In all cases, we find a complex microscopic structure of the particle motion revealing long-time rests and trapping phenomena, sporadically interrupted by the phases of active cross-field propagation reminiscent of Levy-walk statistics. These complex features persist even when the particle dispersion is diffusive. An interpretation of the results obtained is proposed in connection with the fractional kinetics paradigm extending the microscopic properties of transport far beyond the conventional picture of a Brownian random motion. A calculation of the transport exponent for random walks on a fractal lattice is advocated from topological arguments. An intriguing indication of the topological approach is a gap in the transport exponent separating Hamiltonian-like and fractal random walk-like dynamics, supported through the simulation.

Two-dimensional numerical fluid turbulence simulations demonstrating the formation and radial propagation of blob structures in toroidally magnetized plasmas are presented and analysed in detail. A salient feature of the model is a linearly unstable edge plasma region with localized sources of particles and heat, which is coupled to a scrape-off layer with linear damping terms for all dependent variables corresponding to transport along open magnetic field lines. The formation of blob structures is related to profile variations caused by bursting in the global turbulence level, which is due to a dynamical regulation by self-sustained differential rotation of the plasma layer. Radial propagation of the blob structures follows from a vertical charge polarization due to magnetic guiding centre drifts in the toroidally magnetized plasma. Statistical analysis of the particle density, radial electric drift and the radial turbulent particle flux reveals asymmetric conditional waveforms with a steep front and a trailing wake and positively skewed and flattened probability distributions, in agreement with recent experimental investigations. Coarse graining and spectral analysis further indicate the presence of long-range correlations in the particle density fluctuations. Finally, conditional statistics of the particle flux demonstrates the intermittency of the turbulent plasma transport and the quasi-periodic apparency of blob structures due to bursting in the global turbulence level.

In this contribution some recent investigations of two-dimensional thermal convection relevant to ordinary fluids as well as magnetized plasmas are reviewed. An introductory discussion is given of the physical mechanism for baroclinic vorticity generation and convective motions in stratified fluids, emphasizing its relation to interchange motions of non-uniformly magnetized plasmas. This is followed by a review of the theories for the onset of convection and quasi-linear saturation in driven-dissipative systems. Non-linear numerical simulations which result in stationary convective states reveal the process of laminar scalar gradient expulsion, leading to the formation of temperature plumes and vorticity sheets. These dissipative structures are demonstrated to result in temperature profile consistency and power law transport scaling far from the threshold. The last part of this paper deals with the generation of differential rotation by fluctuating motions through tilting of the convective structures. The role of kinetic energy transfer and shearing due to differential advection is pointed out. Numerical simulations for strongly driven systems reveal turbulent states with a bursty behaviour of the fluctuation level which is associated with relaxation oscillations in the kinetic energy of the azimuthally mean flows. This leads to a state of large-scale intermittency manifested by exponential tails in the single-point probability distribution function of the dependent variables. The global bursting is interpreted in terms of a predator–prey regulation from the point of view of energetics. Finally, a discussion is given of the relevance of these phenomena to a variety of magnetized plasma experiments.

Kinetic effects associated with a neutralized plasma beam injected into a neutral background are investigated by numerical methods. We assume that the dominant interactions between ions and neutrals are charge exchange collisions. It is readily noted that by these processes, a fast ion is replaced by a slow one, implying that the injected fast-ion population will generate a new slow one. For a wide parameter range, we find that the combination of these two populations will become unstable with respect to kinetic ion-sound instabilities. The resulting enhanced level of electrostatic fluctuations gives rise to an enhanced scattering of the injected ions, with a resulting very wide velocity distribution. These observations have relevance for instance for chemical processes in the plasma state, where details in the velocity distribution of the constituents can be important. The basic features of the processes outlined here are illustrated by results from a particle-in-cell simulation in one spatial dimension. The results have a wider range of applicability than those outlined here, i.e. similar observations can be made for elastic ion neutral collisions as well.

Passive tracer dynamics are used in numerical simulations of plasma turbulence to describe fundamental anomalous transport processes including diffusive behaviour and up-gradient transport for paradigmatic as well as more realistic plasma turbulence systems. The limits of the applicability of passive tracer dynamics to extrapolate to the overall or even just to impurity transport are discussed. Results are presented on curvature- and inertia-related pinch effects and further on the clustering of passive tracers due to the compressibility of the advecting turbulent velocity fields.

Plausible observations of MHD solitons by means of the Cluster system have recently been reported. The present paper addresses the theory of stationary wave forms obtained from MHD-type equations extended with Hall dispersion. Two aspects will be discussed: (i) the solitary wave solutions come in families, characterized by their velocity–amplitude relationship. The metamorphosis of these relationships will be described, starting with their form for small amplitude models (the KdV equation, the MKdV equation, the DNLS equation, and the triple-degenerate DNLS model), going through the cold plasma model, warm plasma scalar pressure model, and concluding with studies of models with anisotropic pressure. (ii) The predicted wave forms have a series of robust signatures well fitted for experimental tests. These include the polarization of the magnetic field through the structures (i.e., the magnetic hodograph), the relation between magnetic pressure and density perturbation, and the relation between the pressure components in the anisotropic models. These are also characterized in various families and models.

The Third Nordic Symposium on Plasma Physics was organized at Lysebu, Oslo, Norway on 4–7 October 2004, under the auspices of the Norwegian Centre for Advanced Study (CAS). The arrangement was preceded by two similar meetings organized at the Risø National Laboratory in Denmark by one of us (HP): Nonlinear Waves in Plasmas, 13–16 August 1985, and The Second Nordic Symposium on Nonlinear Phenomena in Plasmas and Related Topics, 8–12 August 1988. The proceedings from these two previous meetings were published as Physica Scripta Reprint Series No. 2, and RS 16 (with a few copies still being available). The idea of `Nordic' in the title of this latest meeting was interpreted somewhat liberally, by including also scientific organizations in northern Germany, where a collaboration facing Nordic countries comes naturally, and indeed has solid historical roots pointing also to ongoing activities. We hope that this series of meetings can continue, suggesting that the interval should be kept to a minimum of three years to ensure that all participants present new results. (We hope not to have to wait 16 years until next time, though!) The aim of our meetings is to stimulate collaboration among plasma physicists by creating a forum where the participants can exchange ideas and seek inspiration under relaxed conditions. We have the distinct impression that the meeting was very successful in this respect.

Many Nordic institutes have widespread international collaborations, and we were happy to welcome also foreign representatives for some of these activities. Altogether 28 contributed talks were presented by 30 participants. The abstracts of all talks were distributed at the meeting. The present proceedings cover a selection of the contributions. One participant had to cancel, but the contribution is included in these proceedings. All the papers have been refereed according to the usual standards of the journal

We, the organizers, thank CAS for the generous financial support and also the staff at the centre for the help we received with the practical arrangements. Also we thank the Norwegian Academy of Sciences for their hospitality by letting us arrange the conference dinner at the academy.