Electric probe methods for diagnostics of plasmas are reviewed with emphasis on the link between the appropriate probe theories and the instrumental design. The starting point is an elementary discussion of the working principles and a discussion of the physical quantities that can be measured by the probe method. This is followed by a systematic classification of the various regimes of probe operation and a summary of theories and methods for measurements of charged particle distributions. Application of a single probe and probe clusters for measurements of fluid observables is discussed. Probe clusters permit both instantaneous and time-averaged measurements without sweeping the probe voltage. Two classes of applications are presented as illustrations of the methods reviewed. These are measurements of cross sections and collision frequencies (plasma electron spectroscopy), and measurements of fluctuations and anomalous transport in magnetized plasma.

The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.

A linearized energy-balance model for global temperature is formulated, featuring a scale-free long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parametrized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solution from the observed record is analyzed as a noise process and shown to be consistent with a long-memory time-series model and inconsistent with a short-memory model. By decomposing the forcing record in contributions from solar, volcanic, and anthropogenic activity one can estimate the contribution of each to 20'th century global warming. The LRM model is applied with a reconstruction of the forcing for the last millennium to predict the large-scale features of northern hemisphere temperature reconstructions, and the analysis of the residual also clearly favors the LRM model on millennium time scale. The decomposition of the forcing shows that volcanic aerosols give a considerably greater contribution to the cooling during the Little Ice Age than the reduction in solar irradiance associated with the Maunder minimum in solar activity. The LRM model implies a transient climate response in agreement with IPCC AR4 projections, but the stronger response on longer time scales suggests to replace the notion of equilibrium climate sensitivity by a time-scale dependent sensitivity.

Viscoelastic vortical fluid motion in a strongly coupled particle system has been observed experimentally. Optical tracking of particle motion in a complex plasma monolayer reveals high grain mobility and large scale vortex flows coexistent with partial preservation of the global hexagonal lattice structure. The transport of particles is superdiffusive and ascribed to Lévy statistics on short time scales and to memory effects on the longer scales influenced by cooperative motion. At these longer time scales, the transport is governed by vortex flows covering a wide spectrum of temporal and spatial scales.

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In the BLAAMA" device a wealdy ionized hydrogen plasma is produced by electrons accelerated from a hoL negatively biosed tungsten filament and confined in a toroidal magnetic field of strength up to 0.4 T. The plasma is turbulent, with relative fluctuation levels in ne, # and Tc of 10% or more. The time-averaged state exhibits nested toroidal surfaces of constant potential and pressure, which requires an anomalous cross-field cumeat to remove the spacecharge injected by the cathode and the charge accumulated due to the VB-and C U N ~U E drifts. Typical plusma parameters me n, -10l6 m-3, T, .. 1-20 eV, Z -I eV. The cross-field diffusion coefficient is typically DI -30 m2 s-' -IO4 x Of"""' -10' x DY". Evidence is presented in support of the hypothesis that the placma goes turbulent beuuse it needs to develop an anomalous current channel. nnd this turbulence in tum determines the plasma transport and the time-averaged state.

An experimental study of low-frequency electrostatic fluctuations is presented for a plasma produced by a steady-state discharge in a magnetized toroidal plasma device without a rotational transform. A significant intermittency of the fluctuations is observed. Thus the evolution and propagation of large coherent vortical structures is demonstrated by a conditional sampling technique. The flutelike nature of the structures is explicitly demonstrated. The analysis includes measurements of fluctuations in plasma density, electric potential, and electron temperature. The relevance of the observations to anomalous transport in the device is pointed out. The performance of the conditional sampling technique is compared to a simple correlation analysis by a Monte Carlo simulation.

Transport and confinement within the resistive-g paradigm are investigated by means of two-dimensional numerical simulations. The system is driven by a constant incoming heat flux at the inner radial boundary. Different confinement and transport states are identified, involving self-sustained sheared poloidal flows. At the onset of turbulent convection the probability distribution functions of pressure and radial velocity fluctuations measured in the centre of the plasma layer have a nearly Gaussian form. Further increasing the heat flux drive these distributions become increasingly non-Gaussian, developing exponential tails. This large-scale intermittency is ascribed to the presence of bursting in the domain averaged convective transport and the fluctuation energy integrals. The quasi-periodic bursts are separated by shear-dominated quiescent periods in which the mean flow energy decreases and the confined heat increases on diffusive timescales. The time-averaged thermal energy confined within the plasma layer shows a power law dependence and significant increase with the injected power over the range of turbulent convection investigated.