Table of contents

Several similarity laws for the collisionless interaction of ultra-intense electromagnetic fields with a plasma of an arbitrary initial shape are presented. Both ultra-relativistic and non-relativistic cases are covered. The ion motion is included. A relation to the S-similarity described in Pukhov et al (2004 Plasma Phys. Control. Fusion46 B179) and Gordienko and Pukhov (2005 Phys. Plasmas12 043109) is established. A brief discussion of possible ways of experimental verification of scaling laws is presented. The results can be of interest for experiments and numerical simulations in the areas of ion acceleration, harmonic generation, magnetic field generation and Coulomb explosion of clusters.

High frequency (>100 kHz) modes have been observed for the first time in combined LHCD and ICR-heated minority H (D) plasmas on Tore Supra by means of a correlation ECE diagnostic and by fluctuation reflectometers. These modes have been identified as the toroidicity-induced Alfvén eigenmodes (TAEs) that are destabilized by fast minority hydrogen ions with energies above 250 keV. In reversed central shear plasmas with non-linear oscillations of the central temperature, evolution of the TAE frequency is linked to the development of the local safety factor. This confirms that the central temperature and the q-profile evolve as a non-linearly coupled system in the so-called O-regime in Tore Supra.

In solid targets irradiated by short pulse high intensity lasers, fast electrons have collision times longer than the laser pulse duration and mean free paths much larger than the radius of the laser spot. In these conditions, fast electron transport is dominated by electric and magnetic field. Although the fast electrons are collisionless, collisions of background electrons determine the ability of the background plasma to carry the return current which balances the fast electron current. Hence collisions are important even in this regime. A successful numerical simulation has to be able to model a plasma in which some electrons are collisionless and others are strongly collisional. An expansion of the electron distribution in spherical harmonics in momentum space is well suited to this, and we describe the formulation of the Vlasov–Fokker–Planck equation in terms of spherical harmonics and its solution in our KALOS code. We review the physics that must be modelled in a numerical simulation of fast electron transport and then describe KALOS.

When polarimetric effects are large the Cotton–Mouton and Faraday effects do not combine linearly and it is not possible to separate exactly the pure Cotton–Mouton effect W₁ and the pure Faraday effect, W₃. Four alternative approximate expressions for W₁ and W₃ in terms of measurable quantities are examined for tokamak configurations. Two of these approximations proposed recently are found to be preferable, some previous statements concerning them are corrected and the errors incurred by their use are evaluated.

At the W7-AS stellarator, the neoclassical 'electron-root' was found in discharges with electron cyclotron resonance heating (ECRH) in both O1- and X2-mode. The electron heat diffusivity estimated from the power balance is compared with neoclassical predictions with the radial electric field, E_r, from the ambipolarity condition taken into account. Strongly positive E_r values significantly reducing the electron neoclassical transport coefficients are found in the central region with highly peaked T_e-profiles. Furthermore, the 'electron-root' feature in the ECE time-traces is analysed in the phase when the ECRH is switched off.

The power deposition in phase space is analysed with ray-tracing and bounce-averaged Fokker–Planck calculations. For the O1-mode, the power is almost completely absorbed by passing electrons. These findings are different from the previous X2 results (Maaßberg et al 2000 Phys. Plasmas7 295) for the magnetic configuration with a significant fraction of ripple-trapped electrons in the ECRH launching plane. For these X2 scenarios, fast 'convective' contributions to the radial fluxes had been identified. For the O1-scenarios, a purely 'diffusive' neoclassical modelling of the power threshold for obtaining the 'electron-root' in the different magnetic configurations is described based on the concept of the 'effective helical ripple'. Finally, a simulation of the ECRH switch-off by solving the time-dependent electron energy balance is performed. The results show that the 'electron-root' feature at W7-AS is consistent with the neoclassical predictions.

Experimental observations in stationary ECRH discharges in TCV show that additional heating has a strong effect on the electron density profile. In the absence of MHD activity or strong internal transport barriers, additional electron heating generally leads to a broadening of the density profiles with respect to the Ohmic target plasma profiles. In the ECRH L-mode and in the presence of weak electron internal transport barriers, the density peaking factor depends on the edge safety factor, the power deposition profile and ECRH power. Beyond a critical power of some 0.5 MW, the power dependence saturates. The edge safety factor dependence is supportive of turbulent equipartition (TEP) theory, which predicts inward convection in the presence of turbulence. The observation of a reduction in the peaking with central electron heating supports drift wave turbulence theory, which predicts the decrease of inward particle convection in addition to the inward convection by TEP, when trapped electron modes are destabilized, thereby reducing the net inward convection.

The existence of an electron heat pinch has been experimentally investigated in ASDEX-Upgrade in plasmas with strong off-axis electron cyclotron heating (ECH). Localization of 1.6 MW of ECH power at ρ_dep = 0.65 in plasmas with low Ohmic power (<100 kW) still resulted in peaked electron temperature (T_e) profiles at densities n_e0 ∼ 2.7 × 10¹⁹ m⁻³. Two out of four gyrotrons were modulated in order to study convective effects also on the T_e transient response at different frequencies. Peculiar profiles of the modulation amplitude have been measured, very flat in the region just inside ρ_dep (0.3 < ρ_tor < 0.65) or even increasing rather than decreasing away from ρ_dep on the inner side. The phase profiles instead regularly indicate the propagation of the heat wave in both directions away from ρ_dep. Power balance analysis shows that the heat flux in the core region is very close to zero, but uncertainties do not allow a clear determination of its sign. Modelling steady-state and modulation results with an empirical model featuring a diffusive term characterized by a critical gradient length (L_Te = −T_e/∇T_e) behaviour and a constant Gaussian shaped heat pinch profile allows good reproduction of the data when the region just inside ρ_dep is close to the critical threshold and oscillates around it, and a small convective term U ∼ 1–2 m s⁻¹ is present in the same region. At higher density the T_e profile becomes flatter and the amplitude profiles recover the usual shape with stronger decay inside with respect to outside ρ_dep. In this case no heat pinch is needed and the plasma goes below the critical threshold inside ρ_dep. The results are consistent with the theoretical prediction of a turbulence regulated by a threshold in R/L_Te and a small turbulence generated electron heat pinch term. However initial attempts to perform first principle-based simulations using the quasi-linear electrostatic drift wave Weiland model have failed to reproduce the experimental results.

A linear stability analysis of the RFX-mod equilibrium profiles is carried out in cylindrical geometry for the m = 1 modes resonant inside the reversal surface (dynamo modes). The screening effect of the passive structures surrounding the plasma is taken into account. The results show that magnetic perturbations appear as linear instabilities in the setting up of the reversed field pinch configuration before the reversal of the edge toroidal magnetic field. Later on the equilibrium profiles are found marginally stable for linear tearing modes and completely stable for ideal modes.

To study turbulence, high spatial and temporal resolution are required. In experiments, plasma diagnostics are characterized by low spatial and high temporal resolution. An adapted super-resolution algorithm is proposed to improve the spatial resolution by using temporal information. The performance of the super-resolution algorithm is compared with simple interpolation techniques. By means of synthetic data its performance is benchmarked.

A new straight-magnetic-field-line toroidal coordinate system is introduced by appropriate stretching of the poloidal and toroidal angles (Lamalle P U 2001 Europhys. Conf. Abstracts25 A1145). In this system, the local wavenumber component of every poloidal–toroidal wave Fourier mode along the equilibrium magnetic field, k_||, is rendered by construction constant on all magnetic surfaces.

Semi-analytical expressions are derived for the radio-frequency (rf) response density of tokamak plasmas, providing a convenient description of wave–particle interactions at the fundamental ion cyclotron frequency in general geometry. The new coordinate system makes the analytical developments feasible and remarkably simple: for instance, the cyclotron resonance condition between a particle and a wave Fourier mode is a quadratic equation for the parallel guiding centre (gc) velocity, whereas it is cubic in Boozer coordinates and a transcendent equation in other systems. The theoretical results presented in this paper allow a realistic numerical simulation of rf wave propagation and absorption in the presence of strongly non-Maxwellian distribution functions, such as those created during intense ion cyclotron resonance minority heating scenarios. Extensions of the theory to incorporate finite Larmor radius effects and radial gc drifts are briefly discussed.