This review paper addresses the physics of stochastic boundaries. Although it is focused on the tokamak configuration many features are common to the stochastic boundaries of stellarators. The stochastic properties of magnetic field lines are recalled and related to the spectrum of the radial magnetic perturbation. The stochastic region, referred to as the divertor volume, is shown to be bounded to the edge plasma. Furthermore, the stochastic features discriminate two regions. On short scales, the stochasticity is not effective and parallel transport dominates, this defines the laminar region. On the long scales one recovers the proper stochastic features which characterize the ergodic regime. Theoretical predictions for the transport of energy, current and particles in the divertor volume are analysed for both the laminar and ergodic regimes. A strong increase in electron transport is expected which should lead to a strong increase in the heat diffusivity, a strong increase in the resistivity in the toroidal direction and generally a decrease in the free electron lifetime in the divertor volume. Ambipolarity of particle transport is ensured by a radial electric field. The ion transport, i.e. particle transport, is then more difficult to analyse since one has to consider the strong coupling to the electron temperature field and to the electric potential field. The perturbation level is such that the particle transport induced by the stochasticity remains comparable to the anomalous transport. The experimental data show good agreement with the predictions on electron transport. This translates into a flattening of the edge temperature gradient, a narrowing of the current channel, which probably governs the observed stabilization of MHD activity, and a strong decrease in the lifetime of the runaway electrons. Regarding particle transport, the response is larger than expected and stochastic boundaries are characterized by significant screening properties compared to limiter shots. This property is shown to be a signature of a pumping capability combined with a change of transport properties. Indeed the transport of neutrals is changed since the ratio of the ionization scales to the distance between the recycling surfaces and the separatrix is reduced. Furthermore, a decreased lifetime of the ions at the very edge of the plasma is expected. Screening effects are thus observed for species exhibiting large wall pumping capability, while He and Ne are weakly affected by the stochastic boundary. The plasma properties in the ergodic volume, namely a reduced edge temperature, an increased impurity radiation, an efficient particle screening and the stabilization of MHD activity, have opened the way to radiating layer investigations on Tore Supra. Stable operation has been achieved with 80% of radiated power and radio frequency heating up to 6 MW.

The parallel Kelvin–Helmholtz instability is investigated as a possible explanation for poloidal asymmetries of density fluctuations which reverse with the plasma current direction. It is shown that these modes are localized around the position where the radial gradient of parallel velocity is maximum. Two mechanisms lead to unstable Kelvin–Helmholtz modes; the acceleration of ions in a presheath and the anomalous Stringer spin-up due to asymmetries of the particle flux. Up–down asymmetries are explained by combining these two effects. Depending on the limiter configuration, the Stringer effect amplifies or weakens the flow due to presheath acceleration. This type of asymmetry reverses with the plasma current direction.

Stark broadening of hydrogen lines in the presence of a magnetic field is revisited, with emphasis on the role of the ion component under typical conditions of magnetized fusion devices. An impact theory for ions valid at low density ͑N e Շ 10 14 cm −3 ͒ and taking into account the Zeeman degeneracy removal of the atomic states is developed. It is shown that the Stark widths of the Lorentz triplet components strongly depend on the magnetic field. The model is validated by a computer simulation method. For the lateral components of Ly␣, we show that the impact approximation still holds for densities as high as N e ϳ 10 15 cm −3 . In contrast, for the central component as well as for the other lines from low principal quantum number, significant discrepancies between the proposed theory and the simulation results appear at high density. Application to D␣ in tokamak divertor plasma conditions shows that, in this case, the quasistatic approximation becomes more relevant.