S. Benkadda

Magnetic reconnection and Kelvin–Helmholtz instabilities at the Earth's magnetopause

Kelvin–Helmholtz instability (KHI), driven by the velocity inhomogeneity at Earths magnetopause, has been shown to play a major role in mixing the magnetospheric and the solar wind plasma during northward periods. In fact, when the magnetospheric and interplanetary magnetic fields are mostly perpendicular to the equatorial plane, KHI can develop at a low latitude without being significantly inhibited by the magnetic tension. In contrast, at a high latitude, the more complex magnetic configuration is believed to totally stabilize the instability. This intrinsic 3D dynamics is investigated in a simplified geometry showing that KHI is able to kink the magnetic field lines at a mid-latitude and to create current layers where magnetic reconnection spontaneously develops. It is shown that a mid-latitude reconnection is able to change the global topology of the magnetic field and to connect interplanetary field lines to the Earths cups, allowing the solar wind to directly enter the magnetosphere.

Flux driven turbulence in tokamaks

The work presented deals with tokamak plasma turbulence in the case where fluxes are fixed and profiles are allowed to fluctuate. These systems are intermittent. In particular, radially propagating fronts are usually observed over a broad range of time and spatial scales. The existence of these fronts provides one possible way to understand the fast transport events sometimes observed in tokamaks. It is also shown that the confinement scaling law can still be of the gyro-Bohm type in spite of these large scale transport events. Some departure from the gyro-Bohm prediction is observed at low flux, i.e. when the gradients are close to the instability threshold. Finally, it is found that the diffusivity is not the same for a turbulence calculated at fixed flux as for a turbulence calculated at fixed temperature gradient, with the same time averaged profile.

A signature for turbulence driven magnetic islands

We investigate the properties of magnetic islands arising from tearing instabilities that are driven by an interchange turbulence. We find that such islands possess a specific signature that permits an identification of their origin. We demonstrate that the persistence of a small scale turbulence maintains a mean pressure profile, whose characteristics makes it possible to discriminate between turbulence driven islands from those arising due to an unfavourable plasma current density gradient. We also find that the island poloidal turnover time, in the steady state, is independent of the levels of the interchange and tearing energy sources. Finally, we show that a mixing length approach is adequate to make theoretical predictions concerning island flattening in the island rotation frame.

Dynamics of magnetic islands in large Δ′ regimes

Saturation of magnetic islands at large values of the tearing mode stability parameter Δ′ is investigated numerically. In such regimes, the island dynamics exhibit a number of transient features such as coalescence instability, X-point collapse, and plasmoid generation. It is shown that while conditions for these transient instabilities to appear depend on the viscosity and resistivity, the final width of the saturated island is independent of such phenomena, as well as viscosity and resistivity values. It is found that the saturated island width is strongly influenced by global properties of the current profile and related to the equilibrium reconnected flux across the magnetic island.

Ballistic propagation of turbulence front in tokamak edge plasmas

The flux-driven nonlinear simulation of resistive ballooning mode turbulence with tokamak edge geometry is performed to study the non-steady component in the edge turbulence. The large-scale and dynamical events in transport are investigated in a situation where the mean flow is suppressed. Two types of dynamics are observed. One is the radial propagation of the pulse of pressure gradient, the other is the appearance/disappearance of radially elongated global structure of turbulent heat flux. The ballistic propagation is observed in the pulse of pressure gradient, which is associated with the front of turbulent heat flux. We focus on this ballistic propagation phenomenon. Both of the bump of pressure gradient and the front of heat flux propagate inward and outward direction. It is confirmed that the strong fluctuation propagates with the pulse front. It is observed that the number of pulses going outward is close to those going inward. This ballistic phenomenon does not contradict to the turbulence spreading theory. Statistical characteristics of the ballistic propagation of pulses are evaluated and compared with scaling laws which is given by the turbulence spreading theory. It is found that they give qualitatively good agreement.

Shearless transport barriers in magnetically confined plasmas

Shearless transport barriers appear in confined plasmas due to non-monotonic radial profiles and cause localized reduction of transport even after they have been broken. In this paper we summarize our recent theoretical and experimental research on shearless transport barriers in plasmas confined in toroidal devices. In particular, we discuss shearless barriers in Lagrangian magnetic field line transport caused by non-monotonic safety factor profiles. We also discuss evidence of particle transport barriers found in the TCABR Tokamak (University of S˜ ao Paulo) and the Texas Helimak (University of Texas at Austin) in biased discharges with non-monotonic plasma flows. (Some figures may appear in colour only in the online journal)

Generation of a magnetic island by edge turbulence in tokamak plasmas

We investigate, through extensive 3D magneto-hydro-dynamics numerical simulations, the nonlinear excitation of a large scale magnetic island and its dynamical properties due to the presence of small-scale turbulence. Turbulence is induced by a steep pressure gradient in the edge region [B. D. Scott, Plasma Phys. Controlled Fusion 49, S25 (2007)], close to the separatrix in tokamaks where there is an X-point magnetic configuration. We find that quasi-resonant localized interchange modes at the plasma edge can beat together and produce extended modes that transfer energy to the lowest order resonant surface in an inner stable zone and induce a seed magnetic island. The island width displays high frequency fluctuations that are associated with the fluctuating nature of the energy transfer process from the turbulence, while its mean size is controlled by the magnetic energy content of the turbulence.

Mechanisms and dynamics of the external transport barrier formation in non-linear plasma edge simulations

L-H transition features are reproduced using three-dimensional ă first-principles plasma edge turbulence simulations. A transport barrier ă is observed to form spontaneously above a threshold of the input power. ă The physical mechanism relies on the coupling between the equilibrium ă pressure gradient and the poloidal flow, through both the radial force ă balance and the neoclassical friction. Accounting for the actual radial ă profile and time evolution of the latter is key to the barrier ă formation. It is found that neoclassical friction acts as an energy ă source for the flow, which largely overcomes the sink due to the ă turbulent Reynolds stress during the whole barrier lifetime. ă Importantly, experimentally reported dynamical features are recovered ă during the formation and lifetime of the barrier. This includes ă dithering of the radial electric field, which is reminiscent of ă experimentally observed limit-cycle oscillations and quasi-periodic ă relaxation oscillations showing similarities with type-III ELMs. These ă rich dynamics emerge from interplay between turbulence, ă turbulence-driven flows and the equilibrium flow governed by force ă balance.

Saturation of magnetic islands in equilibria with a finite current gradient. Part II: Numerical simulations

The saturation of magnetic islands is studied numerically for the current profiles with a finite gradient at the rational surface. It is shown that the results of such simulations are in good agreement with analytical theory presented in part I. The effects of plasma viscosity is studied and shown not to affect the final state of the magnetic islands.

Saturation of magnetic islands in equilibria with a finite current gradient. Part I: asymptotic theory

The problem of saturation of magnetic islands for the case of a finite current gradient at the rational surface has been revisited. The asymptotic procedure is presented giving the explicit expressions for the perturbed magnetic flux function at saturation. The resulting nonlinear equation for the island width has been obtained in the form similar to the previous work but with fully analytical expressions for the asymptotic series.