O. Agullo

Global simulations of ion turbulence with magnetic shear reversal

This paper presents the results of three-dimensional fluid global simulations of electrostatic ion turbulence in tokamaks with reversed magnetic shear. It is found that a transport barrier appears at the location of magnetic shear reversal. This is due to a rarefaction of resonant surfaces in this region. For the same reason, the barrier is more pronounced when the minimum of the safety factor is a simple rational number. The barrier is broadened by velocity shear effects. It is also found that large-scale transport events hardly cross a transport barrier. Finally, a significant amount of toroidal rotation is generated by the turbulence. This rotation changes its sign at the position of magnetic shear reversal, as expected from a quasi-linear estimate of the Reynolds stresstensor.

Anomalous transport in Charney-Hasegawa-Mima flows

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around mu = 1.75, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover, the law gamma = mu + 1 linking the trapping-time exponent within jets to the transport exponent is confirmed, and an accumulation toward zero of the spectrum of the finite-time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse-grained picture of the jet, the motion within the jet appears as chaotic, but that chaos is bounded on successive small scales.

Impact of a shear flow on double tearing nonlinear dynamics

The dynamics of global reconnection in the presence of a poloidal shear flow located in between magnetic islands is investigated. Different linear and nonlinear regimes are identified depending on the resistivity, the equilibrium velocity amplitude, and the distance between the low-order resonant surfaces. It is found that nonlinearly, the shear flow can significantly delay DTM generation and global reconnection. It is shown that this delay is linked to a symmetry breaking imposed by the shear flow and the generation of mean poloidal flows in the resistive layers. It is also found that turbulence can be generated by Kelvin-Helmholtz instability in between the resonance layers and enhance magnetic reconnection processes.

Global current profile effects on the evolution and saturation of magnetic islands

The nonlinear evolution of magnetic islands is investigated by means of numerical simulations. The growth and saturation of the island are shown to depend not only on asymptotic tearing mode stability parameter Δ′ but also on the initial global current profile. Presence of the external current sheets leads to the formation of different island state for the same value of Δ′. It is found that the flow vorticity generated by the interacting current sheets is an important feature of nonlocal interactions and nonlocal effects in magnetic islands dynamics.

From chaos of lines to Lagrangian structures in flux conservative fields

Abstract.A numerical method is proposed in order to track field lines of three-dimensional divergence free fields. Field lines are computed by a locally valid Hamiltonian mapping, which is computed using a symplectic scheme. The method is theoretically valid everywhere but at points where the field is null or infinite. For any three dimensional flux conservative field for which problematic points are sufficiently sparse, a systematic procedure is proposed and implemented. Construction of field lines is achieved by means of tracers and the introduction of various Hamiltonians adapted to the “geometrical state” each line or tracer is. The states are artificially defined by an a priori given frame of reference and Cartesian coordinates, and refer to a Hamiltonian which is locally valid at the time step to be computed. This procedure ensures the preservation of the volume (flux condition) during the iteration. This method is first tested with an ABC-type flow. Its benefits when compared to typical Runge-Kutta scheme are demonstrated. Potential use of the method to exhibit “coherent” Lagrangian structures in a chaotic setting is shown. An illustration to the computation of magnetic field lines resulting from a three-dimensional MHD simulation is also provided.

Nonlinear viscoresistive dynamics of the m=1 tearing instability

A numerical investigation of the viscoresistive evolution of the m=1 tearing instability is presented. Its linear growth rate is found to have various power law scalings in different viscoresistive regimes, in agreement with the theoretical results of Porcelli [Phys. Fluids 30, 1734 (1987)]. Our principal focus is on the nonlinear behavior of this instability at a high value of the stability parameter Δ′ and for different values of the Prandtl number Pm. It is found that, depending on the Prandtl regime, and in association with a poloidal oscillation of the magnetic structure, a quadrupolar flow can be generated and/or destroyed outside the current sheet. The reconnection process appears to be influenced by the generation/inhibition dynamics of this external quadrupolar flow. At large enough times, this nonlinear quadrupolar flow can be partially advected in the poloidal direction at the Alfven velocity. However at high Pm values, such an advection is inhibited by viscosity and, as a consequence, the latt...

Higher order and asymmetry effects on saturation of magnetic islands

Higher order asymptotic matching procedure is developed to derive the nonlinear equation for saturated magnetic island with the symmetric profile of the equilibrium current. The theory extends the previous results to include higher order effects such as nonlinear modification of the equilibrium current and asymmetry in the boundary conditions in the outer region. It is shown that due to a finite width of the nonlinear region, the magnitude of the magnetic flux at the rational surface is different from the asymptotic value found from the outer solution, resulting in the suppression of the island growth for higher values of Δ′ parameter.

Nonlinear dynamics of turbulence driven magnetic islands. I. Theoretical aspects

The nonlinear properties of a turbulence driven magnetic island (TDMI) are investigated. Starting from a minimal magnetohydrodynamic fluid model that provides for the generation of a TDMI and using scale separation arguments along with numerical simulation findings, we elucidate the links between the nonlinear transport properties of such magnetic islands and the characteristic features of the small scale turbulence. We also explain the phenomenon of partial pressure flattening inside the TDMI.

Nonlinear dynamics of turbulence driven magnetic islands. II. Numerical simulations

The nonlinear dynamics of a turbulence driven magnetic island (TDMI) is investigated numerically in a reduced magnetohydrodynamic fluid model. The significance of identifying a characteristic signature of a TDMI for its experimental observation is discussed. The principal focus of our simulations is on the nature of the pressure profile flattening inside a TDMI, and we show that, in agreement with analytical predictions, a partial flattening occurs when the island size exceeds a critical value that is a function of the small scale interchange dynamics. We also present a model and test it numerically, which links explicitly the interchange turbulence and the island pressure flattening.

Alpha effect in helically forced turbulence

The effect on large-scale dynamics of small-scale helicity injection in three-dimensional resistive magnetohydrodynamic turbulence is investigated for a weak initial magnetic field. The magnetic configuration of α2 dynamo prototype flows is such that, generally, the energy concentrates on one large-scale mode. However, we obtain that alpha effect is not limited to the dominant mode and that a non-local equation (in Fourier space) is more appropriate to describe it. It gives some insights into the non-local theory of Pouquet et al. [J. Fluid Mech. 77 (1976) 321] where the inverse cascade results from a competition between the helicity and Alfven effects.