Search

A spontaneous heating process is found to arise in a system where a magnetic island is present due to a linearly unstable tearing mode. The parity, the relative phases and the structure of the fields determined linearly by the tearing mode cause the compression of the plasma in the direction parallel to the magnetic field to heat the plasma in the vicinity of the separatrix in the nonlinear phase. Using a six-field electromagnetic fluid model, the process is found to be present in both two-dimensional single-helicity and three-dimensional multi-helicity simulations with both symmetric and asymmetric magnetic equilibrium profiles. A noteworthy feature of the model is that the higher-order compression terms responsible for the heating process are retained in the equations. The process is believed to be linked to experimental observations of localized hot-spots on externally induced magnetic islands.

In space and astrophysical plasmas magnetized coherent structures continuously emerge as an outcome of the nonlinear dynamics. These structures are characterized by the presence of localized strong current density peaks. Here we present a statistical study of the development of such structures resulting in different hybrid-Vlasov 3D-3V simulations of plasma turbulence. In particular, we make use of different methods to characterize the global shape of the 3D structures. Furthermore, we study the local magnetic configuration inside and outside current peak regions, comparing the statistics in the two cases. Finally, we discuss correlations between characteristic dimensions of the current structures and current density, marking the difference between magnetic structures in 2D and 3D simulations.

Context. In space and astrophysical plasmas, turbulence leads to the development of coherent structures characterized by a strong current density and important magnetic shears. Aims. Using hybrid-kinetic simulations of turbulence (3D with different energy injection scales), we investigate the development of these coherent structures and characterize their shape. Methods. First, we present different methods to estimate the overall shape of the 3D structure using local measurements, foreseeing an application on satellite data. Then we study the local magnetic configuration inside and outside current peak regions, comparing the statistics in the two cases. Last, we compare the statistical properties of the local configuration obtained in simulations with the ones obtained analyzing an MMS (Magnetospheric MultiScale mission) dataset having similar plasma parameters. Results. Thanks to our analysis, (1) we validate the possibility of studying the overall shape of 3D structures using local methods, (2) we provide an overview of a local magnetic configuration emerging in different turbulent regimes, (3) we show that our 3D-3V simulations can reproduce the structures that emerge in MMS data for the periods considered.

International audience; The coupling between the poloidal distribution and the collisional flux of impurities can be exploited to derive a simplified analytical model covering toroidal rotation and electrostatic potential asymmetry effects, valid in the Pfirsh-Schlüter regime. This model is compared with earlier works and with the drift-kinetic code NEO, which includes the full Fokker-Planck collision operator. The low computational cost of the model, compared to NEO, is particularly adapted for fast integrated simulation purposes.

International audience; We report on a numerical study of axisymmetric flow of liquid metal in a circular duct with a rectangular cross section. The flow is forced through the combination of an axial magnetic field and a radial current. Sweeping a wide range of forcing parameters, we identify the different regimes which characterize the flows and explicate the associate scaling laws. Results from different studies in the literature are interpreted in the light of our numerical simulations.

International audience; The stability of a microtearing mode (MTM) as a function of collisonality is investigated by means of linear reduced model and numerical simulations using the gyrokinetic code GKW. The study is focused on the role of the electric potential and the magnetic drift, which are potential candidates to explain the destabilization of MTM observed at low collisionality in some recent gyrokinetic simulations. In the simulations, the magnetic drift and electric potential are found destabilizing in the presence of a finite collisionality. This destabilizating role is captured in the analytical calculation, which further highlights the requirement for a finite collisionality.

International audience; 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. Published by AIP Publishing.

International audience; We investigate, through extensive 3D magneto-hydro-dynamics numerical ă simulations, the nonlinear excitation of a large scale magnetic island ă and its dynamical properties due to the presence of small-scale ă turbulence. Turbulence is induced by a steep pressure gradient in the ă edge region [B. D. Scott, Plasma Phys. Controlled Fusion 49, S25 ă (2007)], close to the separatrix in tokamaks where there is an X-point ă magnetic configuration. We find that quasi-resonant localized ă interchange modes at the plasma edge can beat together and produce ă extended modes that transfer energy to the lowest order resonant surface ă in an inner stable zone and induce a seed magnetic island. The island ă width displays high frequency fluctuations that are associated with the ă fluctuating nature of the energy transfer process from the turbulence, ă while its mean size is controlled by the magnetic energy content of the ă turbulence. (C) 2015 AIP Publishing LLC.

The amplification of a turbulence driven seed magnetic island by the bootstrap current is investigated numerically in a reduced magnetohydrodynamic model as a possible additional channel for the excitation and development of a neoclassical tearing mode (NTM) in a tokamak. The novel mechanism for such an excitation involves a two-step process, namely, the formation of a seed island due to a nonlinear beating of interchange turbulence modes followed by an amplification of the seed island by the bootstrap current leading to a large saturated island. Our study indicates that the level of turbulence controls both the critical seed island size and the saturated island size.

International audience; The numerical large eddy simulation (LES) technique is tested on decaying magnetohydrodynamic (MHD) turbulence. The LES approach allows for a strong reduction in computational cost compared to direct numerical simulations by modeling the effects of the smallest turbulent scales instead of computing them directly. Two small-scale models of eddy-viscosity type are presented for this purpose in combination with a procedure for the self-consistent calculation of the model parameters in the course of the simulation. The method is successfully tested by comparing the obtained results to a high-resolution direct numerical simulation of decaying three-dimensional MHD turbulence.

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.

International audience; 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.

The chaotic advection of a passive scalar in a three-dimensional flow is investigated. The stationary velocity field of the incompressible fluid possesses a helical symmetry and satisfies the Beltrami property, and is then an exact solution to the Euler equations. The streamlines of the fluid form a stochastic web which determines the transport properties. In this cylindrical geometry the origin plays a special role. For pure 2{pi}/n symmetry (n is an integer) the particles can return to the origin in finite time, as can be demonstrated analytically. The statistical behavior of the passive scalar is studied by using numerical integrations of the motion equations. Subdiffusive behavior is found, the radial variance growing in time with a characteristic exponent of {approx}0.52 (this exponent is 1 for normal Brownian diffusion). The return probability is also computed. A random walk model, assuming absorption and waiting times proportional to the distance from the origin, appropriately describes the observed features of the particle statistics. In the continuous limit this model gives a diffusion equation with memory effects, highlighting the non-Markovian character of the dynamical system. {copyright} {ital 1997} {ital The American Physical Society}

We investigate the multiscale nonlinear dynamics of a linearly stable or unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small-scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island.

International audience; 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.

Transport properties of passive particles evolving in two dimensional flows are investigated. Flows governed by point vortices and by the Charney-Hasegawa-Mima equation are considered. Transport is found to be anomalous with a non linear evolution of the second moments with time and for all considered cases the characteristic exponent is found to be close to 1.75. The origin of this behavior is traced back to the existence of chaotic jets in these systems.

International audience; Numerical simulations investigating the interaction of co-existent 2/1 and 3/1 neoclassical tearing modes are presented. The results obtained from an initial value 3D toroidal code that solves a set of generalized reduced MHD equations exhibit a host of complex phenomena arising from the coupling of the two modes. These include a modification of the island saturation widths of the two modes, a significant modification in the perpendicular flow patterns in the vicinity of the islands, and the excitation of geodesic acoustic mode like oscillations that lead to concomitant oscillations in the kinetic and magnetic energies of the islands. These oscillations only occur in the presence of the neoclassical stress tensor contribution and are absent for two coupled classical tearing modes.

The drift of ions in a magnetized plasma or the height fluctuations of a rotating fluid layer are described by the conservation equation of a potential vorticity. This potential vorticity contains an intrinsic length scale, the hybrid Larmor radius in plasma, and the Rossby length in the quasigeostrophic flow. The influence of this scale in the evolution of a random initial vorticity field is investigated using a thermodynamic approach. In contrast to the perfect fluid case, where the vorticity tends to a well defined stationary state, complete relaxation towards an equilibrium state is not observed in numerical simulations of quasigeostrophic decaying turbulence. The absence of global thermodynamic equilibrium is explained by the relaxation towards states of local equilibrium where the vorticity is concentrated. The interaction between these separated regions is extremely weak. Explicit, axisymmetric, localized solutions of the mean field integrodifferential equation of extremal entropy states are obtained using asymptotic methods. A comparison of the computed solutions with the observed coherent structures shows that they effectively correspond to states in local thermodynamic equilibrium.

International audience; The effect on large-scale dynamics of small-scale helicity injection in three-dimensional resistive mag-netohydrodynamic turbulence is investigated for a weak initial magnetic field. The magnetic configuration of a 2 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 Alfv e en effects.

The numerical large eddy simulation (LES) technique is applied toisotropic magnetohydrodynamic (MHD) turbulence. Two dynamic MHD subgrid-scale models of gradient diffusion type are presented for this purpose, taking into account the fundamental differences between the dissipation mechanisms of the velocity and the magnetic field. Additional explicit Gaussian filtering in combination with the tensor-diffusivity mixed model approach is also considered. The LES method is successfully tested a posteriori on scalar level by comparing the obtained results to data stemming from high-resolution direct numerical simulations of decaying three-dimensional MHD turbulence.

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.

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.

An exact, unstationary, two-dimensional solution of the Navier-Stokes equations for the flow generated by two point vortices is obtained. The viscosity nu is introduced as a Brownian motion in the Hamiltonian dynamics of point vortices. The point vortices execute a stochastic motion whose probability density can be computed from a Fokker-Planck equation, equivalent to the original Navier-Stokes equation. The derived solution describes, in particular, the merging process of two Lamb vortices, and the development of the characteristic spiral structure in the topology of the vorticity. The viscous effects are thoroughly investigated by an asymptotic analysis of the solution. In particular, the selection mechanism of a specific pattern among the infinity satisfying the nu=0 (Euler) equation is discussed.

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.

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.

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.

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.

We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic β parameter and of curvature effects on the nonlinear evolution of drift tearing islands. We observe a bifurcation phenomenon that leads to an amplification of the pressure energy, the generation of E × B poloidal flow and a nonlinear diamagnetic drift that affects the rotation of the magnetic island. These dynamical modifications arise due to quasilinear effects that generate a zonal flow at the onset point of the bifurcation. Our simulations show that the transition point is influenced by the β parameter such that the pressure gradient through a curvature effect strongly stabilizes the transition. Regarding the modified rotation of the island, a model for the frequency is derived in order to study its origin and the effect of the β parameter. It appears that after the transition, an E × B poloidal flow as well as a nonlinear diamagnetic drift are generated due to an amplification of the stresses by pressure effects.

International audience; A 6-field reduced-MHD model is derived for plasma dynamics. The new model describes coherently both Ion Temperature Gradient mode and Tearing mode, and includes neoclassical effects. The model allows the construction of an energy-like quantity with a linear pressure contribution that is conserved except for dissipative, finite Larmor radius and neoclassical terms. This model may be used to study the nonlinear interaction between ITG microturbulence and neoclassical tearing mode, which is responsible for large-scale magnetic islands in tokamaks, and opens the way to a coherent description of turbulent impurity transport in magnetic islands.