M. Ottaviani

Recent advances in collisionless magnetic reconnection

One of the recurring problems in magnetic reconnection is the identification of the appropriate generalized Ohms law. In weakly collisional plasmas with a strong magnetic guide field component, a fluid model may be adopted, where electron inertia and the electron pressure gradient play important roles. In the absence of collisions, electron inertia provides the mechanism for magnetic field-line breaking. Electron compressibility alters significantly the structure of the reconnection region and allows for faster reconnection rates, which are consistent with the fast relaxation times of sawtooth oscillations in tokamak plasmas. The Hall term may also become important when the guide field is weak. The very possibility of nonlinear, irreversible magnetic reconnection in the absence of dissipation is addressed. We show that in a collisionless plasma, magnetic islands can grow and reach a saturated state in a coarse-grained sense. Magnetic energy is transferred to kinetic energy in smaller and smaller spatial scale lengths through a phase mixing process. The same model is then applied to the interpretation of driven reconnection events in the vicinity of a magnetic X-line observed in the VTF experiment at MIT. The reconnection is driven by externally induced plasma flows in a background magnetic configuration that has a hyperbolic null in the reconnection plane and a magnetic guide field component perpendicular to that plane. In the limit where the guide field is strong, assuming the external drive to be sufficiently weak for a linear approximation to hold, a dynamic evolution of the system is obtained which does not reach a stationary state. The reconnection process develops in two phases: an initial phase, whose characteristic rate is a fraction of the Alfven frequency, and a later one, whose rate is determined by the electron collision frequency.

The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas

A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.

Fast nonlinear magnetic reconnection

The nonlinear evolution of magnetic reconnection in collisionless and weakly collisional regimes is analyzed on the basis of a two‐dimensional incompressible fluid model. The initial equilibria are unstable to tearing modes. In the limit where the stability parameter Δ′ is relatively large, the mode structure is characterized by global convective cells. It is found that the system exhibits a quasiexplosive time behavior in the early nonlinear stage, where the fluid displacement is larger than the inertial skin depth but smaller than the typical size of the convective cells. The reconnection time is an order of magnitude shorter than the Sweet–Parker time for values of the inertial skin depth, of the ion Larmor radius, and of the magnetic Reynolds number typical of the core of magnetic fusion experiments. The reconnection process is accompanied by the formation of a current density sublayer narrower than the skin depth. In the strict dissipationless limit, this sublayer shrinks indefinitely in time. Physic...

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 generic data structure for integrated modelling of tokamak physics and subsystems

The European Integrated Tokamak Modelling Task Force (ITM-TF) is developing a new type of fully modular and flexible integrated tokamak simulator, which will allow a large variety of simulation types. This ambitious goal requires new concepts of data structure and workflow organisation, which are described for the first time in this paper. The backbone of the system is a physics- and workflow-oriented data structure which allows for the deployment of a fully modular and flexible workflow organisation. The data structure is designed to be generic for any tokamak device and can be used to address physics simulation results, experimental data (including description of subsystem hardware) and engineering issues.

Global numerical study of electron temperature gradient-driven turbulence and transport scaling

A three-dimensional, electromagnetic, fluid code with flux boundaries conditions is used to study the scaling of electron thermal transport caused by electron temperature gradient-driven (ETG) turbulence. It is found that close to the ETG threshold, the thermal transport depends weakly on β, which differs from the heuristic formula χe∝1/β. It is shown also that electron thermal losses scale like gyro-Bohm. The observed electron temperature profiles appear more resilient than the ion temperature profiles obtained from previous ITG simulations in similar conditions.

Validating a quasi-linear transport model versus nonlinear simulations

In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.

Rigorous approach to the nonlinear saturation of the tearing mode in cylindrical and slab geometry

The saturation of the tearing mode instability is described within the standard framework of reduced magnetohydrodynamics in the case of an r-dependent or uniform resistivity profile. Using the technique of matched asymptotic expansions, where the perturbation parameter is the island width w, the problem can be solved in two ways: with the so-called flux coordinate method, which is based on the fact that the current profile is a flux function, and with a new perturbative method that does not use this property. The latter is applicable to more general situations where an external forcing or a sheared velocity profile are involved. The calculation provides a new relationship between the saturated island width and the Δ′ stability parameter that involves a lnw∕w0 term, where w0 is a nonlinear scaling length that was missing in previous work. It also yields the modification of the equilibrium magnetic-flux function.

An upgraded 32-channel heterodyne electron cyclotron emission radiometer on Tore Supra

A 32-channel, 1GHz spaced heterodyne radiometer is used on the Tore Supra tokamak to measure electron cyclotron emission (ECE) in the frequency range 78–110GHz for the ordinary mode (O:E‖B,k⊥B) and 94–126GHz for the extraordinary mode (X:E⊥B,k⊥B). The radial resolution is essentially limited by ECE relativistic effects, depending on electron temperature and density, and not by the channels’ frequency spacing. The time resolution depends on the acquisition scheme: the system allows for both 1ms and 10μs acquisition. For example, this leads to precise electron temperature mapping during MHD activity. First experimental results obtained with this upgraded 32-channel radiometer are presented.

Nonlinear magnetohydrodynamic simulation of Tore Supra hollow current profile discharges

Magnetohydrodynamic (MHD) activity often undermines the realization of fully noninductive plasma discharges in the Tore Supra tokamak [J. Jacquinot, Nucl. Fusion 45, S118 (2005)], by producing large degradation of electron energy confinement in the plasma core and the bifurcation to a regime with permanent MHD activity. The nonlinear evolution of MHD modes in these hollow current density profile discharges is studied with the full-scale three-dimensional MHD code XTOR [K. Lerbinger and J.-F. Luciani, J. Comput. Phys. 97, 444 (1991)] and compared with experimental features. Large confinement degradation is predicted when q(0) is close to 2. This derives either from the full reconnection of an unstable double-tearing mode, or from the coupling between a single tearing mode and adjacent stable modes in a region with reduced magnetic shear.