arXiv subjects
Publications and source records attributed to Xavier Garbet.
A novel asymptotic matching procedure is developed to revisit the problem of magnetic island saturation in case of a finite current gradient at the rational surface. Nonlinear dispersion relation is derived for saturated magnetic island. It is shown that arbitrary normalization factors that were present in previous theories are fully specified with the asymptotic matching.
Straightforward method for the derivation of linearized version of stochastic stability analysis of the nonlinear differential equations is presented. Methods for the study of large time behavior of the moments are exposed. These general methods are applied to the study of the stochastic destabilization of the Langmuir waves in plasma.
Inaccurate description of the equilibrium can yield to spurious effects in gyrokinetic turbulence simulations. Also, the Vlasov solver and time integration schemes impact the conservation of physical quantities, especially in long-term simulations. Equilibrium and Vlasov solver have to be tuned in order to preserve constant states (equilibrium) and to provide good conservation property along time (mass to begin with). Several illustrative simple test cases are given to show typical spurious effects that one can observes for poor settings. We explain why Forward Semi-Lagrangian scheme bring us some benefits. Some toroidal and cylindrical GYSELA runs are shown that use FSL.
We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic βparameter 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 \times 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 βparameter 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 βparameter. It appears that after the transition, an E \times B poloidal flow as well as a nonlinear diamagnetic drift are generated due to an amplification of the stresses by pressure effects.
The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the tearing instability are controlled by the properties of the pressure gradient. In these regimes, the interplay between the pressure and the magnetic flux determines the dynamics of the saturated state. A secondary instability can occur and strongly modify the magnetic island dynamics by triggering a poloidal rotation. It is shown that the complex nonlinear interaction between the islands and turbulence is nonlocal and involves small scales.
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the divergence of the fractional order moments of the solution below respectively above some critical exponent. This exponent is computed. In particular models it is the heavy tail exponent. When the equation is linear this exponent determines a new family of weak topologies (stronger compared to the classical one), related to the convergence to the stationary state.
The dynamics of a global reconnection in the presence of a poloidal shear flow which is located in between magnetic islands is investigated. Different linear regimes are identified according to the value of the resistivity and the distance between the low-order resonant surfaces. It is found that the presence of a small shear flow affects and significantly delays the global reconnection processes. It is shown that this delay is linked to a breaking of symmetry imposed by the existence of the shear flow and the generation of a mean poloidal flow in the resistive layers.
The understanding of the mechanisms responsible for particle transport is of the utmost importance for magnetized fusion plasmas. A peaked density profile is attractive to improve the fusion rate, which is proportional to the square of the density, and to self-generate a large fraction of non-inductive current required for continuous operation. Experiments in various tokamak devices (AUG, DIII-D, JET, TCV, TEXT, TFTR) have indicated the existence of an anomalous inward particle pinch. Recently, such an anomalous pinch has been unambiguously identified in Tore Supra very long discharges, in absence of toroidal electric field and of central particle source, for more than 4 minutes [1]. This anomalous particle pinch is predicted by a quasilinear theory of particle transport [2], and confirmed by non-linear turbulence simulations [3] and general considerations based on the conservation of motion invariants [4]. Experimentally, the particle pinch is found to be sensitive to the magnetic field gradient in many cases [5, 6, 7, 8], to the temperature profile [5, 9] and also to the collisionality that changes the nature of the microturbulence [10, 11, 12]. The consistency of some of the observed dependences with the theoretical predictions gives us a clearer understanding of the particle pinch in tokamaks, allowing us to predict more accurately the density profile in ITER.
Lately the question has been raised if a modification of the energy-confinement scaling law with respect to the electron to ion temperature ratio, Te/Ti, is required. Theoretically, like in e.g. the Weiland model, the confinement is thought to degrade with Te/Ti and studies of the hot-ion (Ti>/Te) mode seems to corroborate this. In this paper, it is shown that due to a number of effects that cancel each other out, the energy confinement time remains constant for Te/Ti>~1. The numerical study relies on a series of JET shots specifically designed to reveal an effect of Te/Ti in the hot-electron (Te>Ti) mode. A distinct effort was made to keep all current scaling-law parameters constant, including the total heating power. The effects that provide the constant confinement times have therefore nothing to do with the global properties of the plasma, but are rather due to variations in the temperature gradients which affects the transport locally.