Turbulent transport dynamics and level are investigated with the 5D gyrokinetic global code GYSELA, modelling the Ion Temperature Gradient instability with adiabatic electrons. The heat transport exhibits large scale events, propagating radially in both directions at velocities of the order of the diamagnetic velocity. The effective diffusivity is in agreement with that reported in other gyrokinetic codes such as ORB5. Transition from Bohm to gyroBohm scaling is observed on the turbulence correlation length and time, when the normalized gyroradius $\rho_*$ is decreased from $10^{-2}$ to $5 \cdot 10^{-3}$. The transition value could depend on the distance to the ITG threshold. Collisions are modelled by a reduced Lorentz-type operator. It allows one to recover theoretical neoclassical predictions in the banana and plateau regimes, namely the heat diffusivity and the mean poloidal flow. In the turbulent regime, preliminary results suggest the turbulent transport increases with collisionality close to the threshold, in agreement with previous publications. Finally, the mean poloidal flow can be increased by about 40% as compared to the neoclassical value.
Electromagnetic effects play a key role in tokamak edge turbulence. It has been suggested that the density limit and the L to H mode transition may both be due to an interplay between electromagnetic effects, diamagnetic flows and collisionality. (See, e.g., Ref [1].) The present paper discusses the results of scrape-off layer (SOL) non-linear 3D fluid turbulence simulations including finite beta effects in the shear-less limit. These simulations were carried out using the GBS code [2], which evolves the drift-reduced Braginskii equations for a collisional plasma with cold ions in circular (s-α) geometry with a toroidal limiter in the high-field side midplane. The GBS code has been used to study turbulence in linear devices and in a simple magnetized torus configuration [2, 3]. We have recently adapted the code for tokamak edge geometry, and introduced s-α curvature operators as well as magnetic shear, finite aspect ratio, and finite beta effects. The objective of our work is to describe the phase-space relevant to the tokamak SOL turbulence. In this paper, in particular, the role played by finite beta effects upon the characteristic lengths of the profile gradients, turbulence saturation levels, and other basic turbulence properties, is assessed in the context of fully global non-linear turbulence simulations. The non-linear steady-state turbulent plasma profiles are obtained as the result of a balance between plasma density and heat sources, turbulent fluctuations, and parallel losses at the limiter plates. The turbulence drive is a priori unknown and there is no separation between fluctuations and background profiles. Linear analysis of the fluid equations has been carried out for SOL relevant parameters. In the presence of finite beta effects, we recover three instabilities: drift waves, resistive ballooning modes, and ideal ballooning modes. The onset of ideal ballooning modes is known to correspond to the instability threshold α_MHD = q^2 β R/Lp 1. In the non-linear simulations, however, we observe the onset of catastrophic transport well below the ideal limit. The saturated states in this regime are characterized by large transport due to global ideal modes. These modes are linearly subdominant but non-linearly dominant due to the underlying turbulence saturation mechanism.
Shear flows have a profound influence on turbulence-driven transport in tokamaks. The introduction of arbitrary initial flow profiles into the code ORB5 [Jolliet et al., Comput. Phys. Commun. 177, 409 (2007)] allows the convenient study of how flows on all length scales both influence transport levels and self-consistently evolve. A formulation is presented which preserves the canonical structure of the background particle distribution when either toroidal or poloidal flows are introduced. Turbulence suppression is possible above a certain shearing rate magnitude for homogeneous shear flows, and little evolution of the shearing rate is seen. However, when a flow with a zone boundary, where the shearing rate reverses at mid-radius, is introduced, the shear flow evolves substantially during the simulation. E × B shear flows with a zone boundary of a positive sign decay to a saturation amplitude, consistent with the well known saturation of turbulently generated zonal flows. Unlike the E × B flow, the parallel flows relax diffusively.
We present non-linear self-consistent 3D global fluid simulations of the SOL plasma dynamics using the Global Braginskii Solver (GBS) code. The code solves the drift-reduced Braginkii equations in a collisional plasma, with cold ions. The GBS code, originally developed for an electrostatic, 2D configuration has been recently upgraded to describe the SOL turbulence with the introduction of the variable curvature along the magnetic field lines, the magnetic shear, and the electromagnetic effects. The code peculiarity lies in the capability of evolving self-consistently equilibrium and 3D fluctuations as a results of the interplay among the sources, the turbulent transport and the plasma losses at the limiter plates. The non-linear simulations have been interpreted by means of linear analysis of the fluid equations modeling the system. This points out the presence of two main instabilities driving turbulence: the Drift Wave and the Resistive Balloning instabilities. The dependence of the instabilities growth rate and of their properties on the physical parameters of the system, for example the characteristic length of the plasma density, the magnetic shear and the beta ratio have been explained and the regions where each instability dominates have been identified.
In the context of gyrokinetic flux-tube simulations of microturbulence in magnetized toroidal plasmas, different treatments of the magnetic equilibrium are examined. Considering the Cyclone DIII-D base case parameter set [Dimits et al., Phys. Plasmas 7, 969 (2000)], significant differences in the linear growth rates, the linear and nonlinear critical temperature gradients, and the nonlinear ion heat diffusivities are observed between results obtained using either an s-α or a magnetohydrodynamic (MHD) equilibrium. Similar disagreements have been reported previously [Redd et al., Phys. Plasmas 6, 1162 (1999)]. In this paper it is shown that these differences result primarily from the approximation made in the standard implementation of the s-α model, in which the straight field line angle is identified to the poloidal angle, leading to inconsistencies of order ε (ε=a/R is the inverse aspect ratio, a the minor radius and R the major radius). An equilibrium model with concentric, circular flux surfaces and a correct treatment of the straight field line angle gives results very close to those using a finite ε, low β MHD equilibrium. Such detailed investigation of the equilibrium implementation is of particular interest when comparing flux tube and global codes. It is indeed shown here that previously reported agreements between local and global simulations in fact result from the order ε inconsistencies in the s-α model, coincidentally compensating finite ρ∗ effects in the global calculations, where ρ∗=ρs/a with ρs the ion sound Larmor radius. True convergence between local and global simulations is finally obtained by correct treatment of the geometry in both cases, and considering the appropriate ρ∗→0 limit in the latter case.
Turbulence in the scrape-off-layer (SOL) of magnetic fusion devices is one of the most outstanding issues in magnetic fusion. This open fied lines region determines the boundary condition of the core plasma and controls the plasma refueling, heat losses and impurity dynamics, therefore governing the fusion power output of the entire device. In this work, we present the global fluid code GBS [Ricci et al., Plasma Phys. Control. Fusion 54, 124047, 2012]. It employs a 5 field drift-reduced Braginskii model for both electrostatic and electromagnetic turbulence in a limited configuration. The model simulates a turbulent steady state resulting from plasma sources mimicking the plasma outflow from the core, turbulent perpendicular transport and parallel losses at the limiter sheaths. Unique features of the code are that gradients are a-priori unknown and there is no separation between the background gradient and the fluctuations. We will focus on recent advances to extend GBS from an infinite aspect ratio model to a general geometry model. One of the main features of SOL turbulence is its strong anisotropy characterized by k// /k⊥ << 1, It is therefore crucial to correctly describe the parallel gradient derivative, in particular at the limiter plates where the plasma is lost. In view of more complicated situations such as a diverted geometry, the GBS code does not employ field- aligned coordinates. The fluid fields are discretized on a toroidal and poloidal grid. Using alternative schemes that will be presented. These schemes are tested in a simplified model describing the propagation of shear-Alfven waves, which is the fastest wave propagating for this simulation model. Then, GBS nonlinear simulations using these new schemes will be presented and compared. Among those, we will also discuss some ot the simulation results, focusing on circular geometry with finite aspect ratio. In particular, it is shown that the characteristic pressure length can be well described by the gradient removal theory [Ricci et al., Phys. Plasmas 20, 010702, 2013] that uses the flattening of the gradient by the perturbation as a saturation mechanism.
The scaling of turbulence-driven heat transport with system size in magnetically confined plasmas is reexamined using first-principles based numerical simulations. Two very different numerical methods are applied to this problem, in order to resolve a long-standing quantitative disagreement, which may have arisen due to inconsistencies in the geometrical approximation. System size effects are further explored by modifying the width of the strong gradient region at fixed system size. The finite width of the strong gradient region in gyroradius units, rather than the finite overall system size, is found to induce the diffusivity reduction seen in global gyrokinetic simulations.
Progress in basic understanding of turbulence and its influence on the transport both of the plasma bulk and of suprathermal components is achieved in the TORPEX simple magnetized torus. This configuration combines a microwave plasma production scheme with a quasi-equilibrium generated by a toroidal magnetic field, onto which a small vertical component is superimposed, simulating a simplified form of tokamak scrape-off layers. After having clarified the formation of blobs in ideal interchange turbulence, TORPEX experiments elucidated the mechanisms behind the blob motion, with a general scaling law relating their size and speed. The parallel currents associated with the blobs, responsible for the damping of the charge separation that develops inside them, hence determining their cross-field velocity, have been measured. The blob dynamics is influenced by creating convective cells with biased electrodes, arranged in an array on a metal limiter. Depending on the biasing scheme, radial and vertical blob velocities can be varied. Suprathermal ion transport in small-scale turbulence is also investigated on TORPEX. Suprathermal ions are generated by a miniaturized lithium source, and are detected using a movable double-gridded energy analyser. We characterize vertical and radial spreading of the ion beam, associated with the ideal interchange-dominated plasma turbulence, as a function of the suprathermal ion energy and the plasma temperature. Experimental results are in good agreement with global fluid simulations, including in cases of non-diffusive behaviour. To investigate the interaction of plasma and suprathermal particles with instabilities and turbulence in magnetic configurations of increasing complexity, a closed field line configuration has recently been implemented on TORPEX, based on a current-carrying wire suspended in the vacuum chamber. First measurements indicate the creation of circular symmetric profiles centred on the magnetic axis, and instabilities driven in the region of strong gradients, with a strong ballooning character.
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