Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness $S$ and kurtosis $K$. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the X-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.Comment: 10 pages, 5 figure

Control of Transport-barrier relaxations by Resonant Magnetic Perturbations

Transport-barrier relaxation oscillations in the presence of resonant magnetic perturbations are investigated using three-dimensional global fluid turbulence simulations from first principles at the edge of a tokamak. It is shown that resonant magnetic perturbations have a stabilizing effect on these relaxation oscillations and that this effect is due mainly to a modification of the pressure profile linked to the presence of both residual residual magnetic island chains and a stochastic layer.Comment: 4 page

Angular momentum transport modeling: achievements of a gyrokinetic quasi-linear approach

QuaLiKiz, a model based on a local gyrokinetic eigenvalue solver is expanded to include momentum flux modeling in addition to heat and particle fluxes. Essential for accurate momentum flux predictions, the parallel asymmetrization of the eigenfunctions is successfully recovered by an analytical fluid model. This is tested against self-consistent gyrokinetic calculations and allows for a correct prediction of the ExB shear impact on the saturated potential amplitude by means of a mixing length rule. Hence, the effect of the ExB shear is recovered on all the transport channels including the induced residual stress. Including these additions, QuaLiKiz remains ~10 000 faster than non-linear gyrokinetic codes allowing for comparisons with experiments without resorting to high performance computing. The example is given of momentum pinch calculations in NBI modulation experiments

Stability analysis of secondary modes, driven by the phase space island

We present a new theoretical approach, based on the Hamiltonian formalism, to investigate the stability of islands in phase space, generated by trapping of energetic particles (EPs) in plasma waves in a tokamak. This approach is relevant to MHD modes driven by EPs (EP-MHD) such as toroidal Alfvén eigenmodes (TAEs), EP-driven geodesic acoustic modes (EGAMs) or fishbones. A generic problem of a single isolated EP-MHD mode is equivalent to and hence can be replaced by a 2D Hamiltonian dynamics in the vicinity of the phase space island. The conventional Langmuir wave/bump-on-tail problem is then used as a representative reduced model to describe the dynamics of the initial EP-MHD. Solving the Fokker-Planck equation in the presence of pitch angle scattering, velocity space diffusion and drag and retaining plasma drifts in a model, we find a 'perturbed' equilibrium, associated with these phase space islands. Its stability is then explored by addressing the Vlasov/Fokker-Planck-Poisson system. The Lagrangian of this system provides the dispersion relation of the secondary modes and allows an estimate of the mode onset. The secondary instabilities have been confirmed to be possible but under certain conditions on the primary island width and in a certain range of mode numbers. The threshold island width, below which the mode stability is reached, is calculated. The secondary mode growth rate is found to be maximum when the associated resonant velocity approaches the boundary of the primary island. This, in turn, leads to a conclusion that the onset of the secondary mode can be prevented provided the primary wave number is the lowest available

Comparison between measured and predicted turbulence frequency spectra in ITG and TEM regimes

The observation of distinct peaks in tokamak core reflectometry measurements - named quasi-coherent-modes (QCMs) - are identified as a signature of Trapped-Electron-Mode (TEM) turbulence [H. Arnichand et al. 2016 Plasma Phys. Control. Fusion 58 014037]. This phenomenon is investigated with detailed linear and nonlinear gyrokinetic simulations using the \gene code. A Tore-Supra density scan is studied, which traverses through a Linear (LOC) to Saturated (SOC) Ohmic Confinement transition. The LOC and SOC phases are both simulated separately. In the LOC phase, where QCMs are observed, TEMs are robustly predicted unstable in linear studies. In the later SOC phase, where QCMs are no longer observed, ITG modes are identified. In nonlinear simulations, in the ITG (SOC) phase, a broadband spectrum is seen. In the TEM (LOC) phase, a clear emergence of a peak at the TEM frequencies is seen. This is due to reduced nonlinear frequency broadening of the underlying linear modes in the TEM regime compared with the ITG regime. A synthetic diagnostic of the nonlinearly simulated frequency spectra reproduces the features observed in the reflectometry measurements. These results support the identification of core QCMs as an experimental marker for TEM turbulenc

Anomalous diffusion, clustering, and pinch of impurities in plasma edge turbulence

The turbulent transport of impurity particles in plasma edge turbulence is investigated. The impurities are modeled as a passive fluid advected by the electric and polarization drifts, while the ambient plasma turbulence is modeled using the two-dimensional Hasegawa--Wakatani paradigm for resistive drift-wave turbulence. The features of the turbulent transport of impurities are investigated by numerical simulations using a novel code that applies semi-Lagrangian pseudospectral schemes. The diffusive character of the turbulent transport of ideal impurities is demonstrated by relative-diffusion analysis of the evolution of impurity puffs. Additional effects appear for inertial impurities as a consequence of compressibility. First, the density of inertial impurities is found to correlate with the vorticity of the electric drift velocity, that is, impurities cluster in vortices of a precise orientation determined by the charge of the impurity particles. Second, a radial pinch scaling linearly with the mass--charge ratio of the impurities is discovered. Theoretical explanation for these observations is obtained by analysis of the model equations.Comment: This article has been submitted to Physics of Plasmas. After it is published, it will be found at http://pop.aip.org/pop

Global linear stability analysis of kinetic Trapped Ion Mode (TIM) turbulence in tokamak plasma using spectral method

Trapped ion modes (TIM) which belong to the family of ion temperature gradient (ITG) modes, is one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. It is essential to properly estimate their linear growth rate to understand their influence on ion-scale turbulent transport. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis by considering the exact magnetic flux {\psi} dependency of the equilibrium Hamiltonian H_{eq}({\psi}) in the quasi-neutrality equation and equilibrium gyro-bounce averaged distribution function F_{eq} . Using this spectral method, linear growth-rates of TIM instability in presence of different temperature profiles and precession frequencies of trapped ions, with an approximated constant Hamiltonian and the exact {\psi} dependent equilibrium Hamiltonian, are investigated. The growth-rate depends on the logarithmic gradient of temperature \kappa_{T} , density \kappa_{n} and equilibrium Hamiltonian \kappa_{\Lambda} . With the exact {\psi} dependent Hamiltonian, the growth rates and potential profiles are modified significantly, compared to the cases with approximated constant Hamiltonian. All the results from the global linear analysis agree with a semi-Lagrangian based linear Vlasov solver with a good accuracy. This spectral method is very fast and requires very less computation resources compared to a linear version of Vlasov-solver based on a semi-Lagrangian scheme

L to H mode transition: parametric dependencies of the temperature threshold

The L to H mode transition occurs at a critical power which depends on various parameters, such as the magnetic field, the density, etc. Experimental evidence on various tokamaks (JET, ASDEX-Upgrade, DIII-D, Alcator C-Mod) points towards the existence of a critical temperature characterizing the transition. This criterion for the L-H transition is local and is therefore easier to be compared to theoretical approaches. In order to shed light on the mechanisms of the transition, simple theoretical ideas are used to derive a temperature threshold (Tth). They are based on the stabilization of the underlying turbulence by a mean radial electric field shear. The nature of the turbulence varies as the collisionality decreases, from resistive ballooning modes to ion temperature gradient and trapped electron modes. The obtained parametric dependencies of the derived Tth are tested versus magnetic field, density, effective charge. Various robust experimental observations are reproduced, in particular Tth increases with magnetic field B and increases with density below the density roll-over observed on the power threshold.EURATOM 63305