# Ö. D. Gürcan's research while affiliated with Université Paris-Saclay and other places

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## Publications (94)

The Hasegawa–Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices, is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking, where the phase differences between dominant modes converge to co...

Hasegawa-Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking where the phase differences between dominant modes converge to constant...

Cascade models based on dynamical complex networks are proposed as models of the turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are constructed by adding or replacing some of the existing local interactions by nonlocal ones. The models are then...

Dynamics of the transition from a linear plasma wave to a nonlinear state characterized by the Bernstein-Greene-Kruskal mode is studied within the framework of the Vlasov-Poisson system. In the linear stage, the plasma distribution function (f) develops finer and finer structures in velocity space through a series of “mixing” processes leading to t...

The nonlinear dynamics of beta-induced Alfv\'en Eigenmodes (BAE) driven by energetic particles (EP) in the presence of ion-temperature-gradient (ITG) turbulence is investigated, by means of selfconsistent global gyrokinetic simulations and analytical theory. A tokamak magnetic equilibrium with large aspect ratio and reversed shear is considered. A...

Reduced models, mirroring self-similar, fractal nature of two-dimensional turbulence, are proposed, using logarithmic spiral chains, which provide a natural generalization of shell models to two dimensions. In a turbulent cascade, where each step can be represented by a rotation and a scaling of the interacting triad, the use of a spiral chain whos...

A generalization of curvature modified plasma dispersion functions is introduced in order to express Dupree renormalized dispersion relations used in quasi-linear theory. For instance the Dupree renormalized dispersion relation for gyrokinetic, toroidal ion temperature gradient driven (ITG) modes, where the Dupree's diffusion coefficient is assumed...

Self-similar, fractal nature of turbulence is discussed in the context of two dimensional turbulence, by considering the fractal structure of the wave-number domain using spirals. In loose analogy with phyllotaxis in plants, each step of the cascade can be represented by a rotation and a scaling of the interacting triad. Using a constant divergence...

A logarithmically discretized model, which consists of writing the system in log polar coordinates in wave-number domain and reducing the nonlinear interactions to a sum over neighboring scales that satisfy the triad conditions, is proposed for bounce averaged gyrokinetics, where the energy dependence is kept over a semi-regular grid that allows qu...

A nested polyhedra model has been developed for magnetohydrodynamic turbulence. Driving only the velocity field at large scales with random, divergence-free forcing results in a clear, stationary k−5/3 spectrum for both kinetic and magnetic energies. Since the model naturally effaces disparate scale interactions, does not have a guide field, and av...

This paper presents the results of fluctuation measurements in a toroidal magnetized plasma, using Langmuir probes, and comparisons between the observed frequency modes and a Hasegawa-Wakatani model including curvature, adapted to the specifics of the toroidal device. More precisely, two kinds of signals are detected in the presence of an additiona...

Simultaneous measurements of binormal velocity of density fluctuations using two separate Doppler backscattering systems at the low field side and at the top of the plasma show significant poloidal asymmetry. The measurements are performed in the core region between the radii 0.7 < ρ < 0.95, over a limited number of L-mode discharges covering a wid...

A shell model is derived for the description of nonlinear bounce averaged gyrokinetics, which is one of the simplest kinetic descriptions in magnetized plasmas. In order to validate the numerical implementation, detailed linear evolution of the system is compared with a linear benchmark based on solving the linear dispersion relation numerically. T...

A nested polyhedra model has been developed for magnetohydrodynamic (MHD) turbulence. Driving only the velocity field at large scales with random, divergence free forcing results in a clear, stationary $k^{-5/3}$ spectrum for both kinetic and magnetic energies. Since the model naturaly effaces disparate scale interactions, does not have a guide fie...

A coupled model of transport, turbulence, and mesoscale flows is proposed, including turbulence spreading. The model consists of transport equations for plasma density and pressure coupled to a shell model of drift wave turbulence, which incorporates coupling to mesoscale flows via disparate scale interactions. The model can describe the turbulent...

The general framework of envelope modulations for plasma turbulence in the presence of strong magnetic fields is discussed. It is shown that the problem can be formulated using a functional which is equivalent to the plasma dielectric function for monochromatic waves. Therefore expanding around its linear wave solutions, one can describe the weakly...

Motivated by observations and physics understanding of the phenomenon of intrinsic rotation, it is suggested that similar considerations for electron dynamics may result in intrinsic current in tokamaks. We have investigated the possibility of intrinsic non-inductive current in the turbulent plasma of tokamaks. Ohm's law is generalized to include t...

Geodesic acoustic modes (GAMs) are studied by means of the gyrokinetic global particle-in-cell code ORB5. Linear electromagnetic simulations in the low electron beta limit have been performed, in order to separate acoustic and Alfv\'enic time scales and obtain more accurate measurements. The dependence of the frequency and damping rate on several p...

Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in the quasilinear gyrokinetic transport model QuaLiKiz [C. Bourdelle et al. 2016 Plasma Phys. Control. Fusion 5...

A discretization of the wave-number space is proposed, using nested polyhedra, in the form of alternating dodecahedra and icosahedra that are self-similarly scaled. This particular choice allows the possibility of forming triangles using only discretized wave vectors when the scaling between two consecutive dodecahedra is equal to the golden ratio...

In Tore Supra plasmas, the perpendicular velocity measured by Doppler reflectometry was observed to reverse in a localized zone close to a normalized radius ~0.5–0.6, changing from a negative value (corresponding to a negative radial electric field E r) to a positive value (). This occurs in L-mode, ohmic plasmas with a negligible external momentum...

A detailed systematic derivation of a logarithmically discretized model for two-dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recov...

A discretization of the wave-number space of the Navier-Stokes equation, using a logarithmically spaced chain of alternating icosa-dodeca-hedral spheres is proposed. This strange choice allows the possibility of forming triangles using only discretized wave-vectors when the scaling between two consecutive dodecahedra is equal to the golden ratio, a...

The relationship between the physics of turbulent transport of particles and azimuthal momentum in a linear plasma device is investigated using a simple model with a background density gradient and zonal flows driven by turbulent stresses. Pure shear flow driven Kelvin-Helmholtz instabilities(k∥=0) relax the flow and drive an outward (down gradient...

Geodesic acoustic modes (GAMs) are studied, for the first time, including all
poloidal mode $(m)$ couplings using drift reduced fluid equations. The nearest
neighbor coupling pattern, due to geodesic curvature, leads to a semi-infinite
chain model of the GAM with the mode-mode coupling matrix elements proportional
to the radial wave number $k_{r}$....

We study the steady state spectrum of the Hasegawa-Wakatani (HW) equations that describe drift wave turbulence. Beyond a critical scale k_{c}, which appears as a balance between the nonlinear time and the parallel conduction time, the adiabatic electron response breaks down nonlinearly and an internal energy density spectrum of the form F(k_{⊥})∝k_...

For a comprehensive comparison with theoretical models and advanced numerical turbulence simulations, a large spectrum of fluctuation parameters was measured on the devices ASDEX Upgrade, TCV, and Tore-Supra. Radial profiles of scale-resolved turbulence levels in H-mode discharges are measured and compared with GENE simulations in the transition ra...

The general aspects of zonal flow physics, their formation, damping and interplay with quasi two dimensional turbulence are explained in the context of magnetized plasmas and quasi-geostrophic fluids with an emphasis on formation and selection of spatial patterns. General features of zonal flows as they appear in planetary atmospheres, rotating con...

In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler
backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover,...

We present a theory of turbulence elasticity, which follows from delayed response of drift waves (DWs) to zonal flow (ZF) shears. It is shown that when |〈V〉'ZF|/Δωk ≥ 1, with |〈V〉'ZF| the ZF shearing rate and Δωk the local turbulence decorrelation rate, the ZF evolution equation is converted from a diffusion equation to a telegraph equation. This i...

Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases...

Nonlinear stationary structure formation in the coupled ion temperature gradient (ITG)-zonal flow system is investigated. The ITG turbulence is described by a wave-kinetic equation for the action density of the ITG mode, and the longer scale zonal mode is described by a dynamic equation for the m = n = 0 component of the potential. Two populations...

We present a new, unified model of transport barrier formation in "elastic" drift wave-zonal flow (DW-ZF) turbulence. A new physical quantity-the delay time (i.e., the mixing time for the DW turbulence)-is demonstrated to parameterize each stage of the transport barrier formation. Quantitative predictions for the onset of limit-cycle-oscillation (L...

A particular generalization of the plasma dispersion function, which is linked to the regular plasma dispersion function via recurrence relations is discussed. The generalization allows a fast numerical implementation of a certain two-dimensional integral that appears in the description of the plasma dispersion in curved geometry, by reducing it to...

We present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter |〈v〉'|/Δωk is found to be a measure of the degree of Fickian flux-gradient relation breaking, where |〈v〉'| is the ZF shearing rate and Δωk is...

An overview of the physics of intrinsic torque is presented, with
special emphasis on the phenomenology of intrinsic toroidal rotation in
tokamaks, its theoretical understanding, and the variety of momentum
transport bifurcation dynamics. Ohmic reversals and electron cyclotron
heating-driven counter torque are discussed in some detail. Symmetry
bre...

Understanding the L → H and H → L transitions is crucial to successful ITER operation. In this paper we present novel theoretical and modelling study results on the spatio-temporal dynamics of the transition. We place a special emphasis on the role of zonal flows and the micro → macro connection between dynamics and the power threshold ( P T ) depe...

Various indications on the weakly nonlocal character of turbulent plasma transport both from experimental fluctuation measurements from Tore Supra and observations from the full-f, flux-driven gyrokinetic code GYSELA are reported. A simple Fisher equation model of this weakly nonlocal dynamics can be formulated in terms of an evolution equation for...

We report on model studies of stimulated L→H transitions. These studies use a novel reduced mesoscale model. Studies reveal that L→H transitions can be triggered by particle injection into a subcritical state (i.e., P<P_{Thresh}). Particle injection alters the edge mean flow shear via changes of density and temperature gradients. The change of edge...

We discuss theoretical progress in turbulent transport modelling in tokamaks. In particular, we address issues that the conventional quasilinear type calculation cannot confront, such as (i) the nature of turbulence in the edge-core coupling region of tokamaks (i.e. the so-called 'no man's land'), and the dynamics of incoming structures coupled to...

We propose a novel mechanism to describe E×B flow pattern formation based upon the dynamics of propagation of heat-flux modulations. The E×B flows of interest are staircases, which are quasiregular patterns of strong, localized shear layers and profile corrugations interspersed between regions of avalanching. An analogy of staircase formation to ja...

Simple flux-gradient relations that involve time delay and radial coupling are discussed. Such a formulation leads to a rather simple description of avalanches and may explain breaking of gyroBohm transport scaling. The generalization of the flux-gradient relation (i.e., constitutive relation), which involve both time delay and spatial coupling, is...

An electromagnetic theory of turbulence driven poloidal rotation is developed with particular emphasis on understanding poloidal rotation in finite-β plasmas. A relation linking the flux of polarization charge to the divergence of the total turbulent stress is derived for electromagnetic gyrokinetic modes. This relation is subsequently utilized to...

The effect of a large scale flow shear on a linearly unstable turbulent system is considered. A cubic equation describing the effective growth rate is obtained, which is shown to reduce to well-known forms in weak and strong shear limits. A shear suppression rule is derived which corresponds to the point where the effective growth rate becomes nega...

We investigate the dynamics of the low(L) → high(H) transition using a time-dependent, one dimensional (in radius) model which self-consistently describes the time evolution of zonal flows (ZFs), mean flows (MFs), poloidal spin-up, and density and pressure profiles. The model represents the physics of ZF and MF competition, turbulence suppression v...

Accurate and computationally inexpensive transport models are vital for routine and robust predictions of tokamak turbulent transport. To this end, the QuaLiKiz [Bourdelle et al., Phys. Plasmas 14, 112501 (2007)] quasilinear gyrokinetic transport model has been recently developed. QuaLiKiz flux predictions have been validated by non-linear simulati...

This paper presents the first observation of geodesic acoustic modes (GAMs) on Tore Supra plasmas. Using the Doppler backscattering system, the oscillations of the plasma flow velocity, localized between r/a = 0.85 and r/a = 0.95, and with a frequency, typically around 10 kHz, have been observed at the plasma edge in numerous discharges. When the a...

A simple dynamical cascade model for the evolution of free energy is
considered in the context of gyrokinetic formalism. It is noted that the
dynamics of free energy, that characterize plasma micro-turbulence in magnetic
fusion devices, exhibit a clear predator prey character. Various key features
of predatory prey dynamics such as the time delay b...

Symmetry breaking effects of density gradient on parallel momentum transport is studied via quasilinear theory. It is shown that finite ρs*( ≡ ρs/Ln), where ρs is ion sound radius and Ln is density scale length, leads to symmetry breaking of the ion temperature gradient (ITG) eigenfunction. This broken symmetry persists even in the absence of mean...

An anisotropic shell model has been proposed for two-dimensional (2D) turbulence. It is similar to the 2D version of the Gledzer-Ohkitani-Yamada model but with the angular variable in wave-number space divided into three distinct directions representing structures elongated in different directions. In the case when the drive is isotropic the usual...

We present analyses of mechanisms which convert radial inhomogeneity to broken k||-symmetry and thus produce turbulence driven intrinsic rotation in tokamak plasmas. By performing gyrokinetic simulations of ITG turbulence, we explore the many origins of broken k||-symmetry in the fluctuation spectrum and identify both E × B shear and the radial gra...

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is...

Ripple-induced thermal loss effect on plasma rotation is investigated in a set of Ohmic L-mode plasmas performed in Tore Supra, and comparisons with neoclassical predictions including ripple are performed. Adjusting the size of the plasma, the ripple amplitude has been varied from 0.5% to 5.5% at the plasma boundary, keeping the edge safety factor...

Intrinsic rotation has been observed in I-mode plasmas from the C-Mod tokamak, and is found to be similar to that in H mode, both in its edge origin and in the scaling with global pressure. Since both plasmas have similar edge ∇T, but completely different edge ∇n, it may be concluded that the drive of the intrinsic rotation is the edge ∇T rather th...

Turbulence propagation and temperature profile evolution are studied in heat flux-driven plasmas. A simple model consisting of coupled non-linear reaction–diffusion equations for both turbulence and heat transport is proposed to elucidate several aspects of apparent non-local profile dynamics. Self-consistent E × B shear feedback on turbulence inte...

A collisionality scaling experiment associating a confinement analysis, turbulence measurements across the whole plasma and gyrokinetic modelling is reported. In Tore Supra L-mode plasmas, mid-radius dimensionless collisionality ν* has been varied performing a four-points scan from 0.1 to 0.7. The normalized confinement time exhibits a dependence w...

A model of turbulence intensity spreading with self-consistent nonlinear noise is derived systematically for the simple dynamical model of resistivity gradient driven turbulence. Local effective drive, thermal conduction damping, nonlinear coupling, and spatial scattering effects are included. As a consequence of nonlinear mode coupling processes (...

A better understanding of turbulent transport in a tokamak plasma requires precise comparisons between experimental observation and theoretical prediction of micro-turbulence characteristics. The repartition of fluctuation energy over different spatial scales, which contains detailed information about the character of underlying instabilities and t...

The influence of changing collisionality on density fluctuation characteristics is studied during dedicated nu* scaling experiments, using Doppler backscattering system. First, the repartition of fluctuation energy over different spatial scales, as represented by the wavenumber spectrum, is investigated and a modification of the shape of the perpen...

A kinetic generalization of a Taylor identity appropriate to a strongly magnetized plasma is derived. This relation provides an explicit link between the radial mixing of a four–dimensional (4D) gyrocenter fluid and the poloidal Reynolds stress. This kinetic analog of a Taylor identity is subsequently utilized to link the turbulent transport of pol...

A novel mechanism for driving residual stress in tokamak plasmas based on k(parallel to) symmetry breaking by the turbulence intensity gradient is proposed The physics of this mechanism is explained and its connection to the wave kinetic equation and the wave-momentum flux is described Applications to the H-mode pedestal in particular to internal t...

A theory of the efficiency of the plasma flow generation process is presented. A measure of the efficiency of plasma self-acceleration of mesoscale and mean flows from the heat flux is introduced by analogy with engines, using the entropy budget defined by thermal relaxation and flow generation. The efficiency is defined as the ratio of the entropy...

A variational principle based on an extremum of entropy production rate is derived for an integrable Hamiltonian system in the presence of two perturbations, which are resonant on neighboring or identical resonant surfaces. This method can be used to calculate the neoclassical transport in a magnetic fusion device with a nonaxisymmetric magnetic fi...

A simple unified model of intrinsic rotation and momentum transport in high confinement regime (H-mode) tokamak plasmas is presented. Motivated by the common dynamics of the onset of intrinsic rotation and the L-H transition, this simple model combines E×B shear-driven residual stress in the pedestal with a turbulent equipartition pinch to yield ro...

An extensive study of spectral shell models with possibilities for application to fusion plasmas is discussed. A set of shell models addressing various aspects of the characteristics of fusion plasmas have been derived. Difficulties associated with plasma medium, namely its intrinsic excitability, and importance of mescals have been discussed. The...

A general method of error estimation in the case of multiple point dimensionless scaling experiments, using linear regression and standard error propagation, is proposed. The method reduces to the previous result of Cordey (2009 Nucl. Fusion 49 052001) in the case of a two-point scan. On the other hand, if the points follow a linear trend, it expla...

2] [1] PSFC, MIT; [2] CMTFO, UCSD; [3] NFRI, Korea; [4] LPP, Ecole Polytechnique; [5] Dept. of Engr. Physics, UWM; [6] PPPL; [7] IPP, Abstract. Recent progress towards a physics based phenomenology of intrinsic rotation in H-mode and I-mode is presented. In particular, we aim to elucidate the mechanism of the drive of intrinsic rotation by describi...

Starting from a phase space conserving gyrokinetic formulation, a systematic derivation of parallel momentum conservation uncovers a novel mechanism by which microturbulence may drive intrinsic rotation. This mechanism, which appears in the gyrokinetic formulation through the parallel nonlinearity, emerges due to charge separation induced by the po...

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...

A simple model for the evolution of turbulence fluctuation spectra, which includes neighboring interactions leading to the usual dual cascade as well as disparate scale interactions corresponding to refraction by large scale structures, is derived. The model recovers the usual Kraichnan-Kolmogorov picture in the case of exclusively local interactio...