Ö. D. Gürcan

Transport of parallel momentum by collisionless drift wave turbulence

This paper presents a novel, unified approach to the theory of turbulent transport of parallel momentum by collisionless drift waves. The physics of resonant and nonresonant off-diagonal contributions to the momentum flux is emphasized, and collisionless momentum exchange between waves and particles is accounted for. Two related momentum conservation theorems are derived. These relate the resonant particle momentum flux, the wave momentum flux, and the refractive force. A perturbative calculation, in the spirit of Chapman–Enskog theory, is used to obtain the wave momentum flux, which contributes significantly to the residual stress. A general equation for mean k∥ (⟨k∥⟩) is derived and used to develop a generalized theory of symmetry breaking. The resonant particle momentum flux is calculated, and pinch and residual stress effects are identified. The implications of the theory for intrinsic rotation and momentum transport bifurcations are discussed.

Spatio-temporal evolution of the L → I → H transition

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 via E×B shearing, and poloidal flows driven by turbulence. Numerical solutions of this model show that the L→H transition can occur via an intermediate phase (I-phase) which involves oscillations of profiles due to ZF and MF competition. The I-phase appears as a nonlinear transition wave originating at the edge boundary and propagates inward. Locally, I-phase exhibits the characteristics of a limit-cycle oscillation. All these observations are consistent with recent experimental results. We examine the trigger of the L→H transition, by defining a ratio of the rate of energy transfer from the turbulence to the zonal flow to the rate of energy input into the turbul...

An overview of intrinsic torque and momentum transport bifurcations in toroidal plasmas

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 breaking by lower single null versus upper single null asymmetry is related to the origin of intrinsic torque at the separatrix. (Some figures may appear in colour only in the online journal)

Residual parallel Reynolds stress due to turbulence intensity gradient in tokamak plasmas

A novel mechanism for driving residual stress in tokamak plasmas based on k∥ 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 transport barriers, are discussed. Also, the effect of heat transport on the momentum flux is discussed.

A novel mechanism for exciting intrinsic toroidal rotation

Beginning from a phase space conserving gyrokinetic formulation, a systematic derivation of parallel momentum conservation uncovers two physically distinct mechanisms by which microturbulence may drive intrinsic rotation. The first mechanism, which emanates from E×B convection of parallel momentum, has already been analyzed [O. D. Gurcan et al., Phys. Plasmas 14, 042306 (2007); R. R. Dominguez and G. M. Staebler, Phys. Fluids B 5, 3876 (1993)] and was shown to follow from radial electric field shear induced symmetry breaking of the spectrally averaged parallel wave number. Thus, this mechanism is most likely active in regions with steep pressure gradients or strong poloidal flow shear. The second mechanism uncovered, which appears in the gyrokinetic formulation through the parallel nonlinearity, emerges due to charge separation induced by the polarization drift. This novel means of driving intrinsic rotation, while nominally higher order in an expansion of the mode frequency divided by the ion cyclotron f...

Towards an emerging understanding of non-locality phenomena and non-local transport

In this paper, recent progress on experimental analysis and theoretical models for non-local transport (non-Fickian fluxes in real space) is reviewed. The non-locality in the heat and momentum transport observed in the plasma, the departures from linear flux-gradient proportionality, and externally triggered non-local transport phenomena are described in both L-mode and improved-mode plasmas. Ongoing evaluation of ‘fast front’ and ‘intrinsically non-local’ models, and their success in comparisons with experimental data, are discussed

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.

Analysis of symmetry breaking mechanisms and the role of turbulence self-regulation in intrinsic rotation

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 gradient of turbulence intensity?a ubiquitous radial inhomogeneity in tokamak plasmas?as important k||-symmetry breaking mechanisms. By studying and comparing the correlations between residual stress, E ? B shearing, fluctuation intensity and its radial gradient, we investigate the dynamics of residual stress generation by various symmetry breaking mechanisms and explore the implication of the self-regulating dynamics of fluctuation intensity and E ? B shearing for intrinsic rotation generation. Several scalings for intrinsic rotation are reported and are linked to investigations of underlying local dynamics. It is found that stronger intrinsic rotation is generated for higher values of ion temperature gradient, safety factor and weaker magnetic shear. These trends are broadly consistent with the intrinsic rotation scaling found from experiment?the so-called Rice scaling.

On the efficiency of intrinsic rotation generation in tokamaks

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 destruction rate due to flow generation to the entropy production rate due to ∇T relaxation (i.e., related to turbulent heat flux). The efficiencies for two different cases, i.e., for the generation of turbulent driven E×B shear flow (zonal flow) and for toroidal intrinsic rotation, are considered for a stationary state, achieved by balancing entropy production rate and destruction rate order by order in O(k∥/k⊥), where k is the wave number. The efficiency of intrinsic toroidal rotation is derived and shown to be eIR∼(Mach)th2∼0.01. The scaling of the efficiency of intrinsic rotation generation is also derived and shown to be ρ∗2(q2/s2)(R2/LT2)=ρ∗2(Ls2/LT2), w...

On plasma rotation with toroidal magnetic field ripple and no external momentum input

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 constant. The toroidal flow dynamics is understood as being likely dominated by turbulence transport driven processes at low ripple amplitude, while the ripple-induced toroidal friction becomes dominant at high ripple. In the latter case, the velocity tends remarkably towards the neoclassical prediction (counter-current rotation). The radial electric field is not affected by the ripple variation and remains well described by its neoclassical prediction. Finally, the poloidal velocity is of the order of the neoclassical prediction at high ripple amplitude, but significantly departs from it at low ripple.