Tokamak Plasma Turbulence Research Articles

Nonlinear Interaction of Edge-Localized Modes and Turbulent Eddies in Toroidal Plasma under n=1 Magnetic Perturbation.

The effect of static n=1 resonant magnetic perturbation (RMP) on the spatial structure and temporal dynamics of edge-localized modes (ELMs) and edge turbulence in tokamak plasma has been investigated. Two-dimensional images measured by a millimeter-wave camera on the KSTAR tokamak revealed that the coherent filamentary modes (i.e., ELMs) are still present in the edge region when the usual large scale collapse of the edge confinement, i.e., the ELM crash, is completely suppressed by n=1 RMP. Cross-correlation analyses on the 2D images show that (1)the RMP enhances turbulent fluctuations in the edge toward the ELM-crash-suppression phase, (2)the induced turbulence has a clear dispersion relation for wide ranges of wave number and frequency, and (3)the turbulence involves a net radially outward energy transport. Nonlinear interactions of the turbulent eddies with the coexisting ELMs are clearly observed by bispectral analysis, which implies that the exchange of energy between them may be the key to the prevention of large scale crashes.

A 5D gyrokinetic full-[formula omitted] global semi-Lagrangian code for flux-driven ion turbulence simulations

This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic Gysela code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the Gysela code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.

Optimization of the Gyroaverage operator based on Hermite interpolation

Gyrokinetic modeling is appropriate for describing Tokamak plasma turbulence, and the gyroaverage operator is a cornerstone of this approach. In a gyrokinetic code, the gyroaveraging scheme needs to be accurate enough to avoid spoiling the data but also requires a low computation cost because it is applied often on the main unknown, the 5D guiding-center distribution function, and on the 3D electric potentials. In the present paper, we improve a gyroaverage scheme based on Hermite interpolation used in the Gysela code. This initial implementation represents a too large fraction of the total execution time. The gyroaverage operator has been reformulated and is now expressed as a matrix-vector product and a cache-friendly algorithm has been setup. Different techniques have been investigated to quicken the computations by more than a factor two. Description of the algorithms is given, together with an analysis of the achieved performance.

Self-organized criticality revisited: non-local transport by turbulent amplification

We revise the applications of self-organized criticality (SOC) as a paradigmatic model for tokamak plasma turbulence. The work, presented here, is built around the idea that some systems do not develop a pure critical state associable with SOC, since their dynamical evolution involves as a competing key factor an inverse cascade of the energy in reciprocal space. Then relaxation of slowly increasing stresses will give rise to intermittent bursts of transport in real space and outstanding transport events beyond the range of applicability of the ‘conventional’ SOC. Also, we are concerned with the causes and origins of non-local transport in magnetized plasma, and show that this type of transport occurs naturally in self-consistent strong turbulence via a complexity coupling to the inverse cascade. We expect these coupling phenomena to occur in the parameter range of strong nonlinearity and time scale separation when the Rhines time in the system is small compared with the instability growth time.

The radial propagation of turbulence in gyro-kinetic toroidal systems

In this paper, a conservation equation is derived for the radially dependent entropy in toroidal geometry using the local approximation of the gyro-kinetic equation. This naturally leads to an operative definition for the turbulence intensity. It is shown that the conservation equation can be split into two contributions, one describing the dynamics of the zonal modes and one for the non-zonal modes. In essence the paper provides an operative tool for both analytic as well as numeric studies of the radial propagation of turbulence in tokamak plasmas.

Generation of a magnetic island by edge turbulence in tokamak plasmas

We investigate, through extensive 3D magneto-hydro-dynamics numerical simulations, the nonlinear excitation of a large scale magnetic island and its dynamical properties due to the presence of small-scale turbulence. Turbulence is induced by a steep pressure gradient in the edge region [B. D. Scott, Plasma Phys. Controlled Fusion 49, S25 (2007)], close to the separatrix in tokamaks where there is an X-point magnetic configuration. We find that quasi-resonant localized interchange modes at the plasma edge can beat together and produce extended modes that transfer energy to the lowest order resonant surface in an inner stable zone and induce a seed magnetic island. The island width displays high frequency fluctuations that are associated with the fluctuating nature of the energy transfer process from the turbulence, while its mean size is controlled by the magnetic energy content of the turbulence.

From Non-Markovian Processes to Stochastic Real Time Control for Tokamak Plasma Turbulence Via Artificial Intelligence Techniques

The mathematical approach to the magnetic plasma confinement is considered. In this direction we obtain the interpretation of possible generalizations of Ruelle–Perron–Frobenious theorem and Bayesian inverse method. The aim is to use artificial neural networks for memorize the past history and on such a way the problem of controlled non-Markovian processes is transferred toward fuzzy Markovian processes. If this process is ergodic the we obtain crisp Markovian process good for application of Bayesian method to plasma confinement.

Kinetic Ballooning Mode Turbulence Simulation based on Electromagnetic Gyrokinetics

The kinetic ballooning mode (KBM) turbulence in Tokamak plasma is investigated by electromagnetic gyrokinetic simulations. From the entropy balance analysis, it is revealed that the field-particle interactions transfer a significant fraction of the ion entropy produced by the instability to electrons. Then, the produced ion entropy balances to the sum of the ion and electron dissipations at the saturation of the KBM instability growth, in contrast to ITG turbulence where ion entropy production mostly balances to ion dissipation.

Unraveling Quasiperiodic Relaxations of Transport Barriers with Gyrokinetic Simulations of Tokamak Plasmas

The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability--driven by the temperature anisotropy (T(∥)≠T(⊥)). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.

A possible mechanism responsible for generating impurity outward flow under radio frequency heating

The effect of poloidal asymmetry of impurities on impurity transport driven by electrostatic turbulence in tokamak plasmas is analyzed. It is found that in the presence of in–out asymmetric impurity populations the zero-flux impurity density gradient (the so-called peaking factor) is significantly reduced. A sign change in the impurity flux may occur if the asymmetry is sufficiently large. This may be a contributing reason for the observed outward convection of impurities in the presence of radio frequency heating. This paper extends a previous work (Fülöp and Moradi 2011 Phys. Plasmas 18 030703), by including the effect of ion parallel compressibility on the peaking factor, which is found to have a significant contribution in the presence of poloidal asymmetry. It is shown here that in the ion temperature gradient mode dominated plasmas the presence of an in–out poloidal asymmetry can lead to a negative impurity peaking factor, and it becomes more negative in regions with larger ion temperature gradients. In the trapped electron mode dominated plasmas an in–out poloidal asymmetry results in a strong reduction of the peaking factor; however, it remains positive for typical experimental parameters. Furthermore, it is shown that an up–down asymmetry reduces the peaking factor while an out–in asymmetry increases it.

Predictions on heat transport and plasma rotation from global gyrokinetic simulations

Flux-driven global gyrokinetic codes are now mature enough to make predictions in terms of turbulence and transport in tokamak plasmas. Some of the recent breakthroughs of three such codes, namely GYSELA, ORB5 and XGC1, are reported and compared wherever appropriate. In all three codes, turbulent transport appears to be mediated by avalanche-like events, for a broad range of ρ* = ρi/a values, ratio of the gyro-radius over the minor radius. Still, the radial correlation length scales with ρi, leading to the gyro-Bohm scaling of the effective transport coefficient below ρ* ≈ 1/300. The possible explanation could be due to the fact that avalanches remain meso-scale due to the interaction with zonal flows, whose characteristic radial wavelength appears to be almost independent of the system size. As a result of the radial corrugation of the turbulence driven zonal and mean flows, the shear of the radial electric field can be significantly underestimated if poloidal rotation is assumed to be governed by the neoclassical theory, especially at low collisionality. Indeed, the turbulence contribution to the poloidal rotation increases when collisionality decreases. Finally, the numerical verification of toroidal momentum balance shows that both neoclassical and turbulent contributions to the Reynolds' stress tensor play the dominant role. The phase space analysis further reveals that barely passing supra-thermal particles mostly contribute to the toroidal flow generation, consistently with quasi-linear predictions.

Discoveries from the exploration of gyrokinetic momentum transport

The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.

Effect of poloidal asymmetry on the impurity density profile in tokamak plasmas

The effect of poloidal asymmetry of impurities on impurity transport driven by electrostatic turbulence in tokamak plasmas is analyzed. It is found that if the density of the impurity ions is poloidally asymmetric then the zero-flux impurity density gradient is significantly reduced and even a sign change in the impurity flux may occur if the asymmetry is sufficiently large. This effect is most effective in low shear plasmas with the impurity density peaking on the inboard side and may be a contributing factor to the observed outward convection of impurities in the presence of radio frequency heating.

Impurity dynamics in the presence of transport barriers in tokamaks

Impurity transport in tokamak core plasmas is investigated with a three-dimensional global fluid code. The diffusion coefficient and the pinch velocity of impurity transport in tokamaks are studied using the fluid model for ion temperature gradient and trapped electron mode driven turbulence in tokamak plasmas. It is shown that in the presence of an internal transport barrier created by a reversed magnetic shear configuration or external E×B shear flow, a reversal of impurity pinch velocity is obtained, which changes from inward direction to outward direction. This scenario is favorable for expelling impurities from the central region and decontaminating the core plasma. The pinch reversal is attributed to a change of sign of the curvature pinch velocity. This modification is mostly due to the reversal of magnetic shear for the hollow q profile. When a strong E×B shear flow is externally imposed, it is rather due to a change of the turbulence mean phase velocity.

Characterizing electrostatic turbulence in tokamak plasmas with high MHD activity

One of the challenges in obtaining long lasting magnetic confinement of fusion plasmas in tokamaks is to control electrostatic turbulence near the vessel wall. A necessary step towards achieving this goal is to characterize the turbulence level and so as to quantify its effect on the transport of energy and particles of the plasma. In this paper we present experimental results on the characterization of electrostatic turbulence in Tokamak Chauffage Alfven Bresilien (TCABR), operating in the Institute of Physics of University of São Paulo, Brazil. In particular, we investigate the effect of certain magnetic field fluctuations, due to magnetohydrodynamical (MHD) instabilities activity, on the spectral properties of electrostatic turbulence at plasma edge. In some TCABR discharges we observe that this MHD activity may increase spontaneously, following changes in the edge safety factor, or after changes in the radial electric field achieved by electrode biasing. During the high MHD activity, the magnetic oscillations and the plasma edge electrostatic turbulence present several common linear spectral features with a noticeable dominant peak in the same frequency. In this article, dynamical analyses were applied to find other alterations on turbulence characteristics due to the MHD activity and turbulence enhancement. A recurrence quantification analysis shows that the turbulence determinism radial profile is substantially changed, becoming more radially uniform, during the high MHD activity. Moreover, the bicoherence spectra of these two kinds of fluctuations are similar and present high bicoherence levels associated with the MHD frequency. In contrast with the bicoherence spectral changes, that are radially localized at the plasma edge, the turbulence recurrence is broadly altered at the plasma edge and the scrape-off layer.

Impurity transport driven by ion temperature gradient turbulence in tokamak plasmas

Impurity transport driven by electrostatic turbulence is analyzed in weakly collisional tokamak plasmas using a semianalytical model based on a boundary layer solution of the gyrokinetic equation. Analytical expressions for the perturbed density responses are derived and used to determine the stability boundaries and the quasilinear particle fluxes. For moderate impurity charge number Z, the stability boundaries are very weakly affected by the increasing impurity charge for constant effective charge, while for lower impurity charge the influence of impurities is larger, if the amount of impurities is not too small. Scalings of the mode frequencies and quasilinear fluxes with charge number, effective charge, impurity density scale length, and collisionality are determined and compared to quasilinear gyrokinetic simulations with GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] resulting in very good agreement. Collisions do not affect the mode frequencies, growth rates, and impurity fluxes significantly. The eigenfrequencies and growth rates depend only weakly on Z and Zeff but they are sensitive to the impurity density gradient scale length. An analytical approximate expression of the zero-flux impurity density gradient is derived and used to discuss its parametric dependencies.

Properties of microturbulence in toroidal plasmas with reversed magnetic shear

Electrostatic drift wave turbulence in tokamak plasmas with reversed magnetic shear is studied using global gyrokinetic particle simulations. The linear eigenmode of the ion temperature gradient (ITG) instability exhibits a mode gap around the minimum safety factor (qmin) region, particularly when qmin is an integer, due to the rarefaction of rational surfaces. The collisionless trapped electron mode (CTEM) instability is suppressed in the negative-shear region due to the reversal of the toroidal precessional drift of trapped electrons. However, after nonlinear saturation, the ITG gap is filled up by the turbulence spreading and the CTEM fluctuation propagates into the stable negative-shear region. The steady state turbulence occupies the whole volume without any identifiable gap or coherent structures of the heat conductivity, perturbed temperature, or zonal flows in the qmin location or the reversed shear region. Our finding indicates that the electrostatic drift wave turbulence itself does not support either linear or nonlinear mechanism for the formation of internal transport barriers in the reversed magnetic shear when qmin crossing an integer.

Two distinct regimes of turbulence in HL-2A tokamak plasmas

Two distinct regimes of turbulence are identified with Langmuir probe arrays in the edge plasmas of the HuanLiuqi (HL)-2A tokamak for the first time. The spatial and temporal coherent characteristics of the low frequency fluctuations (LFFs) of 20–100 kHz are found in significant contrast to the high frequency ambient turbulence (HFAT) of 100 kHz or higher. In the LFF regime, the deviations from the regular linear dispersion relations of the HFAT are observed. The poloidal and toroidal correlation lengths of the former are measured one order of magnitude longer than that of the latter. The ratio of the temporal scales of the fluctuations in the LFF and HFAT regimes is estimated to be of the same order as that for the spatial scales. The LFF may coexist with and differentiate from the geodesic acoustic modes. The bispectrum analysis of the data indicates that nonlinear three wave coupling between the LFF and HFAT is a possible creation mechanism for the former. The possible correlation of the results with the theory and simulation predictions on quasimodes is discussed.

Beam emission spectroscopy for density turbulence measurements on the MAST spherical tokamak

Beam emission spectroscopy (BES) of the energetic deuterium (D(0)) heating beams can provide a means of characterizing the density turbulence in tokamak plasmas. First such measurements have been performed on the MAST spherical tokamak using a trial BES system, which shares the collection optics of the charge-exchange recombination spectroscopy system. This system, with eight spatial channels covering the outer part of the plasma cross section, uses avalanche photodiode detectors with custom preamplifiers to provide measurements at 1 MHz bandwidth with a spatial resolution of 4 cm. Simulations of the measurement, including the beam absorption and excitation, line-of-sight integration of the emission spectrum, and the characteristics of the detection system have been benchmarked against the measured absolute intensity of the Doppler shifted Dalpha fluorescence from the 50 keV beam. This gives confidence in predictions of the performance of a two-dimensional imaging BES system planned for MAST. Correlation techniques have also provided information on the characteristics of the density turbulence at the periphery of L-mode plasmas as well as density perturbations due to coherent magnetohydrodynamic activity at the edge of H-mode plasmas. Precursor oscillations of the density in the pedestal region to edge-localized modes occurring during H-mode plasmas with a single-null diverted magnetic configuration are also observable in the raw signals from the trial BES system.

Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence

The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor.