Geodesic Acoustic Mode Amplitude Research Articles

Neoclassical and turbulent E × B flows in flux-driven gyrokinetic simulations of Ohmic tokamak plasmas

The interplay of flows and turbulence in Ohmic FT-2 tokamak plasmas is analysed via gyrokinetic simulations with the flux-driven ELMFIRE code. The simulation predictions agree qualitatively with analytical estimates for the scaling of the neoclassical radial electric field as a function of collisionality for ad hoc parameters. For the experimental parameters, the global full-f modeling agrees well with the analytical estimates in a neoclassical setting, while including kinetic electrons and impurities has a small impact. Allowing turbulence to develop modifies the flow profile through relaxation of profiles caused by turbulent transport, non-adiabatic response of passing electrons around rational surfaces, and turbulent flow drive. Geodesic acoustic mode (GAM) is the main zonal flow component in the simulations, and its frequency and amplitude agree with theoretical predictions and experimental measurements. In the simulations, the non-linear energy transfer from the turbulence to the flows through the Reynolds force is balanced by the collisional flow dissipation. Temporal relationship between the oscillating flow, Reynolds force, and turbulent particle flux is consistent with the fundamental physics picture of GAM modulating turbulent transport on the time scale of the mode. Experimental evidence also suggests anti-correlation of GAM amplitude and turbulent fluctuations.

Microturbulence in DIII-D tokamak pedestal. IV. Electrostatic turbulent transport

Gyrokinetic simulations of electrostatic microturbulence in the edge plasmas of DIII-D shot 131997 find that the geodesic acoustic mode (GAM) is generated after nonlinear saturation both at the pedestal top and in the peak gradient region, and in turn, regulates the turbulence in both regions. Collisions significantly reduce the GAM amplitude and the associated GAM modulation of the turbulence in both regions. Collisions have little effects on the ion temperature gradient turbulent transport level at the pedestal top. On the other hand, collisional damping of the TEM significantly reduces the turbulent transport level in the peak gradient region.

Plasma potential and geodesic acoustic mode evolution with Helium puffing in the ECRH regime on the T-10 tokamak

The evolution of the Geodesic Acoustic Mode (GAM) and mean plasma electric potential were examined in the regime with short (5 ms) Helium puffing into Electron Cyclotron Resonance heated discharge of the T-10 tokamak. It was shown that a Helium pulse leads to temporal perturbation of the plasma electron temperature and density and concomitant evolution of the mean potential, happening in the diffusive time-scale ∼⃒ 30 ms. Afterwards, the potential restores to the new stationary level with the same time-scale. On top of that GAM amplitude reduces sharply (within 2-5 ms) and GAM frequency also decreases within 30 ms after Helium puffing. Afterwards GAM amplitude and frequency relax to a new stationary level within about 50-70 ms. The evolution of electron density, electron and ion temperatures, total stored energy and plasma density turbulence is discussed in order to clarify their links with potential and GAM evolution.

Comparison of experiment and models of geodesic acoustic mode frequency and amplitude geometric scaling in ASDEX Upgrade

In a set of dedicated ASDEX Upgrade shape-scan experiments, the influence of plasma geometry on the frequency and amplitude behaviour of the geodesic acoustic mode (GAM), measured by Doppler reflectometry, is studied. In both limiter and divertor configurations, the plasma elongation was varied between circular and highly elongated states (). Also, the edge safety factor was scanned between 3 < q < 5. The GAM frequency and amplitude are used to test several models (heuristic, fluid and gyrokinetic based), which incorporate various plasma geometry effects. The experimentally observed effect of decreasing with increasing κ is predicted by most models. Other geometric factors, such as inverse aspect ratio ε and Shafranov shift gradient are also seen to be influential in determining a reliable lower boundary. The GAM amplitude is found to vary with boundary elongation and safety factor q. The collisional damping is compared to multiple models for the collisionless damping. Collisional damping appears to play a stronger role in the divertor configuration, while collisional and collisionless damping both may contribute to the GAM amplitude in the limiter configuration.

Fusion Research in Ioffe Institute

In this paper we present the fusion related activities of the Plasma Physics Division at the Ioffe Institute. The first experiments on lower hybrid current drive (LHCD) in a spherical tokamak performed at the Globus-M tokamak (R = 0.36 m, a = 0.24 m, Bt = 0.4 T, Ip = 200 kA) with a novel poloidally oriented grill resulted in an RF driven current of up to 30 kA at (100 kW, 2.5 GHz), exceeding the modelling predictions. At the FT-2 tokamak (R = 0.56 m, a = 0.08 m, Bt = 3 T, Ip = 30 kA) experiments with a traditional toroidally oriented grill revealed no strong dependence of the LHCD density limit on the H/D ratio in spite of LH resonance densities differing by a factor of 3. Microwave Doppler reflectometry (DR) at the Globus-M, and DR and heavy ion beam probe measurements at the tokamak TUMAN-3M (R = 0.53 m, a = 0.24 m, Bt = 1.0 T, Ip = 190 kA) demonstrated geodesic acoustic mode (GAM) suppression at the L to H transition. Observations at FT-2 using Doppler Enhanced Scattering showed that the GAM amplitude is anti-correlated both spatially and temporally to the drift turbulence level and electron thermal diffusivity. For the first time turbulence amplitude modulation at the GAM frequency was found both experimentally and in global gyrokinetic modelling. A model of the L–H transition is proposed based on this effect. The loss mechanisms of energetic ions' (EI) were investigated in the neutral beam injection (NBI) experiments on Globus-M and TUMAN-3M. Empirical scaling of the 2.45 MeV DD neutron rate for the two devices shows a strong dependence on toroidal field and plasma current justifying the Bt and Ip increase by a factor of 2.5 for the proposed upgrade of Globus-M. Bursts of ∼1 MHz Alfvenic type oscillations correlating with sawtooth crashes were observed in ohmic TUMAN-3M discharges. The possibility of low threshold parametric excitation of Bernstein and upper hybrid waves trapped in drift-wave eddies resulting in anomalous absorption in electron cyclotron resonance heating (ECRH) experiments in toroidal plasmas was identified theoretically. A novel method of radial correlation Doppler reflectometry is shown to be capable of measuring the turbulence wave-number spectrum in realistic 2D geometry. On the progress in design and fabrication of three diagnostics for ITER developed in the Ioffe institute is reported: neutral particle analysis, divertor Thomson scattering and gamma spectroscopy.

Comprehensive comparisons of geodesic acoustic mode characteristics and dynamics between Tore Supra experiments and gyrokinetic simulations

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, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation time are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.

Density fluctuation of geodesic acoustic mode on the HL-2A tokamak

The density fluctuations of the geodesic acoustic mode (GAM) have been observed in Ohmic deuterium plasma discharges with a combination of rake-like and three-step Langmuir probe arrays on the HL-2A tokamak. The probe arrays with poloidal and toroidal separations of 36 and 1330 mm are applied to measure the spectral property and intermittency of the GAM density fluctuations. The poloidal and toroidal mode numbers of the fluctuations are simultaneously measured for the first time. The measured fluctuation amplitude is consistent with the theoretical prediction. High coherence and near zero phase shift of the GAM density fluctuations separated toroidally by 37.5° at the same magnetic flux surface was first observed, indicating the symmetric structure of the GAM in the toroidal direction. The peak time delays of the cross-correlation function of the fluctuations above and below the midplane suggest the expected sin θ dependence. The nonlinear three wave coupling between the GAM and the ambient turbulence is shown to be a plausible mechanism for the generation of the GAM density fluctuations. The significant coherence and the corresponding fixed phase shift (∼π) between the original data and the envelope of the high frequency ambient turbulence provide the experimental evidence for the envelope modulation. The GAM amplitude is out of phase with the particle flux. Most of the intermittent frequencies for particle flux are close to the GAM frequency.

Dynamics of kinetic geodesic-acoustic modes and the radial electric field in tokamak neoclassical plasmas

We present edge gyrokinetic simulations of tokamak plasmas using the fully non-linear (full-f) continuum code TEMPEST. A non-linear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson equation. We demonstrate the following. (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high q (tokamak safety factor), and are necessary to explain the damping observed in our TEMPEST q-scans and consistent with the experimental measurements of the scaling of the GAM amplitude with edge q95 in the absence of obvious evidence that there is a strong q-dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and parallel flow characteristics qualitatively like those observed in experiments.

Amplitude behaviour of geodesic acoustic modes in the ASDEX Upgrade tokamak

The amplitude behaviour of the geodesic acoustic mode (GAM), a low frequency (5–25 kHz) coherent plasma turbulence-generated Er × B zonal flow oscillation, is studied in the ASDEX Upgrade tokamak using Doppler reflectometry. Across the tokamak edge the GAM displays one or more maxima a few cm wide, coinciding with radial plateaus in the GAM frequency, suggesting nested zonal flow layers. The GAM peak amplitude ranges between 0.2 and 0.8 km s−1, corresponding to several tens of per cent of the mean E × B flow velocity. In limiter configurations, the GAM amplitude is found to decrease inversely with the plasma vertical elongation 1.1 < κ < 1.4, but rises again in X-point divertor configurations at higher κ ∼ 1.6. At low κ the GAM amplitude increases with the safety factor q, consistent with damping effects, but becomes less sensitive to q at high κ. A positive linear dependence on the electron temperature gradient, an indicator of the linear turbulence drive, is also observed.

Frequency scaling and localization of geodesic acoustic modes in ASDEX Upgrade

The frequency behaviour and localization of the geodesic acoustic mode (GAM), believed to be a coherent plasma turbulence-generated Er × B zonal flow (ZF) oscillation, is studied in the ASDEX Upgrade tokamak using Doppler reflectometry. In typical elongated (1.4 < κ < 1.75) plasmas with an X-point divertor configuration the GAM is observed only in the edge density gradient region 0.95 < ρpol < 1.0 between the density pedestal top and the flux surface boundary. The GAM frequency (5–25 kHz) is found to scale linearly as ω = G cs/Ro (sound speed over major radius) but with an inverse dependence on the plasma elongation κ and a weak direct dependence on the safety factor q. The lower the GAM frequency the more important it is expected to become in moderating the turbulence via shear decorrelation. A heuristic scaling law for the frequency scale factor involving κ and finite aspect ratio ϵ terms has been obtained from dedicated parameter scans. For circular plasmas κ ∼ 1 touching the limiter the density pedestal is weakened and the GAM is seen to reach in radially as far as ρpol ∼ 0.75, depending on the q profile, with a frequency scale consistent with theoretical predictions. Radially the GAM frequency is not a smooth function but displays a series of plateaus a few centimetres wide coinciding with peaks in the GAM amplitude, suggesting several ZF layers. At the plateau edges the GAM spectral peak splits into two frequency branches.

Structure and scaling properties of the geodesic acoustic mode

Characteristics and scaling properties of the geodesic acoustic mode (GAM), a coherent, radially-sheared high frequency (∼15 kHz) zonal flow oscillation, are studied systematically using time-delay-estimation techniques applied to localized, multi-point density fluctuation measurements obtained by beam emission spectroscopy on DIII-D. The GAM amplitude is shown to increase strongly with increasing safety factor, q95, and to likewise become undetectably small for q95 < 4.2, qualitatively consistent with theoretical predictions based on collisional damping as well as simulations. The radial structure of the GAM exhibits peak amplitude in the radial range 0.88 < r/a < 0.95 with a rapid amplitude reduction inside and outside this region. The measured frequency is close to the predicted frequency, though some deviation to higher frequency is observed at lower q. The GAM amplitude is also shown to increase with plasma elongation, κ, while its frequency decreases.