Ralph Kube

Intermittent fluctuations in the Alcator C-Mod scrape-off layer

Fluctuations in the boundary region of the Alcator C-Mod tokamak have been analyzed using gas puff imaging data. It is found that the fluctuation amplitudes in the near scrape-off layer follow a normal distribution while the far scrape-off layer fluctuations are dominated by large amplitude bursts due to radial motion of blob-like structures and have a positively skewed and flattened amplitude probability distribution. Conditional averaging of the time series reveals burst wave forms with a fast rise and slow decay and exponentially distributed burst amplitudes and waiting times. Based on this, a stochastic model of the burst dynamics is constructed. The model predicts that fluctuation amplitudes should follow a Gamma distribution and that there is a parabolic relation between the skewness and the kurtosis moments of the fluctuations. This is shown to compare favorably with the gas puff imaging data over a range of line-averaged plasma densities.

Scrape-off layer turbulence in TCV: evidence in support of stochastic modelling

Intermittent fluctuations in the TCV scrape-off layer have been investigated by analysing long Langmuir probe data time series under stationary conditions, allowing calculation of fluctuation statistics with high accuracy. The ion saturation current signal is dominated by the frequent occurrence of large-amplitude bursts attributed to filament structures moving through the scrape-off layer. The average burst shape is well described by a double-exponential wave-form with constant duration, while the waiting times and peak amplitudes of the bursts both have an exponential distribution. Associated with bursts in the ion saturation current is a dipole shaped floating potential structure and radially outwards directed electric drift velocity and particle flux, with average peak values increasing with the saturation current burst amplitude. The floating potential fluctuations have a normal probability density function while the distributions for the ion saturation current and estimated radial velocity have exponential tails for large fluctuations. These findings are discussed in the light of prevailing theories for filament motion and a stochastic model for intermittent scrape-off layer plasma fluctuations.

Convergence of statistical moments of particle density time series in scrape-off layer plasmas

Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a fixed shape, an exponential distribution of waiting times, and amplitudes represents the radial motion of blob-like structures. With an analytic formulation of the process at hand, we derive expressions for the mean squared error on estimators of sample mean and sample variance as a function of sample length, sampling frequency, and the parameters of the stochastic process. Employing that the probability distribution function of a particularly relevant stochastic process is given by the gamma distribution, we derive estimators for sample skewness and kurtosis and expressions for the mean squared error on these estimators. Numerically, generated synthetic time series are used to verify the proposed estimators, the sample length dependency of their mean squared errors, and their performance. We find that estimators for sample skewness and kurtosis based on the gamma distribution are more precise and more accurate than common estimators based on the method of moments.

Stochastic modelling of intermittent fluctuations in the scrape-off layer: Correlations, distributions, level crossings, and moment estimation

A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process by finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.

Burst statistics in Alcator C-Mod SOL turbulence

Bursty fluctuations in the scrape-off layer (SOL) of Alcator C-Mod have been analyzed using gas puff imaging data. This reveals many of the same fluctuation properties as Langmuir probe measurements, including normal distributed fluctuations in the near SOL region while the far SOL plasma fluctuations are dominated by large amplitude bursts due to radial motion of blob-like structures. Conditional averaging reveals burst wave forms with a fast rise and slow decay and exponentially distributed burst amplitudes and waiting times. Based on this, a stochastic model of burst dynamics is constructed. The model predicts that fluctuation amplitudes should follow a Gamma distribution. This is shown to be a good description of the gas puff imaging data for a range of line-averaged densities.

Effect of dynamical friction on interchange motion of plasma filaments

Theory and numerical simulations are presented for interchange motion of plasma filaments in the presence of dynamical friction and allowing large relative filament amplitudes. When friction is negligible, the filament velocity is proportional to the square root of gravity and its cross-field size. For strong friction, the filament velocity is independent of the cross-field size, proportional to gravity, and inversely proportional to the friction coefficient. In this frictional regime, the filament moves a large distance with nearly constant velocity and shape. The transition between these velocity scaling regimes and the amplitude dependence are revealed. The results presented here complement previous theories for irregularities in the equatorial ionosphere and are in excellent agreement with recent experiments on simply magnetized toroidal plasmas. The relevance to blob-like structures in the scrape-off layer of magnetically confined plasmas is also discussed.

Fluctuation statistics in the scrape-off layer of Alcator C-Mod

Acknowledgements: RK, OEG and AT were supported with financial subvention from the Research Council of Norway under grant 240510/F20. RK would like to thank D Brunner for providing the script used to create figure 1. Work partially supported by US DoE Cooperative agreement DE-FC02-99ER54512 at MIT using the Alcator C-Mod tokamak, a DoE Office of Science user facility. RK and OEG acknowledge the generous hospitality of the Plasma Science and Fusion Center at MIT during a sabbatical stay during which these experiments were performed.

Relationship between frequency power spectra and intermittent, large-amplitude bursts in the Alcator C-Mod scrape-off layer

Fluctuations in the boundary region of the Alcator C-Mod tokamak have been analyzed using gas puff imaging data from a set of Ohmically heated plasma density scan experiments. It is found that the relative fluctuation amplitudes are modest and close to normally distributed at the separatrix but become increasingly larger and skewed towards the main chamber wall. The frequency power spectra are nevertheless similar for all radial positions and line-averaged densities. Predictions of a stochastic model, describing the plasma fluctuations as a super-position of uncorrelated pulses, are shown to be in excellent agreement with the measurements. This implies that the pulse duration is the same, while the degree of pulse overlap decreases radially outwards in the scrape-off layer. The universal frequency power spectral density is thus determined by the shape and duration of the large-amplitude bursts associated with blob-like structures. The model also describes the rate of threshold level crossings, for which the exponential tails underline the intermittency of the fluctuations in the far scarpe-off layer.

Amplitude and size scaling for interchange motions of plasma filaments

The interchange dynamics and velocity scaling of blob-like plasma filaments are investigated using a two-field reduced fluid model. For incompressible flows due to buoyancy the maximum velocity is proportional to the square root of the relative amplitude and the square root of its cross-field size. For compressible flows in a non-uniform magnetic field this square root scaling only holds for ratios of amplitudes to cross-field sizes above a certain threshold value. For small amplitudes and large sizes, the maximum velocity is proportional to the filament amplitude. The acceleration is proportional to the amplitude and independent of the cross-field size in all regimes. This is demonstrated by means of numerical simulations and explained by the energy integrals satisfied by the model.

Intermittent electron density and temperature fluctuations and associated fluxes in the Alcator C-Mod scrape-off layer

Embargo of 12 months from date of publishing on accepted manuscript version. Published version available in https://doi.org/10.1088/1361-6587/aab726> Plasma Physics and Controlled Fusion (2018) 60, (6), 065002 IOP publishing statement: http://ioppublishing.org/wp-content/uploads/2016/05/J-VAR-LF-0216-Author-Rights-New-5.pdf