Universality of Poisson-driven plasma fluctuations in the Alcator C-Mod scrape-off layer

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

Lower hybrid current drive (LHCD) is a potential source of non-inductive off-axis current drive (CD) for tokamaks. Although LHCD has been successfully deployed on a number of tokamaks, it is highly sensitive to the scrape-off layer (SOL) conditions local to the LHCD launcher. Large gaps between the launcher and plasma core, SOL turbulence, or edge density perturbations due to edge-localized modes can hamper CD or cause large reflected power. These coupling issues in part motivated the installation of an LHCD launcher on the high-field side (HFS) of DIII-D. On the HFS, the SOL is less turbulent and more controllable compared to the low-field side. This quiescence may result in more predictable edge conditions and thus a more predictable CD. In this work, HFS SOL reflectometry measurements are predicted from global plasma parameters using machine learning models. The SOL predictions coupled with the full-wave simulation of the LHCD launcher allow for the prediction of reflected power, directivity, and arcing risk before the discharge. Launcher performance is then optimized using multi-objective Bayesian optimization, finding the shot parameters that result in an optimal SOL density that maximizes CD while minimizing the risk of arcing. The predictions and optimizations of LHCD performance are then accelerated using a surrogate model of the full-wave LHCD simulation.

Assessing the performance of lower hybrid current drive (LHCD) at high density is critical for developing non-inductive current drive systems on future steady-state experiments. Excellent LHCD efficiency has been observed during fully non-inductive operation (η=2.0−2.5×1019 AW–1m–2 at n¯e=0.5×1020 m–3) on Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] under conditions (ne, magnetic field and topology, and LHCD frequency) relevant to ITER [S. Shiraiwa et al., Nucl. Fusion 51, 103024 (2011)]. To extend these results to advanced tokamak regimes with higher bootstrap current fractions on C-Mod, it is necessary to increase n¯e to 1.0−1.5×1020 m−3. However, the number of current-carrying, non-thermal electrons generated by LHCD drops sharply in diverted configurations at densities that are well below the density limit previously observed on limited tokamaks. In these cases, changes in scrape off layer (SOL) ionization and density profiles are observed during LHCD, indicating that significant power is transferred from the LH waves to the SOL. Fokker-Planck simulations of these discharges utilizing ray tracing and full wave propagation codes indicate that LH waves in the high density, multi-pass absorption regime linger in the plasma edge, and SOL region, where absorption near or outside the LCFS results in the loss of current drive efficiency. Modeling predicts that non-thermal emission increases with stronger single-pass absorption. Experimental data show that increasing Te in high density LH discharges results in higher non-thermal electron emission, as predicted by the models.

Statistical properties of the scrape-off layer plasma fluctuations are studied in ohmically heated plasmas in the Alcator C-Mod tokamak. For the first time, plasma fluctuations as well as parameters that describe the fluctuations are compared across measurements from a mirror Langmuir probe (MLP) and from gas-puff imaging (GPI) that sample the same plasma discharge. This comparison is complemented by an analysis of line emission time-series data, synthesized from the MLP electron density and temperature measurements. The fluctuations observed by the MLP and GPI typically display relative fluctuation amplitudes of order unity together with positively skewed and flattened probability density functions. Such data time series are well described by an established stochastic framework that models the data as a superposition of uncorrelated, two-sided exponential pulses. The most important parameter of the process is the intermittency parameter, $\gamma = {\tau _{d}} / {\tau _{w}}$ , where ${\tau _{d}}$ denotes the duration time of a single pulse and ${\tau _{w}}$ gives the average waiting time between consecutive pulses. Here we show, using a new deconvolution method, that these parameters can be consistently estimated from different statistics of the data. We also show that the statistical properties of the data sampled by the MLP and GPI diagnostic are very similar. Finally, a synthetic GPI signal using only plasma parameters sampled by the MLP shows qualitatively different fluctuation statistics from the measured GPI signal.

Cross-field particle transport in the scrape-off layer (SOL) of Alcator C-Mod [Phys. Plasmas 1, 1511 (1994)] can be characterized by an effective particle diffusivity (Deff) that increases markedly with distance from the separatrix. As a consequence, recycling onto the main-chamber walls is large compared to plasma flows into the divertor volume. The SOL exhibits a two-layer structure: Steep gradients and moderate fluctuation levels are typically found in a ∼5 mm region near the separatrix (near SOL) where parallel electron conduction typically dominates energy losses. Small gradients and larger fluctuation levels with longer correlation times are found outside this region (far SOL). Deff in the near SOL increases strongly with local plasma collisionality normalized to the magnetic connection length. As the discharge density limit is approached, Deff and associated fluctuation levels become large across the entire SOL and cross-field heat convection everywhere exceeds parallel conduction losses, impacting the power balance of the discharge.

An ad hoc calculation is presented to interpret the growth of sideband waves during lower hybrid current drive (LHCD) experiments on Experimental Advanced Superconducting Tokamak (EAST). We adopt the solution of the non-linear dispersion relation for parametric instabilities to describe the growth rate of ion cyclotron quasi-modes (ICQMs) in the peripheral plasma, and use the WKB solution of the propagation of electrostatic waves in two dimensions to model the variation of the electric field in the scrape-off-layer (SOL). We then calculate the growth rates and amplification factors of the sideband waves associated with ICQM in the parallel and perpendicular coupling limits. The onset and substantial growth of the first down-shifted sideband of lower hybrid waves (LHWs) are associated with elevation of the plasma density in the outer SOL where the growth rate of ICQM in the parallel coupling limit increases sharply after the density is elevated. The peak frequencies associated with the first harmonic of ICQM obtained from calculating the amplification factors in the parallel coupling limit ( A para ) agree very well with the observed frequencies of the first down-shifted sideband of 2.45 GHz LHWs in EAST pulse 43 772 and 86 521. The consistency between the calculation and the observation indicates that the sideband waves are associated with parametric decay instability of ICQM excited in the outer SOL through parallel coupling. The amplitude of A para obtained from a single pass of LHWs through the SOL of EAST is, however, one order of magnitude smaller than unity, meaning that it remains elusive whether the substantial growth of sideband waves mainly occurs in front of the antenna or requires multiple passes of LHWs across the SOL region.

Significant progress on both L- and H-mode long-pulse discharges has been made recently in Experimental Advanced Superconducting Tokamak (EAST) with lower hybrid current drive (LHCD) [J. Li et al., Nature Phys. 9, 817 (2013) And B. N. Wan et al., Nucl. Fusion 53, 104006 (2013).]. In this paper, LHCD experiments at high density in L-mode plasmas have been investigated in order to explore possible methods of improving current drive (CD) efficiency, thus to extend the operational space in long-pulse and high performance plasma regime. It is observed that the normalized bremsstrahlung emission falls much more steeply than 1/ne_av (line-averaged density) above ne_av = 2.2 × 1019 m−3 indicating anomalous loss of CD efficiency. A large broadening of the operating line frequency (f = 2.45 GHz), measured by a radio frequency (RF) probe located outside the EAST vacuum vessel, is generally observed during high density cases, which is found to be one of the physical mechanisms resulting in the unfavorable CD efficiency. Collisional absorption of lower hybrid wave in the scrape off layer (SOL) may be another cause, but this assertion needs more experimental evidence and numerical analysis. It is found that plasmas with strong lithiation can improve CD efficiency largely, which should be benefited from the changes of edge parameters. In addition, several possible methods are proposed to recover good efficiency in future experiments for EAST.

He 3 gas was puffed from the wall into Ohmic low confinement-mode discharges of the Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1551 (1994)] tokamak and the charged states were measured near the wall with the omegatron ion mass spectrometer. Analysis of the data shows that the concentrations of singly- and doubly-ionized helium near the wall are approximately equal. The electron temperature and density at the omegatron are too low to account for ionization of helium in the local flux tube, therefore the helium is ionized in a hotter region of the edge plasma and is transported to the omegatron. A simple one-dimensional radial transport model reproduces the observed values of charge state flux and density, but only if rapid cross-field transport is included, increasing with distance from the separatrix. A constant cross-field diffusion coefficient of order 2 m2/s and an outward convection velocity profile increasing to of order 100 m/s in the far scrape-off layer is implied.

Efficient coupling of lower hybrid (LH) waves in conditions close to those foreseen in ITER has been obtained in advanced scenario plasmas in the JET tokamak. Up to 3 MW of lower hybrid current drive (LHCD) power has been coupled at a distance between the separatrix and the launcher of 11 cm, in the presence of edge localized mode activity. The key to the improved LH wave coupling is local control of the Scrape-Off-Layer (SOL) density through gas injection in the region magnetically connected to the launcher. This increases the electron density in front of the launcher so as to improve the coupling of the LH waves, i.e. reduce the reflected power in the launcher. The average power reflection coefficient was 5.7% with gas injection, at 11 cm distance between the separatrix and the launcher. A change in the gas injection design has made the gas puffing more efficient, making the use of D2 injection possible as an alternative to CD4. At similar injected electrons/s rates, D2 gives higher electron density in the SOL than CD4, resulting in better LH coupling with D2. The possibility of using D2 instead of the earlier used CD4 is an encouraging result in view of ITER operation, as CD4 may not be compatible in ITER due to the problem of tritium retention in deposited carbon layers.

Two aspects of edge turbulence and transport in Alcator C-Mod are explored. The quasi-coherent mode (QCM), an edge fluctuation present in Enhanced Dα H-mode plasmas, is examined with regard to its role in the enhanced particle transport found in these plasmas, its in/out asymmetry, its poloidal wave number and its radial width and location. It is shown to play a dominant role in the perpendicular particle transport. The QCM is not observed at the inboard midplane, indicating that its amplitude there is significantly smaller than on the outboard side. The peak amplitude of the QCM is found just inside the separatrix, with a radial width ≳5 mm, leading to a non-zero amplitude outside the separatrix and qualitatively consistent with its transport enhancement. Also examined are the characteristics of the intermittent convective transport, associated with the larger scale turbulent structures, also called blobs, and typically occurring in the scrape-off-layer (SOL). These turbulent structures are qualitatively similar in L- and H-mode. When their perpendicular extent, occurrence frequencies and magnitudes are compared, it is found that their size is somewhat smaller in ELMfree H-Mode, while their frequency is similar. A clear difference is seen in the magnitude of these turbulent fluctuations in the far SOL, with ELMfree H-mode showing a smaller perturbation there than L-mode. As the Greenwald density limit is approached (n/nGW ⩾ 0.7), blobs are seen inside the separatrix consistent with the observation that the high cross-field transport region, normally found in the far SOL, penetrates the closed flux surfaces at high n/nGW.

An extensive experimental survey of plasma potentials induced by ion cyclotron range-of frequency (ICRF) heating was carried out in the scrape-off layer (SOL) plasmas on the Alcator C-Mod tokamak. Enhanced plasma potentials >100 V are observed at locations where local magnetic fields map to active ICRF antennas. In these cases, the enhanced potential appears only when a local plasma density threshold is surpassed—a threshold that is quantitatively consistent with slow wave (SW) RF rectification theory. However, in many cases large potential enhancements are found in locations that do not map along magnetic field lines to active antennas without obstruction, i.e. locations that are inaccessible to SWs launched by the active antennas. Enhanced potentials in these ‘unmapped’ locations are correlated with local plasma parameters, ICRF electromagnetic fields associated with the fast wave (FW) and SW, launched wave spectra, and the boundary surface geometry. It is found that enhanced plasma potentials in unmapped locations correlate with the FW field strength. These observations are qualitatively consistent with a model that accounts for the conversion of FWs to SWs at conducting surfaces oriented at an oblique angle with respect to the magnetic field, with the SW leading to sheath rectification. In addition, enhanced plasma potentials are found far into the shadow of passive limiter structures. These are correlated with the magnitude of the local FW field strength, yet the effect does not follow any present model. Overall, ICRF-induced plasma potentials may appear in regions far removed from the active antennas, yet due to the complex response of the SOL potentials at a variety of boundary surfaces, it remains unclear what part of the plasma-facing wall should be targeted to mitigate ICRF-induced impurities. The results also suggest that operating active ICRF antennas in a high single pass absorption regime is crucial in minimizing the effects of the FW fields on plasma–material interactions.

At high plasma density, the lower hybrid current drive (LHCD) system in tokamaks suffers significant efficiency loss caused by parametric decay instability (PDI) induced in the scrape-off layer (SOL) plasma. There, the lower hybrid waves (LHWs) launched from the antenna deposit a large fraction of their power through PDI, leading to the phenomenon of nonlinear density limit of LHCD. In this paper, we present a self-consistent modelling of the power deposition of LHWs in the SOL plasma by coupling PDI to the propagation of LHWs, the power loss of LHCD is evaluated quantitively, and a theoretical scaling of the nonlinear density limit n PDI ∝ P 0 −2/3 L y -2/3 T e ω 0 2 B 4/3 0 is acquired.

Scrape-off layer (SOL) data from DIII-D and C-Mod have been acquired and analysed for radial particle transport based on a particle balance model. This has allowed a detailed comparison for L-mode plasmas. The inferred radial particle flux, Γ⊥(r), is parameterized in terms of diffusive [Deff(r) ≡ Γ⊥(r)/∇n(r)] and convective particle transport [veff(r) ≡ Γ⊥(r)/n(r)]. The magnitude of the inferred Deff or veff increases across the SOL for both tokamaks. The inferred Deff or veff in the ‘far’ SOL (one density e-folding length from the separatrix and beyond) are essentially unchanged by changes in core density by factors of 2–3. This corresponds to changes in the far SOL density, collisionality (ν*) and radial fluxes of a factor of 10 or more. Thus ν* does not appear to be an important parameter in determining the radial particle transport in that region.The dimensionlessly-scaled SOL plasma profiles from the two tokamaks overlay for similar dimensionless plasma parameters. The SOL density profile near the separatrix is steeper than in the ‘far’ SOL. The scaled Deff and veff are slightly larger on DIII-D than C-Mod. This difference appears to be within experimental uncertainties.Neutral ionization in the SOL does not appear to affect radial transport but may be related to the observed flattening of the density profiles with increasing .

A stochastic model for a superposition of uncorrelated pulses with a random distribution of and correlations between amplitudes and velocities is analyzed. The pulses are assumed to move radially with fixed shape and amplitudes decreasing exponentially in time due to linear damping. The pulse velocities are taken to be time-dependent with a power law dependence on the instantaneous amplitudes, as suggested by blob velocity scaling theories. In accordance with experimental measurements, the pulse function is assumed to be exponential, and the amplitudes are taken to be exponentially distributed. As a consequence of linear damping and time-dependent velocities, it is demonstrated that the pulses stagnate during their radial motion. This makes the average pulse waiting time increase radially outwards in the scrape-off layer of magnetically confined plasmas. In the case that pulse velocities are proportional to their amplitudes, the mean value of the process decreases exponentially with radial coordinate, similar to the case when all pulses have the same, time-independent velocity. The profile e-folding length is then given by the product of the average pulse velocity and the parallel transit time. Moreover, both the average pulse amplitude and the average velocity are the same at all radial positions due to stagnation of slow and small-amplitude pulses. In general, an increasing average pulse velocity results in a flattened radial profile of the mean value of the process as well as a higher relative fluctuation level, strongly enhancing plasma–surface interactions.

The main goal of this research was to develop and present a general, efficient, mathematical, and theoretical based methodology to model nonlinear forced-vibrating mechanical systems from time series measurements. A system identification modeling methodology for forced dynamical systems is presented based on a dynamic system theory and a nonlinear time series analysis that employ phase space reconstruction (delay vector embedding) in modeling dynamical systems from time series data using time-delay neural networks. The first part of this work details the modeling methodology, including background on dynamic systems, phase space reconstruction, and neural networks. In the second part of this work, the methodology is evaluated based on its ability to model selected analytical lumped-parameter forced-vibrating dynamic systems, including an example of a linear system predicting lumped mass displacement subjected to a displacement forcing function. The work discusses the application to nonlinear systems, multiple degree of freedom systems, and multiple input systems. The methodology is further evaluated on its ability to model an analytical passenger rail car predicting vertical wheel∕rail force using a measured vertical rail profile as the input function. Studying the neural modeling methodology using analytical systems shows the clearest observations from results, providing prospective users of this tool an understanding of the expectations and limitations of the modeling methodology.