Improved profile fitting and quantification of uncertainty in experimental measurements of impurity transport coefficients using Gaussian process regression

The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, but the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We show that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. We also discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.United States. Dept. of Energy. Office of Fusion Energy Sciences (Award DE-FC02-99ER54512)United States. Dept. of Energy. Office of Science (Contract DE-AC05-06OR23177)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Award DE-SC0007099

High-field side scrape-off layer investigation: Plasma profiles and impurity screening behavior in near-double-null configurations

New experiments on Alcator C-Mod reveal that the favorable impurity screening characteristics of the high-field side (HFS) scrape-off layer (SOL), previously reported for single null geometries, is retained in double null configurations, despite the formation of an extremely thin SOL. In balanced double-null, nitrogen injected locally into the HFS SOL is better screened by a factor of 2.5 compared to the same injection into the low field side (LFS) SOL. This result is insensitive to plasma current and Greenwald fraction. Nitrogen injected into the HFS SOL is not as well screened (only a factor of 1.5 improvement over LFS) in unbalanced double-null discharges, when the primary divertor is in the direction of B×∇B. In this configuration, impurity ‘plume’ emission patterns indicate that an opposing E × B drift competes with the parallel impurity flow to the divertor. In balanced double-null plasmas, the dispersal pattern exhibits a dominant E × B motion. Unbalanced discharges with the primary divertor opposite the direction of B×∇B exhibit excellent HFS screening characteristics – a factor of 5 enhancement compared to LFS. These data support the idea that future tokamaks should locate all RF actuators and close-fitting wall structures on the HFS and employ near-double-null magnetic topologies, both to precisely control plasma conditions at the antenna/plasma interface and to maximally mitigate the impact of local impurity sources arising from plasma-material interactions. Keywords: Alcator C-Mod; Impurity screening; Double null; High field side scrape-off layerUnited States. Department of Energy (Contract DE-FC02-99ER54512

Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experimenta)

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.United States. Department of Energy (Contract No. DE-FC02-99ER54512-CMOD)United States. Department of Energy. Office of Science (Contract No. DE-AC02- 05CH11231

Non-local heat transport in Alcator C-Mod ohmic L-mode plasmas

Non-local heat transport experiments were performed in Alcator C-Mod ohmic L-mode plasmas by inducing edge cooling with laser blow-off impurity (CaF2) injection. The non-local effect, a cooling of the edge electron temperature with a rapid rise of the central electron temperature, which contradicts the assumption of 'local' transport, was observed in low collisionality linear ohmic confinement (LOC) regime plasmas. Transport analysis shows this phenomenon can be explained either by a fast drop of the core diffusivity, or the sudden appearance of a heat pinch. In high collisionality saturated ohmic confinement (SOC) regime plasmas, the thermal transport becomes 'local': the central electron temperature drops on the energy confinement time scale in response to the edge cooling. Measurements from a high resolution imaging x-ray spectrometer show that the ion temperature has a similar behaviour as the electron temperature in response to edge cooling, and that the transition density of non-locality correlates with the rotation reversal critical density. This connection may indicate the possible connection between thermal and momentum transport, which is also linked to a transition in turbulence dominance between trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. Experiments with repetitive cold pulses in one discharge were also performed to allow Fourier analysis and to provide details of cold front propagation. These modulation experiments showed in LOC plasmas that the electron thermal transport is not purely diffusive, while in SOC the electron thermal transport is more diffusive like. Linear gyrokinetic simulations suggest the turbulence outside r/a = 0.75 changes from TEM dominance in LOC plasmas to ITG mode dominance in SOC plasmas.United States. Dept. of Energy (DoE Contract No DE-FC02-99ER54512)Oak Ridge Institute for Science and Education (DOE Fusion Energy Postdoctoral Research Program

Experimental data analysis techniques for validation of Tokamak impurity transport simulations

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages [234]-309).This thesis presents two new techniques for analyzing data from impurity transport experiments in magnetically confined plasmas, with specific applications to the Alcator C-Mod tokamak. The objective in developing these new techniques is to improve the quality of the experimental results used to test simulations of turbulent transport: better characterization of the uncertainty in the experimental results will yield a better test of the simulations. Transport codes are highly sensitive to the gradients of the background temperature and density profiles, so the first half of this thesis presents a new approach to fitting tokamak profiles using nonstationary Gaussian process regression. This powerful technique overcomes many of the shortcomings of previous spline-based data smoothing techniques, and can even handle more complicated cases such as line-integrated measurements, computation of second derivatives, and 2d fitting of spatially- and temporally-resolved measurements. The second half of this thesis focuses on experimental measurements of impurity transport coefficients. It is shown that there are considerable shortcomings in existing point estimates of these quantities. Next, a linearized model of impurity transport data is constructed and used to estimate diagnostic requirements for impurity transport measurements. It is found that spatial resolution is more important than temporal resolution. Finally, a fully Bayesian approach to inferring experimental impurity transport coefficient profiles which overcomes the shortcomings of the previous approaches through use of multimodal nested sampling is developed and benchmarked using synthetic data. These tests reveal that uncertainties in the transport coefficient profiles previously attributed to uncertainties in the temperature and density profiles are in fact entirely explained by changes in the spline knot positions. Appendices are provided describing the extensive work done to determine the derivatives of stationary and nonstationary covariance kernels and the open source software developed as part of this thesis work. The techniques developed here will enable more rigorous benchmarking of turbulent transport simulations, with the ultimate goal of developing a predictive capability.by Mark Alan Chilenski.Ph. D

LHCD during current ramp experiments on Alcator C-Mod

The lower hybrid current drive (LHCD) system on Alcator C-Mod is capable of sustaining fully non-inductive discharges for multiple current relaxation times (τ cr ∼ 200 ms) at line averaged densities in the range of 5x10 19 m -3 . Some of these non-inductive discharges develop unstable MHD modes that can greatly reduce current drive performance, particularly in discharges with plasma current of 0.5 MA or less [1,2]. Avoiding these unstable MHD modes motivated an experiment to test if the stable current profile shape of a higher current non-inductive discharge could be achieved in a lower current discharge. Starting from a discharge at 0.8 MA, the plasma current was ramped down to 0.5 MA over 200 ms. The surface voltage of the plasma swings negative during the ramp, with the loop voltage reversal impacting the edge fast electron measurements immediately. Little change can be seen during the I p ramp in the core fast electron measurements, indicating that the loop voltage reversal does not penetrate fully to the magnetic axis on the timescale of the current ramp. The resulting discharge did not exhibit deleterious MHD instabilities, however the existence of this one discharge does not necessarily represent a robust solution to the problem.United States. Department of Energy. Office of Fusion Energy Sciences (Award DE-FC02-99ER54512)United States. Department of Energy. Office of Fusion Energy Sciences (Award DE-AC02-76CH03073

Experimentally testing the dependence of momentum transport on second derivatives using Gaussian process regression

It remains an open question to explain the dramatic change in intrinsic rotation induced by slight changes in electron density (White et al 2013 Phys. Plasmas 20 056106). One proposed explanation is that momentum transport is sensitive to the second derivatives of the temperature and density profiles (Lee et al 2015 Plasma Phys. Control. Fusion 57 125006), but it is widely considered to be impossible to measure these higher derivatives. In this paper, we show that it is possible to estimate second derivatives of electron density and temperature using a nonparametric regression technique known as Gaussian process regression. This technique avoids over-constraining the fit by not assuming an explicit functional form for the fitted curve. The uncertainties, obtained rigorously using Markov chain Monte Carlo sampling, are small enough that it is reasonable to explore hypotheses which depend on second derivatives. It is found that the differences in the second derivatives of and between the peaked and hollow rotation cases are rather small, suggesting that changes in the second derivatives are not likely to explain the experimental results

Core impurity transport in Alcator C-Mod L-, I- and H-mode plasmas

Core impurity transport has been investigated for a variety of confinement regimes in Alcator C-Mod plasmas from x-ray emission following injection of medium and high Z materials. In ohmic L-mode discharges, impurity transport is anomalous (D[subscript eff] ≫ D[subscript nc]) and changes very little across the LOC/SOC boundary. In ion cyclotron range of frequencies (ICRF) heated L-mode plasmas, the core impurity confinement time decreases with increasing ICRF input power (and subsequent increasing electron temperature) and increases with plasma current. Nearly identical impurity confinement characteristics are observed in I-mode plasmas. In enhanced D[subscript α] H-mode discharges the core impurity confinement times are much longer. There is a strong connection between core impurity confinement time and the edge density gradient across all confinement regimes studied here. Deduced central impurity density profiles in stationary plasmas are generally flat, in spite of large amplitude sawtooth oscillations, and there is little evidence of impurity convection inside of r/a = 0.3 when averaged over sawteeth.United States. Department of Energy (Contract DE-FC02-99ER54512)United States. Dept. of Energy. Fusion Energy Postdoctoral Research Program (Oak Ridge Institute for Science and Education

Tungsten impurity transport experiments in Alcator C-Mod to address high priority research and development for ITER

Experiments in Alcator C-Mod tokamak plasmas in the Enhanced D-alpha H-mode regime with ITER-like mid-radius plasma density peaking and Ion Cyclotron Resonant heating, in which tungsten is introduced by the laser blow-off technique, have demonstrated that accumulation of tungsten in the central region of the plasma does not take place in these conditions. The measurements obtained are consistent with anomalous transport dominating tungsten transport except in the central region of the plasma where tungsten transport is neoclassical, as previously observed in other devices with dominant neutral beam injection heating, such as JET and ASDEX Upgrade. In contrast to such results, however, the measured scale lengths for plasma temperature and density in the central region of these Alcator C-Mod plasmas, with density profiles relatively flat in the core region due to the lack of core fuelling, are favourable to prevent inter and intra sawtooth tungsten accumulation in this region under dominance of neoclassical transport. Simulations of ITER H-mode plasmas, including both anomalous (modelled by the Gyro-Landau-Fluid code GLF23) and neoclassical transport for main ions and tungsten and with density profiles of similar peaking to those obtained in Alcator C-Mod show that accumulation of tungsten in the central plasma region is also unlikely to occur in stationary ITER H-mode plasmas due to the low fuelling source by the neutral beam injection (injection energy ∼ 1 MeV), which is in good agreement with findings in the Alcator C-Mod experiments.United States. Department of Energy (DE-FC02-99ER54512