Particle transport constraints via Bayesian spectral fitting of multiple atomic lines.

Optimized operation of fusion devices demands detailed understanding of plasma transport, a problem that must be addressed with advances in both measurement and data analysis techniques. In this work, we adopt Bayesian inference methods to determine experimental particle transport, leveraging opportunities from high-resolution He-like ion spectra in a tokamak plasma. The Bayesian spectral fitting code is used to analyze resonance (w), forbidden (z), intercombination (x, y), and satellite (k, j) lines of He-like Ca following laser blow-off injections on Alcator C-Mod. This offers powerful transport constraints since these lines depend differently on electron temperature and density, but also differ in their relation to Li-like, He-like, and H-like ion densities, often the dominant Ca charge states over most of the C-Mod plasma radius. Using synthetic diagnostics based on the AURORA package, we demonstrate improved effectiveness of impurity transport inferences when spectroscopic data from a progressively larger number of lines are included.

Explaining Cold-Pulse Dynamics in Tokamak Plasmas Using Local Turbulent Transport Models.

A long-standing enigma in plasma transport has been resolved by modeling of cold-pulse experiments conducted on the Alcator C-Mod tokamak. Controlled edge cooling of fusion plasmas triggers core electron heating on time scales faster than an energy confinement time, which has long been interpreted as strong evidence of nonlocal transport. This Letter shows that the steady-state profiles, the cold-pulse rise time, and disappearance at higher density as measured in these experiments are successfully captured by a recent local quasilinear turbulent transport model, demonstrating that the existence of nonlocal transport phenomena is not necessary for explaining the behavior and time scales of cold-pulse experiments in tokamak plasmas.

Efficient design and verification of diagnostics for impurity transport experiments.

Recent attempts to measure impurity transport in Alcator C-Mod using an x-ray imaging crystal spectrometer and laser blow-off impurity injector have failed to yield unique reconstructions of the transport coefficient profiles. This paper presents a fast, linearized model which was constructed to estimate diagnostic requirements for impurity transport experiments. The analysis shows that the spectroscopic diagnostics on Alcator C-Mod should be capable of inferring simple profiles of impurity diffusion DZ and convection VZ accurate to better than ±10% uncertainty, suggesting that the failure to infer unique DZ and VZ from experimental data is attributable to an inadequate analysis procedure rather than the result of insufficient diagnostics. Furthermore, the analysis reveals that even a modest spatial resolution can overcome a low time resolution. This approach can be adapted to design and verify diagnostics for transport experiments on any magnetic confinement device.

Multi-energy SXR cameras for magnetically confined fusion plasmas (invited).

A compact multi-energy soft x-ray camera has been developed for time, energy and space-resolved measurements of the soft-x-ray emissivity in magnetically confined fusion plasmas. Multi-energy soft x-ray imaging provides a unique opportunity for measuring, simultaneously, a variety of important plasma properties (Te, nZ, ΔZeff, and ne,fast). The electron temperature can be obtained by modeling the slope of the continuum radiation from ratios of the available brightness and inverted radial emissivity profiles over multiple energy ranges. Impurity density measurements are also possible using the line-emission from medium- to high-Z impurities to separate the background as well as transient levels of metal contributions. This technique should be explored also as a burning plasma diagnostic in-view of its simplicity and robustness.

Temperature gradient scale length measurement: A high accuracy application of electron cyclotron emission without calibration.

Calibration is a crucial procedure in electron temperature (Te) inference from a typical electron cyclotron emission (ECE) diagnostic on tokamaks. Although the calibration provides an important multiplying factor for an individual ECE channel, the parameter ΔTe/Te is independent of any calibration. Since an ECE channel measures the cyclotron emission for a particular flux surface, a non-perturbing change in toroidal magnetic field changes the view of that channel. Hence the calibration-free parameter is a measure of Te gradient. BT-jog technique is presented here which employs the parameter and the raw ECE signals for direct measurement of electron temperature gradient scale length.

Effects of magnetic shear on toroidal rotation in tokamak plasmas with lower hybrid current drive.

Application of lower hybrid (LH) current drive in tokamak plasmas can induce both co- and countercurrent directed changes in toroidal rotation, depending on the core q profile. For discharges with q(0) <1, rotation increments in the countercurrent direction are observed. If the LH-driven current is sufficient to suppress sawteeth and increase q(0) above unity, the core toroidal rotation change is in the cocurrent direction. This change in sign of the rotation increment is consistent with a change in sign of the residual stress (the divergence of which constitutes an intrinsic torque that drives the flow) through its dependence on magnetic shear.

Formation and stability of impurity "snakes" in tokamak plasmas.

New observations of the formation and dynamics of long-lived impurity-induced helical "snake" modes in tokamak plasmas have recently been carried out on Alcator C-Mod. The snakes form as an asymmetry in the impurity ion density that undergoes a seamless transition from a small helically displaced density to a large crescent-shaped helical structure inside q<1, with a regularly sawtoothing core. The observations show that the conditions for the formation and persistence of a snake cannot be explained by plasma pressure alone. Instead, many features arise naturally from nonlinear interactions in a 3D MHD model that separately evolves the plasma density and temperature.

X-ray imaging crystal spectroscopy for use in plasma transport research.

This research describes advancements in the spectral analysis and error propagation techniques associated with x-ray imaging crystal spectroscopy (XICS) that have enabled this diagnostic to be used to accurately constrain particle, momentum, and heat transport studies in a tokamak for the first time. Doppler tomography techniques have been extended to include propagation of statistical uncertainty due to photon noise, the effect of non-uniform instrumental broadening as well as flux surface variations in impurity density. These methods have been deployed as a suite of modeling and analysis tools, written in interactive data language (IDL) and designed for general use on tokamaks. Its application to the Alcator C-Mod XICS is discussed, along with novel spectral and spatial calibration techniques. Example ion temperature and radial electric field profiles from recent I-mode plasmas are shown, and the impact of poloidally asymmetric impurity density and natural line broadening is discussed in the context of the planned ITER x-ray crystal spectrometer.

Layout and results from the initial operation of the high-resolution x-ray imaging crystal spectrometer on the Large Helical Device.

First results of ion and electron temperature profile measurements from the x-ray imaging crystal spectrometer (XICS) diagnostic on the Large Helical Device (LHD) are presented. This diagnostic system has been operational since the beginning of the 2011 LHD experimental campaign and is the first application of the XICS diagnostic technique to helical plasma geometry. The XICS diagnostic provides measurements of ion and electron temperature profiles in LHD with a spatial resolution of 2 cm and a maximum time resolution of 5 ms (typically 20 ms). Ion temperature profiles from the XICS diagnostic are possible under conditions where charge exchange recombination spectroscopy (CXRS) is not possible (high density) or is perturbative to the plasma (low density or radio frequency heated plasmas). Measurements are made by using a spherically bent crystal to provide a spectrally resolved 1D image of the plasma from line integrated emission of helium-like Ar(16 +). The final hardware design and configuration are detailed along with the calibration procedures. Line-integrated ion and electron temperature measurements are presented, and the measurement accuracy is discussed. Finally central temperature measurements from the XICS system are compared to measurements from the Thomson scattering and CXRS systems, showing excellent agreement.

Edge temperature gradient as intrinsic rotation drive in Alcator C-Mod tokamak plasmas.

Intrinsic rotation has been observed in I-mode plasmas from the C-Mod tokamak, and is found to be similar to that in H mode, both in its edge origin and in the scaling with global pressure. Since both plasmas have similar edge ∇T, but completely different edge ∇n, it may be concluded that the drive of the intrinsic rotation is the edge ∇T rather than ∇P. Evidence suggests that the connection between gradients and rotation is the residual stress, and a scaling for the rotation from conversion of free energy to macroscopic flow is calculated.

Characterization of impurity confinement on Alcator C-Mod using a multi-pulse laser blow-off system.

A new laser blow-off system for use in impurity transport studies on Alcator C-Mod was developed and installed for the 2009 run campaign. Its design included capabilities for multiple impurity injections during a single plasma pulse and remote manipulation of the ablated spot size. The system uses a 0.68 J, Nd:YAG laser operating at up to 10 Hz coupled with the fast beam steering via a 2D piezoelectric mirror mount able to move spot locations in the 100 ms between laser pulses and a remote controllable optical train that allow ablated spot sizes to vary from ∼0.5 to 7 mm. The ability to ablate a wide range in target Z along with Alcator C-Mod's extensive diagnostic capabilities (soft x-ray, vacuum ultraviolet (VUV), charge exchange spectroscopy, etc.) allows for detailed studies of the impurity transport dependencies and mechanisms. This system has demonstrated the achievement of all its design goals including the ability for non-perturbative operation allowing for insight into underlying impurity transport processes. A detailed overview of the laser blow-off system and initial results of operation are presented. This includes an investigation into the characterization of impurity confinement in the I-mode confinement regime recently investigated on C-Mod.

Rotation reversal bifurcation and energy confinement saturation in tokamak Ohmic L-mode plasmas.

Direction reversals of intrinsic toroidal rotation have been observed in diverted Alcator C-Mod Ohmic L-mode plasmas following electron density ramps. For low density discharges, the core rotation is directed cocurrent, and reverses to countercurrent following an increase in the density above a certain threshold. Such reversals occur together with a decrease in density fluctuations with 2 cm(-1)≤k(θ)≤11 cm(-1) and frequencies above 70 kHz. There is a strong correlation between the reversal density and the density at which the Ohmic L-mode energy confinement changes from the linear to the saturated regime.

Vacuum ultraviolet impurity spectroscopy on the Alcator C-Mod tokamak.

Vacuum ultraviolet spectroscopy is used on the Alcator C-Mod tokamak to study the physics of impurity transport and provide feedback on impurity levels to assist experimental operations. Sputtering from C-Mod's all metal (Mo+W) plasma facing components and ion cyclotron range of frequency antenna and vessel structures (sources for Ti, Fe, Cu, and Ni), the use of boronization for plasma surface conditioning and Ar, Ne, or N(2) gas seeding combine to provide a wealth of spectroscopic data from low-Z to high-Z. Recently, a laser blow-off impurity injector has been added, employing CaF(2) to study core and edge impurity transport. One of the primary tools used to monitor the impurities is a 2.2 m Rowland circle spectrometer utilizing a Reticon array fiber coupled to a microchannel plate. With a 600 lines/mm grating the 80<λ<1050 Å range can be scanned, although only 40-100 Å can be observed for a single discharge. Recently, a flat-field grating spectrometer was installed which utilizes a varied line spacing grating to image the spectrum to a soft x-ray sensitive Princeton Instruments charge-coupled device camera. Using a 2400 lines/mm grating, the 10<λ<70 Å range can be scanned with 5-6 nm observed for a single discharge. A variety of results from recent experiments are shown that highlight the capability to track a wide range of impurities.

Development of a spatially resolving x-ray crystal spectrometer for measurement of ion-temperature (T(i)) and rotation-velocity (v) profiles in ITER.

Imaging x-ray crystal spectrometer (XCS) arrays are being developed as a US-ITER activity for Doppler measurement of T(i) and v profiles of impurities (W, Kr, and Fe) with ∼7 cm (a/30) and 10-100 ms resolution in ITER. The imaging XCS, modeled after a prototype instrument on Alcator C-Mod, uses a spherically bent crystal and 2D x-ray detectors to achieve high spectral resolving power (E/dE>6000) horizontally and spatial imaging vertically. Two arrays will measure T(i) and both poloidal and toroidal rotation velocity profiles. The measurement of many spatial chords permits tomographic inversion for the inference of local parameters. The instrument design, predictions of performance, and results from C-Mod are presented.

Objectives and layout of a high-resolution x-ray imaging crystal spectrometer for the large helical device.

A high-resolution x-ray imaging crystal spectrometer, whose concept was tested on NSTX and Alcator C-Mod, is being designed for the large helical device (LHD). This instrument will record spatially resolved spectra of helium-like Ar(16+) and will provide ion temperature profiles with spatial and temporal resolutions of <2 cm and ≥10 ms, respectively. The spectrometer layout and instrumental features are largely determined by the magnetic field structure of LHD. The stellarator equilibrium reconstruction codes, STELLOPT and PIES, will be used for the tomographic inversion of the spectral data.

Calculation of the Johann error for spherically bent x-ray imaging crystal spectrometers.

New x-ray imaging crystal spectrometers, currently operating on Alcator C-Mod, NSTX, EAST, and KSTAR, record spectral lines of highly charged ions, such as Ar(16+), from multiple sightlines to obtain profiles of ion temperature and of toroidal plasma rotation velocity from Doppler measurements. In the present work, we describe a new data analysis routine, which accounts for the specific geometry of the sightlines of a curved-crystal spectrometer and includes corrections for the Johann error to facilitate the tomographic inversion. Such corrections are important to distinguish velocity induced Doppler shifts from instrumental line shifts caused by the Johann error. The importance of this correction is demonstrated using data from Alcator C-Mod.

Observation of self-generated flows in tokamak plasmas with lower-hybrid-driven current.

In Alcator C-Mod discharges lower hybrid waves have been shown to induce a countercurrent change in toroidal rotation of up to 60 km/s in the central region of the plasma (r/a approximately <0.4). This modification of the toroidal rotation profile develops on a time scale comparable to the current redistribution time (approximately 100 ms) but longer than the energy and momentum confinement times (approximately 20 ms). A comparison of the co- and countercurrent injected waves indicates that current drive (as opposed to heating) is responsible for the rotation profile modifications. Furthermore, the changes in central rotation velocity induced by lower hybrid current drive (LHCD) are well correlated with changes in normalized internal inductance. The application of LHCD has been shown to generate sheared rotation profiles and a negative increment in the radial electric field profile consistent with a fast electron pinch.

Spatially resolved high resolution x-ray spectroscopy for magnetically confined fusion plasmas (invited).

The use of high resolution x-ray crystal spectrometers to diagnose fusion plasmas has been limited by the poor spatial localization associated with chord integrated measurements. Taking advantage of a new x-ray imaging spectrometer concept [M. Bitter et al., Rev. Sci. Instrum. 75, 3660 (2004)], and improvements in x-ray detector technology [Ch. Broennimann et al., J. Synchrotron Radiat. 13, 120 (2006)], a spatially resolving high resolution x-ray spectrometer has been built and installed on the Alcator C-Mod tokamak. This instrument utilizes a spherically bent quartz crystal and a set of two dimensional x-ray detectors arranged in the Johann configuration [H. H. Johann, Z. Phys. 69, 185 (1931)] to image the entire plasma cross section with a spatial resolution of about 1 cm. The spectrometer was designed to measure line emission from H-like and He-like argon in the wavelength range 3.7 and 4.0 A with a resolving power of approximately 10,000 at frame rates up to 200 Hz. Using spectral tomographic techniques [I. Condrea, Phys. Plasmas 11, 2427 (2004)] the line integrated spectra can be inverted to infer profiles of impurity emissivity, velocity, and temperature. From these quantities it is then possible to calculate impurity density and electron temperature profiles. An overview of the instrument, analysis techniques, and example profiles are presented.

A spatially resolving x-ray crystal spectrometer for measurement of ion-temperature and rotation-velocity profiles on the Alcator C-Mod tokamak.

A new spatially resolving x-ray crystal spectrometer capable of measuring continuous spatial profiles of high resolution spectra (lambda/d lambda>6000) of He-like and H-like Ar K alpha lines with good spatial (approximately 1 cm) and temporal (approximately 10 ms) resolutions has been installed on the Alcator C-Mod tokamak. Two spherically bent crystals image the spectra onto four two-dimensional Pilatus II pixel detectors. Tomographic inversion enables inference of local line emissivity, ion temperature (T(i)), and toroidal plasma rotation velocity (upsilon(phi)) from the line Doppler widths and shifts. The data analysis techniques, T(i) and upsilon(phi) profiles, analysis of fusion-neutron background, and predictions of performance on other tokamaks, including ITER, will be presented.

Wide-angle point-to-point x-ray imaging with almost arbitrarily large angles of incidence.

The paper describes a new scheme for wide-angle point-to-point x-ray imaging with almost arbitrarily large angles of incidence by a matched pair of spherically bent crystals to eliminate the astigmatism, which is a well-known imaging error of spherical mirrors. In addition to x rays, the scheme should be applicable to a very broad spectrum of the electromagnetic radiation, including microwaves, infrared and visible light, as well as UV and extreme UV radiation, if the crystals are replaced with appropriate spherical reflectors. The scheme may also be applicable to the imaging with ultrasound.