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An economically viable magnetic-confinement fusion reactor will require steady-state operation and high areal power density for sufficient energy output, and elevated wall/blanket temperatures for efficient energy conversion. These three requirements frame, and couple to, the challenge of plasma–material interaction (PMI) for fusion energy sciences. Present and planned tokamaks are not designed to simultaneously meet these criteria. A new and expanded set of dimensionless figures of merit for PMI have been developed. The key feature of the scaling is that the power flux across the last closed flux surface P / S ≃ 1 MW m −2 is to be held constant, while scaling the core volume-averaged density weakly with major radius, n ∼ R −2/7 . While complete similarity is not possible, this new “ P / S ” or “PMI” scaling provides similarity for the most critical reactor PMI issues, compatible with sufficient current drive efficiency for non-inductive steady-state core scenarios. A conceptual design is developed for Vulcan, a compact steady-state deuterium main-ion tokamak which implements the P / S scaling rules. A zero-dimensional core analysis is used to determine R = 1.2 m, with a conventional reactor aspect ratio R / a = 4.0, as the minimum feasible size for Vulcan. Scoping studies of innovative fusion technologies to support the Vulcan PMI mission were carried out for three critical areas: a high-temperature, helium-cooled vacuum vessel and divertor design; a demountable superconducting toroidal field magnet system; and a steady-state lower hybrid current drive system utilizing a high-field-side launch position.

The steady-state current drive system for the Vulcan tokamak concept has been designed, taking into account requirements of high field, small size, and high operational wall temperature (B0 = 7 T, R0 = 1.2 m, Twall > 800 K). This lower hybrid current drive system allows steady-state operation by utilizing high field side launch, high RF source frequency (8 GHz), and dedicated current drive ports. An iterative MHD and current drive solver is used to determine the ideal launching spectra and location to assure strong single pass absorption. It is found that with nominal Vulcan operational parameters (ne ≈ 4 × 1020 m−3, Te ≈ 2.8 keV, Ip = 1.7 MA, PLHCD = 19.8 MW) bootstrap currents of ∼70% and lower hybrid current drive efficiencies of 1.16 × 1019 A W m−2 could be achieved. The optimized solution yielded advanced tokamak profiles with q values on-axis above 2. A conceptual design of the system is presented, which takes into account space, power, cooling, and launched spectrum requirements. The system is found to be compatible with the vacuum vessel design and requires cooling power of

Dimensionless parameter scaling techniques are a powerful tool in the study of complex physical systems, especially in tokamak fusion experiments where the cost of full-size devices is high. It is proposed that dimensionless similarity be used to study in a small-scale device the coupled issues of the scrape-off layer (SOL) plasma, plasma–material interactions (PMI), and the plasma-facing material (PFM) response expected in a tokamak fusion reactor. Complete similarity is not possible in a reduced-size device. In addition, “hard” technological limits on the achievable magnetic field and peak heat flux, as well as the necessity to produce non-inductive scenarios, must be taken into account. A practical approach is advocated, in which the most important dimensionless parameters are matched to a reactor in the reduced-size device, while relaxing those parameters which are far from a threshold in behavior. “Hard” technological limits are avoided, so that the reduced-size device is technologically feasible. A criticism on these grounds is offered of the “P/R” model, in which the ratio of power crossing the last closed flux surface (LCFS), P, to the device major radius, R, is held constant. A new set of scaling rules, referred to as the “P/S” scaling (where S is the LCFS area) or the “PMI” scaling, is proposed: (i) non-inductive, steady-state operation; (ii) P is scaled with R2 so that LCFS areal power flux P/S is constant; (iii) magnetic field B constant; (iv) geometry (elongation, safety factor q*, etc.) constant; (v) volume-averaged core density scaled as n ≈ n ¯ e ∼ R − 2 / 7 ; and (vi) ambient wall material temperature TW, 0 constant. It is shown that these scaling rules provide fidelity to reactor conditions in the divertor of the reduced-size device, allowing for reliable extrapolation of the behavior of the coupled SOL/PMI/PFM system from the reduced-size device to a reactor. The P/S scaling is used as the basis for the Vulcan tokamak conceptual design.

The utilization of tungsten spectroscopy for diagnostics of magnetically confined fusion plasmas requires the radiative properties of tungsten ions to be accurately known. At the Lawrence Livermore National Laboratory, a program to gather spectroscopic data on tungsten ions has been initiated with the purpose to study spectral signatures and identify candidate fusion plasma diagnostics. In this paper, an overview of recent results from the Livermore WOLFRAM spectroscopy project is presented, which includes experimental investigations at the EBIT-I and SuperEBIT electron beam ion traps. In particular, the spectra of highly charged M- and L-shell tungsten ions have been studied. These investigations cover energy measurements of n = 2 to n = 2, 3 transitions in Ne-like W64+ through Li-like W71+ ions and soft X-ray measurements of n = 3 to n = 3, 4 transitions in M-shell ions with emphasis on the Ni-like W46+ and Si-like W60+ through Na-like W63+ ions. The measurements are complemented by atomic-structure calculations and spectral modeling using the Flexible Atomic Code (FAC).

A flat-field grazing-incidence grating spectrometer has been installed on the MIT Alcator C-MOD tokamak, following the installation of such a spectrometer on the Livermore electron beam ion trap facility and on the National Spherical Torus Experiment at Princeton. The spectrometer employs a variable space grating with an average spacing of 2400 lines/mm and covers the 10–70 Å wavelength band. It is being used to monitor the presence of impurity ions such as boron, oxygen, fluorine, argon, calcium, iron, molybdenum, and tungsten, and to calibrate spectral diagnostics of astrophysical plasmas. The Alcator instrument provides spectral emission data in a density regime that is one to three orders of magnitude higher than that covered by the other two instruments and thus produces complementary data.

Application of lower hybrid range of frequencies (LHRF) waves can induce both co- and counter-current directed changes in toroidal rotation in Alcator C-Mod plasmas, depending on the target plasma current, electron density, confinement regime and magnetic shear. For ohmic L-mode discharges with good core LH wave absorption, and significant current drive at a fixed LH power near 0.8 MW, the interior (r/a q95/11.5, and in the co-current direction if ne(1020 m−3) 1, indicating a good correlation with driven current fraction, unifying the results observed on various tokamaks. For high density (ne ≥ 1.2 × 1020 m−3) L-mode target discharges, where core LH wave absorption is low, the rotation change is in the co-current direction, but evolves on a shorter momentum transport time scale, and is seen across the entire spatial profile. For H-mode target plasmas, both co- and counter-current direction increments have been observed with LHRF. The H-mode co-rotation is correlated with the pedestal temperature gradient, which itself is enhanced by the LH waves absorbed in the plasma periphery. The H-mode counter-rotation increment, a flattening of the peaked velocity profile in the core, is consistent with a reduction in the momentum pinch correlated with a steepening of the core density profile. Most of these rotation changes must be due to indirect transport effects of LH waves on various parameters, which modify the momentum flux.

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

In the Alcator C-Mod tokamak, strong, steady-state variations of molybdenum density within a flux surface are routinely observed in plasmas using hydrogen minority ion cyclotron resonant heating. In/out asymmetries, up to a factor of 2, occur with either inboard or outboard accumulation depending on the major radius of the minority resonance layer. These poloidal variations can be attributed to the impurity's high charge and large mass in the neoclassical parallel force balance. The large mass enhances the centrifugal force, causing outboard accumulation while the high charge enhances ion-impurity friction and makes impurities sensitive to small poloidal variations in the plasma potential. Quantitative comparisons between existing parallel high-Z impurity transport theories and experimental results for r/a < 0.7 show good agreement when the resonance layer is on the high-field side of the tokamak but disagree substantially for low-field side heating. Ion-impurity friction is insufficient to explain the experimental results, and the accumulation of impurity density on the inboard side of flux surface is shown to be driven by a poloidal potential variation due to magnetic trapping of non-thermal, cyclotron heated minority ions. Parallel impurity transport theory is extended to account for cyclotron effects and shown to agree with experimentally measured impurity density asymmetries., United States. Dept. of Energy (Agreement DE-FC02-99ER54512), United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program)

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.

Lower hybrid waves launched uni‐directionally into tokamak plasmas impart momentum to the electrons. This momentum can be transferred to the ions, leading to substantial counter current rotation. Observations of LH‐induced counter rotation have been previously reported [1], and the initial rate of increase has been found to be consistent with the calculated rate of wave momentum injection [2]. However, in recent experiments in Alcator C‐Mod it has been found that application of LH waves to relatively low current (Ip∼0.4–0.6 MA) plasmas can result in a co‐current change of rotation, which implies a different mechanism than that described above. This appears to be linked to the so‐called intrinsic rotation commonly observed in Alcator C‐Mod and other tokamaks [3]. In addition to the change in direction at low current, some dependence on the magnetic configuration (USL vs. LSN) has been observed.

International audience; 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.

Imaging x-ray crystal spectrometer #2;XCS#3; arrays are being developed as a US-ITER activity for Doppler measurement of Ti and v profiles of impurities #2;(W, Kr, and Fe)#3; with ~#4;7 cm (a/30)#3; 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 >#2;6000)#3; horizontally and spatial imaging vertically. Two arrays will measure Ti 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.

Summary form only given. The core ion temperature and bulk ion velocity of ITER plasmas will likely be derived from the thermal Doppler broadening and Doppler shift of X-ray lines emitted by highly charged trace elements and recorded by an array of high-resolution spectrometers. Although several elements could be used to seed the plasma for this purpose, we show that the emission of neonlike tungsten provides important advantages. Tungsten is already a plasma constituent due to its use in the divertor region. Moreover, the relevant tungsten lines have wavelengths that are readily analyzed by X-ray crystals and fall into a region where existing detectors have high quantum efficiency, and the abundance of neonlike W64+ is thought to peak for the expected core electron temperatures. Experimental studies of the relevant X-ray emission of tungsten ions confined and excited in an electron beam ion trap confirm these predictions. We have made a conceptual design of an imaging spectrometer, which covers the ITER plasma using six viewing angles to produce a time-dependent radial profile of the ion temperature. Our design is based on a recent development of a core imaging X-ray crystal spectrometer implemented on the Alcator tokamak. Each viewing angle will pick up differing amounts of toroidal and poloidal rotation components in order to allow a determination of the radial profile of bulk ion motion. We will present the design and performance characteristics of the imaging crystal spectrometer. In addition, we will discuss the possibility of utilizing a microcalorimeter for measuring the impurity emission over the entire X-ray band with a resolution sufficient to infer the ion temperature from each line.

Most tokamak-based reactor concepts require the use of noble gases to form either a radiative mantle or divertor to reduce conductive heat exhaust to tolerable levels for plasma facing components. Predicting the power loss necessary from impurity radiation is done using electron temperature-dependent 'cooling-curves' derived from ab initio atomic physics models. We present here a technique to verify such modeling using highly radiative, argon infused discharges on Alcator C-Mod. A novel x-ray crystal imaging spectrometer is used to measure spatially resolved profiles of line-emissivity, constraining impurity transport simulations. Experimental data from soft x-ray diodes, bare AXUV diodes and foil bolometers are used to determine the local emissivity in three overlapping spectral bands, which are quantitatively compared to models. Comparison of broadband measurements show agreement between experiment and modeling in the core, but not over the entire profile, with the differences likely due to errors in the assumed radial impurity transport outside of the core. Comparison of Ar{sup 16+} x-ray line emission modeling to measurements suggests an additional problem with the collisional-radiative modeling of that charge state.

X-ray imaging crystal spectrometers with high spectral and spatial resolution are currently being used on magnetically confined fusion devices to infer the time history profiles of ion and electron temperatures as well as plasma flow velocities. The absolute measurement of flow velocities is important for optimizing various discharge scenarios and evaluating the radial electric field in tokamak and stellarator plasmas. Recent studies indicate that the crystal temperature must be kept constant to within a fraction of a degree to avoid changes of the interplanar 2d-spacing by thermal expansion that cause changes in the Bragg angle, which could be misinterpreted as Doppler shifts. For the instrumental parameters of the x-ray crystal spectrometer on Alcator C-Mod, where those thermal effects were investigated, a change of the crystal temperature by 1 °C causes a change of the lattice spacing of the order of Δd = 1 × 10−5 A introducing a fictitious velocity drift of the order of ~3 km s−1. This effect must be considered for x-ray imaging crystals spectrometers installed on LHD, KSTAR, EAST, J-TEXT, NSTX and, in the future, W7-X and ITER.

Transport in ohmically heated plasmas in Alcator C-Mod was studied in both the linear (LOC) and saturated (SOC) ohmic L-mode confinement regimes and the importance of turbulent transport in the region r/a = 0.5–0.8 was established. After an extensive analysis with TGLF and GYRO, it is found that using an effective impurity ion species with Z[subscript i] = 8, and moderately high Z[subscript eff] (2.0–5.6), in the LOC regime electron transport becomes dominant due to TEM turbulence. The key ingredient in the present results is the observation that dilution of the main ion species (deuterium) by impurity species of moderate charge state reduces dominant ITG turbulence, in contrast to the SOC regime with little, if any dilution. The turbulent spectrum measured with the phase contrast imaging (PCI) diagnostic is in qualitative agreement with predictions of a synthetic PCI diagnostic adopted to Global GYRO. The toroidal rotation in the low-density LOC regime is in the co-current direction but as the density is raised in the SOC regime the rotation reverses to the counter current drive direction. The impurity content of the plasma was measured recently and an effective Z[subscript i] of 9 was deduced., United States. Dept. of Energy (Grant DE-FC02-99ER54512-CMOD)

Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the exper...

Nonlinear gyrokinetic simulations of impurity transport are compared to experimental impurity transport for the first time. The GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) was used to perform global, nonlinear gyrokinetic simulations of impurity transport for a standard Alcator C-Mod, L-mode discharge. The laser blow-off technique was combined with soft x-ray measurements of a single charge state of calcium to provide time-evolving profiles of this non-intrinsic, non-recycling impurity over a radial range of 0.0 ⩽ r/a ⩽ 0.6. Experimental transport coefficient profiles and their uncertainties were extracted from the measurements using the impurity transport code STRAHL and rigorous Monte Carlo error analysis. To best assess the agreement of gyrokinetic simulations with the experimental profiles, the sensitivity of the GYRO predicted impurity transport to a wide range of turbulence-relevant plasma parameters was investigated. A direct comparison of nonlinear gyrokinetic simulation and experiment is presented with an in depth discussion of error sources and a new data analysis methodology.

A numerical modeling of current profile modification by lower hybrid current drive (LHCD) using a fullwave/Fokker-Planck simulation code is presented. A MHD stable LHCD discharge on Alcator C-Mod was analyzed, and the current profile from full wave simulations was found to show better agreement with the experiment than a ray-tracing code. Comparison of full wave and ray-tracing simulation shows that, although ray-tracing can reproduce the stochastic wave spectrum broadening, the full wave calculation predicts even wider spectrum broadening, and the wave spectrum fills all of the kinematically allowed domain. This is the first demonstration of LHCD current profile modeling using a full wave simulation code in a multi-pass absorption regime, showing the clear impact of full wave effects on the LHCD driven current profile.

High-quality spectra of hydrogen-like Ar(17+) have been obtained from Alcator C-Mod tokamak plasmas using a spatially imaging high-resolution x-ray spectrometer system in an extensive study of the ...

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/dE6000) 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.

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

This paper consists of two parts: part I describes the working principle of a recently developed x-ray imaging crystal spectrometer, where the astigmatism of spherically bent crystals is being used with advantage to record spatially resolved spectra of highly charged ions for Doppler measurements of the ion-temperature and toroidal plasma-rotation-velocity profiles in tokamak plasmas. This type of spectrometer was thoroughly tested on NSTX and Alcator C-Mod, and its concept was recently adopted for the design of the ITER crystal spectrometers. Part II describes imaging schemes, where the astigmatism has been eliminated by the use of matched pairs of spherically bent crystals or reflectors. These imaging schemes are applicable over a wide range of the electromagnetic radiation, which includes microwaves, visible light, EUV radiation and x-rays. Potential applications with EUV radiation and x-rays are the diagnosis of laser-produced plasmas, imaging of biological samples with synchrotron radiation and lithography.

Internal transport barriers (ITBs) are seen under a number of conditions in Alcator C-Mod plasmas. Most typically, radio frequency power in the ion cyclotron range of frequencies (ICRFs) is injected with the second harmonic of the resonant frequency for minority hydrogen ions positioned off-axis at r/a > 0.5 to initiate the ITBs. They can also arise spontaneously in ohmic H-mode plasmas. These ITBs typically persist tens of energy confinement times until the plasma terminates in radiative collapse or a disruption occurs. All C-Mod core barriers exhibit strongly peaked density and pressure profiles, static or peaking temperature profiles, peaking impurity density profiles and thermal transport coefficients that approach neoclassical values in the core. The strongly co-current intrinsic central plasma rotation that is observed following the H-mode transition has a profile that is peaked in the centre of the plasma and decreases towards the edge if the ICRF power deposition is in the plasma centre. When the ICRF resonance is placed off-axis, the rotation develops a well in the core region. The central rotation continues to decrease as long as the central density peaks when an ITB develops. This rotation profile is flat in the centre (0 < r/a < 0.4) but rises steeply in the region where the foot in the ITB density profile is observed (0.5 < r/a < 0.7). A correspondingly strong E × B shear is seen at the location of the ITB foot that is sufficiently large to stabilize ion temperature gradient instabilities that dominate transport in C-Mod high density plasmas.

Spontaneous toroidal rotation, self-generated in the absence of an external momentum input, exhibits a rich phenomenology. In L-mode plasmas, the rotation varies in a complicated fashion with electron density, magnetic configuration and plasma current and is predominantly in the counter-current direction. The rotation depends sensitively on the balance between the upper and lower null and plays a crucial role in the H-mode power threshold. Rotation inversion between the counter- and co-current directions has been observed following small changes in the electron density and plasma current, with very distinct thresholds. In contrast, the intrinsic rotation in H-mode plasmas has a relatively simple parameter dependence, with the rotation velocity proportional to the plasma stored energy normalized to the plasma current, and is nearly always directed co-current. In plasmas with internal transport barriers, formed either with off-axis ICRF heating or LHCD, the core rotation velocity increments in the counter-current direction as the barrier evolves.