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Scaling of the power exhaust channel in Alcator C-Moda)
a)Paper JI2 4, Bull. Am. Phys. Soc. 55, 149 (2010).
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Image of FIG. 1.
FIG. 1.

(Color online) In order to facilitate measurements of divertor heat flux “footprints” in Alcator C-Mod, a set of “ramped tiles” was installed in one of the outer divertor cassettes and instrumented with an extensive array of embedded thermal sensors and Langmuir probes (hardware from 2010 installation is shown). An IR camera system was assembled to view the ramped-tile surfaces from above at oblique angles (Refs. 16 and 19).

Image of FIG. 2.
FIG. 2.

(Color online) Heat flux profiles during a plasma discharge (top panels) are deduced from surface temperatures using a thermal analysis code, QFLUX_2D. Surface thermocouple data yield valuable cross-checks on IR measurements. At long times after a discharge (bottom panels), calorimeter and tile temperatures are used to calibrate the IR system and to check the overall consistency of the thermal model.

Image of FIG. 3.
FIG. 3.

(Color online) Representative time traces (top panels) and a corresponding divertor heat flux footprint from a steady EDA H-mode discharge. Heat flux profiles from IR camera (red online color, bottom panel) and Langmuir probe array (blue online color) are shown, mapped to the outer midplane. Parallel heat flux profile widths are characterized by the three different measures shown. (Note: Langmuir probe measurements near the strike-point may be partially shadowed by divertor misalignments in this discharge.)

Image of FIG. 4.
FIG. 4.

(Color online) H-mode discharge exhibiting two different time-evolving EDA phases. Peak parallel heat fluxes vary significantly during the first EDA phase (EDA 1), yet by all measures the width of the footprint remains unchanged. In contrast, a step change in the footprint width is seen in the transition from EDA 1 to EDA 2. Pedestal and SOL electron pressure profiles (averaged over the times indicated by red and blue bars in online color version) are correspondingly different (bottom panel), with the “reduced pedestal height” of the EDA 2 phase displaying a flatter pressure profile in the SOL.

Image of FIG. 5.
FIG. 5.

(Color online) Divertor parallel heat flux profiles at multiple time points from the discharge shown in Fig. 4. Despite the variation in peak parallel heat flux, normalized heat flux profiles during the first EDA phase are identical. Profiles from the EDA 2 phase are also invariant in time, but are distinctly broadened relative to those from EDA 1.

Image of FIG. 6.
FIG. 6.

(Color online) A typical parallel heat flux profile in the divertor is compared with two different estimates of that quantity based on “midplane” temperature and density profiles. Data from C-Mod’s edge Thomson scattering diagnostic are used for this purpose (top panel). The overall width and magnitude of the heat flux footprint is best described by a model that simply maps the midplane pressure profile to the divertor plate and accounts for the parallel heat flux through the sheath using values measured at the divertor to evaluate the local sound speed (). The “two-point model” estimate of the parallel heat flux profile (), i.e., Spitzer–Harm electron parallel conduction (without corrections associated with kinetic effects, cross-field heat spreading or volumetric losses), clearly does not apply—it incorrectly estimates both the peak heat flux and the decay length that is observed. Electron temperature profiles at the “midplane” and divertor locations are shown in the bottom panel.

Image of FIG. 7.
FIG. 7.

(Color online) A separatrix-finding algorithm is employed, which assumes that the divertor heat flux profile matches the shape of the upstream electron pressure profile. As a consistency check, the electron pressures at the last-closed flux surface, along with their corresponding pressure-mapped sheath heat fluxes, are compared to peak parallel heat fluxes arriving at the divertor plate (bottom panel). An approximately linear relationship is found, accommodating discharges with significant variation in heat flux widths, such as those seen in the EDA 1 and EDA 2 time slices of Fig. 4. Plasma thermal energy is also correlated with peak divertor heat flux (top panel), consistent with plasma pressure at the boundary being the common element.

Image of FIG. 8.
FIG. 8.

(Color online) Heat flux footprint widths in EDA H-modes (as defined in Fig. 3) generally decrease with increasing plasma thermal energy, WTH . The smallest widths therefore tend to occur at the highest currents (top panels). In discharges with the highest stored energy per unit current (colored symbols), the e-folding decay of the narrow heat-flux channel near the strike-point exhibits an approximately 1/Ip scaling, with no dependence on toroidal field (bottom panel). Symbols labeled EDA 1 and EDA 2 correspond to data from the two separate time intervals shown in Fig. 4.

Image of FIG. 9.
FIG. 9.

(Color online) A sweep in magnetic topology from lower single-null (LSN) to double-null (DN) is performed in a 1.1 MA ohmic L-mode plasma (left panel). The time history of the x-point balance is shown in the lower left panel, which records the distance between the primary and secondary x-points mapped to the outboard midplane. Snapshots of outer divertor heat flux profiles over the time span of 1.07–1.25 s (indicated as dashed lines) are shown in the right panels. Despite the factor of 2 reduction in magnetic field line length to the divertor surfaces, the heat flux profiles are found to be remarkably resilient, exhibiting little or no change in cross-field decay length, even while the peak heat flux values decrease. For comparison, a typical profile is highlighted (black) and artificially narrowed by factors of 0.707 and 0.5 (red and blue lines overlayed in online color version).

Image of FIG. 10.
FIG. 10.

(Color online) Divertor plasma profiles recorded by embedded Langmuir probes during ohmic L-mode, strike-point sweep experiments. To align the profiles, the separatrix location is taken to be the point where the parallel current density to the divertor surface crosses zero (bottom panel). The parallel heat flux density to the surface is estimated from standard sheath theory, with a heat transmission factor of 7. Despite the factor of two change in toroidal field at fixed current, the electron pressure and parallel heat flux profiles are virtually identical, both in magnitude and in decay length across the scrape-off layer.

Image of FIG. 11.
FIG. 11.

(Color online) Divertor plasma profiles from ohmic L-mode discharges with fixed toroidal field and different plasma currents (data processing identical to that of Fig. 10). Peak plasma pressures and parallel heat fluxes rise with current, as expected for ne /nG  ∼ constant in ohmic plasmas. More significantly, cross-field decay lengths are found to decrease with increasing plasma current over the region of 2–5 mm from the separatrix. (Note: the “shoulder” in the pressure and heat flux profiles for the 1.1 MA that extends beyond 7 mm is caused by plasma conditions changing during the final portion of the strike-point sweep.)

Image of FIG. 12.
FIG. 12.

(Color online) Parallel heat flux and pressure decay lengths at the divertor target plate for a series of ohmic L-mode plasmas in which the strike-point was swept across embedded Langmuir probes. The e-folding lengths are evaluated at the location of 4 mm into the SOL, mapped to the outer midplane (see coordinate axis in Fig. 10). The e-folding lengths are found to scale approximately as 1/Ip for this range of normalized central plasma densities (0.1<< 0.25).

Image of FIG. 13.
FIG. 13.

(Color online) Information on midplane electron pressure profiles obtained from multiple plunges of a scanning Langmuir probe. Discharge conditions correspond to those presented in Figs. 10–12. Approximately five probe scans are performed for each condition; average profiles with corresponding 1-sigma statistical error bars shown. The behavior of the SOL pressure profiles is consistent in detail with the response seen at the divertor plate: a factor of 2 increase in toroidal field at fixed current produces no change, while pressure profiles (top panel) and pressure gradients (middle panel) increase with plasma current. Also pressure gradient scale lengths tend to decrease with increasing current (top panel). As noted in previous studies (Refs. 9 and 10), there is an overall tendency for pressure gradients near the last-closed flux surface to be “clamped” at a fixed value of the MHD ballooning parameter, regardless of engineering parameters (bottom panel). Conditions at the 2 mm location (gray band) are explored in Fig. 14 over a wider range in .

Image of FIG. 14.
FIG. 14.

(Color online) Upstream electron pressure decay lengths (top panel) and MHD ballooning parameter (bottom panel) at a location 2 mm outside the last-closed flux surface, tracked as a function of normalized discharge density, . The approximate value of miplane parallel collisionality, v * || , evaluated at the 2 mm location, is also shown. The corresponding divertor state is noted. The data points represent average values from a number of probe scans; error bars indicate typical ±1 standard deviation in the data sample. Smooth curves shown in the top panel are spline fits to the full set of data points. The strong ∼1/Ip dependence of pressure decay length at low collisionality is found to diminish as the collisionality is raised. Nevertheless, normalized pressure gradients () tend to cluster around a value of this quantity, , which appears to be predominantly a function of parallel collisionality and is statistically independent of plasma current and toroidal field.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Scaling of the power exhaust channel in Alcator C-Moda)