An array of flush-mounted and toroidally elongated Langmuir probes (henceforth called rail probes) have been specifically designed for the Alcator C-Mod’s vertical target plate divertor and operated over multiple campaigns. The “flush” geometry enables the tungsten electrodes to survive high heat flux conditions in which traditional “proud” tungsten electrodes suffer damage from melting. The toroidally elongated rail-like geometry reduces the influence of sheath expansion, which is an important effect to consider in the design and interpretation of flush-mounted Langmuir probes. The new rail probes successfully operated during C-Mod’s FY2015 and FY2016 experimental campaigns with no evidence of damage, despite being regularly subjected to heat flux densities parallel to the magnetic field exceeding ∼1 GW m−2 for short periods of time. A comparison between rail and proud probe data indicates that sheath expansion effects were successfully mitigated by the rail design, extending the use of these Langmuir probes to incident magnetic field line angles as low as 0.5°.

Langmuir probes1 are one of the earliest plasma diagnostics still in use today2 and they maintain significant advantages over other diagnostic systems. They provide measurements of electron temperature (Te), ion density (ni), and surface floating potential (Vf) at well-defined positions in space, allowing for detailed studies of plasma conditions otherwise not achievable. However, with fusion research plasmas getting denser and hotter, the use of Langmuir probes is becoming restricted to peripheral regions of the plasma where heat flux to surfaces may still be acceptable, such as in the scrape-off layer and divertors. Yet, plasma conditions even at these locations are becoming intolerable. Measurements in Alcator C-Mod with surface thermocouples (SFTCs)3 have measured peak parallel heat fluxes in excess of 1 GW/m2. Parallel heat fluxes entering into the divertor of future fusion reactors are expected to be even higher. At these heat fluxes, traditional Langmuir probes that are designed to accept plasma fluxes at a large incident field line angle (≥10°) rapidly melt (Fig. 1). In this regard, an ideal divertor probe would be flush with the divertor surface, reducing the incident field line angle and potentially making the probes as robust as the divertor plates themselves. However, sheath expansion effects4–6 can confound the interpretation of flush-mounted probe current-voltage (I-V) characteristics. Attempts have been made to model these effects using particle-in-cell codes.7 In practice though, experimentalists have relied on fitting an additional free parameter to account for sheath expansion.8,9 More recently, an I-V characteristic model based on the Child-Langmuir law for the sheath thickness has been proposed and shown to fit data well, potentially eliminating the need for an additional fit parameter.10 Based on similar arguments, it has been proposed that sheath expansion may be mitigated by elongating toroidally the collection area of a flush Langmuir probe.11 This concept was further developed and applied at Alcator C-Mod in the design of a new rail probe array for the outer vertical target plate divertor, as described in this paper. The rail-like geometry is found to mitigate sheath expansion effects for incident magnetic field line angles as low as 0.5°. The relatively simple design—which makes use of wire electrical discharge machining (EDM), tungsten plate stock, flame-sprayed ceramic coatings, and stock alumina components—can be readily adapted to other applications. Section II reviews sheath expansion physics and examines how the extended probe geometry can help to mitigate its influence on probe I-V characteristics. Practical considerations for implementing the geometry in the C-Mod divertor target are discussed. Section III documents the design of the Alcator C-Mod rail probe system and how it is assembled. Section IV presents a preliminary analysis of rail probe I-V characteristics obtained in Alcator C-Mod plasmas and compares them to the I-V characteristics obtained from traditional proud probes under identical plasma conditions. Three different models are used to fit the I-V characteristics: the standard model that ignores sheath expansion and two other models that attempt to account for sheath expansion. Finally, integrated heat deposition profiles on the divertor target are compared from four separate diagnostics: surface thermocouples, calorimeters (CAL), tile thermocouples (TILE), and proud Langmuir probes and rail Langmuir probes. These data indicate that the rail Langmuir probe parameters, inferred from the standard I-V characteristic model without sheath expansion, provide consistent results.

FIG. 1.

Standard proud probe design used in Alcator C-Mod with a minimum 10° field line attack angle, ψ. These tungsten electrodes were not able to survive the divertor heat fluxes in C-Mod without melting, despite being exposed to plasma for typically less than 1 s.12 Reprinted with permission from Kuang et al., Nucl. Mater. Energy 12, 1231–1235 (2017). Copyright 2017 Elsevier.

FIG. 1.

Standard proud probe design used in Alcator C-Mod with a minimum 10° field line attack angle, ψ. These tungsten electrodes were not able to survive the divertor heat fluxes in C-Mod without melting, despite being exposed to plasma for typically less than 1 s.12 Reprinted with permission from Kuang et al., Nucl. Mater. Energy 12, 1231–1235 (2017). Copyright 2017 Elsevier.

Close modal

Langmuir probes measure the current (I) collected by an electrode exposed to plasma as the voltage bias is changed. The interpretation of this current-voltage (I-V) characteristic in the presence of a magnetic field has always been difficult.13–15 For cases in which the angle between the electrode surface and field line is large (i.e., greater than ∼5°), the I-V characteristic for a probe, that is biased at voltage V, takes the form,

IV=Apenics1expeVVfkTe,
(1)

where e and k are the electron charge and Boltzmann constant, respectively. However, at low incident field line angles, the ion current fails to saturate due to sheath expansion resulting in the probe projected area (Ap) being a function of V. If unaccounted for, this can produce inferred densities and temperatures that are higher than actually present. Sheath expansion effects arise from the sheath thickness being a function of the applied voltage bias.2 The thickness of the Debye sheath at the probe-plasma interface is expected to depend on the plasma potential (Vplasma) and V, according to the Child-Langmuir law,

xs=cλDe(VplasmaV)kTe34,
(2)

with the coefficient, c, being of order unity and λD, the Debye length. The Child-Langmuir law yields a value for c = 0.8,16 while the perimeter model proposed by Tsui uses c = 1.10 Sheath expansion effects become significant when the variation in xs results in a comparable contribution to the total projected area of the probe surface, as illustrated in Fig. 2. When the probe is negatively biased, the sheath “thickens” and the total projected area increases. In this case, the standard I-V fit model [Eq. (1)] is no longer an appropriate description.

FIG. 2.

Geometric effect of sheath expansion on a probe area projected along a magnetic field.12 Reprinted with permission from Kuang et al., Nucl. Mater. Energy 12, 1231–1235 (2017). Copyright 2017 Elsevier.

FIG. 2.

Geometric effect of sheath expansion on a probe area projected along a magnetic field.12 Reprinted with permission from Kuang et al., Nucl. Mater. Energy 12, 1231–1235 (2017). Copyright 2017 Elsevier.

Close modal

From the geometry shown in Fig. 2, the relative contribution to the projected area due to the expansion of the sheath is

δApAp=Δlprobecotψ,

where Δ is the change in sheath thickness that arises from biasing the probe negative with respect to the adjacent grounded divertor tiles. Using Eq. (2) for the sheath thickness and based on the geometry shown in Fig. 2, an equation for Δ can be formulated as

Δ=cλDekTe34VplasmaV34VplasmaVtile34.

Since the divertor tiles in which the probes are embedded are at ground potential, Vtile=0.

Rearranging

Δ=cλDeVkTe341+VplasmaV34VplasmaV34.

Since V < 0 < Vplasma for a negatively biased probe, the term in the square brackets is always less than or equal to 1. The maximum value of Δ is bounded by

Δmax=cλDeVkTe34,

yielding

δApApmax=cλDlprobeeVkTe34cotψ.
(3)

With all else held constant, Eq. (3) shows how the relative contribution to the projected area depends on the length of the probe, lprobe, and the field line incidence angle, ψ. By increasing lprobe one can reduce this relative contribution to Ap for the same incident field line angle, thus mitigating the effects of sheath expansion. If successful, this can avoid the need for including an additional fitting parameter in the I-V model function to account for the unknown constant, c.

Typically, in Alcator C-Mod, the field line incidence angle on the vertical target plate divertor ranges from 0.5° to 2.5°. In comparison, the proud probe would have an incident field line angle of 10.5°–12.5°. Based on Eq. (3), the maximum relative contribution in the projected area associated with sheath expansion for a traditional proud probe with ψ = 10.5° would be ≈3% (for typical conditions: Te = 30 eV, ne = 1 × 1020 m−3, V = −150 V, and c = 0.8). In order to have an equivalent maximum relative contribution due to sheath expansion for a probe with an incident field line angle of 0.5°, lprobe would have to be increased to 45 mm.

Edge sheath effects are due to the sheath wrapping around the edge of the electrodes as shown in Fig. 3. An assumption made in the above analysis is that the probe is large and that edge effects can be ignored. This is generally true for conventional probe design but with the elongated shape proposed to mitigate the effects of sheath expansion, the perimeter length to probe a surface area ratio has increased and edge effect corrections might then have to be implemented.17 Ignoring area correction terms of order (xs)2 compared to xs, the maximum change in the projected area due to edge effects is given by

δApApEdgeSheath=2lprobe+wcλDeVpkTe34lprobew.
(4)

Here w is the width of the electrode. Like sheath expansion, the edge sheath is approximately proportional to (−Vp)−3/4, but it is also proportional to lprobe. Therefore, edge effects would produce an unsaturated I-V response but, unlike sheath expansion, they are not mitigated by increasing lprobe. For a probe geometry with width 1.5 mm and length 45 mm and for the typical plasma and probe conditions listed above, edge effects could add an additional 1.5% contribution to the projected area. This is within acceptable limits for Langmuir probes, considering that they can typically have intrinsic systematic errors of ∼10% in projected geometric areas.2 

FIG. 3.

The contribution from the edge sheath of the probe is increased when the probe is elongated due to the increased perimeter to surface area ratio. Note that the figure is not to scale and that the sheath thickness has been exaggerated.

FIG. 3.

The contribution from the edge sheath of the probe is increased when the probe is elongated due to the increased perimeter to surface area ratio. Note that the figure is not to scale and that the sheath thickness has been exaggerated.

Close modal

Thus far the analysis has assumed the rail electrode to be perfectly field-aligned. However, if the probe is not field-aligned, the sides of the electrode sheath-expansion volume may produce a significant increase in the projected area, as seen in Fig. 4. To account for this effect, an additional exposed collection area that is a function of the field misalignment, θ, can be added to the projected area total. For the case, when the incident angle, ψ, is small,

δApApFieldMisaligned=cλDeVpkTe34sinθwsinψ.
(5)
FIG. 4.

View of the probe along field-lines at a cross-sectional view starting at the leading edge of the probe. Field misalignment can result in the side of the electrode (shown in green) becoming a current collection surface due to the extended sheath protruding above the adjacent wall surfaces. The inset shows the alignment of the probe with respect to the magnetic field and the section lines for the cross sections shown. The degree of misalignment, θ, is how much the toroidal tilt of the field line deviates from the designed tilt of the probes.

FIG. 4.

View of the probe along field-lines at a cross-sectional view starting at the leading edge of the probe. Field misalignment can result in the side of the electrode (shown in green) becoming a current collection surface due to the extended sheath protruding above the adjacent wall surfaces. The inset shows the alignment of the probe with respect to the magnetic field and the section lines for the cross sections shown. The degree of misalignment, θ, is how much the toroidal tilt of the field line deviates from the designed tilt of the probes.

Close modal

Much like the edge effect contribution, the additional projected area increases with both (−Vp)−3/4 and lprobe. For a probe geometry with width 1.5 mm and length 45 mm and for the typical plasma and probe conditions listed above. A 3° field misalignment can lead to a 4.2% increase in the probe collection area. The toroidal tilt angle of the magnetic field line is defined here as tan−1(Bs/Bφ), where Bφ is the toroidal field component and Bs is the component of the poloidal magnetic field that is tangent to the divertor surface, while the misalignment angle, θ, is the difference between the toroidal tilt angle of the magnetic field lines and the designed tilt of the probes. In Alcator C-Mod, the toroidal tilt angle typically spans the range 0.5°-6°. So if the rail probes were installed with a toroidal tilt angle of 3°, then there is potentially a misalignment between the field lines and the probe of θ ≈ ±3°, dependent on the magnetic geometry.

Since both edge sheath effects and field misalignment can contribute to non-saturation ion collection in the I-V characteristic it is important to consider these factors in optimizing the length of the probe. In practice, the length of the electrodes that can be chosen is often constrained by the geometry available and some compromise must be reached. For the Alcator C-Mod vertical target plate divertor, the toroidal length of the divertor tiles was an important consideration, as discussed in Sec. III.

The final rail probe design has electrodes 1.5 mm wide and ∼64 mm long, tilted at 2.5° for field alignment. The exact electrode length varies with the surrounding tile widths, depending on the location of the probe due to the shape of the Alcator C-Mod divertor modules. Based on Eqs. (3) and (4), the critical incident magnetic field angle at which the relative contribution associated with sheath expansion and edge effects exceed 10% is ∼0.39°. Furthermore, an additional 4.4% contribution in the projected area can result from a ±3° magnetic field-line misalignment.

The rail probes are embedded in the titanium-zirconium-molybdenum (TZM) tiles of the divertor and wire EDM to be flush to the surface. The base of the electrodes is flame sprayed with alumina (0.2 mm thick) to electrically isolate them from the tiles. The overall width of the ceramic coated portion of the electrode is held to tight tolerance by over spraying the coating and grinding to final dimensions. This ensures a high precision fit into the mating grooves on the TZM tile which are machined by wire EDM.

At the location of the rail probes, the toroidal extent of the TZM tiles is expanded to be twice the normal value to accommodating the rails. Normally, consideration of plasma disruption induced eddy currents and resulting forces restricts the allowed tile size in Alcator C-Mod. But in this case, the extensive features machined into the tile to accommodate the rails serve to interrupt the eddy current pathways.

A pin and hook along with Belleville spring washers and a jam nut holds the probes in the tiles. The pins are electrically isolated from the tile with ceramic collars. The dimensions of the ceramic collars are chosen to correspond to stock dimensions of Coors ceramic tubing. Figure 5 shows an exploded view of one probe assembly indicating the various components.

FIG. 5.

Exploded view of a rail probe assembly showing the individual components.

FIG. 5.

Exploded view of a rail probe assembly showing the individual components.

Close modal

To assemble the components, the tungsten electrode is inserted into the groove cut-out of the divertor TZM tile. The grooves have a step profile to help prevent deposited metal from shorting the electrode to the tile. The connection pin and fastening pin are carefully inserted and hooked onto the electrode such that the pin catches in a hole in the electrode. The ceramic and zirconia collars are then placed onto the pins which centers the pins into position and electrically isolates the pins from the divertor tiles. The spring washer and jam nut are then placed over and tightened to lock the entire assembly together. One pin for each probe is extended in length to provide for attachment of a custom coaxial cable connector. Figure 6 shows the rear of an assembled tile with three embedded rail probes. Figure 7 shows the CAD models used in the design process. Note how the nose tile is offset toroidally from the rest of the probes [Fig. 7(a)], this was intentional as it was the only way to get the cable plugs to fit in the rear of the divertor module [Fig. 7(b)].

FIG. 6.

Rear of a rail probe assembly in tile. Shown are the alternating connecting pin layout which allows for a high density of probes on each tile.

FIG. 6.

Rear of a rail probe assembly in tile. Shown are the alternating connecting pin layout which allows for a high density of probes on each tile.

Close modal
FIG. 7.

Different views for the CAD assembly of the Alcator C-Mod divertor module with rail probes installed: (a) front, (b) rear, (c) vertical plate tiles, and (d) nose tile.

FIG. 7.

Different views for the CAD assembly of the Alcator C-Mod divertor module with rail probes installed: (a) front, (b) rear, (c) vertical plate tiles, and (d) nose tile.

Close modal

The tile face and probe were machined together to ensure that the probes are truly flush with the tile surface. The probes were initially machined to protrude above the tile surface. After assembly, the tiles (with probes) were faced using EDM. The EDM process allows for the flexibility to machine the highly asymmetric 3 dimensional pieces with a high level of precision and with no force from the tool on the workpiece. Once faced, the tiles were disassembled and cleaned to remove brass deposits from the EDM wire. The probes and tiles were then reassembled, tack-welding shim stock between the nuts and pins to ensure that they do not loosen, and the divertor module re-installed in Alcator C-Mod (Fig. 8).

FIG. 8.

(a) 21 rail probes were installed on an Alcator C-Mod divertor providing high spatial resolution profiles of divertor plasma conditions. (b) Close up of the rail probes located on the nose and shelf of the divertor. (c) Close up of the rail probes located along the vertical target plate.

FIG. 8.

(a) 21 rail probes were installed on an Alcator C-Mod divertor providing high spatial resolution profiles of divertor plasma conditions. (b) Close up of the rail probes located on the nose and shelf of the divertor. (c) Close up of the rail probes located along the vertical target plate.

Close modal

The rail probe assembly was very robust and reliable throughout the 2015 and 2016 Alcator C-Mod campaigns. It was regularly exposed to divertor parallel heat flux, q, in excess of 1 GW/m2 (Fig. 9) and post-campaign examinations showed no melt damage. In Fig. 9, the divertor plasma heat flux profile measured using by the rail probes is compared against surface thermocouple (SFTC) measurements.3 The Langmuir probe sheath heat flux here is calculated as q = γJsatTe, with the sheath heat flux transmission coefficient assumed as γ = 7, and Jsat and Te are inferred from the I-V characteristics using a standard 3 parameter fit model. There is reasonable agreement between the rail probe and the SFTC heat flux profiles. The profiles have been mapped to the outer midplane and the x-axis coordinate, ρ, is the distance from the last closed flux surface. Note that the proud Langmuir probe data shown are unable to resolve the peak heat flux near the strike point (ρ ∼ 0) and the private zone (ρ < 0) since many of the probes in this array were damaged by this point in the campaign.

FIG. 9.

A comparison of divertor parallel heat flux measurements made using surface thermocouples (SFTC), rail, and proud Langmuir probes. The rail probes were shown to be very robust and reliable throughout the Alcator C-Mod 2015 and 2016 campaigns.

FIG. 9.

A comparison of divertor parallel heat flux measurements made using surface thermocouples (SFTC), rail, and proud Langmuir probes. The rail probes were shown to be very robust and reliable throughout the Alcator C-Mod 2015 and 2016 campaigns.

Close modal

To test the rail probe sheath response, their I-V characteristics were compared with a set of standard proud divertor Langmuir probes located ≈140° toroidally around the Alcator C-Mod tokamak. As can be seen in Fig. 10, the plot on the left shows I-V characteristics of both the rail probe, with an incident field line angle of 0.66°, and proud Langmuir probes, with incident field line angles of 11°. Despite the significant difference in the incident field line angle, the two I-V characteristics have similar shapes and show a similar degree of ion saturation, demonstrating successful mitigation of sheath expansion effects on the flush and extended rail probe. When the incident field line angle approaches the threshold angle for sheath expansion mitigation (calculated for the rail probe to be ∼0.39°), sheath expansion effects are recovered as shown in the middle and right panels of Fig. 10. This is consistent with the scientific basis for the rail probe design which only mitigates sheath expansion effects and does not eliminate them. Overall, from the data collected with the rail probes, sheath expansion effects were successfully mitigated down to ∼0.5°. At these grazing field line angles, uncertainty in deducing the incident field line angles from magnetic flux surface reconstruction combined with geometrical uncertainties in divertor cassette alignment starts to be significant.

FIG. 10.

A comparison of simultaneous rail and proud probe measured I-V characteristics. The dots are the measured data and the solid lines are the least squares fit to Eq. (1) (3 parameter model). Case A—left: Both probes show similar degrees of ion current saturation and similar shapes. Case B—center: At the rail probe cut-off angle, sheath expansion effects begin to be noticeable. Case C—right: Sheath expansion effects are recovered on the rail probes. In this case, the level of ion saturation current inferred from the 3 parameter fit model is clearly displayed as a flat line at large negative bias. However, the data points (dots) do not track this line; ion collection continues to increase with increasing negative bias. Note that at such grazing field line angles other effects begin to become dominate and the projected area is poorly defined.

FIG. 10.

A comparison of simultaneous rail and proud probe measured I-V characteristics. The dots are the measured data and the solid lines are the least squares fit to Eq. (1) (3 parameter model). Case A—left: Both probes show similar degrees of ion current saturation and similar shapes. Case B—center: At the rail probe cut-off angle, sheath expansion effects begin to be noticeable. Case C—right: Sheath expansion effects are recovered on the rail probes. In this case, the level of ion saturation current inferred from the 3 parameter fit model is clearly displayed as a flat line at large negative bias. However, the data points (dots) do not track this line; ion collection continues to increase with increasing negative bias. Note that at such grazing field line angles other effects begin to become dominate and the projected area is poorly defined.

Close modal

Table I compares parameters deduced from fitting the I-V data shown in Fig. 10 (Case A, Case B and Case C) using three models: the standard 3 parameter fit model [Eq. (1)], a 4 parameter fit model using a linear sheath expansion approximation,10,18 and the perimeter model developed by Tsui.10 Comparing the perimeter model to the standard 3 parameter fit, we see that in Case A, there is little to no effect, despite a significant difference in temperature between the two I-V characteristics, indicating that sheath expansion is likely to not be the cause of this temperature difference. In comparison, in Case B where the rail incident field line angle is close to the calculated threshold value, the perimeter model effectively computes comparable Jsat and Te fit parameters between the proud and rail probe data, correcting for the slightly increased Te measurements on the flush probe calculated using the standard 3 parameter fit. For grazing field line angles on the rail probe (Case C), error in the field line mapping and other effects begin to dominate, neither the perimeter model nor a 4 parameter fit can account for this.

TABLE I.

Fit parameters derived for the 3 sets of I-V characteristics shown in Fig. 10. Fit parameters are shown in the format */*/* for three I-V characteristic models: standard 3 parameter fit model, 4 parameter (linear) fit model, and a perimeter sheath expansion model by Tsui.10 

I-V setCase ACase BCase C
ProbeProudRailProudRailProudRail
ψ (deg) 11.0 0.66 10.7 0.41 10.7 0.05 
ρ (mm) ≈0.4 ≈3 ≈−0.1 
Jsat (A/mm20.54/0.33/0.52 0.71/0.45/0.69 0.21/0.11/0.19 0.22/0.16/0.2 0.54/0.47/0.52 10/0.92/10 
Te (eV) 31/23/30 46/35/45 36/25/35 41/28/37 7.6/5.7/7.1 8.4/8.1/8.6 
Vf (V) −20/−20/−20 −26/−27/−26 −35/−35/−35 −12/−12/−12 0.35/0.46/0.36 −1.9/−2/−2 
|ΔJ/ΔV| (mA/V mm2…/2.2/… …/2.4/… …/1/… …/0.5/… …/0.78/… …/36/… 
I-V setCase ACase BCase C
ProbeProudRailProudRailProudRail
ψ (deg) 11.0 0.66 10.7 0.41 10.7 0.05 
ρ (mm) ≈0.4 ≈3 ≈−0.1 
Jsat (A/mm20.54/0.33/0.52 0.71/0.45/0.69 0.21/0.11/0.19 0.22/0.16/0.2 0.54/0.47/0.52 10/0.92/10 
Te (eV) 31/23/30 46/35/45 36/25/35 41/28/37 7.6/5.7/7.1 8.4/8.1/8.6 
Vf (V) −20/−20/−20 −26/−27/−26 −35/−35/−35 −12/−12/−12 0.35/0.46/0.36 −1.9/−2/−2 
|ΔJ/ΔV| (mA/V mm2…/2.2/… …/2.4/… …/1/… …/0.5/… …/0.78/… …/36/… 

When comparing the 3 and 4 parameter fit models, we see that the 4 parameter fit model systematically reduces the Jsat and Te measurement for both probes. Note that in Case A, even with a 4 parameter fit, there remains a significant temperature disparity between the rail and proud Langmuir probe Te measurement. In order, to provide an independent test of the accuracy of fit parameters deduced from Langmuir probe I-V characteristics, the total energy deposited on the divertor over the duration of a discharge was compared across a suite of different diagnostics: proud and rail Langmuir probes, SFTC, calorimeters (CAL), and embedded tile thermocouples (TILE).19 The sheath heat flux was calculated here with heat transmission coefficient γ = 7, and Jsat and Te inferred from the I-V characteristics using a standard 3 parameter fit model. Figure 11 shows the results for a low density sheath limited discharge with minimal divertor radiation, allowing for a fair comparison between the Langmuir probes (fitted with a 3 parameter fit) and the other diagnostics. The x-axis shown is the poloidal distance along the divertor plate instead of the ρ coordinate used earlier since the magnetic geometry changes over the course of a discharge. We see that within the scatter in the data, the proud probe data based on a 3 parameter fit produce a discharge integrated energy deposition that is comparable to the other diagnostics. Since the 4 parameter fit model yields reduced values of Jsat and Te, the model would significantly under predict the total deposited energy—an indication that the model is not able to deduce reliable fit parameters for these I-V characteristics which do not show evidence of sheath expansion effects. In comparison, the rail probes also appear to measure comparable energy deposition densities, an indication that the fitted parameters are fairly accurate, except around the strike point location. This can be traced to the rail probes systematically inferring higher temperatures around the strike point than the proud probes, as seen for the fit parameters for Case A in Table I and discussed in greater detail in a separate publication.12 The reason for this discrepancy is yet to be determined. However, it is not associated with sheath expansion effects which have been shown to have been successfully mitigated by the rail probe design.

FIG. 11.

The discharge integrated divertor energy deposition density of the proud and rail Langmuir probes is compared to other divertor energy deposition diagnostics as a function of poloidal arc length along the divertor. The 3 parameter fit used for the proud and rail Langmuir probes compares well against the other diagnostics, an indication that it is a more accurate than the 4 parameter fit for I-V characteristics that do not show evidence of sheath expansion.

FIG. 11.

The discharge integrated divertor energy deposition density of the proud and rail Langmuir probes is compared to other divertor energy deposition diagnostics as a function of poloidal arc length along the divertor. The 3 parameter fit used for the proud and rail Langmuir probes compares well against the other diagnostics, an indication that it is a more accurate than the 4 parameter fit for I-V characteristics that do not show evidence of sheath expansion.

Close modal

A set of high-heat flux, flush mounted rail probes were designed and installed on Alcator C-Mod. The probes have proven to be robust and reliable, experiencing no damage from plasma operations of the 2015-2016 campaigns—a first for any divertor Langmuir probe diagnostic in Alcator C-Mod. Analysis of the results has shown that the toroidal elongation of the probes has successfully mitigated sheath expansion effects. However, there are ongoing open questions about the physics of probe plasma interactions beyond simple sheath expansion that are being investigated.12 

The authors would like to thank the Alcator C-Mod team, in particular Ronald Rosati and Samuel Pierson who were instrumental in the assembly and installation of the rail probe system.

This work was supported by U.S. DoE cooperative Agreement Nos. DE-SC0014264 and DE-FC02-99ER54512 on Alcator C-Mod, a DoE Office of Science user facility.

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