Imaging divertor strike point splitting in RMP ELM suppression experiments in the DIII-D tokamak

The structure of divertor heat and particle fluxes is a critical issue for ITER and other next-step burning tokamaks.¹ Concerns range from prediction of a radially narrow heat flux between Edge-Localized Modes (ELMs)² to impact of divertor strike point splitting by magnetic field perturbations from locked modes^3,4 and ELM suppression coils^5–7 on particle and heat fluxes, which is problematic for tightly baffled divertors. In addition, the evolution of the wall fuel and impurity source through an ELM cycle is important for understanding the role of different fueling channels in H-mode pedestal recovery, trapping of impurities in the divertor, and providing boundary conditions for integrated core-edge modeling.⁸ Fast visible imaging from above of the photon fluxes at the divertor strike points can be used to constrain modeling of boundary fueling and transport and to validate equilibrium reconstructions and simulations of plasma response to the RMPs used to suppress ELMs in tokamak H-modes.^9–12 

Imaging of emission lines in the visible to near-infrared (400-1000 nm) provides significant advantages for studying transient events requiring either fast temporal response (ELMs), high spatial resolution (arcing or dust), or large toroidal extent (strike point asymmetry). Imaging in DIII-D provides continuous data with high spatial resolution (2–4 mm/pixel) that spans the radial extent of the divertor over a 40° toroidal range, unlike divertor Langmuir probes and Thomson scattering which have limited spatial and/or temporal resolution.

The requirements for effective fast visible imaging of photon fluxes from emission lines in the divertor include high transmission of the optical system and quantum efficiency of the camera at the relevant wavelengths; protection from stray magnetic fields; resistance to γ-ray, hard X-ray, and neutron radiation; the possibility of absolute photon flux calibration; sufficient photon flux to allow high framing rates to study transient events; and a sufficiently wide angle of view to study radial profiles and toroidal asymmetries. Cameras can be used to meet these requirements in either single-color or multi-color mode.

Three Vision Research Phantom cameras are used for these measurements at DIII-D.¹³ Each camera has a CMOS detector with 22 μm pixels that yield 2–4 mm spatial resolution in the divertor and a maximum resolution of 800 × 600 pixels in the (ϕ, R) plane. These cameras have a resolution-dependent minimum exposure time with a minimum of 1 μs. One camera is a Phantom v7.1, with 12 bit image depth and 2.8 GB RAM; the other two cameras are Phantom v7.3s, with 14 bit image depth and 10 and 32 GB RAM, respectively.

The CMOS cameras are sensitive to both magnetic fields and ionizing radiation, so the camera is installed in an enclosure remote (2–3 m) from the vessel that shields magnetic fields, neutrons, and γ-rays (Fig. 1). The magnetic shield consists of 9.525 mm thick low carbon steel, which reduces |B| ∼ 210 G at the camera location to ∼15 G. The radiation shield is wrapped around the magnetic shield and consists of a 76.2 mm thick outer layer of green borated polyethylene (neutron moderation and capture) with an inner layer of 6.35 mm thick lead for shielding γ-rays produced by neutron absorption in the machine hall and inside the neutron shield.

A Schott IG-163 silicate glass wound fiber bundle¹⁴ is used to transfer the image from a Schneider 25 mm objective lens on the 75° R + 2 port of the tokamak [Fig. 2(a)] to the camera inside the shield box. Matched 50 mm relay lens are used to couple the filter wheels to the end of the fiber. The fiber bundle allows the camera to be used for a variety of measurements on several ports within reach of the fiber bundle (2.74 or 4.27 m long), including primarily a tangential view in the co-plasma-current I_p direction at toroidal angle ϕ = 90° [Fig. 2(b)]. A significant drawback of the fiber bundle is the degradation of transmission due to exposure to hard X- and γ-rays and to neutrons in the machine hall. This darkening can be annealed with high temperature baking of the fibers (180–200 °C) for about 20–25 cycles.¹⁵ 

The divertor shelf (1.85 ≤ S ≤ 2.24) obscures the view of the outer strike point for plasmas with the strike point positioned for pumping, as indicated by the discontinuity in the red line in Fig. 2(a). However, the outer divertor can be imaged when the strike point is moved inward from the shelf or placed on the shelf. An important aspect of the camera divertor view [Fig. 2(b)] is the overlap with the infrared TV (IRTV) view at ϕ = 60° used to measure the heat flux to the divertor. This allows the radial profiles of the particle and heat flux to be compared for the first time at the same ϕ, an important capability for studying non-axisymmetric discharges such as those used for RMP ELM suppression.

For fast imaging of transients in the divertor, the FASTCAM system is used with dual Finger Lakes International 5-position filter wheels for 50 mm diameter, narrow-band interference filters to selection emission lines of interest in the visible range. Dual filter wheels allow the use of neutral density filters to reduce the light from very bright objects (e.g., ablating pellets). This capability is not needed for strike point imaging, so one filter wheel is set to an open position. Two common examples for inferring D⁺ ion flux are shown in Fig. 3: (a) molecular D₂ emission from the rotational-vibrational Fulcher band around 601 nm, overlaid in orange on the divertor view for reference, and (b) neutral atomic Balmer-α emission (656.3 nm). For the image resolution shown (512 × 368 pixels), the maximum framing rate is ∼15 kfps. Under typical conditions, the Balmer- α emission allows exposures as low as 3 μs; by reducing the image resolution (FOV), it is possible to frame as fast as 200 kfps. The remaining lines of interest are more than an order of magnitude dimmer. Typical framing rates and exposures are 5 kfps and 198 μs for D₂, and 2–5 kfps and 498–198 μs for Cii and Ciii. These framing rates are fast enough to resolve inter-ELM dynamics, and 32 GB of camera memory yield >20 s of data >2$×$ discharge length at these rates and resolutions.

In Fig. 3(a), the outer strike point (OSP) is placed in the entrance to the pumping plenum under the shelf (Fig. 2) to reduce the discharge density and collisionality via active pumping. As shown in Fig. 2, the OSP is consequently not visible due to the nose tile of the shelf. The inner strike point (ISP), however, is readily visible and shows 4 well-resolved peaks in the D₂ photon flux due to the perturbation of the ISP by the n = 3 applied RMP. In the discharge in Fig. 3(b), the OSP has been pulled to smaller major radius by 2.2 cm, allowing the primary OSP (short dashed line) to be seen. At the ISP (solid line), in place of the emission structures at the divertor surface in Fig. 3(a), the emission extends above the divertor floor along the inner leg of the divertor up to the X-point (large dashed line) and up the plasma edge due to detachment of the plasma at the ISP. This emission pattern during ISP detachment is seen for other emission lines, including D₂, Cii, and Ciii. These results indicate that fast visible imaging of the molecular D₂ Fulcher band can be used to measure the splitting of the ISP provided that the ISP remains attached, as it does during the ITER-like low collisionality and density conditions typical of RMP ELM suppression experiments in DIII-D.^11,16

Photon fluxes are obtained from camera images (Fig. 3) by applying an absolute brightness calibration that accounts for the wavelength-dependent transmission of the vessel port, fiber bundle, and interference filter, as well as the camera exposure time and detector response. In ionizing plasmas, there is a balance between the flux of neutral or low charge state fuel and impurity particles from the wall Γ and ionization sink Γ_i to higher charge states. Thus, the measured photon flux Φ from lower charge state impurities and neutral fuel can be used for calculating the corresponding wall source using the inverse photon efficiency (number of ionization events per photon) S/XB, the ratio of the electron ionization S to excitation X rate coefficients, and the branching ratio B. S/XB is a function of local n_e and T_e at the strike point: S/XB(n_e, T_e) = Γ(n_e, T_e)/Φ(n_e, T_e), where divertor Langmuir probes or Thomson scattering are used to measure n_e and T_e. Applying this method to atomic Balmer-α photon fluxes Φ_D is complicated by contributions to the total deuterium flux from the wall from chemical erosion products C_xD_y and because D is released from the wall in both atomic D and molecular D₂ forms. Consequently, despite the simplicity of the spectroscopic measurement of atomic Balmer-α emission, the total D source must be inferred by using an effective factor $S/XBeff$⁠, such that $ΓtotD=S/XBeff×ΦDα$⁠. Bykov et al. have measured $S/XBeff≈2×S/XB≈40$ for attached divertor plasmas in L and ELMing H-modes in DIII-D.⁸ A similar result was obtained in TEXTOR.⁹ 

The D atom flux due to molecules from the wall $ΓmolD$ can be similarly determined from the total Fulcher band photon flux $ΦFul$ as $ΓmolD=2D/XB×ΦFul$⁠, where D/XB is the photon efficiency for molecular dissociation, and $ΦFul$ is the total Fulcher band intensity, which consists of multiple rotational-vibrational lines spanning the range from 600 to 640 nm. It is not practical to measure the entire Fulcher band intensity with a wide band pass filter because of multiple contaminant lines in that wavelength range. To avoid this problem, we use a filter to measure the intensity of the first diagonal band (around 601 nm), as shown in Fig. 4. The intensity of this first diagonal band (transitions with equal vibrational number v = v′ = 0) can be extrapolated to that of the full Fulcher band $ΦFul$ using a collisional radiative model (CRM).¹⁷ 

The recycling R ∼ 1 locally across the strike point and lobes in attached L and ELMing H-modes. Then what comes to the surface as D⁺ leaves the surface nearly instantaneously as D or D₂. For the molecular photon flux $ΦFul$ to be a good proxy for the D⁺ flux $ΓD+$⁠, to the target, we need locality of the emission, and variation of the emission dominated by $ΓD+$⁠, not by D/XB. The locality of the emission is ensured by the short mean free path (a few mm) to dissociation of the slow D₂ molecules. The particle source rate is a product of $ΦFul$ and D/XB and may be sensitive to local plasma parameters. For attached, non-RMP divertors, the ion saturation current J_sat, electron density n_e, and electron temperature T_e have similar profiles; we assume this holds for the lobes with RMPs as well. Using $ΦFul$ as a proxy for $ΓD+$ without accounting for the D/XB variation reduces the contrast between the lobes so this assumption is a conservative one for measuring the lobe structure on the plate.

Edge resonant magnetic field perturbations (RMPs) are used in DIII-D to control the impulsive power loading to the divertor targets due to edge localized modes (ELMs). In ITER, ELMs are predicted to release 20-30 MJ of plasma stored energy on very short time scales (<1 ms), producing significant erosion and damage to the targets and reducing the divertor lifetime to as little as a single large ELM.^1,18 In 2003, Evans and Moyer demonstrated that ELMs could be suppressed by application of 1 part in 10 000 magnetic field perturbations that were resonant near the top of the H-mode pedestal.¹¹ These magnetic fields perturb the separatrix which forms the topological boundary between closed and open magnetic field lines in a diverted plasma. The non-axisymmetric perturbation lifts the degeneracy of the stable and unstable manifolds [Fig. 5(a)] which define the axisymmetric separatrix, forming lobes which narrow in width and increase in amplitude (magnetic flux-preserving) as the divertor X-point is approached [Fig. 5(a)]. When these lobes are long enough, they intersect the divertor target, causing the axisymmetric strike point to split into multiple lobes.^19–21 These lobes have been shown to change plasma edge profiles^22,23 and to modulate the particle flux to the divertor.^5–7 However, for reasons that are not yet well understood, there is little effect on the divertor heat flux profile in these conditions of ITER-relevant low pedestal electron collisionality. Because such splitting of the divertor heat flux can present problems in ITER and other tokamaks with tight divertor baffling, there is considerable interest in understanding the impact of the plasma response to the applied RMP on these structures and the lack of heat flux dependence on these structures. Fast visible imaging of the divertor particle flux in the (R, ϕ) plane of the divertor, in conjunction with infrared imaging of the divertor heat flux within the same toroidal span, provides a powerful tool for studying the impact of this strike point splitting on divertor heat flux and for validating equilibrium reconstructions and models of the plasma response to the RMPs.

An example of the measured splitting of the particle flux in the divertor of RMP ELM suppression discharge 166450 in DIII-D is shown in Fig. 3(a). In Fig. 6(a), the D₂ photon flux is plotted versus time and S-coordinate in the vicinity of the ISP [Fig. 2(a)] after averaging over Δϕ = 4° centered on ϕ = 60° where the divertor heat flux is measured by the IRTV [Fig. 2(b)]. Blue corresponds to the lowest, and red corresponds to the highest measured photon flux. The ELM behavior is shown by the blue D_α intensity measured by the filterscopes in Fig. 6(b). The RMP is applied at 2.0 s, as shown in Fig. 6(c). At 2.5 s, the current in one quartet of RMP coils is ramped to change the dominant toroidal mode number n of the RMP from 3 to 2. Shortly after the end of this RMP current ramp, the plasma returns to ELMing H-mode at 3.7 s. The dashed line in Fig. 6(a) shows the location of the primary ISP calculated from EFIT equilibrium reconstruction using only the external magnetics data.²⁴ The ELMs transiently broaden the primary strike point until the RMP is applied, after which the ELMs suppress and 4 discrete peaks in the D₂ photon flux are formed at the ISP. As the RMP current is ramped, the plasma control system holds the primary strike point at constant S, while the remaining three lobes move in radius and the D₂ photon flux intensity changes.

The radial structure of the particle and heat fluxes is compared in Fig. 7 at 2750 ms. The 4 peaks in the D₂ photon flux are clearly visible. The IRTV heat flux measurement shows only small “shoulders” near the positions of the well-resolved peaks in the particle flux. Calculations of the radial profile of the magnetic field line hit density using the vacuum magnetic field line integration code TRIP3D²⁵ show excellent agreement with the 4 peaks in the D₂ photon flux when the x-axis (S-S_ISP) of the TRIP3D field line hit density is multiplied by 4, which is consistent with previous DIII-D results.^22,23,26 Because linear plasma response modeling with MHD codes indicates that the plasma response is dominantly a screening response,¹² which has been shown to reduce the strike point splitting below the vacuum model predictions,²³ the measured particle flux splitting presents a challenge for existing plasma response models. Such time-dependent measurements of the particle flux splitting during RMP experiments can be used to validate the plasma response models.

Fast visible imaging of the divertor provides time-dependent, spatially resolved measurements of D and C particle fluxes in attached plasma conditions in DIII-D. These fluxes can be used to study the fueling and recovery of the H-mode pedestal in the inter-ELM period,⁸ to verify equilibrium reconstructions with the strike point positions, and to validate simulations of the plasma response to magnetic field perturbations used to suppress ELMs.

This material is based upon the work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Nos. DE-FG02-07ER54917, DE-FG02-05ER54809, DE-FC02-04ER54698, DE-AC52-07NA27344, DE-NA0003525, and DE-AC04-94AL85000. This research used resources of the DIII-D National Fusion Facility, which is a DOE Office of Science User Facility.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.