Taming the Plasma Material Interface with the "Snowflake" Divertor in NSTX

Steady-state handling of divertor heat flux is a critical issue for ITER and future conventional and spherical tokamaks with compact high power density divertors. A novel ”snowflake” divertor (SFD) configuration was theoretically predicted to have significant magnetic geometry benefits for divertor heat flux mitigation, such as an increased plasma-wetted area and a higher divertor volume available for volumetric power and momentum loss processes, as compared to the standard divertor. Both a significant divertor peak heat flux reduction and impurity screening have been achieved simultaneously with core H-mode confinement in discharges with the SFD using only a minimal set of poloidal field coils. PACS numbers: 52.40.Hf, 52.55.Fa, 52.55.Rk Submitted to: Nuclear Fusion Letters ‡ E-mail: [email protected] Taming the Plasma Material Interface with the ”Snowflake” Divertor in NSTX. 2 The interface between a high-temperature plasma and a material surface is one of the outstanding challenges for magnetically confined fusion energy (MFE) research. A present vision of the plasma-material interface (PMI) for toroidal plasma devices (tokamaks) is a magnetic X-point divertor [1, 2]. In this concept, a region of open magnetic field lines surrounding the confined plasma (the scape-off layer (SOL)) is diverted away by additional divertor magnetic coils to a divertor chamber to minimize the interaction with vacuum vessel walls. The steady-state peak heat flux endured by the divertor chamber surface is limited by the present day divertor material and active cooling technology at qpk ≤ 10 MW/m. At higher heat fluxes the plasma facing component (PFC) lifetime and structural integrity are at risk due to increased material erosion rates and thermal stress. In the collisional SOL plasma, heat transport parallel to the field lines is often dominated by classical electron and ion conduction, whereas turbulence and intermittency set the cross-field heat and particle transport [1, 2, 3, 4]. In order to reduce the power and particle fluxes exhausted in the divertor chamber, a number of solutions based on active techniques, e.g., impurity or D2 seeded radiative divertors, field ergodization and strike point sweeping, and passive techniques, e.g., the number of divertors and divertor geometry, have been developed [1, 2] . These techniques aim to reduce the parallel heat flux q‖ by volumetric power loss processes or SOL power partitioning, and reduce the heat flux qdiv deposited on the PFCs by increasing the plasma-wetted surface area. Spherical tokamaks (STs) impose even greater demands on divertor heat flux handling. The ST is viewed as a candidate concept for future fusion and nuclear science MFE devices [5, 6, 7]. Experiments in the National Spherical Torus Experiment (NSTX), a high-power density medium size ST (R = 0.85 m; a = 0.65 m) with graphite tile PFCs, have demonstrated the challanges of the inherently compact ST divertor: a large out/in SOL power ratio, a small divertor PFC area and reduced divertor volumetric (radiated power and momentum) losses. ITER-scale steady-state divertor heat fluxes qpk ≤ 15 MW/m and q‖ ≤ 200 MW/m have been measured in Ip = 1.0 − 1.2 MA discharges heated by a 6 MW neutral beam injection (NBI) [8, 9]. While a successful reduction of divertor qpk to 0.5-3 MW/m 2 simultaneously with high (H-mode) core confinement has been demonstrated in NSTX with an additional divertor D2 injection [10, 9], the radiative divertor technique alone is limited by the achievable divertor radiated power and does not scale favorably to future MFE devices (e.g., [6, 11]); thus, novel integrated approaches are sought. Several innovative divertor geometries with attractive heat flux handling properties have been proposed recently [11, 12, 13]. One of them is a ”snowflake” divertor (SFD) configuration [13, 14, 15, 16], which uses a second-order poloidal field null created by merging, or bringing close to each other, two first-order poloidal field null points (Xpoints) of a standard two-coil divertor configuration. A poloidal cross-section of the obtained magnetic flux surfaces with a hexagonal null-point has an appearance of a snowflake. The poloidal field Bp increases with distance as r 2 in the vicinity of the second order null (vs r in the vicinity of a first order null in the standard divertor), leading to Taming the Plasma Material Interface with the ”Snowflake” Divertor in NSTX. 3 (1) a higher divertor magnetic flux expansion fm = (Bp/Btot)MP ((Bp/Btot)SP ) −1 (where Btot is the total magnetic field at the strike point (SP) and mid-plane (MP) locations); (2) a higher plasma-wetted surface area Awet = 2πRSPfmλq|| (RSP is the SP radius, and λq|| is the MP (upstream) SOL power width); and (3) a longer X-point connection length Lx [14, 16]. The latter increases the heat diffusive loss into the private flux region, as well as the divertor volume available for impurity radiation and ion momentum losses. The SFD magnetic equilibria have been simulated for several tokamaks with existing divertor coils [15]. The SFD has been already realized in the TCV tokamak using a set of six divertor coils [17]. In this Letter we present an experimental study of the SFD in NSTX. The SFD configuration for the first time 1) was obtained with a minimal number (two) of divertor coils; 2) resulted in a significant reduction of divertor qdiv and q‖ leading to a partial detachment of the outer SP; and 3) proved to be compatible with H-mode core confinement while demonstrating favorable impurity screening properties. Experimental results reported in this Letter fully confirmed the theoretically predicted SFD properties [15, 16]. The two-coil SFD concept thus shows promise as a PMI solution for next-step high-power fusion devices that are likely to have few magnetic coils due to engineering and neutron constraints. Magnetic control is critical for the SFD concept, since a second-order null configuration is topologically unstable [14, 16]. Two stable SFD-like configurations can be realized in practice: a SFD-plus, where the divertor coil currents slightly exceed those of the ideal SFD case, and a SFD-minus, where the corresponding divertor coil currents are slightly lower [14]. A predictive free-boundary axisymmetric GradShafranov equilibrium code ISOLVER was used to model plasma equilibria with the SFD. The boundary shape, normalized pressure and current profiles from an existing medium triangularity discharge (similar to the one shown in Fig. 1a) were used to compute the plasma contribution to the flux ψ on a flux surface. The SFD was obtained by iteratively adjusting the currents in two divertor magnetic field coils PF1A and PF2L (also shown in Fig. 1a). Generally, the SFD-like configurations were generated when a secondary X-point was located on the flux surface within ∆ψN ≤ 0.02 from the separatrix (where normalized flux ψN = 1), and when a separation between the Xpoints in physical space was d ≤ 20 cm (cf. ion Larmor radius rL ≤ 4 mm). The corresponding deviation of the coil currents from those of the standard divertor was within 10-20 %. Shown in Fig. 1 are (a) the standard divertor and (b) the modeled SFD-minus configurations. The benefits of the SFD are apparent from comparison of their magnetic geometry parameters shown in Table 1. The ISOLVER model provided the PF1A and PF2L coil currents as well as the inner and outer SP coordinates for a practical implementation of the SFD in NSTX. In the experiment, the plasma control system (PCS) [18, 19] held the SP positions by real-time variation of the PF1A current for inner SP control, and the PF2L current for outer SP control. A proportional-integral-derivative (PID) controller algorithm with input from magnetic sensor and other diagnostic measurements was used [20]. The Taming the Plasma Material Interface with the ”Snowflake” Divertor in NSTX. 4 SFD-like configurations were obtained in a number of discharges for periods of 50-150 ms. Because of the time-dependent plasma inductance, ohmic transformer flux leakage, and variations in divertor structure eddy currents (none of which were included in the ISOLVER model), both d and ∆ψN changed in time, resulting in intermittent switching between the SFD and standard configuration. For example, the SFD discharge to be discussed below had five periods with the SFD-minus-like (Fig. 1c), and one with the SFD-plus-like (Fig. 1d) configurations. We are presently implementing an improved gain matrix in the PCS PID algorithm, and the real-time tracking and control of the second null-point in the NSTX PCS in order to maintain the SFD for an entire discharge duration (1-2 s). Magnetic and plasma characteristics of the SFD were studied in discharges with Ip = 0.8 MA, Bt = 0.4 T, and 4-6 MW of NBI heating. Lithium coatings evaporated on PFCs in the amount of 80-100 mg per discharge were used for wall conditioning and plasma performance improvements [21, 22]. Two H-mode discharges with similar shaping (κ ∼ 1.9 − 2.0 and δ ∼ 0.6 − 0.7) and SOL power PSOL ' 3 MW, but with different divertor configurations (the standard divertor vs the SFD-minus) will be compared. Core and edge diagnostics used in this study are described elsewhere [10, 9]. The experimental magnetic equilibria confirmed the magnetic geometry properties of the SFD predicted by the ISOLVER model and analytic two-coil SFD theory [13, 14], as shown in Table 1. The experimental equilibria were reconstructed with GradShafranov equilibrium codes EFIT and LRDFIT using standard magnetic and kinetic constraints [23]. Divertor geometries of the standard and SFD discharges are compared in Fig. 2. The presence of a secondary null-point in the SFD reduced Bp/Btot in the divertor separatrix region by up to 90 %, as shown in Fig. 2a. This increased the Xpoint connection length Lx by up to 50 % and the flux expansion fm (as well as Awet) in the outer SP region by up to 90 %. The radial divertor profiles of both Lx and fm in Fig. 2b-c show that the geometry was modified in the SOL radial region near the separatrix (∆ = 2 − 3 mm when mapped to MP using fm), while similar magnetic properties were retained outside of this SOL region at large distances from the nulls in both discharges. The SFD was found to be compatible with high confinement plasma operation, with no degradation in H-mode performance (Fig. 3a). In the standard divertor discharge, ELMs were suppressed as a result of lithium conditioning [24]. These ELM-free H-mode discharges had impurity accumulation leading to Zeff ∼ 2−4 from carbon and radiated power Prad = 1− 3 MW from metallic impurities after 0.5 s [25]. The SFD discharge in contrast showed exceptional impurity screening properties: the core carbon inventory Nc (as well as Prad) was reduced by up to 75 % leading also to a 10-15 % reduction in ne (Fig. 3b-c). The similarity of the carbon density and carbon concentration profiles (up to a scaling factor 1.5-2) suggested an edge carbon source reduction in discharges with the SFD. Divertor measurements in the SFD [26] showed the commonly-observed Taming the Plasma Material Interface with the ”Snowflake” Divertor in NSTX. 5 characteristics of divertor detachment [1, 2, 27, 10, 9]: an increase in divertor radiated power and electron-ion recombination rates, a loss of parallel pressure balance, and as a result, a decrease of heat and particle fluxes to the plate. A good correlation was observed between the SFD periods when the inter-null distance d ≤ 20 cm (Fig. 3d) on one hand, and the increases in the outer SP divertor Dα intensity induced by volume recombination, significant drops in the divertor heat flux averaged over the radial region ∆ = 15 cm adjacent to the outer SP, on the other hand, as shown in Fig. 3e-f. While the heat flux measurements were uncalibrated due to lithium coatings on divertor surfaces, typical qpk = 4−6 MW/m have been measured in similar standard divertor discharges. The averaged divertor heat flux was reduced in the SFD discharges by up to 30-40 % due to increased divertor radiated power. The divertor bolometer signal indicative of divertor Prad showed a 50 % increase in the SFD vs the standard divertor (Fig. 3h). Divertor peak heat fluxes qpk were reduced by up to 90 % in the detachment region adjacent to the separatrix (∆ = 2−3 mm as mapped to MP with fm taken into account), as shown in Fig. 4. In the attached SOL at Rdiv ≥ 0.6 m, similar divertor heat fluxes were measured in the SFD and the standard divertor, due to similar magnetic geometries. Taking the MP SOL width as λq‖ ∼ 6 − 7 mm [28], we conclude that a significant fraction of divertor heat was exhausted through volumetric processes in the SFD. In the SFD discharges, spatially resolved Balmer spectra showed a formation of a large volume recombination region with average Te ' 0.8− 1.1 eV and ne ' 2− 7× 10 m−3 [26] inferred from the modeling with the radiation transport and collisional-radiative code CRETIN [29]. A comparison of the inferred electron pressure in the SP region pe = neTe ∼ 25 − 80 Pa to the measured MP pressure pe ∼ 50 − 120 Pa confirmed a pressure decrease from midplane to target in the SFD. In a partially detached divertor SP region with Te ≤ 1− 2 eV, a significant reduction of divertor physical and chemical sputtering rates, as well as an improved impurity entrainment in a hydrogenic plasma flow are expected [30, 27, 31, 10, 9]. While the physical mechanism is yet to be confirmed, this is consistent with the observed reduction in Zeff and impurity concentration in the SFD discharges. In previous NSTX divertor experiments qpk showed a linear scaling with PSOL and a weak dependence on ne [28, 10]. The outer SP detachment did not occur in standard divertor configurations at the SOL power 1.5 ≤ PSOL ≤ 5 MW, because of insufficient divertor carbon Prad. The SOL power flow from the X-point to the divertor SP is described by ∇ · q‖ = SE, where SE is a sum of volumetric energy sources and sinks, the latter being mainly due to volumetric divertor Prad and ionneutral charge exchange losses. The SFD magnetic properties significantly affected parallel divertor heat transport in the separatrix region by increasing collisionality and the divertor volume, and thus the volumetric losses. This led to a partial detachment of the outer SP, despite the counter-balancing effect of lithium conditioning that tended to reduce recycling and divertor ne. Additionally, the power deposited in the divertor was reduced due the much-increased plasma-wetted area Awet. Applying a simplified 1D model of electron conduction-dominated parallel heat transport with non-coronal Taming the Plasma Material Interface with the ”Snowflake” Divertor in NSTX. 6 carbon radiation (as discussed in [10, 9]), a 50 % increase in Lx and divertor ne is sufficient to increase carbon Prad losses necessary to reduce q‖ to a detachment level of 0.5-1 MW/m−2 [10]. This is also in qualitative agreement with the 2D multi-fluid modeling of the SFD heat transport in a DIII-D tokamak geometry [16]. In summary, the results of this letter provide support for the SFD concept as a promising solution of the PMI problem for next-step high-power fusion devices. We demonstrated that a SFD-like configuration could be obtained with only two existing divertor coils in NSTX, and in comparison with the standard divertor, it significantly reduced both parallel and deposited divertor heat fluxes and improved impurity screening, while maintaining H-mode confinement. This work was performed under the auspices of the U.S. Department of Energy under Contracts DE-AC52-07NA27344, DE-AC02-09CH11466, DE-AC05-00OR22725, W-7405-ENG-36, and DE-FG02-04ER54758. The entire NSTX Team is acknowledged for technical and operational support.