X-point radiator and power exhaust control in configurations with multiple X-points in TCV

Handling the power exhaust of magnetically confined fusion plasmas continues to challenge the safe operation of future reactors. It is accepted that some degree of divertor detachment, defined as a concurrent reduction in target ion flux and temperature,¹ will be required to mitigate the target heat exhaust to within material limits.² Nonetheless, it remains uncertain whether ITER's vertical plate single null (SN) divertor solution would scale favorably to even more powerful devices.^3–5 To mitigate this risk, alternative divertor configurations (ADCs) are being investigated,^3,6,7 some of which facilitate the access to detachment, extend the detachment operational space, and/or reduce peak target heat fluxes, under detached and attached conditions, with the latter reducing the risks associated with divertor reattachment.⁸ Geometric properties of the divertor magnetic flux surfaces can be manipulated to increase volumetric losses and to control the plasma exhaust power and particle distributions at the divertor targets. We use $L | |$ as the parallel connection length, which gives the magnetic field line length from the outboard midplane to its connected target. Simplified analytical models⁹ predict access to higher divertor radiative powers with increased $L | |$⁠, which can reduce the target heat loads. Increasing the target poloidal flux expansion f_X, defined as the ratio of perpendicular flux surface spacing between a location (here the target) and upstream, and/or reducing the target incidence angle, increases the plasma-wetted area at the target.⁷ Additional divertor X-points can further increase f_X in the divertor volume and divide the scrape-off layer (SOL) into multiple channels, directed toward multiple targets, experimentally found to reduce the peak target heat flux.^10,11 Simultaneously, high f_X around the X-point is expected to improve the access to the X-point radiator regime¹² that features a strongly radiating region around the X-point and, typically, a strongly detached divertor.^13,14 The core-edge integration of such scenarios is being studied across multiple devices,^15–19 where control of the position of the radiator is found to be crucial in avoiding core radiative collapse.

The Snowflake minus (SF−) configuration combines these geometric features, by introducing a second divertor X-point in close vicinity to the first.^20,21 This second X-point increases the spatial region of low poloidal field and, thus, increases f_X and $L | |$ over the X-point region, while directing the near- and far-SOL to two targets.^22,23 Previous studies of the SF− in L-mode displayed a radiation region appearing between the two X-points and a strong reduction in peak target heat flux, even for attached conditions.^11,24 However, mixed results in the divertor-core compatibility and divertor radiative power motivated further investigation of the interplay among target conditions, plasma-neutral interactions, and impurity transport.

Previous studies of the SF− configuration exhibit mixed results, which also regard divertor transport. Some studies suggest a stronger cross field transport in the inter-null region,^25,26 as expected for an increased $L | |$⁠. Fast imaging data attribute this increase to the localized inter-null production of filaments that propagate radially between the two X-points.²⁷ However, other experiments infer no increase in turbulent flux in the SF− configuration.²⁸ One question in that study is the possible contribution of the measured turbulent flux in the binormal direction. Simulations suggest an increased inter-null turbulence and infer that this contributes to the heat flux distribution across the additional strike-points.²⁹ The SF− is also expected to feature a convective cell around each X-point, driven by strong E × B drifts^29,30 and an enlargement of a churning mode region.³¹ 

An additional divertor X-point clearly increases the engineering complexity of a device, as additional divertor field coils are required. However, its advantages maintain it as a possible reactor solution, as shown in a proposed divertor design for the ARC pilot power plant, where an additional divertor X-point is placed near the outer target, with the entire outer divertor leg embedded within the neutron shielding blanket.³² Experiments in the Tokamak à Configuration Variable (TCV) have demonstrated that the strongly radiating SF− configuration in H-mode can be accompanied by ELM-suppression³³—strongly desired for the present plans of H-mode operation of future reactors.

The study presented in this paper will focus on the L-mode scenario with multiple X-points, leaving similar studies in H-mode scenarios with multiple X-points as future work. To further elucidate the role of additional divertor X-points on detachment characteristics and core-edge integration, a configuration is developed with three divertor X-points in close vicinity—the “Jellyfish” (JF). This complex configuration is made possible by the high shaping flexibilty of TCV and is facilitated by a state-of-the-art magnetic control system recently developed at TCV in collaboration with DeepMind, leveraging deep reinforcement learning to both design and control that geometry.³⁴ Interpretative modeling is used to study the physics mechanisms behind the operational behavior of configurations with multiple divertor X-points, employing the simplified 1D SOL model, SPLEND1D, together with a more complex edge transport code, EMC3-EIRENE.

Section II presents an overview of the TCV device and diagnostics, followed by a description of the novel Jellyfish geometry developed in TCV and a brief outline of the employed SOL plasma models. Section III investigates the role of connection length using the SPLEND1D model and analyses the experimental power exhaust characteristics and the divertor-core compatibility of the configurations with multiple divertor X-points. Section IV uses EMC3-EIRENE to simulate multiple divertor X-point configurations and explore the role of cross field transport and divertor impurity transport on the power exhaust and divertor-core compatibility. Finally, the conclusions of this study of the role of multiple divertor X-points and increased $L | |$ on divertor conditions and core-edge integration are presented in Sec. V.

This work aims toward a comprehensive approach to study divertor configurations with multiple divertor X-points, leveraging experiments in TCV as well as interpretative modeling, with the goal of furthering the physics understanding of the X-point radiator and power exhaust control. This section presents these methods, starting with an overview of TCV before presenting the experimental development of the JF configuration. The interpretative modeling is then introduced, taking advantage of two codes with varying degrees of complexity. The 1D SOL model SPLEND1D is used to study the role of connection length on target conditions and volumetric momentum and energy sources, and a more complete code—EMC3-EIRENE—is used to capture the effects of complex magnetic geometry to study divertor-core compatiblity and divertor plasma transport.

TCV is a medium-sized tokamak with graphite wall protection tiles (a source of intrinsic carbon impurities), a rectangular vacuum vessel, and 16 independently powered poloidal shaping coils. This unique poloidal shaping capability makes TCV an ideal testbed for ADC studies such as the SF− and JF. Herein, the TCV gas baffle tiles³⁵ were not installed that allowed for a wider range of divertor geometries. This study only employs Ohmic heating, operating in unfavorable B-field direction for H-mode access to facilitate configuration comparisons in the more easily accessible L-mode regime.

A Thomson scattering (TS) diagnostic³⁶ measures the plasma electron temperature, T_e, and density, n_e, along a vertical chord at R = 0.9 m, over both the core and divertor regions (⁠ $− 0.690 < Z < 0.679$ m) shown in Fig. 1(a). Gas valves integrated into the floor of the machine are used to fuel the plasma and seed impurities, Fig. 1(a). Figure 1(b) shows the 120 bolometer lines of sight,³⁷ used to reconstruct the plasma emissivity (assuming toroidal symmetry) to estimate the radiated power. Figure 1(c) shows the diagnostics used to measure target conditions: wall-embedded Langmuir probes (LPs) cover a large poloidal extent of the vessel,^38,39 and infrared (IR) cameras cover the inner divertor wall and vessel floor.⁴⁰ A 10-channel multispectral advanced narrowband tokamak imaging system (MANTIS)⁴¹ has a near toroidal view of the divertor region, see Fig. 1(d), and measures the emissivity of nine spectral lines with an integration time of 4.9 ms. The 2D emissivities from D-Balmer and He neutral and ionized spectral lines are used to infer plasma parameters such as density and temperature assuming a collisional radiative model.^42,43

The JF geometry is a novel divertor configuration featuring three nearby divertor X-points and is used to highlight any effects of additional X-points and the accompanying increased $L | |$ on the divertor power exhaust. This geometry was inspired by a theoretical study of a geometry with a third-order polodial null, termed the “cloverleaf.”⁴⁴ In the same way that the SF− configuration arose from a theoretical conception of an exact SF (with a single second-order poloidal null), a pragmatic cloverleaf became a configuration with three nearby first-order poloidal nulls.

The novel deep reinforcement learning architecture outlined in Ref. 34 was used to facilitate the design and control of such a geometry in TCV.  Appendix A outlines the method used in this novel control architecture, and the steps required to optimize the configuration for divertor studies, in terms of wall gaps and diagnostic coverage.

Two JF configurations were developed with varying X-point separations, to increase the connection length over varying parts of the outer SOL. From SF− studies, the inter-null separation was found to determine the proportion of exhausted power arriving at each additional target.^26,45 This magnetic separation is quantified in the SF− by $d r X 2$⁠, the distance between the first and second separatrices at the outboard midplane. For the JF configuration, we can extend this definition to $d r X 3$⁠, the distance between the first and third separatrices at the outboard midplane. The achieved equilibria are shown in Figs. 2(a) and 2(b), with (a) exhibiting higher X-point separations than (b) (⁠ $d r X 2 ∼ 3.2$⁠, $d r X 3 ∼ 7.0$ and $d r X 2 ∼ 1.6$⁠, $d r X 3 ∼ 3.2$ mm, respectively). This variation in $d r X 2$ and $d r X 3$ enables the study of the outer divertor power handling to be extended to more extreme configurations. To develop reference SF− and SN configurations for direct comparison with the JF, the third and second X-points were sequentially removed—these equilibria are shown in Figs. 2(c) and 2(d). Figure 3 shows the parallel connection length to the outer targets of each configuration as a function of the distance of the flux surface from the primary separatrix at the outboard midplane, dr_u. The JF configurations display extreme connection lengths of up to 130 m, approaching values seen in Wendelstein 7-X.⁴⁶ The two additional separatrices also divide the outer SOL into three channels, with each channel arriving at a separate strike-point, labeled SP2, SP4, SP6 in Fig. 2. Two further outer strike-points are present, but are not magnetically connected to the SOL and, as expected, see a negligible particle flux in these experiments.

The configurations are run for ohmically heated (⁠ $P ohm ∼ 250 − 300$ kW) L-mode discharges in deuterium, with a plasma current $I p = 245$ kA, with a toroidal magnetic field of $B t = 1.44$ T and $∇ B$ ion drift directed upwards (i.e., away from the X-points). The line-averaged core density is increased slowly over the discharge by gas puffing, over the range $⟨ n e ⟩ l = 3.2 − 6.0 × 10 19 m − 3$⁠, corresponding to a Greenwald fraction range of $f G = 0.19 − 0.36$⁠. The time-varying stored plasma energy, due to the density ramp, corresponds to a power level of $∼ 7$ kW across all discharges, and is hence neglected, e.g., for confinement time calculations. Since the density feedback control relies upon an interferometry measurement of the vertical line-integrated density (that can include plasma in the divertor region), applying a density ramp ensures that a steady state plasma with comparable core density (as measured by TS) can be found between all of the configurations.

SPLEND1D⁴⁷ is a simplified SOL plasma model that solves Braginskii-like equations in a 1D flux tube geometry and that enables divertor detachment to be captured. We exploit this code to study the role of connection length on power exhaust in a simplified geometry.

A diffusive neutral model is coupled to the plasma model, allowing for plasma-neutral interactions to be modeled. The plasma and neutral dynamics are driven by source and sink terms that include atomic interactions and external particle and energy sources. Trace impurities are assumed to exist with a constant concentration along the flux tube that generate a loss term in the electron energy balance. The plasma is confined along the field and cross field transport is prohibited. In this study, we impose a flux tube geometry that is symmetric around the outboard midplane, with symmetric boundary conditions upstream and fixed sheath heat transmission coefficients and the Bohm criterion at the target. A recycling boundary condition is imposed on the neutral flux, assuming 99% of ions and 100% of neutrals are recycled at the target. The effect of connection length can be studied in SPLEND1D by varying the length of the flux tube modeled. In this work, we perform density ramps for the set $L | | = { 25 , 50 , 100 }$ m, with constant input power and a constant carbon concentration of 2%.

Momentum and power loss factors are defined as the relative difference in, respectively, total pressure and heat flux along the flux tube, from upstream to the target.⁴⁷ A two-point model formatting⁴⁸ can also be applied to the SPLEND1D model to break down the momentum and power loss factor into individual contributions from each loss channel.

A previous study of the effect of connection length using a simplified SOL model predicted colder target temperatures with increasing $L | |$⁠,⁴⁹ but was unable to capture the target ion flux rollover that is characteristic of divertor detachment, and required the plasma particle, momentum and energy sources to be input from more complex plasma simulations. SPLEND1D is used to study the dependence of target quantities on the flux tube length (i.e., connection length) during the detachment process, calculating plasma sources and losses to self-consistently identify the dominant energy loss channels. Although this model is a great simplification as it analyses a single flux tube, rather than a self-consistent 3D plasma geometry, it can readily be used to interpret the local impact of connection length in isolation of other effects.

In contrast to the simple SOL model presented in Sec. II C, EMC3-EIRENE⁵⁰ is a more complex mean-field plasma edge transport model, coupled to the kinetic neutral model EIRENE. This allows us to study the impact of additional divertor X-points (and the consequential increases in connection length) on impurity transport as well as target conditions and plasma-neutral interactions. Unlike similar mean-field plasma edge transport codes, EMC3-EIRENE uses a 3D grid which is not required to be flux surface-aligned, making it well-suited to model complex divertor geometries, Fig. 4. It implements an advanced trace impurity model to solve for the impurity charge state and velocity spatial distributions. The only feedback of impurities on the main ion species that is included is through electron-impact ionization and radiative losses.

In this study, EMC3-EIRENE is employed to investigate the divertor conditions and core impurity content in the baffled SF− experiments presented in Ref. 11, enabling us to both complement and interpret the complex experimental results. Note that we do not simulate the JF configuration, but use SF− simulations to better understand the features that are intrinsic to configurations with multiple nearby divertor X-points. Two different grids are implemented in the plasma and neutral solvers, with a spatial extent described in terms of the normalized poloidal magnetic flux, $ρ ψ = ( ψ − ψ 0 ) / ( ψ LCFS − ψ 0 )$⁠. ψ is the poloidal magnetic flux and ψ₀ and ψ_LCFS are inferred at the magnetic axis and at the last closed flux surface respectively. The plasma (EMC3) grid is solved from the core edge (⁠ $ρ ψ = 0.95$⁠) until the first flux surface intersecting the first wall (⁠ $ρ ψ = 1.28$⁠). The grid of the neutral solver (EIRENE) covers a larger poloidal cross section, extending from $ρ ψ = 0.78$ to the vacuum vessel wall. The power entering the simulation domain from the core P_in, upstream separatrix density $n e , sep$ and impurity sources are input as user-defined conditions based upon experimental measurements. The requested upstream density results in a target recycling coefficient of R = 0.96 to satisfy the particle balance. In this case, two impurity species are modeled: carbon and optionally nitrogen, each implemented through a different type of source with no target recycling of impurities. Carbon is chemically sputtered with yield, $Y c s C$⁠, chosen to match upstream carbon density measurements; and nitrogen is injected upon request as a neutral gas flux as in the reference experiments.¹¹ Cross-field transport is described in EMC3-EIRENE as a diffusive flux, governed by $D ⊥ , χ ⊥ , e$⁠, and $χ ⊥ , i$⁠, respectively, the particle, electron heat, and ion heat diffusivity coefficients.

These user-defined quantities are tuned such that the experimental upstream and target conditions of a reference SN geometry are reasonably well reproduced. This results in a good match between experiment and simulation in upstream electron temperature and density, even when applying spatially uniform transport coefficients. At the targets, simulations underestimate the electron temperature and overestimate the electron density, as is commonly observed in edge transport modeling.^51,52 This discrepancy may originate from an incomplete treatment of neutrals in EIRENE.⁵³ The selected input parameters, given in Table I and again with spatially uniform transport coefficients, are applied to the SF− geometry to first study the effect on divertor conditions of magnetic geometry alone, and then $D ⊥ , χ ⊥ , e , χ ⊥ , i$ are varied spatially to study the hypothesized variation in cross field transport in the SF−.^{25–27,29,54}

This section looks to explore the expected dependence of connection length on the power exhaust in a simplified flux tube geometry, before turning to the experimental observations in Subsections III B–III E. The connection length is scanned in SPLEND1D simulations for plasma parameters relevant to the present experiments. This shows an earlier detachment onset for increasing $L | |$⁠, with the target ion flux rollover occurring at $∼ 30 %$ lower upstream density for $L | |$ increased by a factor four, from $25$ to $100$ m, Fig. 5. This is approximately the increase in $L | |$ in the near-SOL (at $d r u ∼ 3$ mm) from the reference SN to the JF configurations. This earlier rollover is accompanied by an earlier increase in momentum and power loss factors, Figs. 5(b) and 5(c). The two-point model formatting of the SPLEND1D model indicates charge exchange as the dominant plasma momentum loss mechanism and radiation (both from main ion species and impurities) as the dominant power loss mechanism. It should be noted that cross field transport should become a significant loss channel for configurations with enhanced $L | |$⁵⁵ but is not accounted for by the SPLEND1D model.

For a given upstream density, the radiated power fraction increases strongly with connection length. Figure 6 shows the radiation profiles along the flux tube length for the range of $L | |$ studied, at $n e , u ∼ 0.8 × 10 19 m − 3$ (attached) and $n e , u ∼ 2.4 × 10 19 m − 3$ (detached). Under attached conditions, the radiation peak increases with connection length in front of the target due to more favorable radiative conditions (increased plasma and neutral densities, reduced electron temperature), rather than an increase in radiative volume, consistent with Ref. 56. Meanwhile, under detached conditions, the radiation peak region begins to move away from the target where we see a weakening of the effect of connection length on radiated power, as the power loss fraction saturates (⁠ $f power → 1$⁠).

These results are consistent with the generally observed reduction in peak target heat flux in SF− configurations.^11,24 In the SF− experiments presented in Ref. 11, a weakening of these SF− power exhaust benefits is also observed as detachment deepens, consistent with the saturation of f_power found in the SPLEND1D modeling.

LP measurements reveal a strong reduction in peak target parallel heat flux, $q | | peak$⁠, for the JF configuration compared to the reference SN, Fig. 7. Reductions in peak parallel target heat flux of at least 50% are observed for both JF configurations (with different X-point separations) across the whole range of upstream density achieved. Since the JF SP6 spans a larger wetted area than the SN SP2, the heat flux in Fig. 7 is mapped upstream to account for differences in target total flux expansion. The strong heat flux reduction occurs primarily in regions of the SOL with the stronger increase in $L | |$⁠. Note that the SN reference in these experiments features a longer poloidal leg and higher flux expansion than a standard SN configuration in TCV, compared to which the reduction in peak heat flux would be expected to be even greater. When the JF is compared to the reference SF− configuration in Fig. 2(c), not shown here, a strong heat flux reduction is seen in the near-SOL of $∼ 75 %$⁠, while the far-SOL heat flux profiles (⁠ $d r u > 11$ mm) are very similar in the SF− and JF configurations.

LP measurements also reveal an earlier detachment onset in the JF compared to the reference SN, consistent with the predictions from the SPLEND1D modeling presented in Sec. III A. The peak target ion flux decreases with $⟨ n e ⟩ l$ at the JF near-SOL target (SP2), Fig. 8, indicating that this target is already detached. Furthermore, the LPs measure a target temperature $T e , t ∼ 6$ eV at SP2 at the start of the density ramp, decreasing below 4 eV throughout the ramp, further supporting the detachment of this target as plasma-neutral interactions become significant momentum sinks at this temperature.¹ The far-SOL targets in the JF configuration (SP4, SP6) exhibit an increasing target ion flux with $⟨ n e ⟩ l$⁠, with $T e , t < 10$ eV at the start of the density ramp. Meanwhile, the SN outer target remains attached, with an increasing target ion flux and $T e , t ∼ 18$ eV at the end of the density ramp. The stronger divertor cooling in the JF, with respect to the SN configuration, is supported by divertor spectroscopy.⁵⁷ The temporal evolution and spatial extent of CIII emission indicates that SN SP2 is beginning to detach, while the JF SP2 is already detached, with a movement of the peak emissivity further toward the core. Meanwhile, little CIII emission is observed in the JF far-SOL, indicating $T e < 8$ eV.²⁴ The SF− configuration, similarly to the SN, exhibits an increase in peak target ion flux throughout the density ramp, not shown here. With a peak target temperature starting at 16 eV and decreasing to 11 eV by the end of the density ramp, the two SF− outer strike-points remain under attached conditions, likely ascribed to the configuration's fairly high X-point separation. The results from LPs and divertor spectroscopy suggest an earlier detachment onset in flux tubes with higher connection lengths.

The divertor radiated power (⁠ $P rad , div$⁠) normalized to the power entering the SOL (⁠ $P SOL = P ohm − P rad , core$⁠), shown in Fig. 9, does not indicate any direct correlation to the peak $L | |$ in the JF experiments. Although the radiative power dissipation is not increased in geometries with additional divertor X-points, we recall here the overarching importance of the reduction of peak target heat fluxes, demonstrated for these geometries in Fig. 7, for a well-protected divertor. To study the localized effect of $L | |$ on radiative power losses, as tested in the SOL modeling in Sec. III A, we estimate the radial distribution of radiated power per flux tube. The plasma emissivity in the outer SOL is integrated over the volume between two flux surfaces, separated radially by an upstream distance of $Δ r u ∼ 1.25$ mm, and extended poloidally from the outboard midplane to the connected divertor target—further information in  Appendix B. The radiated power per flux tube, Fig. 10, demonstrates a strong correlation with $L | |$⁠. Similarly, the radiated power per flux tube for the SF− dataset presented in Ref. 11 is also found to be strongly correlated with $L | |$ for attached conditions ( Appendix B). A comparable increase is seen in the experimental radiated power per flux tube and in the SPLEND1D modeling. For an increase in connection length from 25 to 100 m, SPLEND1D predicts 1.4 × (detached conditions) and 3.6 × (attached conditions) increase in radiated power (see Fig. 6), whereas the JF experimental measurements are between 1.6 and 2 × (see Fig. 10).

Experimentally, the JF with higher X-point separation features a radiation region that is broadly spread across the SOL, in the divertor volume rather than at the target. Conversely, the JF with lower X-point separation features stronger peaking near the separatrix, Fig. 10. This is visually observed in the tomographic inversions of plasma emissivity, not shown, and is consistent with the broadened radiation distribution commonly observed in the SOL of the SF− configuration in previous experiments.^24,58 Although the near-SOL radiated power is greater in the JF compared to the reference SN and SF− configurations, as mentioned above, this does not result in an overall increase in divertor radiated power fraction. Here, the SN configuration features a strongly radiating inner strike-point compared to the JF whose intensity increases with core density. This may indicate, or perhaps even drive, a change in in-out power sharing in the JF, which is expected to be dependent on X-point separation and, hence, connection length.²⁶ The JF exhibits between 1.3 and 1.9 times higher peak parallel inner target heat flux than the SN and SF− references. However, the total power (integrated perpendicular heat flux) arriving at the inner target is comparable across the geometries.

Although the correlation of radiated power per flux tube to connection length does not necessarily result in an increase in total divertor radiated power, it does provide a new control over the radial location of the radiation region, with the magnetic configuration an actuator, in addition to e.g., impurity seeding.

Spectroscopic imaging in TCV reveals “finger-like structures” extending across the additional separatrices in the JF configuration. These cross field striations are observed in the raw radiation from multiple spectral lines (HeI, CIII, D_α,…) from the MANTIS diagnostic. Within the camera field of view, the striations are periodically generated in the same poloidal positions for around 600 ms; a snapshot at 1.125 s is shown in Fig. 11. The tomographic inversions of multiple spectral lines measured by MANTIS can be used to infer the distribution of plasma parameters, assuming a calibrated collisional radiative model.^42,43 The inferred electron temperature in the JF, shown in Fig. 12(a), clearly shows the radial striations seen in the raw data. In contrast, both the SN configuration, Fig. 12(b), and the SF− (termed herein SF−_JF) configuration, not shown here, exhibit the more usual monotonic poloidal and radial SOL temperature profiles. The presence of the radial striations in the raw data, Fig. 11, confirms that these are not artifacts of the inversion process.

Multi-spectral imaging data from the SF− discharges presented in Ref. 11 (termed herein SF₁₁) also reveal radial striations in the inter-null region, similar to those seen in the JF. These features were also seen with the fast imaging camera,⁵⁹ in the same location as seen in the MANTIS data, but on a turbulent timescale. It appears that there is an increased localized production of turbulent filaments in the inter-null region that remain visible over the time-scales of the MANTIS system. Note that both imaging diagnostics have the same field of view. The raw data of these imaging diagnostics, in the form of short videos, are provided in the data repository accompanying this work.

These radial striations are similar to the lobes of homoclinic tangles⁶⁰ seen in tokamaks with non-axisymmetric features, such as for toroidal field pertubations induced by RMPs,^61–63 MHD activity, non-axisymmetric currents, or error fields. Such striations are consistently observed across the inter-null region in configurations with multiple X-points if the inter-null separation is sufficiently low. This would be consistent with the increased significance of error fields in regions of low poloidal field. The relatively high X-point separation in the SF−_JF results in a much weaker reduction in the inter-null poloidal field, compared to in the SF−₁₁, which may explain the absence of striations. Further investigation of the impact of these striations is left to future work.

The effect of multiple divertor X-points on divertor-core compatibility has previously yielded mixed results in experiments on TCV,¹¹ both in terms of the core impurity content and energy confinement time. Although the SF− features a radiative region further from the core than in the SN, it does not necessarily see a lower core impurity content.

The core effective charge is defined in the usual manner as $Z eff = Σ i n i Z i 2 n e$⁠, where n_i, Z_i are the density and charge number of each ion species and charge state. $Z eff$ is estimated from $V loop$ measurements and the profile-averaged core T_e measured by TS, assuming steady state conditions and neo-classical conductivity,^64,65 shown in Fig. 13(a) for each configuration. The JF configurations (both X-point separations) recover a similar core effective charge to the SN reference, clearly lower than the SF− reference. This indicates that the increase observed in the SF− is a particular feature of this geometry, rather than an intrinsic property of configurations with multiple divertor X-points.

The energy confinement time, defined as the ratio of plasma stored energy to the input heating power,¹¹ is shown in Fig. 13(b). Each configuration exhibits a similar energy confinement time, within the experimental scatter, differing by $< 5 %$⁠.

This section looks to interpret the experimental results of configurations with multiple divertor X-points using a more complex SOL model that implements kinetic neutrals, diffusive cross field transport and impurity transport, as well as the magnetic geometry, much more realistically than for the simplified SOL modeling presented in Sec. III A. We use the EMC3-EIRENE code for this purpose, extending the SN simulations presented in Sec. II D to the SF− configuration. We first simulate the SF− configuration using the same input parameters as given in Sec. II D to investigate the features that can be accessed through a change in magnetic geometry only, comparing the simulated results with those obtained in experiment (presented in Ref. 11). We then increase the inter-null cross field diffusive transport coefficients to mimic the increased convective and turbulent cross field transport inferred in some previous works, and study the resultant trends in power exhaust and core impurity content. Finally, the divertor impurity characteristics, such as the impurity density and ionization source, are studied to explain the increased core impurity content observed in the SF− configuration.

Simulations of the SF− are first performed with EMC3-EIRENE using the same input parameters as the SN reference, discussed in Sec. II D, including spatially constant diffusive transport coefficients, shown in Table I. Following the expectation that cross field transport differs between the SN and SF− configurations, this first step aims to highlight the effects of magnetic geometry rather than achieve a good match with experimental measurements. Two SF− configurations are compared: one with a relatively low X-point separation, $d r X 2 ∼ 3.0$ mm, close to the heat flux decay width, λ_q, and one with $d r X 2 ∼ 6.6$ mm. Section IV focuses on the lower $d r X 2$ case unless stated otherwise. These simulated scenarios are ohmically heated L-mode with constant core density, $⟨ n e ⟩ l = 4.7 × 10 19 m − 3$—further experimental details can be found in Ref. 11.

Considering the change in magnetic geometry with respect to the SN reference simulations, EMC3-EIRENE is able to recover some, but not all, of the experimental features of the SF−. The secondary strike-point SP4 is activated in the simulations, seen in the plasma density distribution shown in Fig. 14(a). The simulated radiated power distribution, Fig. 15(b), indicates a strong radiation peak around the second separatrix, consistent with the experimentally observed radiation peak at the secondary X-point.¹¹ 

As in the experimental cases reported in Ref. 11, nitrogen seeding was added to the SF− simulations to study the evolution of the radiation region with increasing impurity content. The modeled radiated power, shown in Fig. 15, increases and moves toward the confined region for each configuration with N₂ seeding. Nonetheless, in simulations with and without nitrogen impurities, the SF− maintains a radiation region further from the core than in the SN, consistently with the experimental observations.¹¹ 

Not all of the SF− experimental features are reproduced by the simulations while retaining constant divertor transport. Although the radiated power peaks at the second separatrix in the unseeded case, shown in Fig. 15(b), inter-null radiation is absent and a deficit of impurities in the inter-null region is obtained, Fig. 14(c). TS profiles of electron density, measured vertically across the divertor, indicate that the simulated electron density is under-estimated in the far-SOL, Fig. 16(a). Note that the upstream electron density and temperature (⁠ $Z > − 0.4$ m in Fig. 16) provide a good match to the experimental measurements. Furthermore, target heat flux profiles predict $∼ 2 ×$ lower peak heat flux at SP4 than seen experimentally from LPs, with an overestimation of the heat flux at SP2, Fig. 17. Therefore, the target heat flux distribution between the two active outer targets is not well reproduced, and there is no reduction in peak parallel heat flux with respect to the SN configuration. These transport-related discrepancies are likely ascribable to the unchanged cross field transport coefficients taken from the SN reference.

The diffusive transport is now increased in the entire poloidal extent of the inter-null region, Fig. 18, with $5 ×$ higher particle and heat diffusivities than in the reference case (⁠ $D ⊥ = 0.75 m 2 s − 1 , χ ⊥ , e = χ ⊥ , i = 5.0 m 2 s − 1$⁠). When applied to the main ion species, D⁺, the match between experiment and simulation in the SF− improves. The far-SOL plasma density increases, better matching the TS measurements, shown by the dashed lines in Fig. 16. Furthermore, a stronger redistribution of particles from SP2 to SP4 improves the match to the target heat flux distribution, shown by a dashed line in Fig. 17. When applied to the impurity ion species, C^k+ (⁠ $k ∈ [ 1 , 6 ]$⁠), in addition to D⁺, an increase in inter-null cross field diffusivity fills the inter-null impurity void observed in Fig. 14(c) (not shown), a requirement for a strongly radiating inter-null region. Note that the electron temperature in the divertor region (⁠ $Z < − 0.4$ m) is largely insensitive to changes in cross field transport coefficients, implying weak perpendicular heat transport with respect to that parallel to the magnetic field in these scenarios.

While an increase in diffusive transport in the inter-null region brings the simulations closer to experimental observation, it is clear that further physics is necessary, for example more realistic effective transport coefficients, to fully capture the plasma divertor transport to achieve a quantitative match with experiment. For example, the spatial offset between experiment and simulated results in Figs. 16 and 17 are likely due to the lack of particle drifts in EMC3.^54,66 Nonetheless, a change in transport coefficients in areas other than the inter-null region of the SF− configuration result in unrealistic target heat flux profiles under attached conditions. As such, an increase in the SF− inter-null cross field transport coefficients results in the best qualitative agreement obtained in these simulations. Discrepancies between the simulated and experimental radiated power distribution may be due to an incomplete treatment of neutral interactions in EIRENE or limitations of the trace impurity model in EMC3.

The EMC3-EIRENE simulations of the SF− configuration observe a radiation region that is further from the core than in the SN, described in Sec. IV A. Consistently with experiment,¹¹ this is not accompanied by a reduction in core impurity content. Indeed, modeling actually predicts $∼ 50 %$ higher core-averaged impurity concentration in the SF− compared to the SN.

The impurity sources modeled are intrinsic carbon, sputtered primarily from the targets and HFS baffle, and in some cases also externally seeded nitrogen. For simplicity, we focus on the former case. The impurity neutral density profiles shown in Figs. 19(a) and 19(c) highlight the targets and the HFS baffle as key impurity sources. In the SN configuration, the impurities are then ionized close to the targets, Fig. 19(b). In the SF− configuration, the impurity ionization source is significant in the LFS near-SOL region at the height of the LFS baffle, highlighted by a magenta oval in Fig. 19(d). The increased mean free path of ionization in the SF− configuration compared to the SN is attributed to the strike-point location, with the SF− SP4 located in a much colder region of the SOL than SP2 in the SN configuration. With the ionization source closer to the core than in the SN, we expect a higher probability of core impurity penetration. While the SN appears to have a stronger ionization source in the private flux region compared to the SF−, this does not appear to strongly affect the core impurity content, perhaps due to significant plasma flow in this region, as well as a less direct access to the core plasma.

In EMC3-EIRENE simulations of the SF− configuration with higher $d r X 2$ presented in Ref. 11, we recover the same impurity concentration at the separatrix as for the SN. The simulated ion flux arriving at the far-SOL strike-point (SP4) in this configuration is much lower than for the lower $d r X 2$ case, resulting in a weak neutral impurity sputtering source, and therefore without a strong ionization source near the confined region. This supports the result of the SF− with lower $d r X 2$⁠, where the higher core impurity content is linked to the impurity source location—which could be improved with further optimization—rather than being an intrinsic property of the SF− configuration.

The first configuration with three nearby divertor X-points, named the Jellyfish, has been developed in TCV. The experimental study of this configuration has elucidated the role of additional divertor X-points and high L_|| on power exhaust and divertor-core compatibility. A strong reduction is seen in parallel target heat flux, with an earlier detachment onset compared to a reference SN. Within a given flux tube, a strong correlation is observed experimentally between the local radiated power and connection length. Simplified 1D SOL modeling predicts this localized increase in radiated power with connection length and attributes this to more favorable radiative conditions rather than an increase in radiative volume. While this does not necessarily result in an overall greater divertor radiated power in configurations with enhanced connection length, it does give control over the radial position of the radiation region, that has the potential to help avoiding core radiative collapse. In experimental multi-spectral imaging data, we observe radial striations in configurations with multiple divertor X-points, similar to homoclinic tangles observed in other tokamaks.

The divertor-core compatibility of configurations with multiple divertor X-points is not found to be necessarily worse than a comparable SN, as the SF− study in Ref. 11 indicated. In the present experiments, the energy confinement time is not significantly affected by divertor geometry. Meanwhile, the JF experiments maintain a similar core impurity content to the SN. Although the SF− features a worsened core impurity shielding than the other configurations, in both experiment and simulation, the latter attributes this to the impurity source location rather than an intrinsic property of configurations with multiple X-points. This implies that optimization of the impurity source location may be sufficient to ensure good divertor-core compatibility. Interpretative simulations and comparison with the experiment also support the idea of enhanced cross field transport in the inter-null region of configurations with multiple X-points, but further physics is necessary to achieve a quantitative match between the two approaches.

The detachment onset and divertor-core compatibility in configurations with multiple divertor X-points continue to be studied in TCV, with experiments currently ongoing to attain nitrogen-seeded divertor detachment in the JF configuration and to map the parameter space of the ELM-free H-mode SF−. These works aim to further the physics understanding required for scenario development of the SF− configuration as an alternative divertor solution.

See the supplementary material for the following: divertor imaging data are included in.avi format for the experiments in TCV presented in this article, as well as the SF− experiment presented in Ref. 11. Imaging data from the MANTIS diagnostic are shown for the SN (77067_SN_MANTIS.avi) and the JF (77021_JF_MANTIS.avi) configurations. The data in these videos have been compressed and scaled. Note that the poloidal field of view is mirrored horizontally about the central column with respect to the standard TCV cross section, with the machine LFS on the left of the image. A snapshot of the video in the JF configuration at t = 1.125 s is presented in Fig. 11, and the video further demonstrates the radial striations. Imaging data from the MANTIS diagnostic are also shown for the SF− configuration presented in Ref. 11 (70424_SF-_MANTIS.avi), demonstrating the recurrence of such striations. This is complemented by raw imaging data from the fast imaging camera67 in the same discharge (70424_SF-_Fastcam.avi) that measures the HeI line (587.5 nm). With an exposure time of ∼ 0.01 ms, this system is capable of imaging the plasma on a turbulent timescale. The data in this video have been scaled and are not absolutely calibrated. Note that, unlike the MANTIS data, the images have been mirrored horizontally about the central column. MANTIS and the fast imaging camera both have the same field of view. They image the divertor, part of the central column, and the lower part of the confined region, see Fig. 1(d).

This work was supported in part by the Swiss National Science Foundation. This work has been carried out within the framework of the EUROfusion Consortium, partially funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200-EUROfusion). The Swiss contribution to this work has been funded by the Swiss State Secretariat for Education, Research and Innovation (SERI). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union, the European Commission or SERI. Neither the European Union nor the European Commission nor SERI can be held responsible for them.

The authors have no conflicts to disclose.

Sophie Gorno: Conceptualization (lead); Data curation (equal); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (equal); Project administration (lead); Software (supporting); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Olivier Février: Methodology (supporting); Software (equal); Validation (equal); Writing – review & editing (equal). Christian Theiler: Conceptualization (equal); Project administration (equal); Supervision (lead); Writing – review & editing (equal). Timo Ewalds: Methodology (supporting); Software (lead); Writing – review & editing (supporting). Federico Felici: Conceptualization (equal); Methodology (supporting); Software (equal); Writing – review & editing (supporting). Tilmann Lunt: Software (equal); Supervision (supporting). Antoine Merle: Investigation (equal); Methodology (equal); Software (equal); Writing – review & editing (supporting). Filippo Bagnato: Data curation (supporting); Investigation (supporting); Writing – review & editing (supporting). Claudia Colandrea: Investigation (supporting). Jonas Degrave: Methodology (supporting); Software (equal); Writing – review & editing (supporting). Richard Ducker: Data curation (supporting). Garance Durr Legoupil Nicoud: Writing – review & editing (supporting). Basil P. Duval: Methodology (supporting); Writing – review & editing (equal). Kenneth Lee: Investigation (supporting). Lorenzo Martinelli: Data curation (supporting); Investigation (supporting). Diego Sales Oliveira: Investigation (supporting); Writing – review & editing (supporting). Artur Perek: Data curation (supporting); Formal analysis (supporting); Investigation (supporting); Visualization (supporting). Holger Reimerdes: Investigation (supporting); Writing – review & editing (supporting). Luke Simons: Data curation (supporting); Formal analysis (supporting); Writing – review & editing (supporting). Guangyu Sun: Investigation (supporting). Brendan Tracey: Methodology (supporting); Software (equal); Writing – review & editing (supporting). Marco Wischmeier: Funding acquisition (supporting). Curdin Wüthrich: Data curation (supporting); Visualization (supporting).

The data that support the findings of this study are openly available in Zenodo at http://doi.org/10.5281/zenodo.10496926.

We first attempted to develop a magnetic geometry with three nearby divertor X-points using TCV's conventional control system.^68,69 The method started with a manually driven design of a magnetic equilibrium that employed a suite of tools—Free Boundary Tokamak Equilibrium (FBTE)⁷⁰ and Matrix Generation Algorithm and Measurement Simulation (MGAMS)⁷¹—to calculate poloidal field coil currents from given inputs, such as the number and position of X-points, and boundary points of the confined core region. A set of independent PID controllers was then tuned to control the plasma shape, together with the plasma current and vertical and radial plasma positions. Using this conventional control system, we attempted to develop a geometry with one additional X-point in the LFS SOL and a further X-point in the HFS SOL. However, within this parameter space, no stable configuration was found with the conventional approach. We then applied a novel control architecture recently developed at TCV in collaboration with DeepMind³⁴ that uses deep reinforcement learning to generate non-linear feedback controllers. This technique identified a point in the operational parameter space of TCV encompassing three nearby divertor X-points, with the two additional X-points in the LFS SOL and at a greater distance to the primary X-point. While different from the original target geometry, this novel configuration generated physics interest through its exceptionally high connection length. This highlights the potential for such methods in the design of novel divertor configurations.

The novel deep reinforcement learning architecture outlined in Ref. 34 was used to train a control policy by acting and exploring in a simulated tokamak environment (involving a Forward Grad–Shafranov solver). In this environment, it learns the plasma's reaction to certain actions, while trying to achieve a goal specified using targets and a reward function. The policy is implemented as a simple feed-forward neural network. The targets describe the desired plasma parameters, for example: plasma shape, number and position of X-points, and minimum/maximum inner wall gaps, and are fed into the control policy and training environment. The reward function specifies the tolerance and priority of several objectives and returns a scalar quality measure to the plasma state given the targets. When targeting three nearby divertor X-points, the policy consistently produced a magnetic equilibrium where the two additional divertor X-points are in the LFS common flux region with respect to a SN configuration.

The trained control policy was then deployed on TCV, where it is fed real-time measurements (flux loop, magnetic probe and coil current measurements) and directly outputs voltage commands, inferring the plasma state from measurements without solving real-time equilibria. The first attempt to execute this geometry was successful (No. 74587), with the Jellyfish geometry shown in Fig. 20 held in a reasonably stable state for approximately 1 s.

The JF design in Fig. 20 required further development to be better suited for divertor studies in TCV, as the initial wall gaps were too narrow (leading to an almost limited situation) and the divertor design was not optimized for divertor diagnostic coverage. By assuming that small modifications to the geometry would not substantially affect its vertical stability, it is possible to manually tune the design using the conventional control methods that remain easier to perform and assess. The plasma volume was thus moderately reduced using conventional methods to increase the inner and outer wall gaps. The plasma was also placed downwards within the machine to improve divertor diagnostic coverage. Here, a trade-off arises between vertical stability and data quality (where greater diagnostic coverage improves the data spatial resolution), so a trial-and-error approach was taken to maximize data quality whilst maintaining a long discharge duration—avoiding disruption. In a second step, the additional X-points of the JF configuration were brought radially closer to the primary X-point in order to generate a JF configuration with reduced X-point separation in magnetic-flux space.

Estimates of the radiated power per flux tube allow the study of the radial variation of plasma radiation, enabling the role of geometric properties such as connection length to be explored. Since this work presents geometries with a variation in LFS connection length, we focus on the radiated power in the outer SOL. The SOL is divided into flux tubes of finite width, corresponding to a width of $Δ r u ∼ 2.5$ mm when mapped to the outboard midplane. An illustration of this division is shown in Fig. 21, with the white lines delimiting the flux tubes. The plasma emissivity within each flux tube is then integrated over its volume.

The radiated power per flux tube in the JF experiments is presented in Sec. III C. For the SF− experiments presented in Ref. 11, a strong correlation in radiated power per flux tube with connection length is also seen, Fig. 22.