Carbon Chemist

Tag: Magnetically confined plasmas

  • A high-density and high-confinement tokamak plasma regime for fusion energy

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    Fusion energy is the ultimate energy source for humanity16. A promising approach is a steady-state fusion reactor using magnetic confinement in the tokamak configuration17,18. With a deeper understanding of tokamak plasma physics and the development of reactor-relevant technologies, many fusion reactor designs have been proposed3,4,5,6,7,8,9,10. When the ion temperature is above 13 keV (1.5 × 108 K) in D–T fusion reactions, the thermonuclear power density19 Pfus = nfuel2⟨σv⟩E/4 is proportional to the fuel density (nfuel) squared, as the change of normalized reaction rate ⟨σv⟩ with temperature is relatively small. Here, E is the fusion energy released per reaction. Detailed definitions of all variables mentioned in this paper can be found in Extended Data Table 1. Therefore, to achieve attractive fusion goals, most of the recent fusion pilot plant (FPP) designs require very high plasma densities, higher than the empirical edge density limit known as the Greenwald density11 (nGr), in tokamak high-confinement mode (H-mode) plasmas13. The energy confinement quality, represented by the H-factor20 (for example, H98y2), is believed to be the highest leverage parameter for fusion capital cost8. H98y2 is usually required to exceed the standard H-mode level (H98y2 = 1.0) for good fusion economy. FPP designs3,4,5,6,7,8,9,10 simultaneously require 1 ≤ Greenwald fraction (fGr) ≤ 1.3 and 1 ≤ H98y2 ≤ 1.65. However, such a tokamak operating regime is an uncharted area that has never been verified in experiments.

    The empirical nGr is a density limit for the pedestal density in an H-mode plasma21,22. The pedestal is a narrow region of plasma at the edge with suppressed turbulent transport and a steep pressure gradient. When approaching nGr at the pedestal, various unfavourable phenomena can be observed in experiments. These cause a strong decrease of the confinement quality or even a sudden, complete loss of plasma energy (disruption)22. A peaked core density profile is, therefore, required to achieve a line-averaged density above the pedestal density limit. Possible approaches include relying on the natural peaking at low collisionality23 and the potential inward particle pinch24. The previous DIII-D experiment24 can achieve a transient fGr of about 1.4 with D2 gas puffing. A large pinch velocity has been measured. H98y2 in this case is around 1. ASDEX Upgrade experiments took a different approach by using pellet injection to improve the core fuelling. The experimental results show a transient fGr ≈ 1.5 with pellet injection25,26. However, the H98y2 values in those discharges were less than 1. More examples with H98y2 < 1 at high density are well documented22. As no tokamak experiment has yet attained a sustained fGr above 1 and H98y2 well above 1 (for example, 1.5) at the same time, experimentally verifying the desired operating regime in FPP designs is a great challenge for the magnetic confinement fusion community.

    Another challenge with H-mode reactor plasmas is the very high transient heat load produced by quasi-periodic edge magnetohydrodynamic (MHD) instabilities known as type-I edge-localized-modes (ELMs). Without control, ELMs in a reactor can severely damage plasma-facing-components, for example, the first wall27,28. ELM control is an active research area and various approaches have been proposed29,30,31,32,33. However, compatibility among small/no ELM solutions, high density (above nGr) and high confinement quality (H98y2 well above 1, for example, 1.5) has not been demonstrated in experiments.

    We report a new experimental approach for achieving a line-averaged density above nGr. It exploits an operating regime recently established in the DIII-D tokamak that allows simultaneous fGr > 1.0, H98y2 ≈ 1.5 and small ELMs and could support many existing designs for future reactors3,4,5,6,7,8,9,10. The approach elevates the plasma density in the core while keeping the pedestal fraction of the Greenwald density at moderate levels (for example, fGr,ped ≈ 0.7), thus not violating the empirical density limit. It does so by exploiting self-organized internal transport barriers (ITBs) at large minor radius in the high poloidal-beta (βP) scenario15,34,35,36. More information about the high-βP research can be found in Methods. In experiments, the on-axis fraction of the Greenwald density (fGr,0) can reach up to 1.7, resulting in a line-averaged fGr of 1.3. ITBs in the density and temperature profiles also greatly improve the energy confinement quality (H98y2 up to 1.8), compared to the standard H mode (H98y2 = 1) at the same engineering and operating parameters.

    Figure 1 shows a plot of the DIII-D database and illustrates the progress made in extending the plasma operating space towards high fGr and high H98y2. The 2019 high-βP experiments with impurity injection15 have simultaneously achieved fGr > 1.0 and H98y2 > 1.0. However, in these experiments, too much impurity injection also increases the radiative energy loss in the plasma core, limiting H98y2 at high density. Of the violet diamonds in Fig. 1, some have H98y2 ≤ 1.2 when fGr ≥ 1.15. However, these results are not good enough for FPP designs. A major improvement in the 2022 DIII-D high-βP experiment used additional D2 gas puffing (Fig. 2) instead of impurity injection. This approach effectively reduces the core radiation and improves H98y2, as shown in Fig. 1 (blue squares). Thus, this paper reports a clear experimental demonstration of an accessible operating point in an existing tokamak that can meet a few of the FPP requirements, including simultaneous fGr > 1 and H98y2 ≈ 1.5. For comparison, other scenarios presented run on DIII-D have not achieved such simultaneous normalized performance (yellow circles).

    Fig. 1: Database of H98y2 and fGr for DIII-D discharges.
    figure 1

    More than 3,600 discharges are included. Violet diamonds show high-βP experiments performed in 2019 with impurity injection. Blue squares are the new high-βP experiments performed in 2022 without impurity injection. Yellow circles represent all other experiments performed in 2019–2022. The area shaded in orange indicates the parameter space for attractive FPP designs. Vertical and horizontal dashed lines show fGr = 1.0 and H98y2 = 1.0, respectively.

    Fig. 2: Time history of experimental parameters and plasma profiles of DIII-D 190904.
    figure 2

    a, fGr in blue and H98y2 in green. b, βN in blue, βP in green and q95 in violet. c, D2 gas puffing in feedback control in black and dedicated feedforward D2 gas puffing in vermillion. d, Peak pedestal electron density gradient in blue and pedestal total pressure in vermillion. e, Separatrix electron density in green and ratio between pedestal electron density and separatrix electron density in violet. f–i, Profiles of electron temperature (f), ion temperature (g), electron density (h) and carbon density (i) at the time slices shown in the vertical dashed lines in a. Dots with error bars are measurements. j–l, Dα data for the three periods shown in the shaded area in d. a.u., arbitrary units. m–o, Total pressure profiles at the time slices of the vermillion dots in d.

    Figure 2 shows detailed data from an example discharge (190904) in 2022. The striking feature in this discharge is the dynamic synergy between energy confinement quality and plasma density. That is, H98y2 increased along with fGr (Fig. 2a) until the ramping down of the heating power (Extended Data Fig. 1e). This is opposite to the common observation of reduced energy confinement quality in higher density H modes22, especially for experiments close to the Greenwald density. The plasma was maintained at fGr > 1.0 and H98y2 > 1.0 for about 2.2 s, which was 2.2 times the current diffusion time (τR) or 24 times the energy confinement time (τE). Thus, the high normalized density and confinement phase was not transient, which is imperative for application in future long-pulse FPPs. A normalized plasma pressure βN ≈ 3.5 and βP ≈ 2.9 was achieved at safety factor q95 ≈ 8.5 (Fig. 2b) with plasma current Ip = 0.73 MA and toroidal magnetic field BT = 1.89 T, and with mixed co- and counter-Ip neutral beam injection (NBI). Note that nGr = 6.7 × 1019 m−3 in this discharge, close to the Greenwald density of the ITER 9 MA steady-state scenario at 7.2 × 1019 m−3. The dedicated D2 gas puffing time trace is shown in vermillion in Fig. 2c. This approach ensures that there is a sufficient source of particles in the plasma, and it pushes the plasma density to a higher level, regardless of the change in the feedback gas (black line in Fig. 2c).

    Profiles of the temperature and density for electrons, deuterium (main ion) and carbon (main impurity) are shown in Fig. 2f–i and Extended Data Fig. 2a. The evolution of the on-axis densities for electrons, deuterium and carbon is displayed in Extended Data Fig. 1c. One can see that ITBs developed in all density channels. The increased deuterium density in this experiment suggests the promising application of this scenario in future FPPs, as it can attain a higher fuel density to give a higher fusion power. A related piece of experimental evidence is shown in Extended Data Fig. 1d. It is clear that with increased plasma density and energy confinement, the neutron rate, an indicator of fusion performance, increased substantially (67% higher, from 0.6 × 1015 to 1.0 × 1015 s−1) from 2 to 4.8 s, whereas the injected power (blue line in Extended Data Fig. 1e) was almost constant. Moreover, a very mild increase of the radiated power was observed in the very-high-density phase of the experiment (Extended Data Fig. 1e). The core radiated power as a fraction of the injected power increased from 10% to 20% as fGr increased from 0.7 to 1.1. The edge radiation remained about 25% of the injected power. Note that for either Bremsstrahlung radiation or impurity line emission, the radiated power was roughly proportional to the electron density squared. Therefore, some increase in the radiated power was expected even with the same impurity level, when the plasma density was increased significantly. Regarding the impurity behaviour, one can see a well-developed ITB at large radius in the carbon density profiles (Fig. 2i). Despite the ITB at large radius, the carbon density inside the ITB did not have a significant central peak, which would usually cause a large amount of core radiation and a reduction of core performance. The ratio between carbon density and electron density stayed around 4–5% during the evolution (Extended Data Fig. 2b). This is consistent with the well-controlled radiated power in the phase with fGr > 1.0.

    The evolution of the safety factor profile (q-profile) is shown in Extended Data Fig. 2c. The figure shows the self-organized q-profile evolution, which reflects the change of the local bootstrap current density associated with the development of a large-radius ITB. The local minimum q (qmin) in the outer half of the plasma was at ρ ≈ 0.6 for around 2τR. qmin in this discharge stayed above 2.

    When a density ITB built up over time and was sustained, the total pedestal pressure at ρ = 0.88 did not change significantly (Fig. 2d). However, other pedestal parameters and the ELM behaviour changed. At fGr < 0.8, typical standard H-mode pressure profiles and typical large type-I ELMs were observed (Fig. 2j,m). At 0.8 ≤ fGr < 1.0, pressure profiles with an ITB and compound ELMs emerged (Fig. 2k,n). Finally, pressure profiles with a large ITB and small ELMs dominated the fGr ≥ 1.0 phase (Fig. 2l,o). During the evolution, a decreased peak pedestal electron density (ne,ped) gradient, increased separatrix electron density (ne,sep) and decreased ratio between ne,ped and ne,sep were observed, as shown in Fig. 2d,e. These parameter evolutions are consistent with the favourable conditions needed to access the small-ELM regime discussed in the literature29. A more detailed modelling analysis of the pedestal for different ELM behaviours will be discussed later in this paper.

    Although addressing the transient heat load is crucial, mitigating the stationary heat load is equally important for an FPP. Divertor detachment is widely considered to be a necessary solution for realizing an acceptable stationary heat load in the operation of future FPPs. Even without detachment-oriented impurity seeding, Extended Data Fig. 3 shows that the electron temperature at the divertor plates (Te,div) clearly reduced from over 35 eV (before 1.8 s) to 20–25 eV (1.8–2.8 s) and finally to 10–15 eV (after 2.8 s) in the fGr > 1.0 and H98y2 ≈ 1.5 phase, and there were small ELMs. The lowest Te,div phase is consistent with the existence of an ITB at large radius. Although Te,div ≤ 15 eV is not yet considered as divertor detachment (usually Te,div < 10 eV), it already suggests that there would be mitigation of tungsten erosion under the experimental stationary heat load, if a tungsten wall had been used. Note that although the integration of full divertor detachment and high-confinement core has been achieved in previous DIII-D high-βP experiments and reported15,37, the experimental approach and the operating parameter space were both different. The previous results used impurity seeding and fGr ≈ 0.9, which are not sufficient for FPP designs.

    Therefore, the analysed typical DIII-D high-βP discharge has demonstrated a sustained, accessible operating point in a present tokamak that integrates high normalized density and confinement quality, small ELMs and reduced divertor electron temperature, thus addressing the key requirements of FPP designs for simultaneous high-performance core and excellent core-edge integration.

    To understand the physics that enables high confinement quality at high normalized density, we performed a gyro-fluid transport analysis using the TGLF code38 on the experimental data from the discharge shown in Fig. 2. Figure 3a,b shows the dependence of the normalized electron turbulent heat flux Qe/QGB (where QGB is the Gryo-Bohm heat flux) on the fractional contribution of the density gradient to the pressure gradient (Fp = T∇n/∇p) at mid-minor radius in the plasma. The gyro-fluid modelling indicates that when using either numerical approach to vary Fp (constant ∇T or constant ∇p), the decreasing trend of Qe for increasing Fp is robust. A similar result was obtained for the ion energy transport. These results reveal an important feature in the high-βP scenario, namely that anomalous turbulent transport, which leads to poor global confinement, can be reduced with a high density gradient, that is, a high density in the core with the pedestal density maintained below nGr. This is consistent with the experimental observation of synergy between high confinement quality and high density. If Fp were increased by 30%, the normalized Qe would decrease by a factor of 2 compared with the prediction at the experimental value, when the normalized pressure gradient αMHD (approximately −q2/BT,unit2Rdp/dr) was moderate (1.13), as shown in Fig. 3a. However, the reduction of the transport can be 2–3 orders of magnitude stronger when αMHD is high (2.75) in the experimental equilibrium (Fig. 3b). Note that this finding is also consistent with the previous nonlinear gyro-kinetic theoretical modelling39, which found an extreme reduction in the transport coefficient when high αMHD was combined with moderate density gradients. The underlying physics includes 1) the low drive of the ion-temperature-gradient turbulence at high density gradient (that is, there is a low ratio between the density gradient scale length and the ion temperature scale length (ηi)), and 2) less effective coupling between trapped electrons and the trapped-electron-mode turbulence owing to the much narrower turbulence eigenfunction at high αMHD.

    Fig. 3: Transport modelling of the dependence of normalized electron turbulent heat flux on the normalized electron density gradient.
    figure 3

    a, Moderate αMHD case from the high-βP discharge in Fig. 2. Fp scan with the constant ∇p approach in blue and with the constant ∇T approach in vermillion. The experimental (Exp.) value of Fp is indicated by the black arrow. b, High αMHD case from the high-βP discharge in Fig. 2. Same colour coding as in a. c,d, Temperature (c) and density (d) profiles for the low-q95 H-mode case analysed in e and f. Dashed lines show the radial location for transport analysis. e,f, Two-dimensional scans of normalized electron turbulent heat flux on Fp and local q based on the low-q95 H-mode data shown in c and d. Full experimental βe (e) and half experimental βe (f). The experimental data point from the low-q95 discharge is indicated by a blue star in e.

    We also applied the same gyro-fluid transport analysis to a standard H-mode discharge to reveal the requirement for realizing the favourable conditions for low transport at high density. A low-q95 standard H-mode discharge (DIII-D 187019) with strong D2 gas puffing and high density was investigated. Compared with the high-βP discharge discussed above, this discharge had the same heating power (9 MW), comparable line-averaged density (5.0–6.5 × 1019 m−3), slightly lower βN (approximately 2.5), but much lower q95 (4 versus 8.5). This was because of a much higher Ip (1.3 versus 0.73 MA). Typical standard H-mode profiles are shown in Fig. 3c,d, which are different from the ITB profiles in Fig. 2. Figure 3e presents the transport analysis of a two-dimensional scan on Fp and local q at ρ = 0.65. The modelling uses the experimental βe value. As illustrated by the horizontal dashed lines, the figure can be roughly divided into three regimes. At low local q, such as for the standard H-mode experimental data point, the modelling predicts high turbulent transport at high Fp. This is consistent with the experimental observation of decreased H98y2 at high density in this discharge. At medium q, transport is predicted to be almost independent of Fp. Finally, low transport at high Fp can be found in the high-q regime (top right corner of this figure highlighted by the blue dashed line). This example suggests that a minimum of the local q ≈ 4.4 is required to access this regime. Note that the analysed high-βP case has local q ≈ 5.1. However, high local q alone is insufficient to access this regime. Figure 3f indicates the importance of sufficient βe, or the plasma pressure (β). Note that β changes accordingly in the modelling when scanning βe. The range of the two-dimensional scan is the same. However, this scan uses half of the experimental βe in the modelling. As one can see, the results are significantly different. For most of the q values in the scan, high turbulent transport at high Fp is predicted. The favourable low transport at high Fp may still exist but probably requires very high local q, which is less realistic in present tokamak experiments or future machine designs.

    In summary, the transport analysis suggests that the standard H-mode could access the favourable low-transport regime at high density, with the following necessary conditions: high local q and high plasma pressure β, which are two key components in the expression of αMHD. Thus, sufficient αMHD is essential for realizing the favourable operating regime. As summarized in the literature15,37,40, α-stabilization is considered as the primary turbulence suppression physics in the high-βP scenario, as it provides a reactor-relevant rotation-independent mechanism for high confinement40. On the other hand, given that βP ∝ βNq95, high q95 and high βN lead to high βP. Therefore, the high-βP scenario is naturally an excellent candidate for pursing this goal.

    We performed a pedestal analysis to evaluate the pedestal stability and understand the evolution of the ELM behaviour in the high-βP discharge described in Fig. 2. The ELITE calculations41 shown in Fig. 4a predict the stability boundary for peeling–ballooning modes in the pedestal, for each of the three ELM states. In the type-I ELM state, the pedestal lies near the unstable ballooning region. Evolving to the small-ELM state, the experimental point moves along the ballooning boundary towards a lower pedestal pressure gradient and lower pedestal current density. Moving further away from the peeling boundary is consistent with the observation of no giant ELMs in the later phase. Modelling with BOUT++ (refs. 42,43,44) provides details on the instability growth rate in Fig. 4b. The dominant low-n peeling–ballooning mode was identified at n ≈ 10, which agrees with the ELITE result. The predicted low-n growth rate is smallest for small ELMs. BOUT++ modelling also resolves high-n resistive ballooning modes near the separatrix, when considering the plasma resistivity. It is clear that the high-n separatrix modes are dominant in the small-ELM case in contrast to other results in Fig. 4b. The modelling suggests that the high-n separatrix modes played an essential role in the observation of small ELMs in high-βP plasmas.

    Fig. 4: Pedestal modelling of the three types of ELM behaviours in DIII-D 190904.
    figure 4

    a,b, Results for the type-I ELM in blue, the compound ELM in green and the small ELM in violet. a, Pedestal stability versus normalized pedestal current density (y axis) and normalized pressure gradient at the pedestal peak gradient location (x axis). jmax, jsep and ⟨j⟩ are the maximum pedestal current density, the current density at the separatrix and the average current density in the pedestal region, respectively. Stability boundaries are shown as solid lines. Experimental points are indicated as open squares with error bars. b, Linear mode growth rate (normalized by Alfvén frequency, ωA) at different toroidal mode numbers.

    In this paper, we have extended the operating space of a tokamak plasma towards a regime with simultaneous fGr up to 1.25 and H98y2 ≈ 1.3–1.8, using the high-βP scenario in DIII-D. The achievement of entering this previously uncharted regime provides essential support to many attractive FPP designs all over the world. The increased deuterium density and neutron rate in the experiment confirm the promising application of this scenario for higher fusion performance in future FPPs. Unlike many previous high-density H-mode experiments, the high-βP scenario uniquely features a synergy between high confinement quality and high density, especially around the Greenwald value. We have also elucidated the important role of α-stabilization in this achievement, showing that the favourable regime of low turbulent transport at high density is predicted and achieved only at relatively high local q and high β, namely for sufficient αMHD at high βP. This successful experiment not only addresses a few of the key requirements on FPP core plasma parameters but also suggests a potential solution for core-edge integration by demonstrating sustained small ELMs together with fGr > 1.0 and H98y2 > 1.0. Realizing the small-ELM regime is understood as a combination of the reduced growth rate of low-n modes and the predominance of the high-n resistive ballooning mode near the separatrix because of the decreased peak density gradient in the pedestal, increased separatrix density and high βP. During the natural small-ELM phase with a high normalized density and confinement, the plasma is close to divertor detachment, which is believed to be the most promising solution for achieving steady-state plasma–wall-interactions in FPPs37,45. The natural proximity of detachment conditions shows the potential of a fully integrated scenario with high-performance core and cool edge. As the divertor detachment was not optimized in the discussed experiment, doing so will be important work for future experiments. Note that the compatibility of the high-βP scenario with full divertor detachment has been demonstrated37. So far, neither a significant central peak in the density profile of the impurity (carbon) nor a significant increase in the core radiated power has been observed when the density is above the Greenwald value. Dedicated impurity transport experiments and modelling work are also under consideration for this operating regime. Fast-particle confinement is important for future FPPs. Experiments on the high-βP scenario in DIII-D usually exhibit classical fast-ion transport. More discussion of previous results is presented in ‘DIII-D high-βP experiments’ (Methods).

    We fully appreciate that further work is needed to address other critical issues related to FPP compatibility, for example, operating with a metal wall and helium exhaust. On DIII-D, limited experiments with high-βP plasmas operating with a divertor strike point on a (temporary) ring of tungsten tiles have shown promising results, with no significant degradation of core performance. However, to fully address the compatibility with a metal wall, we are collaborating closely with the Experimental Advanced Superconducting Tokamak (EAST) and Korea Superconducting Tokamak Advanced Research programme in the development of high-βP scenarios so that we can exploit their metal wall and long-pulse operation capabilities. Long-pulse operation (over 10 s) will further address the alignment for steady-state q-profiles and pressure profiles with ITB in the high-βP scenario. With regard to the helium exhaust, several review papers give favourable conclusions for high-βP plasmas with ITBs in JT-60U46,47. The results for JT-60U high-βP ITB plasmas show that the helium density in the core was controlled well and that no helium accumulation was observed, even with helium NBI for the core helium source. Moreover, the results also emphasize the importance of helium exhaust techniques, such as pumping, for controlling the helium content in the core.

    Furthermore, there has been recent activity on extending the high-βP scenario towards true long-pulse operation, including modelling work for EAST48, ITER49,50 and FPPs under design10. Depending on the design philosophy of each group, the high-βP scenario can be applied in a wide range of FPP designs, from large conventional tokamaks14 to relatively small and compact devices9,10. One example from CAT-DEMO (Case D)9 shows a possible design point of an FPP using the high-βP scenario: R = 4 m, R/a = 3.1, BT = 7 T, Ip = 8.1 MA, q95 = 6.5, fGr = 1.3, fGr,ped = 1.0, βN = 3.6, H98y2 = 1.51, fusion gain Q = 17.3 and output electric power 200 MWe. The experimental achievement and the increased understanding reported in this paper may open a potential avenue to an operating point for producing economically attractive fusion energy.

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  • Avoiding fusion plasma tearing instability with deep reinforcement learning

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    DIII-D

    The DIII-D National Fusion Facility, located at General Atomics in San Diego, USA, is a leading research facility dedicated to advancing the field of fusion energy through experimental and theoretical research. The facility is home to the DIII-D tokamak, which is the largest and most advanced magnetic fusion device in the United States. The major and minor radii of DIII-D are 1.67 m and 0.67 m, respectively. The toroidal magnetic field can reach up to 2.2 T, the plasma current is up to 2.0 MA and the external heating power is up to 23 MW. DIII-D is equipped with high-resolution real-time plasma diagnostic systems, including a Thomson scattering system45, charge-exchange recombination46 spectroscopy and magnetohydrodynamics reconstruction by EFIT37,39. These diagnostic tools allow for the real-time profiling of electron density, electron temperature, ion temperature, ion rotation, pressure, current density and safety factor. In addition, DIII-D can perform flexible total beam power and torque control through reliable high-frequency modulation of eight different neutral beams in different directions. Therefore, DIII-D is an optimal experimental device for verifying and utilizing our AI controller that observes the plasma state and manipulates the actuators in real time.

    Plasma control system

    One of the unique features of the DIII-D tokamak is its advanced PCS47, which allows researchers to precisely control and manipulate the plasma in real time. This enables researchers to study the behaviour of the plasma under a wide range of conditions and to test ideas for controlling and stabilizing the plasma. The PCS consists of a hierarchical structure of real-time controllers, from the magnetic control system (low-level control) to the profile control system (high-level control). Our tearing-avoidance algorithm is also implemented in this hierarchical structure of the DIII-D PCS and is integrated with the existing lower-level controllers, such as the plasma boundary control algorithm39,41 and the individual beam control algorithm40.

    Tearing instability

    Magnetic reconnection refers to the phenomenon in magnetized plasmas where the magnetic-field line is torn and reconnected owing to the diffusion of magnetic flux (ψ) by plasma resistivity. This magnetic reconnection is a ubiquitous event occurring in diverse environments such as the solar atmosphere, the Earth’s magnetosphere, plasma thrusters and laboratory plasmas like tokamaks. In nested magnetic-field structures in tokamaks, magnetic reconnection at surfaces where q becomes a rational number leads to the formation of separated field lines creating magnetic islands. When these islands grow and become unstable, it is termed tearing instability. The growth rate of the tearing instability classically depends on the tearing stability index, Δ′, shown in equation (2).

    $${\varDelta }^{{\prime} }\equiv {\left[\frac{1}{\psi }\frac{{\rm{d}}\psi }{{\rm{d}}x}\right]}_{x=0-}^{x=0+}$$

    (2)

    where x is the radial deviation from the rational surface. When Δ′ is positive, the magnetic topology becomes unstable, allowing (classical) tearing instability to develop. However, even when Δ′ is negative (classical tearing instability does not grow), ‘neoclassical’ tearing instability can arise due to the effects of geometry or the drift of charged particles, which can amplify seed perturbations. Subsequently, the altered magnetic topology can either saturate, unable to grow further48,49, or can couple with other magnetohydrodynamic events or plasma turbulence50,51,52,53. Understanding and controlling these tearing instabilities is paramount for achieving stable and sustainable fusion reactions in a tokamak54.

    ITER baseline scenario

    The ITER baseline scenario (IBS) is an operational condition designed for ITER to achieve fusion power of Pfusion = 500 MW and a fusion gain of Q ≡ Pfusion/Pexternal = 10 for a duration of longer than 300 s (ref. 12). Compared with present tokamak experiments, the IBS condition is notable for its considerably low edge safety factor (q95 ≈ 3) and toroidal torque. With the PCS, DIII-D has a reliable capability to access this IBS condition compared with other devices; however, it has been observed that many of the IBS experiments are terminated by disruptive tearing instabilities19. This is because the tearing instability at the q = 2 surface appears too close to the wall when q95 is low, and it easily locks to the wall, leading to disruption when the plasma rotation frequency is low. Therefore, in this study, we conducted experiments to test the AI tearability controller under the conditions of q95 ≈ 3 and low toroidal torque (≤1 Nm), where the disruptive tearing instability is easy to be excited.

    However, in addition to the IBS where the tearing instability is a critical issue, there are other scenarios, such as hybrid and non-inductive scenarios for ITER12. These different scenarios are less likely to disrupt by tearing, but each has its own challenges, such as no-wall stability limit or minimizing inductive current. Therefore, it is worth developing further AI controllers trained through modified observation, actuation and reward settings to address these different challenges. In addition, the flexibility of the actuators and sensors used in this work at DIII-D will differ from that in ITER and reactors. Control policies under more limited sensing and actuation conditions also need to be developed in the future.

    Dynamic model for tearing-instability prediction

    To predict tearing events in DIII-D, we first labelled whether each phase was tearing-stable or not (0 or 1) based on the n = 1 Mirnov coil signal in the experiment. Using this labelled experimental data, we trained a DNN-based multimodal dynamic model that receives various plasma profiles and tokamak actuations as input and predicts the 25-ms-after tearing likelihood as output. The trained dynamic model outputs a continuous value between 0 and 1 (so-called tearability), where a value closer to 1 indicates a higher likelihood of a tearing instability occurring after 25 ms. The architecture of this model is shown in Extended Data Fig. 1. The detailed descriptions for input and output variables and hyperparameters of the dynamic prediction model can be found in ref. 5. Although this dynamic model is a black box and cannot explicitly provide the underlying cause of the induced tearing instability, it can be utilized as a surrogate for the response of stability, bypassing expensive real-world experiments. As an example, this dynamic model is used as a training environment for the RL of the tearing-avoidance controller in this work. During the RL training process, the dynamic model predicts future βN and tearability from the given plasma conditions and actuator values determined by the AI controller. Then the reward is estimated based on the predicted state using equation (1) and provided to the controller as feedback.

    Figure 4b–d shows the contour plots of the estimated tearability for possible beam powers at the given plasma conditions of our control experiments. The actual beam power controlled by the AI is indicated by the black solid lines. The dashed lines are the contour line of the threshold value set for each discharge, which can roughly represent the stability limit of the beam power at each point. The plot shows that the trained AI controller proactively avoids touching the tearability threshold before the warning of instability.

    The sensitivity of the tearability against the diagnostic errors of the electron temperature and density is shown in Extended Data Fig. 2. The filled areas in Extended Data Fig. 2 represent the range of tearability predictions when increasing and decreasing the electron temperature and density by 10%, respectively, from the measurements in 193280. The uncertainty in tearability due to electron temperature error is estimated to be, on average, 10%, and the uncertainty due to electron density error is about 20%. However, even when considering diagnostic errors, the trend in tearing stability over time can still be observed to remain consistent.

    RL training for tearing avoidance

    The dynamic model used for predicting future tearing-instability dynamics is integrated with the OpenAI Gym library55, which allows it to interact with the controller as a training environment. The tearing-avoidance controller, another DNN model, is trained using the deep deterministic policy gradient56 method, which is implemented using Keras-RL (https://keras.io/)57.

    The observation variables consist of 5 different plasma profiles mapped on 33 equally distributed grids of the magnetic flux coordinate: electron density, electron temperature, ion rotation, safety factor and plasma pressure. The safety factor (q) can diverge to infinity at the plasma boundary when the plasma is diverted. Therefore, 1/q has been used for the observation variables to reduce numerical difficulties42. The action variables include the total beam power and the triangularity of the plasma boundary, and their controllable ranges were limited to be consistent with the IBS experiment of DIII-D. The AI-controlled plasma boundary shape has been confirmed to be achievable by the poloidal field coil system of ITER, as shown in Extended Data Fig. 3.

    The RL training process of the AI controller is depicted in Extended Data Fig. 4. At each iteration, the observation variables (five different profiles) are randomly selected from experimental data. From this observation, the AI controller determines the desirable beam power and plasma triangularity. To reduce the possibility of local optimization, action noises based on the Ornstein–Uhlenbeck process are added to the control action during training. Then the dynamic model predicts βN and tearability after 25 ms based on the given plasma profiles and actuator values. The reward is evaluated according to equation (1) using the predicted states, and then given as feedback for the RL of the AI controller. As the controller and the dynamic model observe plasma profiles, it can reflect the change of tearing stability even when plasma profiles vary due to unpredictable factors such as wall conditions or impurities. In addition, although this paper focuses on IBS conditions where tearing instability is critical, the RL training itself was not restricted to any specific experimental conditions, ensuring its applicability across all conditions. After training, the Keras-based controller model is converted to C using the Keras2C library58 for the PCS integration.

    Previously, a related work17 employed a simple bang-bang control scheme using only beam power to handle tearability. Although our control performance may seem similar to that work in terms of βN, it is not true if considering other operating conditions. In ITER and future fusion devices, higher normalized fusion gain (G ∝ Q) with stable core instability is critical. This requires a high βN and small q95 as \(G\propto {\beta }_{{\rm{N}}}/{q}_{95}^{2}\). At the same time, owing to limited heating capability, high G has to be achieved with weak plasma rotation (or beam torque). Here, high βN, small \({q}_{95}^{2}\) and low torque are all destabilizing conditions of tearing instability, highlighting tearing instability as a substantial bottleneck of ITER.

    As shown in Extended Data Fig. 5, our control achieves a tearing-stable operation of much higher G than the test experiment shown in ref. 17. This is possible by maintaining higher (or similar) βN with lower q95 (4 → 3), where tearing instability is more likely to occur. In addition, this is achieved with a much weaker torque, further highlighting the capability of our RL controller in harsher conditions. Therefore, this work shows more ITER-relevant performance, providing a closer and clearer path to the high fusion gain with robust tearing avoidance in future devices.

    In addition, the performance of RL control in achieving high fusion can be further highlighted when considering the non-monotonic effect of βN on tearing instability. Unlike q95 or torque, both increasing and decreasing βN can destabilize tearing instabilities. This leads to the existence of optimal fusion gain (as G ∝ βN), which enables the tearing-stable operation and makes system control more complicated. Here, Extended Data Fig. 6 shows the trace of RL-controller discharge in the space of fusion gain versus time, where the contour colour illustrates the tearability. This clearly shows that the RL controller successfully drives plasma through the valley of tearability, ensuring stable operation and showing its remarkable performance in such a complicated system.

    Such a superior performance is feasible by the advantages of RL over conventional approaches, which are described below.

    1. (1)

      By employing a ‘multi-actuator (beam and shape) multi-objectives (low tearability and high βN)’ controller using RL, we were able to enter a higher-βN region while maintaining tolerable tearability. As shown in Extended Data Fig. 5, our controlled discharge (193280) shows a higher βN and G than the one in the previous work (176757). This advantage of our controller is because it adjusts the beam and plasma shape simultaneously to achieve both increasing βN and lowering tearability. It is notable that our discharge has more unfavourable conditions (lower q95 and lower torque) in terms of both βN and tearing stability.

    2. (2)

      The previous tearability model evaluates the tearing likelihood based on current zero-dimensional measurements, not considering the upcoming actuation control. However, our model considers the one-dimensional detailed profiles and also the upcoming actuations, then predicts the future tearability response to the future control. This can provide a more flexible applicability in terms of control. Our RL controller has been trained to understand this tearability response and can consider future effects, while the previous controller only sees the current stability. By considering the future responses, ours offers a more optimal actuation in the longer term instead of a greedy manner.

    This enables the application in more generic situations beyond our experiments. For instance, as shown in Extended Data Fig. 7a, tearability is a nonlinear function of βN. In some cases (Extended Data Fig. 7b), this relation is also non-monotonic, making increasing the beam power the desired command to reduce tearability (as shown in Extended Data Fig. 7b with a right-directed arrow). This is due to the diversity of the tearing-instability sources such as βN limit, Δ′ and the current well. In such cases, using a simple control shown in ref. 17 could result in oscillatory actuation or even further destabilization. In the case of RL control, there is less oscillation and it controls more swiftly below the threshold, achieving a higher βN through multi-actuator control, as shown in Extended Data Fig. 7c.

    Control of plasma triangularity

    Plasma shape parameters are key control knobs that influence various types of plasma instability. In DIII-D, the shape parameters such as triangularity and elongation can be manipulated through proximity control41. In this study, we used the top triangularity as one of the action variables for the AI controller. The bottom triangularity remained fixed across our experiments because it is directly linked to the strike point on the inner wall.

    We also note that the changes in top triangularity through AI control are quite large compared with typical adjustments. Therefore, it is necessary to verify whether such large plasma shape changes are permitted for the capability of magnetic coils in ITER. Additional analysis, as shown in Extended Data Fig. 3, confirms that the rescaled plasma shape for ITER can be achieved within the coil current limits.

    Robustness of maintaining tearability against different conditions

    The experiments in Figs. 3b and 4a have shown that the tearability can be maintained through appropriate AI-based control. However, it is necessary to verify whether it can robustly maintain low tearability when additional actuators are added and plasma conditions change. In particular, ITER plans to use not only 50 MW beams but also 10–20 MW radiofrequency actuators. Electron cyclotron radiofrequency heating directly changes the electron temperature profile and the stability can vary sensitively. Therefore, we conducted an experiment to see whether the AI controller successfully maintains low tearability under new conditions where radiofrequency heating is added. In discharge 193282 (green lines in Extended Data Fig. 8), 1.8 MW of radiofrequency heating is preprogrammed to be steadily applied in the background while beam power and plasma triangularity are controlled via AI. Here, the radiofrequency heating is towards the core of the plasma and the current drive at the tearing location is negligible.

    However, owing to the sudden loss of plasma current control at t = 3.1 s, q95 increased from 3 to 4, and the subsequent discharge did not proceed under the ITER baseline condition. It should be noted that this change in plasma current control was unintentional and not directly related to AI control. Such plasma current fluctuation sharply raised the tearability to exceed the threshold temporarily at t = 3.2 s, but it was immediately stabilized by continued AI control. Although it is eventually disrupted owing to insufficient plasma current by the loss of plasma current before the preprogrammed end of the flat top, this accidental experiment demonstrates the robustness of AI-based tearability control against additional heating actuators, a wider q95 range and accidental current fluctuation.

    In normal plasma experiments, control parameters are kept stationary with a feed-forward set-up, so that each discharge is a single data point. However, in our experiments, both plasma and control are varying throughout the discharge. Thus, one discharge consists of multiple control cycles. Therefore, our results are more important than one would expect compared with standard fixed control plasma experiments, supporting the reliability of the control scheme.

    In addition, the predicted plasma response due to RL control for 1,000 samples randomly selected from the experimental database, which includes not just the IBS but all experimental conditions, is shown in Extended Data Fig. 9a,b. When T > 0.5 (unstable, top), the controller tries to decrease T rather than affecting βN, and when T < 0.5 (stable, bottom), it tries to increase βN. This matches the expected response by the reward shown in equation (1). In 98.6% of the unstable phase, the controller reduced the tearability, and in 90.7% of the stable phase, the controller increased βN.

    Extended Data Fig. 9c shows the achieved time-integrated βN for the discharge sequences of our experiment session. Discharges until 193276 either did not have the RL control applied or had tearing instability occurring before the control started, and discharges after 193277 had the RL control applied. Before RL control, all shots except one (193266: low-βN reference shown in Fig. 3b) were disrupted, but after RL control was applied, only two (193277 and 193282) were disrupted, which were discussed earlier. The average time-integrated βN also increased after the RL control. In addition, the input feature ranges of the controlled discharges are compared with the training database distribution in Extended Data Fig. 10, which indicates that our experiments are neither too centred (the model not overfitted to our experimental condition) nor too far out (confirming the availability of our controller on the experiments).

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