Accessing the density-free regime with ECRH-assisted ohmic start-up on EAST

Abstract

High plasma density operation is crucial for a tokamak to achieve energy breakeven and burning plasma. However, there is often an empirical upper limit of electron density in tokamak operation, namely, the Greenwald density limit $n_{\mathrm{G}}$, above which tokamaks generally disrupt. Achieving high-density operation above the density limit has been a long-standing challenge in magnetic confinement fusion research. Here, we report experimental results on the Experimental Advanced Superconducting Tokamak (EAST) achieving line-averaged electron density in the range of (1.3 to 1.65) $n_{\mathrm{G}}$, significantly above the typical EAST operational range of (0.8 to 1.0) $n_{\mathrm{G}}$. This is performed with electron cyclotron resonance heating (ECRH)–assisted ohmic start-up and sufficiently high initial neutral density. These experiments are shown to operate in the density-free regime first predicted by a recent plasma-wall self-organization theory. These results suggest a promising scheme for substantially increasing the density limit in tokamaks, a critical advancement toward achieving burning plasma.

Experiments in the density-free regime offer a promising scheme to break through the density barrier toward fusion ignition.

INTRODUCTION

Achieving high plasma density is essential for satisfying the Lawson criterion in magnetic confinement fusion, yet density limits often constrain tokamak performance, potentially leading to disruptive terminations (1). Over decades, understanding and predicting these limits have remained a focal point of fusion research. For the past decades, the Greenwald density limit $n_{\mathrm{G}}\left({\mathrm{m}}^{-3}\right)=I_{\mathrm{p}}\left(\text{MA}\right)\times {10}^{20}/\left[\mathrm{\pi }\mathrm{a}{\left(\mathrm{m}\right)}^2\right]$ has been widely used as an empirical scaling law for the tokamak density limit (1). However, this scaling law does not account for the heating power dependence of the density limit that has been observed in many experiments (2–7) and confirmed by many theoretical models (8–14). For example, the power balance model (8–10) considering impurity radiation effects introduces a modified scaling for the density limit, ${(I_{\mathrm{p}}P/a^4)}^{(4/9)}$, where P is the heating power. This radiative scaling is in better agreement with the tokamak experimental databases compared with the Greenwald density limit [figure 4 of (10)]. Besides, more experiments have exceeded the Greenwald density limit, such as those on T-10 (15), Frascati Tokamak Upgrade (FTU) (16), Doublet III-D (DIII-D) (17), and Madison Symmetric Torus (MST) (18). One common approach to increasing the density limit is pellet fuelling. For instance, Axially Symmetric Divertor Experiment (ASDEX) Upgrade achieved H-mode operation at densities up to about 1.5 $n_{\mathrm{G}}$ using pellet injection in combination with edge localized mode (ELM) mitigation, and DIII-D obtained discharges approaching 1.5 $n_{\mathrm{G}}$ through density profile control enabled by pellet injection and divertor pumping (19, 20).

In the wake of (8–10), a recent plasma-wall self-organization (PWSO) theory was built under the assumption that the primary factors influencing the power balance limits stem from impurity radiation, which is largely controlled by plasma-wall interactions (21). This theory provides important insights into the interaction between plasma dynamics and wall conditions through impurity radiation (21). It shows that there are two attraction basins for the density: the density-limit basin corresponding to a higher target-region plasma temperature and the density-free basin corresponding to a lower target-region plasma temperature, where the density limit moves up to an extremely high value as the target temperature decreases. In particular, the power-dependent scalings of density limit have been derived from this theory and are able to match the experimental results in multiple tokamak devices (22). Besides, a relatively higher density limit is reached in stellarator when the start-up is performed by using higher electron cyclotron resonance heating (ECRH) power (23, 24). This higher density limit might be due to their mode of breakdown at start-up phase: the massive use of ECRH power with high neutral density producing less impurities (8, 21). Both PWSO theory and stellarator results were an incentive to perform experiments in Joint Texas Experiment Tokamak (J-TEXT), which directly validated key aspects of PWSO theory in ECRH-assisted ohmic start-up discharges (25, 26). These experiments demonstrate that increasing ECRH power or prefilled gas pressure enhances the achievable density limit by decreasing impurity radiation and increasing target region plasma temperatures but by remaining in the density limit basin of PWSO theory. Building on the success of these experiments, the EAST tokamak provides a unique platform to extend the validation of the PWSO model. With the tungsten plasma-facing components, the EAST tokamak allows the exploration of PWSO-induced density limits under conditions distinct from those of J-TEXT. Whereas with carbon walls, the chemical sputtering is important, and for tungsten walls, the physical sputtering dominates, which might enable reaching the density-free basin predicted by the PWSO theory.

In this study, we present the EAST experimental results, with a focus on the role of ECRH power and prefilled gas pressure in achieving high-density regimes. Comparative analysis with the PWSO theory is conducted to elucidate the mechanisms underpinning observations and to further refine our understanding of density limits in tokamaks. The EAST experimental results show that increasing the prefilled neutral gas pressure and/or the ECRH power can increase the density limit up to 1.3 $n_{\mathrm{G}}$ to 1.65 $n_{\mathrm{G}}$, while the usual range in EAST is (0.8 to 1.0) $n_{\mathrm{G}}$ (27, 28). The experimental data for density limit $n_{\mathrm{c}}$ and plasma temperature around divertor $T_{\mathrm{t}}$ are consistent quantitatively with the prediction of PWSO theory. Moreover, as expected, these discharges are found to operate in the density-free regime of PWSO theory, which implies that a substantial enhancement in the density limit of tokamaks may be attainable through achieving detachment without actively introducing impurities.

RESULTS

Experimental results

There are two main series of discharges in our experiments (Table 1), namely, the one with varied prefilled neutral gas pressure at a fixed ECRH power and the other with varied ECRH heating powers at a fixed prefilled pressure. We selected a reference discharge #143069 to serve as a point of comparison, which is based on an ECRH-assisted ohmic start-up scenario similar to those reported in references (29, 30). The time history of its key parameters, including total radiation levels, plasma current $I_{\mathrm{p}}$, ECRH power, and line-average electron density $n_{\mathrm{e}}$, are shown in Fig. 1. The line-averaged density, $n_{\mathrm{e}}$, used in this article is measured by the central chord of the vertical interferometers unless otherwise specified. This discharge starts at 0.0 s, with a toroidal magnetic field of 2.5 T, a prefilled gas puffing voltage $V_{\text{gas}}$ of about 3 V with the corresponding number of injected deuterium (D₂) of 6.6 × 10¹⁹, an ECRH power of about 600 kW with the pulse width [0.0 s, 4.5 s], and a plasma current of 250 kA. Hydrogen gas is injected as the working gas, and no other kind of gas or impurity is injected throughout the discharge. During the current plateau period, the gas injection continues until the plasma density limit of about 1.5 $n_{\mathrm{G}}$ is reached. At this point, the plasma density starts to decrease and then rapidly drops to zero, without any prior manifestation of MHD activities. During the whole discharge, the feedback control technique is used to make sure that the time evolution of line-averaged electron density follows the designed path (31). In the following analysis, the density limit, defined as the maximum density immediately reached before the disruption, is taken at the onset of the collapse. The prefilled gas amount is defined as that of the total injected gas before t = 0 s. Other parameters, including the target temperature $T_{\mathrm{t}}$, effective charge number $Z_{\text{eff}}$, and the averaged radiated power, are evaluated as time-averaged values over the interval [5 to 6] s when the plasma is close to the disruption.

Table 1. Summary of key parameters for the density limit discharges analyzed in this study.

The first column lists the shot numbers. $P_{\text{EC}}$ in the second column indicates the applied ECRH power. The third column shows the prefilled gas amount, which is positively correlated with, and controlled by, the applied prefill voltage. The fourth column presents the achieved line-averaged electron density, taken as a measure of the density limit.

Shot number (1430xx)	${\mathit{P}}_{\mathbf{\text{EC}}}$ (kW)	Prefilled gas (D2) amount (1020 molecules)	Density limit (1019 m−3)
64	0	0.66	4.8
69	600	0.66	5.2
73	600	1.0	5.3
74	600	1.37	5.4
75	600	1.73	5.4
77	0	0.66	5.5
79	600	0.66	5.6
80	600	0.66	5.6

Fig. 1. Time histories of key parameters in density limit discharges with varied ECRH power.

$I_{\mathrm{p}}$: plasma current; Z_eff: averaged effective charge number; $P_{\text{EC}}$: injected ECRH power; $V_{\text{gas}}$: voltage applied to control gas puffing, which is positively correlated with the puffed gas amount; $n_{\mathrm{e}}$: line-averaged electron density measured using the central chord of vertical interferometers; Total Rad.: relative intensity of total radiation measured using bolometer.

For discharges with varied prefilled neutral gas and an ECRH power of about 600 kW, the experimental results indicate that the density limit increases with the prefilled gas pressure until saturation (Fig. 2A). This saturation should be attributed to the limited ECRH power, instead of an absolute limit. Higher ECRH power should lead to higher pressure thresholds where saturation occurs, much like the relation between gas pressure threshold and ECRH power during the startup phase (29, 30). This enhancement of density limit is related to the decrease of total radiation power (Fig. 2B) and the higher plasma cleanliness, as indicated by the effective charge number $Z_{\text{eff}}$ (Fig. 2C). The cleanliness of plasma and the enhanced density limit should be mainly influenced by the plasma-wall interaction, which is related to the plasma temperature around the divertor target. This can be inferred from Fig. 2D, which shows that the plasma temperature around the low-outer divertor target is lower when the prefilled gas pressure is higher and the final density limit is higher.

Fig. 2. Relationship between the density limit and several key parameters in discharges with varying prefilled gas pressure levels during the start-up phase and two different ECRH powers.

The density limit $n_{\mathrm{c}}$ is shown as a function of (A) the corresponding particle number of prefilled gas (D₂) with an ECRH power of about 600 kW; (B) the time-averaged relative radiation in time interval (5 to 6 s); (C) the time-averaged effective charge number $Z_{\text{eff}}$; (D) the time-averaged plasma temperature near the lower outer divertor $T_{\mathrm{t}}$. The number label next to each symbol denotes the last two digits of the shot number 1430xx. The horizontal lines in (B) to (D) represent the measurement error bars. a.u., arbitrary units.

For discharges with varied ECRH heating powers and the lowest prefilled gas pressure of all cases, the experimental results indicate that the density limit weakly increases with the ECRH power. For instance, from shot #143064 to shot #143069, density limit increases from 4.9 × 10¹⁹ to 5.2 × 10¹⁹ m⁻³ as the ECRH power increases from 0 to 600 kW; from shot #143077 to shot #143079, density limit increases from 5.5 × 10¹⁹ to 5.6 × 10¹⁹ m⁻³ with the ECRH power increasing from 0 to 600 kW (Fig. 2). The lowest prefilled gas pressure might be the reason for the weak density limit increase, since there would be less amount of gas from the outset available for later density increase. Lower prefilled gas pressure is also known to restrict the upper limit of the accessible density range during start-up, thus even with increased ECRH power, the plasma can only reach relatively lower densities (30). This density limit enhancement is also related to the decrease of total radiation (Fig. 2B), the higher plasma cleanliness (Fig. 2C), and the lower plasma temperature around the low-outer divertor target (Fig. 2D), which can all be attributed to the reduced strength of plasma-wall interaction.

It is noted that shots #143079 and #143069 have identical input parameters yet yield different plasma temperatures around the divertor target or density limit. A similar observation can be made regarding shots #143064 and #143077. These differences may be due to alterations in wall conditions over time (32), because there are several density limit discharges between shots #143064 and #143079, which can have potential impacts on the wall conditions. The successive effective discharges shown in Fig. 3 demonstrate a notable point that the target region plasma temperature $T_{\mathrm{t}}$ and the effective charge number $Z_{\text{eff}}$ decrease with a discharge number, and the density limit $n_{\mathrm{e}}$ increases with a discharge number. This indicates the wall condition is improving with time. Therefore, the above technique improves the density limit, but this improvement is not a simple function of ECRH power and prefilled gas pressure. In addition, the electron density at the separatrix, with its position determined fromequilibrium fitting (EFIT) equilibrium reconstruction (33, 34), remains below 0.75 $n_{\mathrm{G}}$ in all the discharges discussed above.

Fig. 3. Parametric dependence of edge plasma temperature, impurity level, and density limit on ECRH power and prefilled gas voltage in successive effective discharges.

The 3D diagrams displaying (A) the target region plasma temperature $T_{\mathrm{t}}$, (B) the effective charge number $Z_{\text{eff}}$, and (C) the density limit $n_{\mathrm{e}}/n_{\mathrm{G}}$ of successive effective discharges as a function of both ECRH power $P_{\text{EC}}$ and prefilled gas voltage. The black dotted line is the projection of the colored line in the $P_{\text{EC}}$-prefilled gas voltage plane. The number label next to each symbol denotes the last two digits of the shot number 1430xx. The color bar represents the value of $T_{\mathrm{t}}$, $Z_{\text{eff}}$, and $n_{\mathrm{e}}/n_{\mathrm{G}}$. The vertical lines in (A) and (B) represent the measurement error bars.

In summary, these experimental results demonstrate that increasing prefilled gas or/and ECRH power leads to lower plasma temperature around the divertor target and higher density limit well above the Greenwald density limit (Fig. 2D). This enhancement of density limit is related to the improved wall condition. In the following, we will compare the experimental results with the predictions of PWSO theory.

Comparison with PWSO theory

PWSO theory describes the plasma-wall interaction through the relationship between sputtered impurities’ radiation and heating power (21, 25).

PWSO 0D model and comparison

The basic idea of the PWSO theory [section 4.1 of (21)] is that the existence of a time delay in the feedback loop relating impurity radiation and impurity production on divertor/limiter plates yields the following equation in a zero-dimensional (0D) model

$$R_{+}=\mathrm{\alpha }(P-R)$$ (1)

where P is the total input power to plasma, R is the total radiated power, and $R_{+}$ is the delayed radiation power during the next cycle of the feedback loop. The coefficient α quantifies the radiation power $R_{+}$ generated by the impurity produced from the plasma-wall interaction that is proportional to the deposition of the outflow power $(P-R)$ onto the wall targets, which can be modeled as (21, 25)

$$\mathrm{\alpha }=\frac{\mathrm{f}\mathrm{\lambda }}{{\mathit{aD}}_{\perp }{T}_{\mathrm{t}}}I\left(T_{\mathrm{t}}\right){\displaystyle \underset{0}{\overset{a}{\int }}}\mathit{rn}\left(r\right)R_{\text{coe}}\mathrm{d}r$$ (2)

Here, a is the wall radius in unit of meters, n is the electron density in unit of cubic meters, $D_{\perp }$ is the perpendicular diffusion coefficient in unit of square meters per second, $T_{\mathrm{t}}$ is the plasma temperature around the target plate location in unit of electron volts, f is the fraction of the sputtered atoms that reach the main plasma and become ionized at a distance λ inward from the plasma target location, $R_{\text{coe}}$ is the impurity radiation rate coefficient in unit of electron volts per second per cubic meter, and $I\left(T_{\mathrm{t}}\right)$ is an average of the yield function of impurity $Y\left(E\right)$ over the energies of the impinging particles

$$I\left(T_{\mathrm{t}}\right)=\sqrt{\frac{m}{2\mathrm{\pi }{T}_{\mathrm{t}}}}{\displaystyle \underset{0}{\overset{\infty }{\int }}}Y(\frac{{\mathit{mv}}^2}{2}+\mathrm{\gamma }{T}_{\mathrm{t}})\text{exp}\frac{-{\mathit{mv}}^2}{2T_{\mathrm{t}}} \mathrm{d}v$$ (3)

where γ is the total energy transmission coefficient (35), $\mathrm{\gamma }{T}_{\mathrm{t}}$ is a measure of the Debye sheath height, and m is the ion mass. The fixed point of Eq. 1 $R=R_{+}$ corresponds to the PWSO equilibrium, which becomes unstable for α > 1 as predicted from Eq. 1. So the threshold α = 1 establishes an upper radiation density limit

$$n_c=\frac{2D_{\perp }}{f\mathrm{\lambda }{R}_{\text{coe}}}\frac{T_{\mathrm{t}}}{I\left(T_{\mathrm{t}}\right)a}$$ (4)

that can be reached for a ratio of total radiated power to total input power as low as 1/2 (21). There are two density limit basins of PWSO. One is the regime of density limit corresponding to the higher temperature of target, whereas the other is the regime of density freedom corresponding to the lower temperature of target, in particular in machines where the target plates are made of high-Z materials (21, 25). For high–discharge number impurity, such as tungsten, the yield function Y(E) is dominated by the physical sputtering (36). So in the following calculation, the contribution from chemical sputtering is ignored. The empirical formula for Y(E) at normal incidence are provided in equation 15 of (37) for physical sputtering

$$Y_{\text{phy}}\left(E\right)=0.042\frac{Q\left(Z_2\right){\mathrm{\alpha }}^{\ast }(M_2/M_1)}{U_{\mathrm{s}}}\frac{S_{\mathrm{n}}\left(E\right)}{1+\mathrm{\Gamma }{k}_{\mathrm{e}}{\mathrm{ϵ}}^{0.3}}\times {[1-\sqrt{\frac{E_{\text{th}}}{E}}]}^s$$ (5)

where the numerical coefficient 0.042 is in unit of per angstrom squared, $Z_1$ and $Z_2$ are the atomic numbers, $M_1$ and $M_2$ are the masses of the projectile and the target atoms, respectively, $S_{\mathrm{n}}$ is the reduced nuclear stopping cross section, $U_{\mathrm{s}}$ is the surface binding energy of the target solid, $k_{\mathrm{e}}$ is the Lindhard electronic stopping coefficient, E is the projectile energy, $E_{\text{th}}$ is the threshold energy for sputtering, the $\mathrm{\Gamma }$ factor has the form $W\left(Z_2\right)/\left[1+{(M_1/7)}^3\right]$, W and Q are dimensionless fitting coefficients, and $\mathrm{ϵ}$ is the value of the reduced energy in unit of electron volts

$$\mathrm{ϵ}=\frac{0.03255}{Z_1{Z}_2{\left\{Z_1^{2/3}+Z_2^{2/3}\right\}}^{1/2}}\frac{M_2}{M_1+M_2}E\left[\text{eV}\right]$$ (6)

where E[eV] denotes the value of the projectile energy in unit of electron volts.

According to the impurity radiation measured using the extreme ultraviolet (EUV) spectrometer, the main impurities in the plasma include carbon and tungsten, which is sputtered from the divertor target plates. Previous experimental and modeling results demonstrate that carbon is a dominant impurity causing tungsten sputtering in L-mode plasmas on EAST (38, 39). Thus, in the calculation of PWSO model, we consider the sputtering of tungsten by carbon ions. The impurity radiation rate $R_{\text{coe},\mathrm{W}}$ is estimated to be a constant value ${10}^{-30}/(1.602\times {10}^{-19})$ $\text{eV}\cdot {\mathrm{s}}^{-1}\cdot {\mathrm{m}}^3$ based on the simulation results using the FLYCHK code (40). We further assume that the perpendicular diffusion coefficient $D_{\perp }$ of target impurities is 3 m² s⁻¹ (41), and 1% of the sputtered atoms penetrate the main plasma (42), undergoing ionization at a distance λ = 0.01 m away from the target (43). A maximal projectile energy E of 740 keV, well above the thermal energy, is used as the upper limit in the integral in Eq. 3. For these experiments on EAST, the radius a = 0.45 m. With the above EAST parameters, the PWSO 0D model predicts that there are two density limit basins. The EAST experimental results are located in the density-free regime, exceeding the Greenwald density limit (Fig. 4), and are in good agreement with the PWSO 0D model prediction. The decreasing target region plasma temperature $T_{\mathrm{t}}$ with a discharge number (Fig. 3A) also means that EAST is working in the virtuous process of the density freedom basin indicated by the PWSO model [section 4.1 of (21)].

Fig. 4. Experimental and theoretical comparison of the density limit dependence on target region plasma temperature.

The density limits are shown as functions of the target region plasma temperature $T_{\mathrm{t}}$ predicted from the PWSO 0D (solid line) and 1D (dashed line) model in comparison with the experimental data (symbols) for various $V_{\text{gas}}$ and $P_{\text{EC}}$. $V_{\text{gas}}$ represents the gas puffing voltage which is proportional to the prefilled gas amount.

PWSO 1D model and comparison

The PWSO 1D model describes a more detailed evolution of the radiation power and the temperature toward the PWSO equilibrium (21). The impurity density and the plasma temperature evolution are determined from the following 1D transport equations

$${\mathrm{\partial }}_t{n}_i-D{\mathrm{\partial }}_x^2{n}_i=C_i[{\mathrm{\partial }}_{x}T(r_{\text{LCFS}},t-{\mathrm{\tau }}_{\text{delay}})+T_{\text{loss}}^{\prime }]\mathrm{\delta }(x-a+\mathrm{\lambda })$$ (7)

$$n{\mathrm{\partial }}_{\mathrm{t}}T-K{\mathrm{\partial }}_x^{2}T=C_{\mathrm{T}}{T}^{3/2}+P_{\text{add}}-{\mathit{nn}}_{\mathrm{i}}{R}_{\text{coe}}$$ (8)

where $n_{\mathrm{i}}$ is the impurity density, T is the plasma temperature, n is the uniform plasma number density, ${\mathrm{\tau }}_{\text{delay}}$ denotes the propagation time of heat from the LCFS to the targets plus the flight time for sputtered atoms to reach the ionization position, $C_i=-\mathit{\text{faKI}}\left(T_{\mathrm{t}}\right)/\left[(a-\mathrm{\lambda })T_{\mathrm{t}}\right]$ represents the plasma-wall interaction, K is a uniform diffusion coefficient, $C_T=E_0^2/\left[\mathrm{\eta }\left(T\right)T^{3/2}\right]\simeq {6.510}^2{E}_0^2/Z$, with $E_0$ the electric field corresponding to the loop voltage, $\mathrm{\eta }\left(T\right)$ is the transverse Spitzer resistivity, and $P_{\text{add}}$ is the additional power density. For EAST experiments, the transport coefficient $\mathrm{\chi }=K/n=0.5 {\mathrm{m}}^2{\mathrm{s}}^{-1}$ and ${\mathrm{\tau }}_{\text{delay}}$ = 200 ms are assumed. The same parameters as those used in the 0D model are applied to obtain the following results, and the resistivity η is considered to be a constant. Applying the following initial and boundary conditions

$$\begin{array}{cc}{n}_i(t=0)=0;\hfill & T(t=0)=T_0\hfill \\ n_i(x=a)=0;\hfill & {\left.\frac{\mathrm{\partial }{n}_i}{\mathrm{\partial }x}\right|}_{x=0}=0\hfill \\ T(x=a)=T_0;\hfill & {\left.\frac{\mathrm{\partial }T}{\mathrm{\partial }x}\right|}_{x=0}=0\hfill \end{array}$$ (9)

at plasma center x = 0 and edge x = a, the 1D model equations are numerically solved with various number density levels. The density limit is identified when the evolution of radiation power becomes unstable. A relation between the density limit and the target region temperature has been thus obtained and compared with the experimental data as shown in Fig. 4.

The PWSO 1D model gives predictions similar to the PWSO 0D model. The EAST experimental data are located in the density-free basin, as in the case of the 0D model. So, further altering the wall conditions, including increasing the prefilled gas pressure and ECRH power, should result in a cleaner plasma and lower plasma temperature around divertor and lead to a higher density limit.

DISCUSSION

These EAST experiments show that a moderate increase of ECRH power and/or prefilled gas pressure at start-up enhances the density limit at the flat-top phase of discharge. This enhancement of the density limit is related to the lower plasma temperature around the divertor target and can be explained using the PWSO model. Whereas the experimental results on J-TEXT tokamak are found to locate in the density limit basin predicted by the PWSO theory (25), the EAST experimental results are located in the density-free regime, which further validate the PWSO theory and highlight the significance of high-Z materials in the targets for accessing the enhanced density limit and the density-free regime as expected in (21). These experiments demonstrate and validate a practical scheme to raise the density limit, which can be extended and applied to other magnetic confinement fusion devices in the future.

In both EAST and J-TEXT experiments, some discharges with identical prefilled gas pressure and ECRH power at start-up can yield different plasma temperatures around the target, which ultimately leads to different density limits. These differences signify the effect of wall conditions in the high-density discharges. How the varying wall conditions can affect the target region plasma temperature and the corresponding density limit may be used to further validate the PWSO model.

Compared with W7-X (21, 23), which has a plasma volume V = 30 m³, a magnetic field B = 3 T, and a minor radius a = 0.53 m, EAST has V = 9 m³, B = 2.5 T, and a = 0.45 m. The magnetic field B and minor radius a are close for the two machines. Then, it makes sense to compare the injected power per unit volume P/V for EAST and W7-X experiments. One finds respectively P/V = 0.6 MW/9 m³ for EAST and 2 MW/30 m³ for W7-X, which are exactly the same ratio P/V = 1/15 MW/m⁻³. In addition, in W7-X experiments, a density of 2 × 10¹⁹ m⁻³ (an order of magnitude higher than in tokamak breakdown) is reached with a single gas puff, right before injecting waves [section 7 of (21)]. In EAST, almost the same density is reached at the end of the ECRH pulse (Fig. 1), which further increases to about 5 × 10¹⁹ m⁻³. These results demonstrate that tokamaks can operate in a way similar to stellarators and reach likewise a higher density limit. The big difference is in the duration of the pulse: For W7-X, the start-up takes about 100 ms, while it is more than an order of magnitude longer in EAST to reach the same density with ECRH assisted start-up. This is reasonable because a tokamak needs a finite poloidal magnetic field to confine, while the confinement is available in a stellarator from the outset.

Stellarator and tokamak experiments also find that the density limit increases with the heating power during flat top (8, 23, 24, 44). For EAST experiments in this paper, the ECRH power is only up to 600 kW. Together with the predictions of the PWSO theory (Fig. 4), it is expected that higher ECRH power and prefilled gas pressure in EAST experiments might lead to a detached plasma state with a notably higher density limit.

In conclusion, we report on the experimental results on EAST tokamak that have achieved line-averaged electron density in the range of 1.3 to 1.65 Greenwald density limit and our quantitative comparison with the predictions of PWSO theory that shows good agreement. Increasing ECRH power and/or prefilled gas pressure are confirmed to lead to lower plasma temperature around the divertor target and higher density limit at the flat top. The experiments are found to locate in the density-free regime of PWSO model from both 0D and 1D predictions. These results demonstrate the potential of a practical scheme for substantially increasing the density limit in tokamaks, which is also germane to the stellarator start-up. Although ultimately it is the triple product $\mathit{nT}{\mathrm{\tau }}_E$ that governs the fusion ignition condition, the breaking of Greenwald density limit and the successful access to the density-free regime as demonstrated in this work opens a promising path advancing toward achieving the fusion ignition condition.

MATERIALS AND METHODS

Experimental Advanced Superconducting Tokamak

The EAST is a superconducting tokamak with a major radius of R₀ ≤ 1.9 m, a minor radius a ≤ 0.45 m, plasma current I_p ≤ 1 mega-ampere (MA), and toroidal field B_t ≤ 3.5 T (45, 46). Two full tungsten divertors are located at the top and bottom of the toroidal vacuum chamber with full metal walls (47–49). Various wall conditioning techniques, like lithiation (50) and boronization, can be used in experiments. EAST is equipped with an auxiliary heating system with four gyrotrons (51, 52). The working frequency of the ECRH system is chosen to be 105 or 140 GHz, and the second harmonic extraordinary mode (X2) is used for electron heating and current drive (53, 54).

Basic experimental conditions

The experiments in this work are conducted in a lower single null divertor configuration with purely or ECRH-assisted ohmic start-up. The details of ECRH-assisted ohmic start-up can be found in (29, 30). The plasma density is feedback-controlled using gas puffing (27), and the #2 ECRH system is used for auxiliary heating (52). The wall conditioning technique, lithiation (50), is used in our experiments. The typical parameters in EAST experiments are as follows: plasma current I_p of ~250 kA, plasma elongation ratio κ of ~1.5, triangularity δ of ~0.5, and toroidal magnetic field B₀ of ~2.5 T.

Techniques to obtain diagnostic data

The line-averaged density is measured using 3 vertical chord interferometers and 11 horizontal chord polarimeter-interferometers (55, 56). A divertor triple probe system with 16 channels covering different poloidal positions is embedded in the divertor target plates for the measurement of electron temperature $T_{\mathrm{t}}$ and heat flux (57, 58). In the discharges of our experiments, 5 of 16 channels show high values in the 5- to 6-s interval, and $T_{\mathrm{t}}$ is taken as the average over these five channels. The time and space resolved evolutions of radiation are measured using 64 channel absolute extreme ultraviolet photodiode arrays, and the total radiation power is measured using a metal foil resistive bolometer (59, 60). The impurities in the core plasma are monitored with a flat-field EUV spectrometer (61). The effective ion charge $Z_{\text{eff}}$ is measured with the visible bremsstrahlung system (62).

Key parameters for density limit discharges

Table 1 summarizes the set of EAST discharges designed to explore the density limit with varying ECRH power and prefilled D₂ amounts, along with the corresponding achieved density limits.

Calculation of PWSO 1D model

The PWSO 1D model, which consists of an impurity particle transport equation (Eq. 7) and a heat transport equation (Eq. 8), is solved using an implicit finite difference method. The resulting system of linear equations is solved using the Thomas algorithm (tridiagonal matrix algorithm).

Supplementary Materials

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