Disruption prediction and mitigation strategies in the EHL-2 spherical torus

1.   Introduction

A major disruption is a global instability in a tokamak plasma that leads to an uncontrolled termination of the plasma discharge. During a disruption, the thermal quench (TQ) phase results in the rapid loss of most of the plasma’s stored thermal energy, causing excessive heat loads that could potentially melt the divertor wall material. This is quickly followed by the current quench (CQ) phase, where the rapid decay of the plasma current induces significant electromagnetic forces due to the generation of eddy currents. Furthermore, halo currents arising from vertical plasma displacements impose additional mechanical stress on the first wall structure. The generation of runaway currents during the current quench is another critical issue since these currents can strike the first wall, potentially leading to severe damage and affecting its operational lifetime. These disruptions are particularly concerning for large devices such as EHL-2, a next-generation spherical torus designed by ENN to study proton-boron (p-¹¹B) fusion reactions [1, 2]. The name EHL stands for ‘ENN He-Long’, which literally means ‘Peaceful Chinese Loong’.

EHL-2 is designed to operate with plasma currents of up to 3 MA and can hold thermal energy approaching 3.3 MJ. To protect EHL-2 from excessive thermal loads and electromagnetic forces associated with plasma disruptions, effective mitigation strategies are essential to ensure its safe operation. A key aspect of disruption mitigation lies in the precise prediction of these events before they occur, enabling the timely activation of the disruption mitigation system (DMS) to minimize potential damage to EHL-2. Data-driven neural networks have been successfully employed for disruption prediction in smaller spherical tokamaks, such as EXL-50 [3] and EXL-50U, both designed by ENN. Due to the limited data set of disruptive discharges resulting from EHL-2’s low tolerance to unmitigated disruptions, a promising strategy involves learning disruptive patterns from these existing tokamaks and applying this knowledge to EHL-2.

The vacuum vessel and internal components of EHL-2 are designed to endure the maximum anticipated halo and eddy current forces. However, the maximum pessimistic energy impact factor far exceeds the melting threshold of the divertor plate materials, underscoring the urgency of active disruption mitigation for thermal loads. Among the various methods available for disruption mitigation, the injection of a large amount of impurity into the plasma before a disruption is a leading technique. This approach, which aims to increase the plasma core density, dissipates energy more evenly, thereby reducing the overall impact of the disruption. For EHL-2, two primary DMS candidates are massive gas injection (MGI) and shattered pellet injection (SPI). It is critical to evaluate the DMS characteristics, including the response time, applicability and overall performance, to determine their feasibility in mitigating electromagnetic force and thermal loads associated with plasma disruptions on EHL-2.

The outline for the rest of this paper is as follows. Section 2 describes impact estimates associated with disruptions on EHL-2. Section 3 presents the performance requirements for the disruption prediction system, along with the details of disruption prediction strategies for EHL-2. Section 4 discusses the characteristics of the disruption mitigation system on EHL-2. Finally, section 5 provides the discussion and conclusion.

2.   Impacts associated with disruptions in the EHL-2 spherical torus

EHL-2 aims to explore the potential of a novel compact p-¹¹B nuclear fusion reactor based on a high-field, spherical tokamak design. The primary target parameters of the EHL-2 physical design are listed in table 1 as follows: the plasma major radius is 1.1 m, the plasma minor radius is 0.61 m, the maximum central toroidal magnetic field strength is 3 T, the plasma toroidal current is 3 MA, the target thermal energy during high-confinement mode (H-mode) operation is 3.3 MJ. Although the physics underlying disruptions is complex, the approximate magnitudes of key characteristics relevant to disruption dynamics, such as time scales, electromagnetic force and thermal loads, can be estimated using empirical and physical scaling laws, as shown in table 2. These estimates facilitate a deeper understanding that informs and optimizes the device’s engineering design.

Table  1.  The main design parameters of EHL-2 spherical torus.

R (m)	$a$ (m)	$\kappa$	Ip (MA)	Bt (T)	W (MJ)
1.1	0.61	2.27	3	3	3.3

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Table  2.  The main characteristic parameters of unmitigated thermal quench and current quench in the EHL-2 spherical torus.

Disruption characteristic parameters	Values
Minimum current quench time	4.8 ms
Minimum thermal quench time	0.1 ms
Axisymmetric vertical force by halo current	4.05 MN
Eddy current force on single inboard tile	10.3 kN
Eddy current torque on single inboard tile	0.5 kN·m
Maximum energy impact factor	400 MJ·s−0.5·m−2

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2.1   Estimate of thermal loads

In an unmitigated major disruption, thermal loads on EHL-2 arise from the thermal energy released during the thermal quench phase of the disruption. The duration of the thermal quench tends to increase roughly in proportion to the plasma minor radius, according to scaling laws derived from current tokamaks [4]. Given the minor radius of a = 0.61 m, the thermal quench duration τ_tq on EHL-2 is estimated to be in the order of 0.1 ms.

The target thermal energy on EHL-2 during H-mode operation is 3.3 MJ, and it is assumed pessimistically that all thermal energy is lost during the thermal quench phase. During steady-state operation, the characteristic heat flux width of the EHL-2 divertor is approximately λ ~ 6 mm, and under a symmetric X-point configuration, the total wetted area on the divertor target plates is about 0.33 m². During the thermal quench, the thermal load will be distributed over a significantly larger area, typically ranging from 5 to 10 times the wetted area of the divertor under steady-state operation. For this calculation, we assume the lower limit of 5 [5]

Therefore, the average thermal loads on the divertor target plates can be estimated as 2 MJ·m⁻². Considering the dominant n = 1 toroidal asymmetry that may exist during the thermal quench, the peak heat flux at the most impacted point could be twice the average value, leading to maximum energy loads of approximately Q_max $\simeq$ 4 MJ/m². Assuming that the heat flux remains constant during the thermal quench, the maximum energy impact factor can be estimated as,

In the most pessimistic case, the maximum energy impact factor significantly exceeds the melting thresholds of tungsten and carbon-fiber composites (CFC), which are 40 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$ and 48 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$, respectively [6]. This would undoubtedly cause significant damage to the divertor target plates.

2.2   Estimate of electromagnetic forces

During the current quench phase of a disruption, significant electromagnetic (EM) force is generated. This force arises from halo currents generated during vertical displacement events (VDEs) and from the rapid decay of plasma current, which induces eddy currents in the first wall structure. While the vacuum vessel experiences the greatest force from halo currents, the first wall is more significantly impacted by eddy currents, which induce poloidal force on its support structures.

In the 2007 ITER Physics Basis (IPB) [7], the minimum current quench time, ${\tau }_{\mathrm{c}\mathrm{q}}$, normalized by the cross-sectional area in the database, is bounded by 1.8 ms·m⁻²:

where $a$ is the minor radius and $\kappa$ is the elongation, with the values shown in table 1. Based on the scaling law, the minimum current quench time for EHL-2 is found to be 4.8 ms. The magnitude of the forces resulting from eddy currents and halo currents can be estimated using some simple zero-dimensional (0D) models.

The maximum assumed halo current is ${I}_{\mathrm{h}\mathrm{a}\mathrm{l}\mathrm{o}}= 0.5{I}_{\mathrm{p}}= 1.5\;\mathrm{M}\mathrm{A}$, with a toroidal magnetic field of 3 T and a poloidal path length of 0.9 m. The total electromagnetic force on the vacuum vessel caused by the halo current is calculated to be 4.05 MN based on the following equation:

In addition, the eddy current circulating in a discrete component generates radial currents that interact with the toroidal field, producing the following force [8]：

and torque

Here, $w$ represents the component’s dimension perpendicular to the wall, Δθ and Δϕ spanned by the component, and R_c is the major radius at which the component is mounted. Taking the first-wall tiles on the inboard side as an example, with $w=0.02\;\mathrm{m}$, $\Delta \theta =$ 0.36 and $\Delta \phi \cdot {R}_{\mathrm{c}}=0.05\;\mathrm{m}$, the resulting poloidal force is 10.3 kN and the corresponding torque is 0.5 kN·m. It is evident that the vertical forces from halo currents have a more significant impact on the vacuum vessel compared to the influence of eddy currents on the first-wall components. However, we should bear in mind that these are only order-of-magnitude estimates; more precise calculations of the vertical and lateral forces could be conducted in DINA simulations, with detailed information of the coil system, vacuum vessel and in-vessel components. This, in turn, will help accelerate the iterative engineering design process.

2.3   Estimate of runaway electrons

The generation of runaway electrons could be significant during disruptions on EHL-2. Experimental results from the KSTAR device indicate that approximately 80% of the initial plasma current can be converted into runaway current during a disruption [9]. Similarly, the conversion rate of initial plasma current to runaway current reaches up to 60% in JET [10], and the ASDEX-Upgrade (AUG) also shows a conversion rate as high as 50% during disruptions [11]. Moreover, research shows that the magnitude of runaway current during disruptions is approximately linear with the size of the devices [12]. Therefore, for the EHL-2 spherical torus, with plasma current of up to 3 MA, a runaway electron beam of 2 MA could be generated during a disruption.

3.   The disruption prediction strategies on EHL-2

A qualitative estimation of the potential hazards posed by disruptions on EHL-2 has been made, demonstrating that the mitigation of disruptions is essential to ensure the safe operation of the machine. The successful disruption mitigation heavily depends on the reliability of disruption prediction. However, the complexity of the disruption causes and the non-linearity of evolvement still make it impracticable to give a quantitative prediction of impending disruption based on the first-principles approach. Recently, data-driven neural networks have been used in many devices for disruption prediction, such as JET [13], ASDEX [14], DIII-D [15, 16], Alcator C-Mod [17], JT-60U [18, 19], EAST [20, 21] and J-TEXT [22, 23].

To evaluate the performance of the disruption mitigation system on EHL-2, three key metrics are employed. The first is the warning time, defined as the interval between the alarm triggered by the prediction system and the actual occurrence of a disruption. The second metric is the number of correct predictions, quantified by the true positive rate (TPR). The third metric assesses the number of false alarms, measured by the false positive rate (FPR).

Since it is challenging to predict disruptions with limited disruptive cases on EHL-2, a promising approach would be to explore transfer learning techniques to integrate models developed from existing experimental data to EHL-2. To this end, data-driven models have been successfully employed to predict disruptions on EXL-50U, the existing device used to support the physics design of EHL-2 [24, 25]. Neural network models and disruption databases are currently being established on EXL-50U, with the disruption databases serving as a reference for the EHL-2 spherical torus. The goal is to learn from the disruptive patterns observed on EXL-50U and apply this knowledge to the EHL-2 case, even with a limited number of disruptive discharges.

3.1   The database and architecture of neural network

To estimate the risk of impending disruptions in advance, only real-time measured diagnostics are utilized. Table 3 presents the signals used for the predictive model, along with their sampling rates. Thirteen signals serve as input features for predicting disruptions, most of which are associated with the underlying causes of disruptions, such as locking modes, density limit, radiation limit and vertical displacement events, while others are basic plasma control signals.

Table  3.  Signals used as the input features in the CNN-LSTM model.

Quality	Symbol	Sampling rate
Radiation at the core (a.u.)	AXUV016	1 kHz
Radiation at the edge (a.u.)	AXUV001	1 kHz
Soft-X radiation at the core (a.u.)	SXR016	1 kHz
Soft-X radiation at the edge (a.u.)	SXR001	1 kHz
Plasma current (kA)	Ip	1 kHz
Reference plasma current (kA)	Ip	1 kHz
Plasma density (1017 m−2)	ne	1 kHz
Current of toroidal field coil (kA)	Itf	1 kHz
Vertical displacement (cm)	Zp	1 kHz
${B}_{\theta }$ probe, toroidal array ($\phi ={0} {\text{°}}$)	MIR073	20 kHz
${B}_{\theta }$ probe, toroidal array ($\phi ={90} {\text{°}}$)	MIR077	20 kHz
${B}_{\theta }$ probe, toroidal array ($\phi ={180} {\text{°}}$)	MIR081	20 kHz
${B}_{\theta }$ probe, toroidal array ($\phi ={270} {\text{°}}$)	MIR085	20 kHz

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The Long Short-Term Memory (LSTM) network, a specialized type of Recurrent Neural Network (RNN), is designed to learn time correlations, enabling it to focus on the temporal evolution of the input signals and provide earlier warnings of potential disruptions. In this study, we integrate convolutional neural network (CNN) and LSTM to develop a state-of-the-art model. A sketch of the hybrid CNN-LSTM model architecture is shown in figure 1.

Figure  1.  Sketch of the CNN-LSTM hybrid model architecture. For Mirnov data with dimensions of (200, 4), we apply 32 sliding convolutional filters of size (20, 4). Filter size of 20 acts as a window function to extract frequency information from the signals, while the size of 4 captures mode information from the toroidal positions. Output from the CNN has dimensions of (10, 32). This output is then concatenated with other input features, which have dimensions of (20, 10), resulting in a combined feature set of (20, 42). This combined feature set is fed into the LSTM network, which consists of three layers of LSTM units, each with 32 units.

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Four toroidal Mirnov probes are utilized to detect the m/n = 2/1 tearing mode, as mode locking is the most frequent early indicator. The Mirnov signals have a resolution of 20 kHz, while other diagnostic signals have a resolution of 1 kHz. To accommodate the multi-dimensional nature of these input signals, the network architecture is designed to process and merge data effectively before feeding it into the LSTM for sequential analysis.

For Mirnov signals, a CNN utilizing 32 sliding convolutional filters is employed to reduce dimensionality and extract key features. Additional input features are concatenated with the CNN output to create a unified feature representation. The combined feature set is then passed to the LSTM network, which consists of three layers of LSTM units, each with 32 units. These layers are designed to analyze temporal dependencies and capture sequential patterns crucial for prediction tasks. The main hyper-parameters used in the CNN-LSTM model are presented in table 4.

Table  4.  The main hyper-parameters used in the CNN-LSTM model.

Hyper-parameters	Values
Number of CNN layers	1
Number of CNN filters per layer	32
Kernel size of CNN	(20,4)
Strides of CNN kernel	(20,1)
Number of LSTM layers	3
Number of LSTM units per layer	32
Batch size	128
Learning rate	0.001
Activation function	ReLU
Optimizier	Adam
Loss function	Cross-entropy loss

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The model is designed for sequence-to-label prediction, where a binary label (disruptive or non-disruptive) is assigned to each input plasma sequence with a duration of 10 ms. Time sequences occurring within 150 ms of a disruption event (t_disrupt–t < 150 ms) are labeled as disruptive, while all other time sequences are labeled as non-disruptive. The CNN-LSTM model is trained to learn a functional mapping from the input plasma sequences to these binary labels, enabling it to classify sequences based on the likelihood of an impending disruption.

The database consists of 1043 discharges, which is split into training (70%), validation (15%) and test (15%) data sets. The distribution of disruptive and non-disruptive discharges within each data set is presented in table 5. The training data set is utilized to optimize the model parameters by minimizing the loss function while the validation data set is utilized to select the best predictive model. Finally, the test data set serves as an independent benchmark to assess the model’s generalization ability on unseen data.

3.2   The performance requirements of the disruption prediction system on EHL-2

The performance requirements of the disruption prediction system must be thoroughly evaluated to ensure the demands of disruption mitigation on EHL-2. First, a high true positive rate is required to accurately predict the disrupted discharges before the warning time on EHL-2. The criteria for the recall rate (true positive rate) can be given as,

where R_tol is the ratio of disruption that can be allowed or tolerated without mitigation, and R_dis is the natural disruption rate [26]. In addition, to minimize the interruptions to successful discharges, the false alarm rate should not exceed 50% of the natural disruption rate.

On EHL-2, a low tolerance of 1% is required, and the minimum required TPR and the maximum allowable FPR are expressed as a function of the natural disruption rate, as shown in figure 2. Considering a natural disruption rate of 10%, a high TPR ($\geqslant$ 90% ) is required, along with an FPR (< 5% ). To ensure the model’s performance on EHL-2, it is essential that the model performance requirements are achieved on EXL-50U as a foundation for knowledge transfer training.

Figure  2.  Blue line indicates the required minimum value of TPR with tolerance of 0.01, while the red line indicates the maximum allowable value of FPR.

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The CNN-LSTM model has been trained using the dataset presented in table 5, with the receiver operating characteristic (ROC) curve shown in figure 3. The area under the curve (AUC) value of the CNN-LSTM model is 0.943. Notably, the optimal point on the ROC curve, characterized by a TPR of 83.3% and an FPR of 5.5%, has been identified. This point is particularly significant since it maximizes the F0.5 score, a weighted harmonic mean of precision and recall, to 0.862. For experimental machines like the EHL-2 spherical torus, where it is critical to avoid interrupting the machine during a successful plasma discharge, the F0.5 score is preferred since it places more emphasis on precision than recall.

Table  5.  Distribution of disruptive and non-disruptive discharges in training, validation and test datasets.

Category	Training	Validation	Test	Total
Disruption	272	63	48	383
Non-disruption	457	94	109	660
Total	729	157	157	1043

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Figure  3.  ROC curve of EXL-50U on the test dataset, and the star indicates the optimal point.

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To successfully mitigate the thermal quench on EHL-2, the disruption mitigation system must be triggered at least 24 ms before the onset of disruption. This accounts for the thermal time (less than 1 ms), the computation time for a single forward pass of the CNN-LSTM model (less than 3 ms on the CPU) and the time delay between activation and initiation of the mitigated TQ (10–20 ms). As a precaution, the warning time for the EHL-2 trigger should exceed the minimum requirement, which has been increased to 30 ms. The advance warning time distributions given by the CNN-LSTM model on the test data set are shown in figure 4. It is noteworthy that warnings of most disruptions (above 83%) predicted by the model are given more than 30 ms in advance. However, the optimal TPR and FPR achieved by the CNN-LSTM model are still far short of the requirements for EHL-2, considering a natural disruption rate of 10%. The results suggest that additional data sets, model fine-tuning and the incorporation of advanced feature engineering are necessary to enhance the model’s predictive accuracy and achieve the desired performance standards.

Figure  4.  Cumulative distribution of disruption warning times for the test data set using the CNN-LSTM model on EXL-50U. Fraction of disruptions detected by time X corresponds to the percentage of disruptions in the test data set that were successfully predicted at least X ms before the disruption. Dashed line represents the minimum warning time required for effective disruption mitigation.

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3.3   The considerations of knowledge transfer to EHL-2

For disruption predictions on EHL-2, the disruptive discharges are insufficient for training due to the low tolerance to unmitigated disruptions ($R_{\mathrm{t}\mathrm{o}\mathrm{l}}\leqslant1\%$). To overcome the insufficiency of disruptive cases, a potential approach is to learn the disruptive patterns from existing tokamaks, such as EXL-50U, and transfer the knowledge to the cases on EHL-2 using a limited number of disruptive discharges.

Cross-device training has been explored in several previous works. A Fusion Recurrent Neural Network (FRNN) was trained with a combination of discharges from DIII-D and a ‘glimpse’ of discharges from JET, achieving high accuracy in predicting disruptions for JET [27]. A Hybrid Deep-Learning (HDL) architecture utilized 20 disruptive and thousands of non-disruptive discharges from EAST, combined with over a thousand discharges from DIII-D and Alcator C-Mod, enhancing disruption prediction performance for EAST [28]. In addition, an adaptive disruption predictor was developed based on extensive databases of AUG and JET discharges, successfully transferred from AUG to JET, achieving a 98.14% success rate for mitigation and a 94.17% success rate for prevention [29]. A deep parameter-based transfer learning method in disruption prediction was used on the J-TEXT tokamak and transferred to EAST with only 20 discharges [30]. The results demonstrate that the proposed method is expected to contribute to predicting disruptions in new machines with knowledge learned from existing tokamaks with different configurations.

Mixing data from both the target machine and existing machines presents the first issue to be addressed in standardizing input data. To facilitate transfer learning from the disruption model of the EXL-50U tokamak to the EHL-2 spherical torus, it is essential to standardize the input data across different devices. For example, density can be normalized by the Greenwald density limit, radiation signals by the total input power, vertical displacement by the minor radius, and magnetic signals by the poloidal magnetic field.

Another challenge is the difficulty of labeling across different devices due to the varied disruption triggers and device conditions. To address the challenges of overfitting and overconfidence caused by the inaccurate labeling across machines, a technique called cross-machine label smoothing (CMLS) was proposed to account for uncertainty by manually modifying the target value with the hyper-parameter smoothing parameters [31]. While label smoothing helps prevent overconfident predictions by encouraging small logit gaps and tolerance for uncertainty [32], CMLS is limited by its use of uniform smoothing parameters across all instances within the same machine. To improve upon this, an instance-specific label smoothing method has been proposed on EXL-50, assigning disruption risk based on learned patterns [3]. This approach uses knowledge-rich predictions from a teacher model to guide a student model, combining soft labels with hard labels for misclassified instances, leading to a more accurate and reliable labeling process.

4.   Disruption mitigation strategies on EHL-2

To address the impact of disruptions on EHL-2, the disruption mitigation system (DMS) is designed with three primary objectives: to reduce thermal loads on the plasma-facing components (PFCs) during the thermal quench, to minimize electromagnetic forces during the current quench, to suppress or mitigate the formation of runaway electrons. While the vacuum vessel and all internal components are designed to withstand the highest expected halo and eddy current forces, the maximum energy impact factor significantly exceeds the melting threshold of the PFC material. This underscores the critical importance of mitigating heat loads for the safe operation of EHL-2.

When triggered by the alarm of the CNN-LSTM model, the DMS system will inject a large number of impurities to increase the radiation and rapidly shut down the plasma. Successful and effective disruption mitigation is crucial for ensuring the safe operation of EHL-2. Therefore, it is necessary to study the characteristics of the disruption mitigation system, including its response time, applicability and overall mitigation performance.

4.1   Disruption mitigation techniques

The disruption mitigation system aims to mitigate disruptions by injecting a large number of impurities into the plasma, with two injection technologies currently under consideration: MGI and SPI. MGI works by injecting impurities as a high-pressure gas pulse using a fast valve into the plasma through the delivery tube. The objective of rapid shutdown using MGI is to dissipate the stored thermal and magnetic energy of the plasma by enhancing the radiation fraction over the entire surface of the first wall. This method has been successfully demonstrated on numerous devices [33–38].

On EHL-2, it might be challenging for the injected gas to reach deeper plasma due to high-pressure gradients. To address this challenge, another injection technology, SPI, has also been considered. SPI works by injecting frozen pellets that shatter upon entering the plasma. These pellets, created by condensing impurity gas into solid form, are propelled into the plasma using high-pressure gas. Upon impact with a bent tube or strike plate, the pellets break apart, allowing the solid fragments to penetrate deeper into the plasma due to their greater momentum and reduced diffusion compared to gas. This enables SPI to deliver the cooling material more effectively to regions with higher plasma density and steep gradients, providing more efficient disruption mitigation.

SPI was first applied in 2009 on the DIII-D tokamak to increase the depth of impurity injection for mitigating disruptions [39]. This demonstrated that SPI, using similar quantities of neon, provided a faster and stronger density perturbation and higher neon assimilation, which resulted in a lower conducted energy to the divertor and a quicker onset of thermal quench. Subsequently, JET [40, 41], KSTAR [41], HL-2A [42] and J-TEXT [43] developed their own SPI systems, and numerous significant results through experiments utilizing SPI have been achieved on these facilities.

An essential design consideration for the DMS is the time delay between DMS triggering and the onset of the mitigated thermal quench, commonly known as the response time. For MGI, the response time is influenced by gas flow in the delivery tube and cooling duration. It depends on several factors, including gas species, plasma thermal energy, minor radius, edge safety factor (q₉₅) and distance between valve and plasma edge, all of which vary between different tokamaks. On EHL-2, the speed of neon gas jet is assumed to be about 500–600 m/s [44], with a delivery tube length of 1–2 m, resulting in flight times of less than 4 ms. Furthermore, the scaling law indicates that the normalized cooling duration (t_cool/a/q₉₅) depends on the thermal energy normalized to the number of injected particles [45]. An empirical cooling duration on EHL-2 is estimated to be 3–5 ms, assuming that 10²² neon atoms are injected at the time of the thermal quench.

In the case of SPI, this includes both the flight time from the injector to the plasma and the time required for assimilation and MHD growth. Typically, pellets are gas-accelerated using room temperature low-Z gas, with their velocities well described by the ideal gas gun formula [46]. The pellets could achieve velocities of 300–600 m/s, depending on the tube length, pellet mass, and propellant gas [47] . Given that the distance from the injector to the plasma is 3–4 m, the corresponding flight time would be under 13 ms. In addition, simulations have indicated that SPI’s faster mixing rate can significantly shorten the TQ onset time in ITER [47].

4.2   Thermal quench mitigation

According to previous estimates in the worst case, the energy impact factor far exceeds the melting thresholds for tungsten and CFC. We can further relax the restriction on thermal quench energy flux by considering that not all the plasma thermal energy is lost at the beginning of the thermal quench, with 1.65 MJ as an approximation here. This results in a maximum thermal energy impact factor on the divertor target plates of ∆Q_max ~ 200 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$. In addition, if there is toroidal rotation of the dominant mode phase during the thermal quench, it would average out the toroidal asymmetry of the heat flux, leading to a more optimistic energy impact factor estimate of ∆Q_max ~ 100 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$. The estimated thermal quench energy loads are nearly twice the melting thresholds for tungsten and CFC, indicating that the energy loads on the divertor must be reduced at least by a factor of 2.

The energy impact on the divertor during thermal quench could be mitigated by the massive gas injection of a noble gas into the confined plasma. The gas ionizes in the core and the contamination of the plasma leads to a fast loss of thermal energy by photon radiation. A simple 0D model indicates that the minimum number of impurity atoms in the mantle needed for complete thermal quench mitigation is proportional to the total thermal energy and the width of the mantle ($\Delta x$) [6]:

For example, in the case of Ne injection on EHL-2 with ${W}_{\mathrm{t}\mathrm{h}}=$ 3.3 MJ and $\Delta x/a= 0.1$, the minimum number of assimilated neon atoms in the mantle required for full thermal quench mitigation would be the order of 10²¹. To account for the assimilation factor, the injection of approximately 10²² neon atoms via MGI or SPI would be sufficient for full thermal quench mitigation, which are typical injection quantities for current machines.

Experimental tests of massive noble gas injection for disruption mitigation have been carried out on several tokamaks, during which 80%–100% radiative losses were achieved by radiation deposited over the first wall [35, 48–50]. These encouraging results provide strong support for the development of effective disruption mitigation systems for the EHL-2 spherical torus. However, while the thermal energy is highly radiated over the first wall, it would pose a threat to the first wall if the radiation is too localized. Table 6 summarizes key parameters relevant to mitigating thermal loads in EHL-2, including energy impact factors on both the divertor and the first wall.

Table  6.  Parameters relevant to mitigation of the thermal loads in the EHL-2 spherical torus.

Mitigation parameters	Values
Optimistic energy impact factor on divertor	100 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$
Thermal energy of H-mode	3.3 MJ
Assimilated neon for full thermal quench mitigation	1021 ${\mathrm{m}}^{-3}$
Area of the first wall	46.4 m2
Energy impact factor on the first wall for 90% radiation	6 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$

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For 90% radiated power, the energy impact factor for an isotropically radiated TQ is only 6 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$, distributed over the 46.4 m² area of the first wall on EHL-2. In comparison, an energy impact factor of 35 MJ·${\mathrm{s}}^{-0.5}{\cdot \mathrm{m}}^{-2}$ is estimated on SPARC under a similar assumption of 80% radiated power [8]. Even accounting for a radiation peaking factor as high as 4, the resulting energy impact factor on EHL-2 remains well within the acceptable limits for its first wall material, CFC.

4.3   Current quench mitigation

Thermal quench mitigation aims to rapidly terminate discharges and shorten the current quench time compared to natural disruptions, thereby effectively reducing halo currents. A long quench time allows the post-thermal quench plasma to drift a considerable vertical distance, eventually contacting the upper or lower divertor and generating high halo currents. In contrast, a shorter quench time ensures a limited vertical drift, preventing the plasma from reaching the divertor surfaces. As a result, it significantly reduces halo currents.

The unmitigated vertical force on the vacuum vessel due to halo currents on EHL-2 is estimated to be nearly 4 MN, which is an order of magnitude smaller compared to 90 MN on ITER [51] and 45 MN on SPARC [8]. Consequently, force loads are not a primary consideration in disruption mitigation for EHL-2, and the vacuum vessel is being designed to withstand the expected force by halo current in unmitigated disruption. Furthermore, experiments on many tokamaks have demonstrated that MGI could significantly reduce the total vertical mechanical force acting on the vessel [33, 36, 37] .

4.4   Runaway electron suppression

During the thermal and current quench phases, a significant toroidal electric field, reaching several tens of volts per meter, is generated in the plasma. This can be estimated using a 0D toroidal electric field model as follows:

where $L=\dfrac{{\mu }_{0}{Rl}_{i}}{2}$ represents the plasma internal inductance. Assuming l_i = 1, E = 62.5 V/m could be derived. When the acceleration force on electrons exceeds the frictional force from collisions with background particles, the electrons can become runaway. To effectively suppress the avalanche multiplication of runaway electrons, sufficient impurities must be injected before the current quench. The critical electron density required to prevent relativistic electrons from running away can be expressed as,

Using $\mathrm{l}\mathrm{n}\varLambda$ = 18, we obtain n_c = 6.8×10²² m⁻³. This value is an order-of-magnitude estimate, considering that the internal inductance may underestimate the effective inductance by up to a factor of 2.

Current experiments with MGI can only achieve about 20% of the critical density required for effective runaway electron suppression. For instance, in the AUG tokamak, the injection of over 8×10²² neon atoms by MGI resulted in an effective electron density that reached only 24% of the critical density [50]. Similarly, by optimizing MGI with multiple small gas valves firing simultaneously on DIII-D, the line-averaged electron density reached 15% of the critical density [52]. These results underscore the necessity for more advanced injection techniques to improve mitigation effectiveness.

Currently, there are significant challenges in suppressing the generation of runaway electrons solely through current injection methods. Therefore, an externally applied three-dimensional magnetic perturbation system has been proposed to enhance the radial loss of runaway electrons, ensuring that they strike the wall before they can avalanche and accelerate to high energies during the current quench. Promising preliminary results were obtained in various tokamaks. For instance, the generation of runaway electrons was suppressed in TEXTOR disruptions by applying perturbation fields with toroidal mode numbers n = 1 and n = 2 [53]. Similar results were achieved on J-TEXT by applying m/n = 2/1 mode external magnetic perturbation fields and JT-60U with m/n = 3/2 mode external magnetic perturbation [38, 54]. Currently, an external magnetic perturbation system has been designed for EHL-2, aimed not only at suppressing runaway electrons, but also at controlling Edge Localized Modes (ELMs) [55].

5.   Discussion and conclusion

EHL-2 is designed to explore the potential of an advanced, compact p-¹¹B nuclear fusion reactor, utilizing a high-field, high-plasma-current spherical tokamak configuration, where the impact of disruptions must be carefully considered and addressed. Key characteristics relevant to disruptions, such as the time scales of thermal quench and current quench, as well as forces and thermal loads on EHL-2 have been estimated using scaling laws and 0D physical models. The vacuum vessel and internal components of EHL-2 are designed to endure the unmitigated anticipated halo and eddy current forces. The most critical issue arises from thermal loads, where unmitigated disruptions could result in the PFC materials exceeding their melting threshold.

In this paper, the performance requirements of the disruption prediction system on EHL-2 are discussed. A hybrid CNN-LSTM model is employed for disruption prediction using real-time diagnostics from EXL-50U, with the aim of leveraging transfer learning techniques to adapt the model for application on EHL-2. For the majority of disruptive cases on EXL-50U, the warning time given by the model on EXL-50U is long enough to ensure effective mitigation of disruptions on EHL-2. However, the optimal TPR and FPR achieved by the model still fall far short of the requirements for EHL-2, suggesting that additional data sets, model fine-tuning and the incorporation of advanced feature engineering are necessary to achieve the desired performance standards.

Active disruption mitigation methods are necessary to reduce the heat flux on the divertor on EHL-2, and this study explores two main techniques of DMS: MGI and SPI. Both techniques could effectively reduce the heat flux on the divertor to tolerable material limits by radiating the energy across the first wall. Even with 90% radiated power, the energy impact factor of the first wall on EHL-2 remains within the tolerable limits of the first-wall materials considering a high radiation peaking factor of up to 4. Furthermore, installing multiple injectors along the toroidal direction could help reduce radiation asymmetries and ensure a more uniform distribution of impurity radiation over the wall surface. These estimates provide valuable insight for optimizing the engineering design of EHL-2 and identifying its optimal operational regime.

Currently, a significant challenge in disruption mitigation is that the electron density required for complete runaway suppression cannot be achieved through current injection methods alone. Consequently, a passive runaway suppression strategy utilizing an externally applied three-dimensional magnetic perturbation system has been proposed. On EHL-2, an external magnetic perturbation system has been designed to not only suppress runaway electrons, but also to control ELMs.