Simulation and Comparative Analysis of Advanced Scenarios for High- and Low-Temperature Superconducting Tokamak Using METIS Code

1. Introduction

Breakthroughs in rare-earth barium copper oxide (REBCO) high-temperature superconducting (HTS) tape technology have significantly advanced the development of compact, high-field tokamaks such as SPARC and ARC [1,2]. These devices offer a potentially faster and more economical path to fusion energy. A strong magnetic field ($B > 10 \mathrm{T}$) can significantly enhance plasma confinement and fusion reaction rates. Consequently, devices can achieve high fusion gain (Q) or even ignition with smaller size and lower auxiliary heating power [3,4].

However, high magnetic fields introduce new physics and engineering challenges. Higher fields typically lead to higher plasma density and pressure, which alters the physics of wave heating and current drive. For example, high fields affect the density cut-off for lower hybrid (LH) waves [5,6] and the absorption location of electron cyclotron (EC) waves [7,8,9]. Simultaneously, high-power-density operation places extreme demands on first-wall and divertor heat load management. Therefore, it is vital to systematically explore operational scenarios in high-field regimes using integrated modeling tools. Comparing these with conventional LTS device operation modes during the pre-design phase is of great importance.

Traditional high-fidelity 1.5D integrated codes (e.g., TRANSP, CRONOS) offer high accuracy but require long computation times, making extensive parameter scans difficult [10,11]. In contrast, the METIS code employs simplified physics models and empirical scaling laws. It achieves computation speeds far exceeding real-time while maintaining reasonable fidelity for key physical processes [12]. This makes METIS well-suited for rapid exploration of operational spaces and sensitivity analysis.

Based on this, this paper employs the METIS code to conduct a comparative study of advanced operation scenarios for an HTS-based device (using SPARC parameters as a reference) and an LTS-based device (using BEST parameters as a reference). We first validate the METIS configuration against published simulation data for SPARC. We then simulate the respective conditions required for each device to reach $Q\approx 5$, comparing their demands on auxiliary heating power, density, and confinement level. Finally, we establish a common set of core physics parameters (aiming to control for the primary variable of magnetic field strength) to compare the ultimate fusion power and operational mode achievable by both devices. This study aims to reveal the impact of magnetic field strength on fusion device performance and provide reference for the physics design of subsequent high-field tokamak.

2. Materials and Methods

2.1. METIS Code Introduction

METIS (Minute Embedded Tokamak Integrated Simulator) is a fast integrated modeling code designed to simulate a full tokamak discharge lasting hundreds of seconds within minutes [12]. It adopts a hybrid 0D-1D approach: global 0D equations describe the evolution of integral quantities like plasma stored energy and current, while 1D diffusion equations calculate the transport of profile quantities such as temperature and current density.

Although METIS uses scaling laws to simplify physics models, its results remain reliable and consistent with 1.5D transport codes [12,13]. This is due to METIS’s 0D-1D approach to describing the transport of physical quantities, which are greatly influenced by turbulence and for which there are still large uncertainties in the simulation results of other first-principle based codes. The energy transport in METIS begins with a time-dependent 0D equation:

$${\displaystyle \frac{d{W}_{th}}{dt}}=-{\displaystyle \frac{W_{th}}{{\tau }_E}}+P_{loss}$$

(1)

where $W_{th}$ is the plasma thermal energy content, ${\tau }_E$ is the energy confinement time, and $P_{loss}$ is the total power loss through the plasma separatrix. Plasma confinement is modified by various processes, resulting in the total thermal energy expression:

$$W_{th}=H_{MHD}{H}_{li}{H}_{ref}{\tau }_E{P}_{th}+\left(H_{ITB}-1\right)W_{core}$$

(2)

where $H_{ref}$ is a prescribed factor, $H_{MHD}$ is an internally computed confinement factor that takes into account the confinement degradation due to MHD phenomena (not considered in our simulations, i.e., $H_{MHD}=1$), $H_{ITB}$ is an internally computed confinement factor that takes into account the enhancement of the confinement due to the magnetic shear (considered in our simulations), $H_{li}$ allows to take into account the effect of internal inductance on energy confinement (not considered in our simulations i.e., $H_{li}=1$). ${\tau }_E$ is calculated using the ITER-98P(y,2) scaling law for the H-mode discharges. $W_{core}$ is defined as ${\tau }_E\times P_{th}-W_{ped}$, where $W_{ped}$ is the thermal energy in the pedestal region predicted by the scaling expression. The derivatives of electron and ion temperature with respect to the radial coordinate are then solved using diffusion transport equations, respectively. Although only the diffusion part is considered in the energy transport equation, the modified diffusion coefficients ${\chi }_e$ and ${\chi }_i$, or alternatively conductivity coefficients ${\kappa }_{e,i}=n_{e,i}{\chi }_{e,i}$, can be expressed by a prescribed analytical equation or theoretical model. In our simulations, the Current Diffusion Ballooning Mode (CDBM) [14] model is used to describe the shape of the transport coefficient. Thus, the temperature profiles are obtained by integrating the solved derivatives in the heat transport equations. The current diffusion component of METIS is completely implemented using the same method as the traditional 1.5D transport code, which evolves as a function of poloidal flux whose transport combines a 2D magnetic surface equilibrium with a 1D poloidal flux transport equation. The current diffusion equation includes several source terms that can be described by various physical models. The Sauter model [15] is used in this article to compute the bootstrap current. This model simplification is core to METIS’s computational speed. Although it sacrifices some first-principles detail, it has proven reliable for predicting overall performance trends [12,16].

2.2. Model Validation Based on SPARC Simulation Data

To ensure the reliability of the parameter settings and physics models used for the subsequent SPARC and BEST simulations, we first used METIS to reproduce a published full H-mode operational scenario for SPARC. The key parameters for this operating point are from published integrated modeling results [1,17], including: plasma current $I_P=8.7 \mathrm{MA}$, toroidal field $B_t=12.2 \mathrm{T}$, major radius $R=1.85 \mathrm{m}$, minor radius $a= 0.57 \mathrm{m}$, Greenwald density fraction $f_{GW}\approx 0.37$, confinement factor $H_{98}=1.0$, total heating power $P= 12.8 \mathrm{MW}$ (of which$P_{ICRH} = 11.1 \mathrm{MW}$, $P_{ohmic}= 1.7\mathrm{MW}$).

We configured METIS using the data from Table 1 and parameters from the references. The simulation was run for 35 seconds to reach a steady state. The outputs were compared with reference data for the same scenario, particularly the fusion power $P_{fusion}$, fusion gain Q, and the current safety factor profile at the 95% flux surface$q_{95}$. Figure 1 shows the fusion gain Q and the comparison between METIS simulation results and SPARC reference data for the evolution of safety factors $q_0$ and $q_{95}$. It can be seen that the simulated $q_0$ and $q_{95}$ trends align well with the reference data, with minor numerical differences. In our simulation results, the central electron temperature is close to 25 keV, the central electron density is approximately $3.4\times {10}^{20} m^{-3}$, and the fusion gain $Q\approx 12$. The differences from the reference data are within an acceptable margin of error（$<10\%$）, thereby validating our METIS configuration.

2.3. Simulation Setup for BEST $Q\approx 5$ Scenarios

To explore the differences in parameters, performance, and operational scenarios between high-temperature superconducting (high-field) and low-temperature superconducting devices, we selected the SPARC (representing HTS high-field) and BEST (representing LTS) devices. Using METIS, we performed parameter scans to find operational scenarios achieving $Q\approx 5$. During the scan, we first fixed some engineering and geometric parameters: BEST references published design parameters ($R=3.6$m, $a=1.1$m, $B_t=6.15 \mathrm{T}$, $I_P=7 \mathrm{MA}$) [18], and SPARC parameters are as previously described. Secondly, we selected the same energy scaling (ITER-98P(y,2) scaling law and ITER-89P(y,2) scaling law), density model (Angioni) [19,20], and transport model (CDBM). The core variables scanned were: line-averaged density (representing the Greenwald density fraction), impurity fraction, effective nuclear charge number $Z_{eff}$, and heating power (including frequency, deposition location, width, etc.). Table 2 presents the key design parameters for operational scenarios., derived from literature references and parameter scan results. The parameter scan for BEST was conducted based on the $Q\approx 5$ operational scenario outlined in the BEST research plan. Figure 2 shows the METIS simulation results for the high fusion gain $Q\approx 5$ scenario in BEST. The results of the simulation profiles further reveal central electron temperatures $T_{e0}$ of 26 keV and ion temperature $T_{i0}$ of 33 keV at 45 s, accompanied by the formation of an internal transport barrier(ITB). A reversed-shear safety factor profile is also established with $q_0 \approx 2$ and $q_{min} \approx 1$. The parameter scan for SPARC was performed in accordance with the relevant SPARC literature, and the results are presented in Section 3.

3. Results and Discussion

3.1. Simulation Results for HTS Device (SPARC) at $Q\approx 5$

Referring to SPARC design literature, auxiliary heating of SPARC employs only the ICRH minority ion heating scheme. Under its very high magnetic field (12.2 T) condition, it requires only a relatively low density to achieve a relatively high fusion power. Our scans indicate that SPARC, within the range of $f_{GW}\approx 0.3-0.4$, $H_{98}\approx 1.0$, requires only about 15-20 MW of external heating power to achieve $Q\approx 5$. Figure 3 illustrates some key parameters of a $Q\approx 5$ operating scenario ($f_{GW}=0.37,H_{98}=1.0,$ $P_{ICRH}= 16.6 \mathrm{MW}$). The results of the simulation profiles further reveal central electron density $n_{e0}$ of $3.1\times {10}^{20},$electron temperatures $T_{e0}$ of 26 keV and ion temperature $T_{i0}$ of 32 keV at 16 s. Compared with the SPARC $Q=11$ reference data, this result shows an increased auxiliary heating power, a slightly reduced electron density, a significantly lower temperature, and consequently, a decreased fusion gain. The reductions in density and temperature diminish the fusion power, thereby lowering the fusion gain, while the increase in auxiliary heating power also contributes to a lower gain. The combined effect of these two factors results in a reduction of SPARC’s fusion gain from 11 to 5. This outcome is consistent with the underlying physics and represents a valid scientific result. It also can be seen that even with a confinement factor $H_{98}=1.0$, which is lower than BEST ($H_{98}=1.2$), SPARC can still achieve the same $Q\approx 5$ fusion gain target at a lower Greenwald density fraction. This is due to the high plasma pressure and fusion cross-section enabled by the high magnetic field. Unfortunately, a reversed-shear safety factor profile was not achieved in our simulations.

3.2. Comparison of $Q\approx 5$ Results for LTS(BEST) and HTS(SPARC) Devices

As shown in Figure 4, at the same fusion gain, the volume-averaged electron density of SPARC is higher than that of BEST, while its Greenwald density fraction is significantly lower. This is because the high magnetic field generated by SPARC’s high-temperature superconductors enables a more compact device with a smaller minor radius and a higher plasma current, meaning that SPARC’s Greenwald density limit is substantially higher than that of BEST. This implies that, compared to BEST, SPARC offers a wider operating parameter space—a key advantage of the high-temperature superconducting high-magnetic-field approach.

Overall, the comparison of simulation results clearly reveals the core advantages of the high-temperature superconducting high-field path:

(1)

Lower auxiliary heating power requirement: SPARC requires about 50%–60% less auxiliary heating power ($P_{aux}=16.6 \mathrm{MW}$) than BEST ($P_{aux}=40 \mathrm{MW}$). This directly reduces the cost and complexity of external heating systems.

(2)

Lower operational density: SPARC can operate at $f_{GW}\approx 0.37$, while BEST needs to operate near the Greenwald density limit ($f_{GW}\approx 0.87$). Lower density operation favors wave heating (e.g., EC, LH) coupling and propagation, reduces plasma-wall interaction intensity, and may mitigate instabilities like edge-localized modes (ELM) [21].

(3)

More relaxed requirement on confinement factor: SPARC can achieve its target with $H_{98}\approx 1$, while BEST requires $H_{98}\approx 1.2$. This indicates that HTS high-field devices have higher “tolerance” for plasma confinement performance.

The physical root of these differences lies in the fusion triple product $n{\tau }_{E}T\propto {\beta }_N{B}^3/H_{98}$ (for a fixed normalized beta ${\beta }_N$). To achieve a given fusion power (Q), a high magnetic field (B) can “compensate” for stringent requirements on density (n), temperature (T), or confinement time (${\tau }_E$, linearly related to $H_{98}$). Our simulation results quantitatively validate this fundamental relationship, proving that increasing the magnetic field strength is one of the most effective levers for enhancing fusion performance.

3.3. Comparison of Fusion Performance Under Identical Physics Parameters

To further isolate the effect of the magnetic field variable on enhancing fusion device performance, we designed a more “fair” comparison: applying an identical set of core physics parameters to both SPARC and BEST. These parameters include: volume-averaged heating power density ($P_{aux}/V_{plasma}$), confinement factor $H_{98}$, Greenwald density fraction $f_{GW}$, and impurity content ($Z_{eff}$). This means both devices operate in “similar” physical states but within different magnetic fields and sizes. We selected a typical high-density operating point from BEST as the parameter set: $H_{98}\approx 1.2$, $f_{GW}\approx 0.87$, $Z_{eff}\approx 1.5$

3.3.1. Fusion Power and Confinement

The simulation results (Figure 5) show that under the identical “BEST-like” physics parameters, SPARC, leveraging its 12.2 T field, achieved a very high fusion gain of $Q\approx 27$ ($P_{fusion}\approx 420 \mathrm{MW}$) , whereas fusion gain of BEST was $Q\approx 5$ ($P_{fusion}\approx 200 \mathrm{MW}$). This visually demonstrates the enormous potential of a strong magnetic field for boosting fusion power.

However, high power density also brings challenges. The simulation shows that at such high density and pressure, the L-H transition power threshold $P_{LHth}$ for SPARC increases dramatically. The auxiliary heating power we initially set was insufficient to bring it into H-mode operation; that is, SPARC could only operate in L-mode under the initially set parameters. To better control the variables, we increased the auxiliary heating power of SPARC ($P_{ICRH}$ from 11.1 MW to 14.0 MW) to enable it to enter H-mode.

3.3.2. Discussion on the Feasibility of L-Mode Operation

Our simulations show that under high-field, high-density conditions, SPARC has a higher L-H transition threshold power. This makes entering H-mode more difficult. However, SPARC still achieves decent fusion gain in L-mode. Specifically, under conditions of high density ($f_{GW}= 0.85$), and $H_{89}=1.0$, the fusion gain reached approximately $Q\approx 5.2$ (Figure 6). This finding is significant: an operational strategy combining a strong magnetic field and high density can enable a device to achieve engineering-relevant fusion gain ($Q>5$) without entering H-mode.

This has important implications for HTS device design. While H-mode offers better confinement, it often involves periodic edge-localized modes (ELM) [21]. ELM generate large thermal transients that can damage the first wall and divertor in compact devices like ARC or SPARC [1,22]. Therefore, proactively choosing to operate in an ELM-free L-mode may be a more robust and viable scheme [22]. By appropriately increasing the operational density ($f_{GW}$), the fusion power loss from poorer L-mode confinement can be compensated for.

3.4. Challenge of Current Drive and Profile Control

Another prominent issue in our simulation process is current profile control. Under high-density ($f_{GW}\approx 1.0$) conditions, EC and LH waves face limitations due to density cut-offs and wave accessibility issues, making it difficult to effectively heat and drive core plasma current [23]. NBI (neutral beam injection) heating also struggles to heat the core plasma [24]. Therefore, the primary method for auxiliary heating of SPARC is ICRH. The ICRH minority ion heating scheme can efficiently heat ions, but its contribution to current drive is limited, and its driven current profile is broad and difficult to tailor flexibly. This makes it difficult for the final current distribution to exhibit an inverse shear configuration, and also hinders the formation of the internal transport barrier (ITB)—resulting in the inability to achieve advanced operating modes.

Because BEST employs four auxiliary heating methods (ECRH, LH, NBI, and ICRH) and has higher total auxiliary heating power, it can drive more current and provide more flexible current profile control. This makes it easier for the final current profile to exhibit a reverse magnetic shear shape.

This highlights a key dilemma: The high-density operational mode pursued by HTS devices for high power density inherently restricts the use of tools most commonly used for fine control of the current profile (e.g., off-axis ECCD, LHCD). In the SPARC simulation, the total current profile is dominated by ohmic and bootstrap currents, with a low fraction of auxiliary driven current that is difficult to adjust flexibly. This makes it very challenging to actively control the current profile to form and sustain advanced operational modes with reverse magnetic shear [25] or internal transport barriers (ITB) [26]. Developing effective methods for current profile control under high-density, high-field conditions is a major challenge that must be addressed in the future physics design of HTS devices.

3.5. Overview and Discussion

The study quantitatively demonstrates the performance leverage provided by high magnetic fields in tokamak. The HTS path (exemplified by SPARC) significantly lowers the entry barriers to high fusion gain by reducing demands on auxiliary heating power, plasma density, and confinement quality compared to the conventional LTS path (exemplified by BEST). This advantage stems directly from the $B^3$ scaling of the fusion triple product, which our simulations have validated.

However, the pursuit of high-power density through high fields and high densities introduces significant trade-offs. The most critical is the challenge to active current profile control. High densities render common tools like EC and LH waves ineffective, forcing reliance on ICRH, which is a poor current driver. This limits the ability to establish and sustain advanced, high-performance scenarios like those with reverse magnetic shear or internal transport barriers, which are often desired for steady-state operation.

Furthermore, the increased L-H transition power threshold at high field and density may preclude H-mode operation, forcing the device into L-mode. While our simulations show that $Q>5$ is still achievable in L-mode for HTS devices, this operational regime typically has poorer energy confinement. This necessitates even higher density to compensate, which in turn exacerbates the current drive challenges. Therefore, the operational space for compact high-field devices like SPARC or ARC may involve a complex optimization between confinement mode, density, and current drive capability. The potential benefit of avoiding ELM-induced heat loads by operating in L-mode [22] must be carefully weighed against the confinement penalty and the increased difficulty in controlling the current profile.

4. Conclusions

This study employed the fast integrated modeling code METIS to systematically compare the physical characteristics and requirements for achieving high fusion gain operation in high-temperature superconducting (SPARC) and low-temperature superconducting (BEST) tokamak, representing different technological paths. The main conclusions are as follows:

The high-field HTS device (SPARC) demonstrates significant advantages in achieving the same fusion gain ($Q\approx 5$): it requires 50-60% less auxiliary heating power, operates at a lower Greenwald density fraction requirement ($f_{GW} \approx 0.37 \mathrm{vs}. \approx 0.87$), and has a more relaxed requirement for the energy confinement factor ($H_{98} \approx 1.0 \mathrm{vs}. \approx 1.2$). This quantitatively validates the strong dependence of fusion performance on magnetic field strength.

Under an identical set of high-density physics parameters, fusion power potential of SPARC far exceeds that of BEST, but H-mode transition power threshold of SPARC is also significantly increased, likely forcing operation in L-mode. However, simulations indicate that even in L-mode, SPARC can still achieve $Q > 5$ through high-density operation. This suggests a potential fallback operational strategy for compact HTS devices facing severe first-wall heat load challenges: proactively choosing to operate in an L-mode without large ELM.

However, high-density operation severely limits the application of heating methods such as ECRH and LH, making HTS devices heavily reliant on ICRH. This single auxiliary heating scheme cannot drive sufficient current to adjust the current profile, making it difficult to establish and maintain advanced operating modes such as reverse shearing [25] or ITB (internal transport barriers) [26]. This poses new challenges for current profile control. Developing efficient, controllable non-inductive current drive methods suitable for high-density, high-field plasmas may be a key point for future research.

Looking ahead, HTS magnet technology opens a new development path for fusion energy characterized by high magnetic fields and compactness. This study reveals the great potential of this new path compared to the previous LTS path in lowering the barriers to fusion (auxiliary heating power, confinement requirements), and also identifies its core physics challenges (current drive and profile control at high density, higher L-H transition threshold power). Follow-up work needs to incorporate more precise wave physics and current drive calculations to explore possible current profile control schemes at high density. Simultaneously, for future higher-parameter steady-state operation devices like ARC and CFEDR, it is necessary to further explore the operational characteristics and scenarios of HTS and LTS devices to provide guidance for the design of commercial fusion reactor.