The fixed boundary plasma equilibrium basis for a one Gigawatt electric stellarator power plant

Abstract: A fixed boundary stellarator equilibrium capable of producing 3 GW of fusion power (1 GW-electric) is presented as the design basis for the GIGA fusion power plant being developed by Gauss Fusion GmbH. The stellarator concept provides a steady-state, transient free, low recirculating power approach to a fusion power plant, which builds on 50 years of progress in plasma physics. A set of requirements for a fixed boundary equilibrium were determined through application of 0.5 D modeling. Optimization of a modified Wendelstein 7-X (W7-X) equilibrium was performed to achieve these requirements including alpha power confinement greater than $85\%$, neoclassical effective ripple below 0.01, bootstrap current below 50 kA, and reduced turbulent heat fluxes. In order to fix the plasma volume of $1500~m^3$ during optimization, the VMEC code was modified to renormalize the boundary coefficient to the desired plasma volume. The STELLOPT stellarator optimization code was modified as well to include new bootstrap current targets, a new target for the radial electric field, and the capability to hold the magnetic field on axis at a fixed value. An intermediary conceptual design plasma and final evolved fixed boundary equilibria are compared to the original modified W7-X equilibrium. The final evolved equilibrium is shown to achieve all the necessary requirements for the GIGA fusion power plant through more detailed modeling of stability, fast ion confinement, and transport.

• The paper presents a fixed-boundary plasma equilibrium design using advanced numerical optimization to minimize bootstrap current and ensure robust MHD stability.
• It employs a systems engineering approach with genetic and gradient-based minimization, achieving 3 GW fusion power while meeting stringent plasma shape and reactor requirements.
• The final design ensures high alpha retention, low neoclassical and turbulent transport, and positive radial electric fields, positioning the reactor at TRL 6 for pilot demonstration.

Fixed-Boundary Plasma Equilibrium Design for the GIGA Stellarator Power Plant

Overview and Motivation

This work provides the fixed-boundary magnetic equilibrium basis for the GIGA stellarator, a 1 GWe electric fusion power plant under development by Gauss Fusion GmbH. Stellarators are uniquely positioned among magnetic confinement approaches to offer steady-state, disruption-free operation with low recirculating power requirements, leveraging decades of plasma physics and engineering advances. However, optimal performance in stellarators is a function of complex three-dimensional shaping, requiring advanced optimization for adequate plasma confinement, stability, and reactor performance. This paper establishes the detailed systems engineering, physics modeling, and numerical optimization routes that underpin the viability of stellarator-based gigawatt-class fusion plants, focusing on the synthesis of plasma shape with reactor-scale performance requirements.

Systems Engineering Approach and Physics Requirements

A systems engineering methodology is adopted to structure the plasma design process, emphasizing the quantification and traceability of requirements from plant-level needs to plasma specification. Key plant-level requirements comprise:

• Continuous net electric power output of 1 GWe (assuming ~33% conversion efficiency and 90% availability),
• Achievement of 3 GW fusion power in steady-state,
• Utilization of feasible, high-maturity magnet technology.

The derived plasma-level requirements (quantified via 0.5D scaling and predictive modeling) include:

• 3 GW total fusion power with plasma volume fixed at 1500 m³,
• On-axis magnetic field of 6 T in a 4-field-period configuration,
• Alpha power confinement ≥85%,
• Effective helical ripple $\epsilon_{\mathrm{eff}}^{3/2} < 0.01$,
• Net bootstrap current <50 kA,
• Core rotational transform $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$,
• Avoidance of low-order rational surfaces and large core-edge Alfvén eigenmode gaps,
• Stability to ballooning, kink ($n=0,1,2$), and Alfvénic modes,
• Core electron root conditions (outward-pointing $E_r$),
• Compatibility with modular-coil-accessible island divertor geometries,
• Peak heat flux <600 kW/m², low impurity concentration (<8% He, <0.01% W).

These requirements constrain both plasma profiles (densities, temperatures) and geometric quantities (shape harmonics, transform profiles).

Optimization Methodology and Tools Enhancements

Numerical optimization is performed using the STELLOPT code framework [doecode_12551], targeting figures of merit encompassing MHD stability (ballooning, kink), fast-ion confinement, rotational transform profile, neoclassical transport, bootstrap current, turbulent transport proxies, and radial electric field. The key computational elements include:

• VMEC for ideal MHD equilibrium [hirshman_steepest-descent_1983],
• Modified STELLOPT incorporating new targets for bootstrap current and $E_r$ (interfacing PENTA/BOOTSJ [shaing_bootstrap_1989, spong_generation_2005]),
• Direct control of plasma volume via online boundary renormalization,
• Use of both genetic and gradient-based minimization algorithms,
• Gyrokinetic turbulence proxies ($g^{rr}$) as indirect minimization of nonlinearly computed fluxes [mynick_optimizing_2010, xanthopoulos_controlling_2014].

Notable code modifications introduced include enforced plasma volume, self-consistent equilibrium-bootstrap coupling during optimization, and the addition of new targets for $E_r$ and on-axis $B$.

Equilibrium Development and Evolution

Starting from a high-iota/high-mirror W7-X equilibrium modified for plant-scale (20 m major radius, 6 T central field, 1500 m³ plasma), successive rounds of optimization produced:

1. Initial Equilibrium (GIGA_v500): Provided a feasible starting point, but with excessive bootstrap current (~-1.5 MA) and low fast-ion confinement.
2. Conceptual Design (GIGA_v515): Reduced bootstrap current, improved geometric and neoclassical performance. However, suffered marginal kink stability at $n=1,2$ and only just met alpha confinement requirements.
3. Evolved Equilibrium (GIGA_v549): Achieved all design targets after incorporating direct minimization of bootstrap current (PENTA/DKES proxies), explicit targeting of core $E_r>0$ (CERC conditions), and further suppression of turbulent proxies and deeply trapped particle losses.

The final equilibrium retains strong geometric and magnetic resemblance to the conceptual design but with critical improvements in neoclassical and fast-ion metrics, reduction of core resonance crossings, and robust stability signatures.

Physics Performance and Modeling Outcomes

Confinement and Transport

• Alpha Particle Confinement: Predictive modeling (slowing-down simulations with BEAMS3D and ASCOT5) demonstrates deeply trapped alpha loss fractions below 1% in the evolved equilibrium, comfortably surpassing the 85% retention criterion [vtt_2026]. Improved alignment of fast-ion orbits with flux surfaces is confirmed by rigorous drift orbit analysis [nemov_poloidal_2008, bader_modeling_2021].
• Neoclassical Transport: $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$0 remains $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$1 throughout the plasma, indicating effective suppression of $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$2 losses at low collisionality [ho_neoclassical_1987, nemov_evaluation_1999]. Bootstrap current, computed with current-equilibrium self-consistency (THRIFT+PENTA), is minimized to $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$3 kA for reactor-core profiles, reducing transform variation and divertor strike-line sensitivity [helander_bootstrap_2009, van_ham_modeling_2025].
• Core Radial Electric Field: Positive $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$4 (CERC) achievable at $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$5 for typical reactor conditions, facilitating outward impurity convection and inner fueling [lee_direct_2024, beidler_reduction_2024].
• Turbulence Optimization: Gyrokinetic simulations (stella code) indicate reduced ion heat and particle fluxes across relevant gradient regimes compared to current experimental baselines (e.g., W7-X), corresponding to operational improvements in plasma performance [garcia-regana_reduced_2024].

Stability Analysis

• Ballooning/Kink/Interchange Stability: Full-spectrum analyses (COBRAVMEC, TERPSICHORE) confirm absence of unstable $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$6 modes in the low-to-moderate $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$7 operational window; robust magnetic well and Mercier criterion satisfied everywhere except deep core [sanchez_cobra_2000, anderson_terpsichore_1990].
• Alfvén Eigenmode Spectrum: No significant core-edge continuum gaps detected (STELLGAP), mitigating fast particle redistribution risk [spong_shear_2003, slaby_perturbative_2024].
• Integrated Transport: 1D transport modeling yields peak heat fluxes $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$8 kW/m² for reference profiles, and operating windows with auxiliary heating requirements well below $$0.8 < \iota_{\mathrm{core}} < \iota_{\mathrm{edge}} < 1$$9 MW at full power (assuming ISS04 scaling).

System Integration and Reactor Implications

The equilibrium design supports integration with island divertor geometries, with edge transform and resonance control critical for efficient power and particle exhaust [feng_review_2022]. Wall loading, neutron flux, and radial build analyses indicate that material limits, not plasma physics, set the ultimate device compactness for fixed net electric output—higher field operation allows for smaller machines but increases complexity and wall loading risk [kappel_magnetic_2024]. The strict self-consistency of transport, transform, and heating scenarios achieved here minimizes operational risk during reactor startup and burn.

Readiness and Future Prospects

Analysis of technical readiness indicates that neoclassical, equilibrium, alpha confinement, and stability physics are at or approaching TRL 6 in current experiments, while full electromagnetic turbulence optimization remains at TRL 4–5. The equilibrium and physics performance achieved here positions the GIGA plant for direct transition to integrated coil-divertor-plasma engineering and industrial-scale prototype demonstration [donne_beyond_2025, grulke_overview_2026].

Anticipated next steps involve:

• Coil set optimization for field accuracy and radial build,
• Full free-boundary equilibrium and coil self-consistency,
• Detailed divertor and blanket integration,
• Nuclear (tritium breeding) and thermal optimization,
• Industrial pilot demonstration, potentially staged via intermediate Q~5 device.

Conclusion

A robust, numerically optimized fixed-boundary equilibrium basis for a 3 GW fusion, 1 GWe electric, 4-field-period stellarator power plant has been established, achieving all necessary physics and engineering constraints at the plasma level. The design demonstrates simultaneously minimized alpha losses, bootstrap current, and neoclassical/turbulent transport, with comprehensive MHD stability, CERC access, and reactor compatibility. The systematic optimization methodology, coupling advanced physics models with systems requirement flowdown, serves as a template for future stellarator reactor designs and supports the practical realization of steady-state fusion electricity.

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References:

• “The fixed boundary plasma equilibrium basis for a one Gigawatt electric stellarator power plant” (2607.09346)
• Associated references in text for specific modeling codes and physics principles.