Features of spherical torus p 11B burning plasmas

Abstract: A spherical torus (ST) p B11 plasma model that satisfies multi-magnetofluid force balance is developed, which includes small fractions of suprathermal ions with temperatures around 0.5 MeV and suprathermal electrons in the MeV range. Alongside the primary thermal plasma with ion temperatures exceeding 100 keV and densities above 10E20 m-3, these components enhance fusion reaction rates by leveraging the p B11 double-peak fusion cross section. Suprathermal ions and strong toroidal rotation driven by neutral beam injection have been observed in devices such as START, MAST, NSTX, Globus-M2, and ST40. Central-solenoid-free plasma initiation, ramp-up, and sustainment were tested on EXL-50 and replicated on EXL-50U with partial central induction, demonstrating efficient current drive and consistent with the multi-magnetofluid equilibrium model. Motivated by ENN's aneutronic commercial fusion roadmap, this paper presents a rotating, thermally un-equilibrated ST p B11 plasma with unique properties: fluid components experience separate balance under centripetal, electrostatic, and Lorentz forces with common electric and magnetic fields, leading to large rotation speed differences between thermal boron ions and suprathermal protons; a large outboard region with magnetic well and omnigeneity is created, affecting neoclassical transport and gradient-driven turbulence; suprathermal charged particles can extend beyond the last closed flux surface and be limited by plasma-facing components, influencing recycling and pedestal conditions; and the superposition of these plasma components modifies sources and sinks of free energy, prompting renewed evaluation of stability, turbulence, transport, heating, current drive, and flux diffusion. Challenges and opportunities for sustained burn are discussed for a compact p B11 ST with 1.4-meter major radius, 13-MA current, and 3-T toroidal field.

• The paper introduces a six-component equilibrium model that integrates thermal and suprathermal species for p–11B fusion plasmas.
• The paper demonstrates non-local, orbit-based reactivity modeling which accurately captures finite-orbit effects and differential flow dynamics.
• The paper reveals that strong E×B and precessional shear, combined with advanced edge physics, can suppress turbulence and stabilize plasma confinement.

Multi-Component Magnetofluid Equilibria and Non-Local Reactivity in Spherical Torus p-11B Fusion Plasmas

Introduction and Motivation

This work establishes a comprehensive multi-component magnetofluid equilibrium model for spherical torus (ST) plasmas burning proton–boron-11 (p-11B) fuel, motivated by the pursuit of aneutronic fusion power. The ST configuration is leveraged for its high-beta capabilities, compactness, and ability to sustain strong toroidal rotation and suprathermal particles through neutral beam injection (NBI) and electron cyclotron resonance heating (ECRH), as recently demonstrated in EXL-50/EXL-50U and related devices. The physical rationale for this modeling approach is the double-peaked nature of the p-11B fusion cross section, which incentivizes the inclusion of both thermal and suprathermal ion populations to optimize reactivity at realistic input power levels.

Model Formulation and Numerical Implementation

The authors extend their previously validated four-fluid axisymmetric equilibrium framework to a six-component system: thermal protons, suprathermal protons, thermal 11B, suprathermal 11B, thermal electrons, and relativistic suprathermal electrons. This model self-consistently integrates centrifugal, electrostatic, and magnetostatic effects within force balance equations for each population, thereby resolving differential flows, multi-temperature species, and non-local effects crucially absent in single-fluid magnetohydrodynamics (MHD).

An iterative solution method with a three-grid Successive Over-Relaxation (SOR) approach achieves $1\%$ numerical convergence for physically plausible profiles. Reference parameters for burning ST p-11B equilibria are presented with major radius $R \approx 1.43$ m, current $I_p = 12.6$ MA, $B_T = 3.38$ T, $$\langle n_{e,0} \rangle = 1.04 \times 10^{20}~\mathrm{m}^{-3}$$, bulk ion $T \sim 130$ keV, and minority suprathermal energies near 0.9 MeV. The suprathermal electron fraction is computed to carry about $21\%$ of the total plasma current, extending significantly beyond the last closed flux surface (LCFS).

Suprathermal-Driven Reactivity: The Necessity of Orbit-Based Modeling

A central technical contribution is the demonstration of the inadequacy of local (0D) Maxwellian-based reactivity models when suprathermal ions on finite-orbit-width (FOW) trajectories comprise a non-negligible plasma fraction. For suprathermal protons, drift orbits can traverse wide radial regions, sampling variable 11B densities, with co-current orbits drifting inward and counter-current orbits often lost at the wall. The computed differential rotation exceeds $2 \times 10^6$ m/s between suprathermal protons and thermal boron ions near the LCFS, further enhancing non-Maxwellian effects.

A more accurate fusion power computation is performed via full orbit integration—tracking suprathermal proton trajectories in 3D, averaging cross-section weighted fusion probabilities along each orbit, and integrating over initial conditions. This non-local treatment corrects the local model's tendency to underestimate inward-drifting, high-reactivity suprathermal proton events and overestimate lost counter-current orbit contributions.

In the sample scenario, whereas the local model yields a volume-averaged $\langle P_{pB} \rangle = 0.0306$ MW/m$^3$ with only $R \approx 1.43$0 from suprathermal/thermal reactions, orbit-based modeling indicates this underestimates the net suprathermal contribution given the non-local enhancements and loss mechanisms.

Macroscopic Equilibrium and New Transport Regimes

The equilibrium analysis reveals several interlinked features with significant consequences for confinement and transport:

• Outboard |B| Well and Omnigeneity: The computed equilibria feature a pronounced outboard magnetic well and omnigenous region, consistent with theoretical predictions for reduced neoclassical and turbulence-driven transport in axisymmetric low-aspect-ratio plasmas. This enhances orbit squeezing and can enable elevated pedestal gradients for both ions and electrons.
• Reversed $R \approx 1.43$1 and Precessional Shear: Strong toroidal rotation generates reversed core $R \approx 1.43$2 shear, which, combined with precessional shear, is expected to suppress both ion and electron-scale turbulence, possibly enabling internal transport barriers under appropriate conditions.
• Multi-Temperature Components and Strong Differential Flow: The co-existence of thermal and suprathermal populations, each with their own force balance, fundamentally modifies stability and transport, impacting tearing mode drive, energetic particle physics, and edge conditions.

Edge Physics, Current Distribution, and Wall Interactions

The multi-component force balance leads to several unique edge and pedestal features:

• Plasma Potential: The model self-consistently produces a positive electrostatic potential peaking at $R \approx 1.43$3 kV, which modifies the confinement of low-energy ions, influences helium ash and impurity exhaust, and affects energetic particle orbit termination points.
• Current Distribution: Suprathermal electron and ion currents extend beyond the LCFS, with implications for edge stability, rational surface structure, and potential interaction with plasma-facing components (PFCs).
• Pedestal and Recycling: The penetration of suprathermal populations beyond the LCFS, combined with positive $R \approx 1.43$4, likely alters recycling, pedestal fueling, and neutral dynamics, deviating from conventional H-mode SOL physics. Suprathermal orbit loss may localize edge heat flux but also reduce pedestal neutrals, potentially raising the pedestal height.

Neoclassical, Turbulent, and Stability Implications

The standard separation of equilibrium and neoclassical theory is challenged in this regime, as strong rotation, non-conventional $R \approx 1.43$5 topology, and suprathermal FOW populations require orbit-averaged rather than purely local transport coefficients. As Suprathermal populations interact strongly with MHD modes, modifying moment of inertia and driving/damping instabilities, stability thresholds—especially for tearing and resistive wall modes—are altered.

High-fidelity axisymmetry becomes a critical design goal, as non-axisymmetric fields (error fields, ripple, etc.) can severely degrade orbit-confinement and rotation, thereby compromising the predicted transport and stability improvements. Experimental validation in upcoming EHL-2 ST experiments will be required to quantify these effects.

Implications and Future Directions

The results indicate several new directions for p-11B ST research:

• Non-Local Reactivity and Transport Modeling: Next-generation transport modeling must fully integrate FOW, non-local fusion reactivity, and self-consistent electrostatics, particularly in regimes where suprathermal populations are significant.
• Confinement Optimization: Theoretical and experimental studies should target regimes with strong $R \approx 1.43$6 and precessional shear, large $R \approx 1.43$7 wells, and omnigeneity, coupled with enhanced edge control via plasma potential engineering.
• Edge and Pedestal Physics: Investigation of suprathermal-induced recycling suppression, impurity/ash exhaust, and localized heat flux will be crucial for viable reactor operation.
• Stability and Control: The impact of extended current profiles, differential flows, and energetic minority populations on tearing mode and resistive wall mode thresholds must be addressed with dedicated kinetic-MHD analysis.

The major practical challenge remains the relatively low volumetric fusion reactivity of p-11B compared to D-T under comparable plasma densities. This necessitates substantially longer global energy confinement times and places stringent demands on turbulence suppression, impurity control, and edge/SOL heat flux management.

Conclusion

This paper presents a technically rigorous, multi-component analysis of ST p-11B equilibria, emphasizing the necessity of non-local orbit-based fusion reactivity modeling, the critical role of suprathermal populations, and the implications of coupled axisymmetric magnetofluid force balance for transport, edge physics, and stability. The modeling framework delivers quantitative predictions for future high-current, high-beta, p-11B burning ST experiments and identifies both opportunities (enhanced confinement, potential turbulence suppression, raised pedestal) and challenges (non-locality, wall interactions, low fusion power density). The results motivate significant further investigation, both experimental and theoretical, to quantitatively assess the feasibility of sustained, net-positive p-11B ST operation.