Timothy Stoltzfus-Dueck

ST-E1 is Tokamak Energy’s concept for a fusion power plant. As part of the pre-concept design, a series of reference flat-top plasma operating points have been developed and analysed in [McNamara et al (2026 Nucl. Fusion 66 086008)]. The present work focuses on the low-density baseline conceptual power plant (BCP) operating point of [McNamara et al (2026 Nucl. Fusion 66 086008)] selected as a representative operating point for the ST-E1 pilot plant and investigates its micro-stability, turbulent transport and transport-informed optimisation using first-principles spectral flux-tube electromagnetic gyrokinetic simulations. Linear gyrokinetic calculations, involving electrons, thermal ions, impurities, and thermal and fast helium ions, complemented by dynamic mode decomposition (DMD) to identify subdominant and stable drift-wave eigenmodes, reveal two principal long-wavelength electromagnetic instability branches: hybrid h-ITG modes driven by thermal gradients and FI-KBMs, i.e. kinetic-ballooning-like modes strongly influenced by the plasma beta (a ratio of thermal to magnetic energy) and the fast-ion (FI) population. At shorter wavelengths, electron-temperature-gradient (ETG) modes become unstable towards the plasma edge while remaining stable in the core. A comprehensive sensitivity analysis identifies the principal equilibrium parameters governing these instabilities. Building on these linear predictions, nonlinear electromagnetic gyrokinetic simulations are performed to quantify the resulting turbulent transport of the thermal plasma and fast helium ions. The reference operating point is found to exhibit saturated, rather than runaway, electromagnetic turbulence, establishing it as a physically meaningful baseline for further optimisation. The nonlinear simulations show that turbulent transport is governed primarily by the combined effects of the plasma beta, safety factor and fast-ion fraction, with intrinsic-rotation-driven E × B shear providing an additional, complementary reduction in transport. Although fast ions provide the free energy driving the FI-KBM branch, increasing the fast-ion fraction is found to reduce the saturated turbulent transport across all species through nonlinear self-organisation. To efficiently explore the resulting multidimensional parameter space, defined by the plasma beta, safety factor and fast-ion fraction, a physics-informed interpolation framework constrained and validated by nonlinear gyrokinetic simulations has been developed, enabling the identification of transport-favourable operating points without requiring exhaustive nonlinear parameter scans. The resulting framework yields a family of transport-favourable operating points for the ST-E1 low-density BCP equilibrium and provides quantitative targets for future self-consistent equilibrium optimisation.

As part of the U.S. Department of Energy’s Milestone-Based Fusion Energy Development Program, Tokamak Energy has completed the pre-concept design of the ST–E1 fusion power plant. ST–E1 is envisaged to operate in two phases: a pilot plant phase, targeting sustained net power production of 300 − 500 MWe for a duration > 1 hr , followed by a commercial power plant phase targeting steady-state operations and a normalised overnight capital cost of ⩽ 12 000 $ / kWe . The design process adopted was highly iterative, integrating all major plant systems and progressing in a phased fidelity approach. At the pre-conceptual stage, the emphasis has been on exploring the design space, identifying the main system-level trade-offs, and making the key decisions that define the overall plant concept, rather than optimising a single operating point. This paper, part of a focused collection detailing the ST–E1 pre-concept design, addresses the development of a series of reference flat-top plasma operating points for the pilot plant phase. A modelling workflow was established to develop and assess candidate plasma design points and explore key dependencies. The workflow includes integrated core plasma modelling, magnetohydrodynamic (MHD) stability assessment, equilibrium generation, scrape-off-layer and exhaust modelling, heating & current drive design and optimisation, and turbulent transport modelling. Using this framework, the impact of several key parameters on the flat-top operating space was investigated, including the density limit, core radiation fraction and divertor power loading, level of external heating and curent drive power and assumed pedestal characteristics. The MHD stability, controllability and micro-stability characteristics of these plasmas were also analysed. These investigations informed the definition of a set of fully non-inductive, flat-top reference operating points that satisfy the high-level ST–E1 mission, including a low and high density case, a case that is stable to resistive wall modes and a case with reduced divertor power loading.

One practical challenge for the centrifugal-mirror confinement concept is the large radial voltage necessary to drive supersonic azimuthal rotation. In principle, the addition of a strong azimuthal field could reduce the required voltage, since the simple azimuthal E × B drift would be replaced by more rapid azimuthal trapped-particle precession. Also, if the mirror ratio is large enough, newly ionized ions are accelerated to the necessary parallel velocities in their first bounce orbit, both confining and significantly heating them. Unfortunately, MHD analysis shows that the centrifugal-force-confining plasma current is purely azimuthal. This implies that only the axial magnetic field contributes to the confining magnetic pressure, severely limiting the usefulness of the azimuthal magnetic field in a beta-limited plasma scenario.

Using the assumption of a weak normalized turbulent viscosity, usually valid in practice, the modulated-transport model (Stoltzfus-Dueck 2012 Phys. Plasmas 19 055908) is generalized to allow the turbulent transport coefficient to vary in an arbitrary way on radial and poloidal position. The new approach clarifies the physical interpretation of the earlier results and significantly simplifies the calculation, via a boundary-layer asymptotic method. Rigorous detailed appendices verify the result of the simple boundary-layer calculation, also demonstrating that it achieves the claimed order of accuracy and providing a concrete prediction for the strong plasma flows in the immediate vicinity of the last closed flux surface. The new formulas are used to predict plasma rotation at the core-edge boundary, in cases with and without externally applied torque. Dimensional formulas and extensive discussion are provided, to support experimental application of the new model.

The modulated transport model, a model kinetic ion transport equation for the pedestal and scrape-off layer (SOL), is generalized to self-consistently include effects of a single neutral particle species. The neutrals contribute additional transport terms, modifying the v ∥ -dependent orbit-averaged ion diffusivities of the original work and the resulting predicted intrinsic rotation of the ions. After making simplifying assumptions of the neutral transport, in particular taking the continuous transport limit via a short charge-exchange step expansion, we derive relatively simple analytic expressions that capture the diffusive neutral physics. Within the scope of the model’s validity, the neutral-driven intrinsic rotation can compete with the turbulence-driven intrinsic rotation. However, for physically motivated parameters, the neutral-driven intrinsic rotation appears negligible, either on a term-by-term basis or due to a strong cancellation between the neutral-driven momentum diffusion and pinch terms. It appears that a treatment containing finite charge-exchange steps is necessary to capture neutral transport of strong flow momentum into the confined region from the SOL.

Ion orbit loss has been used to model the formation of a strong negative radial electric field E _r in the tokamak edge, as well as edge momentum transport and toroidal rotation. To quantitatively measure ion orbit loss, an orbit-flux formulation has been developed and numerically applied to the gyrokinetic particle-in-cell code XGC. We study collisional ion orbit loss in an axisymmetric DIII-D L-mode plasma using gyrokinetic ions and drift-kinetic electrons. Numerical simulations, where the plasma density and temperature profiles are maintained through neutral ionization and heating, show the formation of a quasisteady negative E _r in the edge. We have measured a radially outgoing ion gyrocenter flux due to collisional scattering of ions into the loss orbits, which is balanced by the radially incoming ion gyrocenter flux from confined orbits on the collisional time scale. This suggests that collisional ion orbit loss can shift E _r in the negative direction compared to that in plasmas without orbit loss. It is also found that collisional ion orbit loss can contribute to a radially outgoing (counter-current) toroidal-angular-momentum flux, which is not balanced by the toroidal-angular-momentum flux carried by ions on the confined orbits. Therefore, the edge toroidal rotation shifts in the co-current direction on the collisional time scale.

Ion orbit loss is considered important for generating the radially inward electric field E _r in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code XGC. As the first application of this diagnostic, a neoclassical DIII-D H-mode plasma is studied using gyrokinetic ions and adiabatic electrons. The validity of the diagnostic is demonstrated by studying the collisional relaxation of E _r in the core. After this demonstration, the loss-orbit current is numerically measured in the edge pedestal in quasisteady state. In this plasma, it is found that the radial electric force on ions from E _r approximately balances the ion radial pressure gradient in the edge pedestal, with the radial force from the plasma flow term being a minor component. The effect of orbit loss on E _r is found to be only mild.