31 Search Results

This paper describes new modeling capabilities for predicting H-mode pedestal profiles in spherical tokamaks. Temperature profiles for NSTX discharges 132543 and 132588 are modeled by coupling the \textsc{astra} transport solver with neoclassical transport and gyrokinetic-based reduced models for electron temperature gradient (ETG) and kinetic ballooning mode (KBM) instabilities. A quasi-linear surrogate model for ion-scale transport is developed using linear \textsc{gene} simulations, requiring only a single free parameter calibrated to one discharge. Time-evolving the temperatures with fixed density yields good agreement with experiments for both discharges. Systematic analysis of the transport mechanisms reveals that neoclassical transport is huge across the entiremore » pedestal region for the ion channel. ETG turbulence is large in the plasma edge and low density gradient region, contributing substantially to the electron channel. However, KBM/MHD-like modes also drive significant transport in both the ion and electron thermal channels, making them essential for accurate pedestal modeling. Further refinements, including explicit E×B shear suppression and scaled ETG transport, produce quantitative but not qualitative improvements. This work lays the foundation for predictive modeling of future devices. This paper is on arxiv and has been submitted to Nuclear Fusion.« less

The National Spherical Torus Experiment Upgrade (NSTX-U) is preparing to resume operation, representing a crucial step toward realizing compact, cost-effective fusion pilot plants. In advance of this, extensive modeling and data analysis have been conducted to advance the physics basis for low-aspect-ratio, high-performance plasma regimes, focusing on three core objectives: confinement and stability, power and particle handling, and steady-state operation. Significant progress has been made in understanding the electron temperature flattening in high-β plasmas, which is shown to be driven by a complex interplay of magnetohydrodynamic instabilities (e.g. non-resonant infernal modes), fast-ion-driven Alfvén eigenmodes, and electron and ion-scale micro-instabilities, particularlymore » Kinetic Ballooning Modes (KBMs), whose destabilization is strongly dependent on parallel magnetic field fluctuations (δB_∥). Furthermore, a new gyrokinetic critical pedestal model was developed, accurately predicting pedestal structure by identifying KBMs as the primary stability limit, offering a critical constraint for future high-confinement scenarios. To address the challenge of high heat flux, novel liquid lithium plasma-facing components were modeled. The analysis confirmed that lithium vapor shielding is a self-regulating mechanism for heat mitigation, while also emphasizing that strong main ion parallel flow is essential to minimize core lithium contamination. Finally, progress toward steady-state operation was anchored by developing the required physics basis and control tools. This includes predictive modeling for reversed magnetic shear sustainment, demonstrating that magnetic island-induced bootstrap current reduction is negligible in STs, and advancing real-time control and disruption avoidance capabilities. The development of high-speed surrogate models (e.g. MMMNet) provides computationally efficient tools vital for non-inductive scenario optimization and integrated, low-disruptivity operations planned for NSTX-U.« less

This study employs electron-scale gyrokinetic simulations to investigate the electron temperature gradient (ETG) driven instabilities, turbulence, and transport in the pedestal region of the National Spherical Torus Experiment, comparing non-lithiated (narrow pedestal) and lithiated (wide pedestal) scenarios. Our findings reveal that, in the non-lithiated case, a branch of strongly unstable ETG modes exhibiting finite parallel magnetic field fluctuations ($$\delta B_{\parallel} \neq 0$$) emerges at the pedestal top and upper density pedestal region. This branch is uncovered only when $$\delta B_{\parallel}$$ is retained in the simulations and is associated with substantial electrostatic electron heat flux. This region of strong ETG transportmore » corresponds to the only region in the plasma where the pressure gradient is far below the critical gradient for kinetic ballooning modes. We investigated the origin of this finite $$\delta B_{\parallel}$$ ETG branch by analyzing the gyrokinetic field equations. Nonlinear saturation is also analyzed and contrasted for simulations with and without $$\delta B_{\parallel}$$. In contrast with the nonlithiated case, ETG modes in the lithiated case produce substantial transport in the steep gradient region, but are negligible at the pedestal top.« less

Microtearing modes can play a crucial role in electron heat transport in tokamak plasmas, affecting both energy confinement and overall performance. This study investigates microtearing modes (MTM) stability and turbulence in a JET pedestal through gyrokinetic simulations using the Gene code, complemented by a reduced eigenvalue model. The focus is on how MTM properties depend on key plasma parameters, including collisionality and plasma beta β—the ratio of plasma pressure to magnetic pressure—the normalized toroidal wavenumber k_yρ_s⁠, where ρ_s denotes the ion sound gyroradius (typically a few millimeters in edge plasmas) and isotope mass. Collisionality enhances MT growth rates, while increasingmore » β leads to a shift from MTMs to kinetic-ballooning modes, typically for k_yρ_s⁠, where ρ_s ≲ 0.2⁠. A purely collisionless branch of MTMs persists at low k_yρ_s⁠, where ρ_s with distinctive properties including non-negligible particle flux and ion thermal transport. Isotope mass scans reveal modest reduction of MTM growth rates as ion mass decreases. Nonlinear simulations produce experimentally relevant transport levels. Numerical experiments turning off zonal flows and fields identify the critical role of zonal flows and zonal fields in regulating MTM turbulence. Their removal leads to a significant increase in electron heat flux. These findings provide new insight into MTM-driven transport and its impact on tokamak confinement and lay a foundation for reduced modeling and predictive capabilities.« less

A velocity dependent, kinetic model for line radiation is developed for continuum kinetic codes. It has been implemented in the full-f gyrokinetic code Gkeyll. The total radiation for a charge state is modeled as an advection in velocity space with a form of $$\nabla_v \cdot(v\nu(v)f(v))$$, guaranteeing particle conservation. The velocity dependence (in the form of an effective frequency $$\nu(v)$$) is found through fitting the energy loss of the operator, i.e. the second velocity moment, to the radiation data in the OpenADAS database. Therefore, each individual transition does not need to be evaluated every time step, significantly reducing the computational costmore » of including line radiation in a kinetic model. The dependence on velocity instead of the usual, temperature, allows the radiation to be computed from non-Maxwellian electron distribution functions: We benchmark the model against a collisional radiative model using isotropic non-Maxwellian distribution functions. A velocity dependent model of radiation can more accurately describe the radiation in the more kinetic regimes expected in reactor-scale devices. The velocity dependence qualitatively captures the quantum mechanical need for a minimum velocity before any radiation occurs.« less

Typically, fluid simulations are used for tokamak divertor design. However, fluid models are only valid if the scrape-off layer (SOL) is highly collisional. This assumption is valid in many present-day experiments but is questionable in the upstream SOL of some high-power scenarios envisioned for burning plasmas and fusion pilot plants. This paper reports on comparisons between fluid and kinetic simulations of the SOL for upstream parameters and geometry representative of the Spherical Tokamak for Energy Production fusion pilot plant. The SOLPS-ITER (fluid) and Gkeyll (gyrokinetic) codes are operated in a two-dimensional axisymmetric mode, which replaces turbulence with ad-hoc diffusivities. Inmore » kinetic simulations, we observe that the ions in the upstream SOL experience significant mirror trapping. This substantially increases the upstream temperature and has important implications for impurity dynamics. We show that the mirror force, which is excluded in SOLPS’s fluid equations, enhances the electrostatic potential drop along the field line in the SOL. We also show that the assumption of equal main ion and impurity temperatures, which is made in commonly used fluid codes, is invalid for the regimes explored here. The combination of these effects results in superior confinement of impurities to the divertor region in kinetic simulations, consistent with our earlier predictions [Kotschenreuther et al., in 29th IAEA 29 Fusion Energy Conference (IAEA, London, UK, 2023)]. This effect can be dramatic, reducing the midplane impurity density by orders of magnitude. These results indicate that in lower collisionality SOL’s the tolerable downstream impurity densities may be higher than would be predicted by fluid simulations, allowing for higher radiated power while avoiding unacceptable core contamination. Our results highlight the importance of kinetic simulations for divertor design and optimization for fusion pilot plants.« less

Abstract A fundamental dynamical constraint—that fluctuation induced charge-weighted particle flux must vanish- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density gradients, when large enough, lead to a violation of the constraint and hence preclude unstable modes and turbulent transport. This mechanism, then, broadens the class of configurations (in magnetized plasmas) where these high confinement states can be formed and sustained. The need for velocity shear, the conventional agent for TB formation, is obviated. The most important ramifications of the constraint is to permit a charting out of the domains conducivemore » to TB formation and hence to optimally confined fusion worthy states; the detailed investigation is conducted through new analytic methods and extensive gyrokinetic simulations.« less

Abstract A gyrokinetic threshold model for pedestal width–height scaling prediction is applied to multiple devices. A shaping and aspect ratio scan is performed on National Spherical Torus Experiment (NSTX) equilibria, finding ${\mathrm{\Delta }}_{\mathrm{ped}}=0.92A^{1.04}{\kappa }^{-1.24}{0.38}^{\delta }{\beta }_{\theta ,\mathrm{ped}}^{1.05}$ for the wide-pedestal branch with pedestal width ${\mathrm{\Delta }}_{\mathrm{ped}}$ , aspectmore » ratio A , elongation κ , triangularity δ , and normalized pedestal height ${\beta }_{\theta ,\mathrm{ped}}$ . The width–transport scaling is found to vary significantly if the pedestal height is varied either with a fixed density or fixed temperature, showing how fueling and heating sources affect the pedestal density and temperature profiles for the kinetic-ballooning-mode (KBM) limited profiles. For an NSTX equilibrium, at fixed density, the wide branch is ${\mathrm{\Delta }}_{\mathrm{ped}}=0.028{(q_{\text{e}}/{\mathrm{\Gamma }}_{\text{e}}-1.7)}^{1.5}\sim {\eta }_{\text{e}}^{1.5}$ and at fixed temperature ${\mathrm{\Delta }}_{\mathrm{ped}}=0.31{(q_{\text{e}}/{\mathrm{\Gamma }}_{\text{e}}-4.7)}^{0.85}$ $\sim {\eta }_{\text{e}}^{0.85}$ , where $q_{\text{e}}$ and ${\mathrm{\Gamma }}_{\text{e}}$ are turbulent electron heat and particle fluxes and ${\eta }_{\text{e}}=\mathrm{\nabla }\ln T_{\text{e}}/\mathrm{\nabla }\ln n_{\text{e}}$ for an electron temperature $T_{\text{e}}$ and density $n_{\text{e}}$ . Pedestals close to the KBM limit are shown to have modified turbulent transport coefficients compared to the strongly driven KBMs. The role of flow shear is studied as a width–height scaling constraint and pedestal saturation mechanism for a standard and lithiated wide pedestal discharge. Finally, the stability, transport, and flow shear constraints are combined and examined for an NSTX experiment.« less

Abstract This paper reports on the refinement (building on (Hatch D.R. et al 2022 Phys. Plasmas 29 062501)) and application of simple formulas for electron heat transport from electron temperature gradient (ETG) driven turbulence in the pedestal. The formulas are improved by (1) improving the parameterization for certain key parameters and (2) carefully accounting for the impact of geometry and shaping in the underlying gyrokinetic simulation database. Comparisons with nonlinear gyrokinetic simulations of ETG transport in the MAST pedestal demonstrate the model’s applicability to spherical tokamaks in addition to standard aspect ratio tokamaks. We identify bounds for model applicability: themore » model is accurate in the steep gradient region, where the ETG turbulence is largely slab-like, but accuracy decreases as the temperature gradient becomes weaker in the pedestal top. We use the formula to model the electron temperature profile in the pedestal for four experimental scenarios while extensively varying input parameters to represent uncertainties. In all cases, the predicted electron temperature profile exhibits extreme sensitivity to separatrix temperature and density, which has implications for core-edge integration. The model reproduces the electron temperature profile for high ${\eta }_e=L_{ne}/L_{Te}$ scenarios but not for low η _e scenarios in which microtearing modes (MTMs) have been identified. We develop a proof-of-concept model for MTM transport and explore the relative roles of ETG and MTM in setting the electron temperature profile.« less

Global linear electromagnetic gyrokinetic simulations of micro-tearing modes (MTMs) growing in the wide pedestal of the ELM-free NSTX discharge #132 588 are reported. Two micro-tearing branches growing near the surfaces of safety factor q = 4 (pedestal top) and q=5–6 (pedestal) are simulated. The frequencies of these MTMs with low toroidal mode number (n ranging from 3 to 6) are in agreement with the ones of quasi-coherent fluctuations present on the magnetic spectrogram. No kinetic ballooning mode (KBM) is observed at experimental values of β; instead, the experimental plasma lies 20% below the critical global KBM threshold. This confirms local simulation results statingmore » that experimental NSTX profiles lie in the KBM stability region. Carbon impurities, which are abundant in this plasma, were found to play a significant role. Neglecting them leads to a ∼50% error in the growth rates.« less