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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Validation of NSFsim as a Grad-Shafranov equilibrium solver at DIII-D

Plasma shape is a significant factor that must be considered for any Fusion Pilot Plant (FPP) as it has significant consequences for plasma stability and core confinement. A new simulator, NSFsim, has been developed based on a historically successful code, DINA [1], offering tools to simulate both transport and plasma shape. Specifically, NSFsim is a free boundary equilibrium and transport solver and has been configured to match the properties of the DIII-D tokamak. This paper is focused on validating the Grad-Shafranov (GS) solver of NSFsim by analyzing its ability to recreate the plasma shape, the poloidal flux distribution, and the measurements of the simulated diagnostic signals originating from flux loops and magnetic probes in DIII-D. Five different plasma shapes are simulated to show the robustness of NSFsim to different plasma conditions; these shapes are Lower Single Null (LSN), Upper Single Null (USN), Double Null (DN), Inner Wall Limited (IWL), and Negative Triangularity (NT). The NSFsim results are compared against real measured signals, magnetic profile fits from EFIT [2], and another plasma equilibrium simulator, GSevolve [3]. EFIT reconstructions of shots are readily available at DIII-D, but GSevolve was manually ran by us to provide simulation data to compare against.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Grad-Shafranov model for compact quasisymmetric stellarators

A Grad-Shafranov equation (GSE) valid for compact quasisymmetric stellarators is derived by an asymptotic expansion around a vacuum field carried to first order. We obtain an equation for the existence of flux surfaces leading up to the GSE. The flux surface label must simultaneously satisfy the existence equation and the GSE, which generally leads to an overdetermined problem. We show how the overdetermined problem can be resolved within our model for a class of hybrid devices similar to that studied by Henneberg and Plunk [Phys. Rev. Res. 6, L022052 (2024)]. We are also able to solve the existence equation for flux surfaces analytically in the most general case by introducing a special coordinate system. This will enable us to carry out an optimization seeking to minimize the error in our GSE while obeying the flux surface existence equation, which will allow us to find solutions outside the class of hybrid devices. This will allow for a coarse-grained approximate search in the space of quasisymmetric equilibria that should be faster than a conventional stellarator optimization. Nevertheless, it would still be necessary to fine-tune the approximate solutions using conventional tools to obtain a more precise optimized equilibrium.

Nikulsin, N. (ORCID:0000000318611777)↗
DOE OSTI2025

Feedforward equilibrium trajectory optimization with GSPulse

One of the common tasks required for designing new plasma scenarios or evaluating capabilities of a tokamak is to design the desired equilibria using a Grad-Shafranov (GS) equilibrium solver. However, most standard equilibrium solvers are time-independent and do not include dynamic effects such as plasma current flux consumption, induced vessel currents, or voltage constraints. Another class of tools, plasma equilibrium evolution simulators, do include time-dependent effects. These are generally structured to solve the forward problem of evolving the plasma equilibrium given feedback-controlled voltages. In this work, we introduce GSPulse, a novel algorithm for equilibrium trajectory optimization, that is more akin to a pulse planner than a pulse simulator. GSPulse includes time-dependent effects and solves the inverse problem: given a user-specified set of target equilibrium shapes, as well as limits on the coil currents and voltages, the optimizer returns trajectories of the voltages, currents, and achievable equilibria. This task is useful for scoping performance of a tokamak and exploring the space of achievable pulses. The computed equilibria satisfy both Grad-Shafranov force balance and axisymmetric circuit dynamics. The optimization is performed by restructuring the free-boundary equilibrium evolution equations into a form where it is computationally efficient to optimize the entire dynamic sequence. GSPulse can solve for hundreds of equilibria simultaneously within a few minutes. GSPulse has been validated against NSTX-U and MAST-U experiments and against SPARC feedback control simulations, and is being used to perform scenario design for SPARC. The computed trajectories can be used as feedforward inputs that are connected to the feedback controller to inform and improve feedback performance. The code for GSPulse is available open-source at github.com/jwai-cfs/GSPulse_public.

equilibrium↗
DOE OSTI2024

EFIT‐AI: Machine Learning and Artificial Intelligence Assisted Equilibrium Reconstruction for Tokamak Experiments and Burning Plasmas (Final Report)

The EFIT-AI project is creating a modern advanced equilibrium reconstruction code suitable for tokamak experiments of burning plasmas. EFIT [1,2] was the first and is the most extensively used equilibrium reconstruction code in the world. This project builds on the production-level experience and adds key elements as follows. 1. A Model Order Reduction (MOR) version of the two-dimensional (2D) Grad-Shafranov equation solver (EFIT-MORNN) using physics-informed neural networks. 2. Improved optimization and data analysis capabilities using a Bayesian framework enhanced with machine learning. 3. A MOR version of the three-dimensional (3D) perturbed equilibrium reconstruction tool.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Centrifugal-mirror confinement with strong azimuthal magnetic field

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 x 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.

Grad-Shafranov↗