F. Carpanese | Searcharxiv

arXiv2026

A tutorial on inversion-based shape control with design application to NSTX-U

One of the most common designs for magnetic control in tokamaks is to ``linearize an equilibrium'' to obtain a sensitivity mapping, then invert this mapping in order to determine the feedback control currents or voltages. For this work, we refer to this broad class of methods as inversion-based shape control (IBSC). In this work we describe the IBSC framework in a comprehensive manner and show how variations such as using dynamic voltage mappings and quadratic-program constrained control fit naturally into the framework. Despite the prevalence of IBSC, some of these extensions and the challenges associated with specific variations of IBSC are less widely known. We pay special attention to the challenge of decoupling the interaction between shape control and vertical control, which was a source of degraded vertical control performance on NSTX-U. This work is intended to provide a systematic overview of IBSC, and to that end, we have provided background material, proposed design procedures, and tutorials on the magnetic control design process within the appendices. Applying the systematic design procedure to NSTX-U, we find that the vertical control bobble on NSTX-U can be removed via decoupling, and that the vertical control phase margin can be improved by 6 degrees just by including PF1A and PF2 as vertical actuators.

physics.plasm-ph↗

arXiv2025

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 (FBEE) 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 to inform and improve feedback performance. The code for GSPulse is available open-source at https://github.com/jwai-cfs/GSPulse_public.

physics.plasm-ph↗