In the quest for clean, sustainable energy, tokamaks—doughnut-shaped devices that confine hot plasma with magnetic fields—have long been a promising avenue for fusion power. However, their efficiency and stability can be disrupted by tiny misalignments in the magnetic fields, known as error fields. A recent study published in the journal *Nuclear Fusion* (translated from the original title) and led by J. Halpern of Columbia University sheds new light on how to accurately model these error fields, potentially paving the way for more robust and efficient tokamak designs.
The research focuses on the critical assumption of axisymmetry in tokamak modeling. Axisymmetry refers to the symmetry of the magnetic field around the tokamak’s central axis. The study reveals that the choice of reference frame for axisymmetry significantly impacts the accuracy of perturbed equilibrium models, which predict how the plasma will respond to error fields. “The incorrect choice of reference frame can lead to incorrect predictions of the plasma response,” Halpern explains. “This is a crucial detail that can affect the overall performance and stability of the tokamak.”
To determine the correct reference frame, Halpern and his team used fully 3D equilibria generated by the VMEC code, a sophisticated tool for modeling tokamak plasmas. They analyzed two specific cases: the SPARC tokamak, which has independently offset toroidal field (TF) coils and central solenoid (CS)/poloidal field (PF) coils, and the NSTX-U tokamak, which features an independent centerpost consisting of the inner legs of the TF coils and CS. Their findings suggest that the appropriate reference frame can be well approximated by the centroid of the TF coil set in SPARC and by the radial location of the TF coil inboard legs at the midplane in NSTX-U.
The study also delves into the limits of linearized magnetohydrodynamic (MHD) theory, which is commonly used to model plasma behavior. By analyzing the magnetic field line displacement, the researchers identified the point at which linear theory begins to break down. They found that linear theory remains valid for existing tokamak tolerances, validating the use of perturbative codes to set these tolerances. However, they caution that for future devices with relative tolerances larger than approximately 1% of the minor radius, the margin becomes notably small.
This research has significant implications for the energy sector, particularly for companies and research institutions developing tokamak-based fusion reactors. By providing a clearer understanding of how to model error fields, the study enables engineers to set more accurate assembly tolerances, ultimately leading to more stable and efficient tokamak designs. “This study gives engineers the confidence to use 3D perturbative models for determining assembly tolerances,” Halpern notes. “It provides insight into the correct applications of the theory, which is essential for advancing fusion energy technology.”
As the world continues to seek sustainable energy solutions, the insights from this research could play a pivotal role in shaping the future of fusion power. By refining the modeling of error fields, scientists and engineers can work towards overcoming one of the key challenges in tokamak design, bringing us one step closer to harnessing the power of fusion energy.