Scientists measured the lateral forces that hinder the progress of nuclear fusion ignition in a tokamak reactor.

The work is published in Nuclear Fusion. The origins of research into plasma disruptions trace back to the JET experiment era, where it was first observed that lateral forces could reach significant amplitudes, leading to horizontal displacements of the tokamak torus. These forces were linked to asymmetric magnetic perturbations caused by plasma deformations that disrupt the symmetry of the design. Early models described the plasma as a rigid current-carrying ring, allowing for force estimation using classical formulas; however, experiments demonstrated that these models yielded incorrect force values.

Over the past decades, scientists have proposed various theoretical approaches to explain the observed phenomena. Recently, a new model was introduced by Pustovitov and his student Mironov—at that time a student at MIPT, which is based on the principle of the absence of an integral electromagnetic force acting directly on the plasma. This principle establishes a strict constraint on the allowable modes of deformation, thereby offering a more conservative estimate of the lateral force. However, the tokamak also contains a complex array of conductive structures, making the task of force estimation particularly challenging.

In a recent study, a group of scientists under the aegis of an international consortium conducted a unique experiment aimed at investigating the lateral forces that arise during plasma disruptions and act on the vacuum chamber walls. In the experiment, physicists explored the dynamics of the plasma discharge. The primary objective was to measure and analyze the lateral (horizontal) force resulting from asymmetric magnetic perturbations, as well as to compare the experimental results with the theoretical predictions of various models.

The unique experiment was conducted in Italy by an international team that included a Russian group of scientists working under the auspices of the international ITER project.

The study examined three cases: VV, TSS, and PSS. The VV case refers to the estimation of the lateral (horizontal) force calculated by considering only the resistive vacuum vessel (VV) as the conductive structure. Thus, in this approach, the influence of other elements (such as the passive stabilizing shell—PSS, and the toroidal support structure—TSS) is not taken into account. The parameters of VV (its geometry, material, wall time, and electrical resistance) are used to determine the contributions to the lateral force arising during plasma disruption, based on measurements of the magnetic field outside the vessel.

The force in the TSS case refers to the estimation of the lateral (horizontal) force calculated by considering only the resistive toroidal support structure (TSS) as the sole conductive wall. In this approach, the parameters of TSS (its material, geometry, wall time, and electrical conductivity) are used to compute the force acting on this structure, without accounting for the influence of other structures (such as VV or PSS). However, it is important to note that in the TSS analysis, contributions are often overlooked, as they are considered to be shielded by the more effective passive stabilizing shell (PSS).

The force in the PSS case is the estimation of the lateral (horizontal) force calculated on the condition that only the passive stabilizing shell (PSS) is considered as the conductive structure.

The researchers aimed to compare the magnitude of the lateral force computed using magnetic measurements with the predictions of three different models. These included the Mironov–Pustovitov model, which lacks an integral electromagnetic force, linking the lateral force to bending harmonics; the Riccardo–Walker–Nolla model, in which the plasma is treated as a current-carrying ring; and the Zakharov model, which evaluates the average toroidal magnetic field as the source of the force.

The integral lateral force on the wall was calculated using a surface integral over the entire toroidal surface of the vessel. This method allows for obtaining a "reference" value of the force against which the results from theoretical models were compared.

It was found that during the discharge phase, the amplitude of the radial component of the magnetic field increased exponentially, indicating a rise in lateral force. During the decay phase, a sharp decrease in the amplitude of bending modes was observed as the plasma transitioned to a more stable state.

A comparison of the models was conducted. It turned out that the Riccardo–Walker–Nolla model overestimates the lateral force by about 20 times compared to the reference data. The Zakharov model provides an estimate exceeding the experimental data by approximately three times, and its predictions often have the opposite sign when transitioning to a stable state. The Mironov–Pustovitov model systematically underestimated the force by about three times; however, its temporal variation qualitatively matched the experiment, indicating that it is the best of the three models.

The results demonstrate that traditional models, which do not account for the complex geometry and interaction of multiple conductive structures (vacuum vessel, PSS, and TSS), are unable to accurately describe the observed lateral force.

“Our experiment confirms that the lateral force arising during plasma disruptions significantly differs from the predictions of classical models. This indicates the necessity to consider not only the dynamics of individual bending modes but also the interaction of multiple conductive structures surrounding the plasma. We are confident that further research into these phenomena will enhance the stability of plasma discharges and bring us closer to the successful realization of nuclear fusion. Accounting for the complex interaction of multiple conductive walls (resistive vacuum vessel, passive stabilizing shell, and toroidal support structure) is a key factor for accurately calculating the lateral force in real installations,” emphasized Vladimir Pustovitov, a researcher at the Department of Plasma Physics and Chemistry at MIPT.

The results of the study are significant for the advancement of plasma control technologies in nuclear reactors. Understanding the mechanisms behind the formation of lateral forces will aid in developing new active plasma stabilization systems capable of correcting displacements and preventing unwanted disruptions. The use of magnetic sensors for direct measurement of lateral forces demonstrates the potential of such techniques for widespread application in plasma physics experiments, allowing for more accurate data collection without the need for mechanical sensors.

To reduce the discrepancy between experimental and theoretical estimates of lateral force, researchers will need to develop more complex modified models that can account for the interaction of multiple conductive structures and the influence of halo currents. Future experiments may focus on a more detailed study of the temporal evolution of bending modes and their impact on plasma displacement, which will help better understand nonlinear effects in discharge dynamics. Combining magnetic measurements with other diagnostic methods (such as optical and X-ray) may provide a more comprehensive understanding of the processes occurring in the plasma and facilitate the creation of integrated control systems.