FPGA-Enhanced Stabilization of High-Temperature Superconducting Coil Levitation for Magnetic Confinement Applications

Magnetic levitation using high-temperature superconducting (HTS) coils holds incredible promise in fields like plasma physics and fusion research, where stable and high-precision magnetic confinement is essential. However, achieving sustained magnetic levitation presents significant technical challenges, particularly when it comes to stability and control. The inherent instability of magnetic levitation, famously encapsulated in Earnshaw’s theorem, means that maintaining a levitated state requires some form of active feedback. Without such control, levitating objects are prone to drift or destabilize due to slight shifts in gravitational and magnetic forces. This instability becomes a critical issue for research environments, where even minute positional shifts can disrupt sensitive experiments and affect the accuracy of results. For HTS coils in particular, maintaining stable levitation for extended periods has been a long-standing obstacle, as small vertical fluctuations can compromise the field’s effectiveness.

Authored by A. Card, A. Deller, Matthew Stoneking, Jens von der Linden, and Dr. E. V. Stenson from Germany’s Max Planck Institute for Plasma Physics, introduces a creative, highly effective way to achieve stable magnetic levitation of HTS coils using real-time feedback control based on field-programmable gate array (FPGA) technology. Published in IEEE Transactions on Applied Superconductivity, this work has significant implications, particularly in magnetic confinement research for plasma physics and in applications related to fusion energy. Their study was driven by the need to create a stable magnetic levitation platform capable of supporting HTS coils over extended periods without significant positional drift. The primary application of this research centers around magnetic confinement of electron-positron plasmas in the Advanced Pair EXperiment – Levitating Dipole (APEX-LD). This experiment requires a highly controlled magnetic field generated by a levitated coil to study unique properties of low-energy plasmas. Given the critical role of magnetic confinement in plasma research, creating a stable levitation system would allow the researchers to explore plasma behavior with precision that was previously unattainable. A major challenge the researchers aimed to address was achieving a consistent and sustained magnetic lift while minimizing energy loss and handling thermal variations that can disrupt HTS coil stability. High-temperature superconductors like rare-earth barium copper oxide (ReBCO), which lose resistance at cryogenic temperatures, are particularly sensitive to heat. Any temperature fluctuations can result in current decay, which reduces the magnetic lift force and risks destabilizing the levitated coil. The use of an FPGA-based feedback system allowed the researchers to actively control the lifting force by adjusting current in the lifting coil, countering the effects of gravitational forces and enabling precise vertical positioning of the HTS coil. By combining this real-time feedback with laser displacement sensors to monitor the coil’s position, they hoped to overcome the limitations of traditional magnetic levitation and push the boundaries of what’s possible with superconducting technology. Their work not only seeks to advance the field of plasma physics but also lays the groundwork for future applications of stable, long-duration magnetic levitation in other high-precision research domains.

The authors focus on achieving long-term, stable levitation for an HTS coil designed to create a magnetic field that can confine electron-positron plasmas. The HTS coil, constructed from ReBCO without any insulation, functions under vacuum conditions, and the team leverages a carefully positioned water-cooled copper lifting coil to stabilize it. Through a PID (proportional-integral-derivative) feedback loop implemented directly on an FPGA, running at a 1 kHz refresh rate, the levitation is stabilized with impressive precision. They managed to sustain levitation for more than three hours with only minimal vertical displacement, which is no small feat when it comes to magnetic levitation. The backbone of this setup is the FPGA-based system, which continuously adjusts the current within the lifting coil to counteract gravitational pull and correct any vertical instability in the HTS coil’s position. This level of stabilization effectively addresses Earnshaw’s theorem, which traditionally asserts that magnetic levitation is inherently unstable without some form of active feedback. By integrating a real-time feedback loop, the researchers overcame this hurdle, achieving a stable vertical position for the coil with a mean displacement of -3 micrometers and a standard deviation of only 18 micrometers. This level of control is remarkable and opens doors for sustained, stable levitation in setups requiring long durations of uninterrupted magnetic fields. The magnetic levitation system centers around two essential coils: the floating HTS coil (F-coil) and the lifting coil (L-coil). The F-coil generates a magnetic dipole field when it’s energized by a persistent current, enabling it to confine charged particles effectively. Meanwhile, the L-coil, placed above the F-coil, provides the lifting force needed to counteract the HTS coil’s weight. This F-coil, crafted with a no-insulation design, achieves superconductivity around 91 K, ideal for the vacuum conditions needed for the research. A key part of this setup involves using laser displacement sensors to track the F-coil’s vertical position with precision. These sensors feed real-time data to the FPGA, which then adjusts the lifting coil’s current to hold the F-coil in place. The feedback loop’s operation at 1 kHz, combined with PID control fine-tuned through simulations, ensures a quick response time and precise control over vertical stability. The adaptability of the FPGA system also means that real-time parameter adjustments are possible, which helps maintain levitation stability over prolonged periods.

 To create an effective feedback mechanism, the authors performed extensive simulations to hone in on the most effective PID parameters. Using a one-dimensional model of the system, they tested a wide range of parameter sets to see which configurations would keep vertical displacement to a minimum. The team adjusted proportional, integral, and derivative parameters to optimize the balance and keep the coil stable within a range of ±22.5 mm, with the system instantly correcting any deviations thanks to the feedback loop. These simulations not only provided insights into how the system would behave but also revealed crucial adjustments needed to minimize any fluctuations in vertical positioning. Simulating various noise factors and response delays allowed the researchers to further refine the system, helping ensure a low risk of destabilization or accidental coil drop during real-world operation. In practice, the FPGA-controlled feedback system achieved stable levitation for over three hours, demonstrating impressive robustness and reliability in a real-world setup. Throughout the entire levitation period, the coil showed minimal drift, which validated the effectiveness of the feedback loop under operating conditions. The coil’s vertical displacement held within a standard deviation of just 18 micrometers, closely matching the stability predicted during simulations. During operation, the F-coil maintained a lifting force in equilibrium with gravity, keeping the HTS coil stable. As the persistent current in the HTS coil decayed over time, the lifting current was automatically adjusted to maintain position. While cooling and warming cycles inevitably affected current retention, the FPGA system’s constant monitoring and corrections ensured that even after approximately 3.5 hours, when thermal effects caused the F-coil to quench, the system handled the process smoothly.

In conclusion, the work by Max Planck Institute for Plasma Physics tea sets the stage for exciting advancements in stable, precision magnetic levitation, which is especially relevant for high-precision plasma physics experiments. The team’s APEX-LD experiment—intended to confine low-energy electron-positron plasmas—benefits directly from the stable confinement conditions this system enables, making it feasible to study plasma behavior in ways that would otherwise be challenging. The insights gained here could also extend to other magnetic confinement systems, particularly those that need to maintain stable magnetic fields over lengthy periods. Looking ahead, possible improvements include introducing active cooling mechanisms to extend levitation times well beyond the current 3.5-hour limit. Real-time adaptive tuning of PID parameters could further enhance stability, potentially adjusting for current decay and other dynamic changes within the system. We believe the study presents a meaningful leap forward in the field of magnetic levitation. Through precise, real-time stabilization using FPGA-based control and fine-tuned PID settings, the team at Max Planck Institute has addressed the unique challenges of levitating HTS coils within vacuum environments. This accomplishment not only sets a new benchmark for stability in magnetic confinement systems but also lays a solid foundation for future plasma and fusion research, promising new possibilities in stable, high-energy magnetic environments.