Recently, after more than a decade of intensive research, the team led by Professor Jian Liu from the Weihai Institute for Interdisciplinary Research at Shandong University, in collaboration with the computational mathematics team from Beijing Jiaotong University, has successfully established a general canonical guiding center theory that is independent of the specific magnetic field configuration. This work has paved a new path for the fundamental research and applications of guiding center dynamics and gyrokinetics in magnetized plasmas. Titled “Canonical Hamiltonian guiding center theory and classical intrinsic magnetic moment”, the research was published in Frontiers of Physics, a prestigious comprehensive physics journal, and has attracted widespread attention from the international academic community. Professor Jian Liu from Shandong University is the corresponding author of the paper. Associate Professor Ruili Zhang from Beijing Jiaotong University is the first author. Professor Xiaogang Wang, adjunct chair professor at Shandong University, is the key collaborator.
Guiding center dynamics is a key framework for describing and addressing multi-scale problems in magnetized plasmas, providing a crucial theoretical foundation for frontier fields such as controlled nuclear fusion, space physics, and astrophysics. To date, the predominant plasma guiding center theory is still based on the guiding center Lagrangian system proposed by Littlejohn in the early 1980s. Despite continuous efforts by many renowned plasma physicists to establish a complete canonical guiding center theory, traditional canonical methods have long been confined to the reduced four-dimensional phase space and are highly dependent on the specific magnetic field form, making it difficult to form a universal theoretical framework. This bottleneck has not only severely restricted the completeness of guiding center theory but also hindered the establishment of long-term and accurate gyrokinetic descriptions for complex magnetized plasma systems. Furthermore, it has posed a fundamental obstacle to exploring the physical structure of guiding center systems and developing numerical algorithms with excellent structural properties.
To address this core scientific challenge, Professor Jian Liu's team leveraged the advantages of interdisciplinary collaboration, integrating plasma physics and computational mathematics. By synthesizing multidisciplinary theoretical approaches such as gyrokinetics, Hamiltonian systems, and multi-scale analysis, the team conducted sustained research. Using two different derivation methods, the team obtained three equivalent canonical expressions of guiding center dynamics, laying a solid foundation for the systematic development of guiding center symplectic algorithms and canonical gyrokinetics.
This work contributes scientific value in several key dimensions. From the perspective of fundamental theory, it derives a new guiding-center Lagrangian via two independent methods, and for the first time demonstrates that guiding-center dynamics form a canonical Hamiltonian system with two constraints in six-dimensional phase space, yielding three equivalent expressions. A clear "pseudo-particle" model beyond gyro-scale is established, making the dynamics self-consistent and physically complete. Furthermore, for the first time, the study reveals the origin of the intrinsic magnetic moment from a multi-scale modeling perspective, offering a fresh perspective for understanding the nature of the interaction between microscopic particles and magnetic fields.
From the perspective of fundamental theory, the canonical framework clarifies the symplectic structure, enabling the systematic development of guiding center symplectic algorithms with a theoretical foundation. Through guiding center numerical simulations of plasma distribution evolution in magnetic mirror fields, it has been verified that the symplectic mid-point method based on this theory maintains energy relative errors within an extremely small range during long-term simulations. In contrast, traditional non-geometric algorithms (such as RK4) exhibit significant error growth due to coherent accumulation as the simulation progresses. Guiding center symplectic algorithms will become an essential method for long-term, accurate simulation of guiding center dynamics in complex magnetic fields, providing technical support for key challenges such as magnetic field design, confinement optimization, and control prediction in controlled nuclear fusion devices. Furthermore, this theory serves as a core basis for developing canonical gyrokinetic theory and symplectic gyrokinetic PIC simulation algorithms and codes.
Original link: https://doi.org/10.15302/frontphys.2026.026200
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