Research Background
When walking through a dense forest, a compass is indispensable for knowing which direction to take, and it works because the Earth has a magnetic field. By around the second century, it was already known that a magnetic compass points north, and in the seventeenth century the idea that the Earth is a single giant magnet had been suggested by William Gilbert. Albert Einstein regarded the origin of the Earth's magnetic field as one of the major unsolved problems in science. The dipole magnetic field of the Earth*1 (upper left Fig. 1) was shown to be generated by magnetohydrodynamic interactions associated with thermal convection of liquid iron in the Earth's outer core - that is, by the dynamo process*2 - through magnetohydrodynamic simulations*3 almost simultaneously by the simulation group at the National Institute for Fusion Science (NIFS) and a group at the University of California, Los Angeles (UCLA). On the other hand, paleomagnetism studies to date have shown that the geomagnetic field reverses its direction (polarity) at irregular intervals of roughly once every several hundred thousand to ten million years (lower left Fig. 1), and that each polarity reversal takes place over a timescale of the order of one thousand years. Many magnetohydrodynamic simulation studies have investigated both the generation of such a dipole magnetic field and its periodic reversals. A quarter century ago, the NIFS simulation group succeeded in reproducing the phenomenon in which an Earth-like magnetic field undergoes repeated irregular (aperiodic) polarity reversals [Li, Sato & Kageyama, Science (2002)] (right Fig. 1). Unfortunately, however, the trigger mechanism that causes the magnetic poles to reverse irregularly again and again remains completely unknown, making this a problem of exceptional difficulty. In the present study, in order to move closer to clarifying the reversal phenomenon, a research team at NIFS and the Graduate University for Advanced Studies, SOKENDAI, focused on how magnetic-field polarity is determined and carried out magnetohydrodynamic simulations under a simplified setting with simple convection without the complexity of the Earth.
Research Results
Using a three-dimensional magnetohydrodynamic simulation code in which the Yin-Yang grid*4 is adopted, the NIFS/SOKENDAI research team led by Assistant Professor Hiroki Hasegawa, Associate Professor Hiroaki Ohtani, and Professor Emeritus Tetsuya Sato carried out a detailed investigation of the mechanism that determines magnetic-field polarity in a convective dynamo in a spherical-shell plasma with the same geometry as the Earth's outer core. The calculations were performed on NIFS supercomputers - the Plasma Simulator "Raijin" and "Sosei"*5. In the simulations, nearly steady helical convection shown in Fig. 2 was imposed, and 50 different random weak magnetic perturbations were used as the initial magnetic field. As a result, every run evolved into a state dominated by a dipole magnetic field, and the two polarities - northward and southward - appeared with nearly equal probability. Even when the direction of convection was reversed, this probability did not change, showing that the polarity is determined not by the background convection but by the initially imposed weak magnetic perturbations. The research team also found that the magnetic-field growth process can be divided into two stages: an initial stage in which polarity reversals recur periodically on the magnetic-diffusion timescale*6, and a later stage in which the polarity becomes fixed and the magnetic field reaches a stable state. Furthermore, when the research team performed additional calculations in which weak magnetic perturbations were again imposed after the stable state had been reached, no significant change was observed in the already formed dipole magnetic field. This indicates that the stable state of the dipole magnetic field is extremely robust, and that small magnetic perturbations do not cause a polarity reversal (Fig. 3).
This study shows that, in a spherical-shell dynamo, the dipole magnetic field exists as two stable equilibrium states. It also suggests that the polarity of the Earth's magnetic field may have been determined by tiny initial fluctuations and then robustly maintained thereafter. The research team therefore believes that, to trigger magnetic reversals, this stable state must be broken by mechanisms outside the standard framework of magnetohydrodynamic theory - for example, anomalous magnetic diffusivity*6 or viscosity produced by microscopic plasma instabilities.
Significance of the Results and Future Prospects
Previous simulation studies have mainly understood magnetic-field reversals as periodic phenomena occurring on the magnetic-diffusion timescale. In contrast, actual geomagnetic reversals are known to occur irregularly on far longer timescales, and their physical mechanism remains unresolved. In the early 2000s, the NIFS simulation group succeeded in reproducing such long-timescale irregular magnetic reversals (right Fig. 1). The bi-stability of the magnetic field revealed in the present study may seem at first glance to contradict such reversal phenomena. The research team, however, believes that this very relationship contains an important clue to understanding the trigger mechanism of geomagnetic reversals.
In the future, identifying the factors that break this stable state is expected to lead to elucidation of the physical mechanism of geomagnetic reversals.
Magnetohydrodynamic simulations inevitably contain finite-difference (numerical) errors. In fluid simulations, continuous space is represented by dividing it into many grid points (a process called discretization), and this finite differencing (discretization) brings locally numerical dissipation of the magnetic field. The research team believes that previously reported simulation results showing irregular reversal phenomena may have been caused by such discretization errors. In fluid simulations, these errors become amplified in regions where energy concentrates (stagnation points). In the real world, however, plasmas are not continua but composed of particles, and in regions like these "stagnation points," microscopic plasma instabilities may arise when the particle distribution departs from equilibrium. The research team considers it possible that such microscopic effects act as the trigger for magnetic reversals. Going forward, they plan first to use high-accuracy magnetohydrodynamic simulations to examine carefully how much can be reproduced within the range of conventional models, and to clarify the limits of those models, before developing new models that incorporate microscopic physical processes.
This study was conducted as part of the "Future-Telescope Project" launched by the Japan Society for Simulation Technology (JSST) and NIFS. One of the goals of this project is to predict natural phenomena such as earthquakes, which can cause disasters, and to minimize the damage resulting from them. Once a geomagnetic reversal begins, the Earth's magnetic field becomes extremely weak for the roughly thousand years required for the reversal to complete, and may no longer be able to shield the Earth from high-energy cosmic rays arriving from space. This could have major impacts on ecosystems and on humankind. Elucidating the mechanism of geomagnetic reversals is therefore of great importance also for predicting and minimizing such adverse effects.
Glossary
*1 Dipole magnetic field: The most basic magnetic-field configuration, produced by a bar magnet or a coil, in which a north pole and a south pole appear as a pair. The Earth's magnetic field is dominated by its dipole component, but it is not a pure dipole; rather, it is a superposition of many components, including quadrupole and octupole terms.
*2 Dynamo process: The process by which the motion of an electrically conducting fluid, such as liquid metal or plasma, generates and sustains a magnetic field.
*3 Magnetohydrodynamic simulation: A simulation that reproduces on a computer the behavior of an electrically conducting fluid such as plasma, based on the equations describing the interaction between fluid motion and electromagnetic fields (the magnetohydrodynamic, or MHD, equations).
*4 Yin-Yang grid: In the computational grid of an ordinary spherical polar coordinate system, the grid spacing becomes extremely narrow near the poles, making numerical treatment very difficult. The Yin-Yang grid was developed to avoid this problem by Prof. A. Kageyama of Kobe Univ. et al. It consists of one spherical-polar grid excluding the polar regions (Yin) and another spherical-polar grid tilted by 90 degrees (Yang), overlapped in a baseball-like arrangement.
*5 Plasma Simulator "Raijin" and "Sosei": "Raijin" was a vector-type supercomputer operated from July 2020 through June 2025 (consisting of 4,320 high-speed computational units called vector engines, with a theoretical peak performance of 10.5 petaflops). It is especially powerful for fluid calculations such as those in the present study. Heterogeneous computing in combination with scalar processors was also possible. "Sosei" is the latest-generation supercomputer jointly procured by NIFS and the National Institutes for Quantum Science and Technology (QST), and it began operation in July 2025. It consists of three subsystems with different hardware (A, B, and C) and reaches a total theoretical peak performance of 40.4 petaflops.
*6 Magnetic diffusion time / magnetic diffusivity: In an electrically conducting fluid, finite electrical resistance causes the magnetic field not to move perfectly with the fluid, but instead to diffuse and decay. The time required for this diffusion is the magnetic diffusion time, and the quantity describing the rate of diffusion is the magnetic diffusivity. If there is no electrical resistance, the magnetic field moves with the fluid and does not diffuse (the so-called frozen-in condition).
Acknowledgments
This work is supported by the NINS (National Institutes of Natural Sciences) program of Promoting Research by Networking among Institutions (Grant Number 01422301). Numerical simulations were carried out on the "Plasma Simulator (PS)" (NEC SX-Aurora TSUBASA and LX series) of NIFS under the auspices of the NIFS Collaboration Research programs (NIFS24KISM005).
