This is a self-sustaining planetary dynamo. A convecting, electrically conducting fluid swirling inside a rotating core converts motion into magnetic energy. A tiny seed field is amplified, sustained, and — because the underlying equations are chaotic — occasionally flips polarity, just like Earth's geomagnetic field has done hundreds of times.
Rikitake two-disk dynamo (dimensionless):
dx1/dt = -mu·x1 + x2·y
dx2/dt = -mu·x2 + (y - k)·x1
dy/dt = 1 - x1·x2
Magnetic Reynolds: Rm = U·L / eta — dynamo onset needs Rm > Rm_crit.
Earth's magnetic poles have swapped over 180 times in the last 80 million years. The most recent full reversal, the Brunhes–Matuyama event, happened about 780,000 years ago — and the field strength has dropped roughly 9% over the last 150 years.
This simulation models the planetary dynamo process, in which a rotating, convecting, electrically conducting fluid — such as the molten iron in Earth's outer core — generates and sustains a global magnetic field through electromagnetic induction. The underlying engine is the Rikitake two-disk dynamo, a set of coupled nonlinear differential equations that capture the self-exciting feedback loop: field drives current, current reinforces field, and nonlinear saturation combined with chaos produces irregular polarity reversals. Users can adjust rotation rate, magnetic Reynolds number, convection drive, and coupling strength to explore how each parameter shifts the dynamo between active, decaying, and reversal-prone regimes.
The dynamo effect is fundamental to planetary science and space weather: Earth's geomagnetic field shields life from solar wind particles, and its history of reversals is preserved in magnetized ocean-floor rocks, giving geophysicists a tape recording of the core's behaviour stretching back hundreds of millions of years.
The dynamo effect is the process by which a rotating, convecting, electrically conducting fluid converts kinetic energy into magnetic energy, sustaining a magnetic field against ohmic decay. It is responsible for the magnetic fields of Earth, the Sun, and most planets in the solar system. Without a continuous energy input from convection and rotation, the field would decay away within tens of thousands of years.
Use the Rotation rate (Omega) slider to speed up or slow down the core's spin — higher values drive stronger helical columns and faster field evolution. The Magnetic Reynolds number (Rm) slider is the most critical: drag it below 10 to watch the dynamo shut off and the field decay; raise it above 10 to sustain dynamo action. Convection drive (mu) and Coupling (k) tune the Rikitake engine's dissipation and feedback strength, which changes how frequently polarity reversals occur. Click Pause to freeze the simulation and inspect the timeline plot, or Reset to restart with a fresh seed field.
During a reversal the field magnitude shown on the timeline plot drops toward zero, the polarity indicator switches from NORTH to SOUTH (or vice versa), and the dipole axis arrow flips direction on the planet graphic. The reversal counter increments each time the dominant field component changes sign. In the real geomagnetic record such events unfold over 1,000 to 10,000 years, but in the simulation the chaotic Rikitake equations produce reversals on simulation-time scales that depend on the coupling parameter k.
The magnetic Reynolds number is defined as Rm = U L / eta, where U is the fluid velocity, L is the length scale of the flow, and eta is the magnetic diffusivity of the conductor. It compares how fast the moving fluid advects (carries) magnetic field lines relative to how fast ohmic diffusion smooths them out. When Rm exceeds a critical threshold (typically 10 to 100 depending on flow geometry), advection wins and dynamo action becomes possible. Below the critical value the field simply diffuses away faster than the fluid can regenerate it, which this simulation demonstrates when you drag the Rm slider below 10.
The alpha-omega dynamo is the dominant conceptual framework for planetary and stellar dynamos. The omega effect refers to differential rotation shearing a poloidal magnetic field (running from pole to pole through the interior) into a toroidal field (wrapping around the spin axis like a doughnut). The alpha effect refers to small-scale helical convection — driven by the Coriolis force in a rotating system — which twists toroidal field lines back into poloidal field, closing the regeneration loop. Without both effects operating together no sustained dipole field is possible, which is why slowly rotating or non-convecting planets like Venus lack a global magnetic field today.
The Rikitake model, published by Tsuneji Rikitake in 1958, consists of two coupled homopolar disk dynamos in which each disk's output current powers the other disk's coil. The governing equations — dx1/dt = -mu*x1 + x2*y, dx2/dt = -mu*x2 + (y-k)*x1, dy/dt = 1 - x1*x2 — form a three-dimensional autonomous chaotic system. It was one of the first mathematical models to reproduce irregular polarity reversals qualitatively similar to the geomagnetic paleomagnetic record, making it a canonical analogue dynamo despite being far simpler than full magnetohydrodynamic simulations of Earth's core.
Mars had an active dynamo and a global magnetic field for the first few hundred million years of its history, evidenced by strongly magnetized ancient crust in the southern highlands. The dynamo appears to have shut down around 4 billion years ago, most likely because Mars's smaller size allowed its core to cool below the threshold needed to sustain vigorous convection. Without convective overturn in the liquid outer core, Rm fell below critical and the field decayed. Earth retains its dynamo because its larger core is still losing heat slowly, and because solidification of the inner core releases latent heat and light elements that drive compositional convection.
Walter M. Elsasser and Edward Bullard independently developed the magnetohydrodynamic dynamo theory for Earth in the late 1940s and early 1950s. Bullard and Gellman produced the first numerical dynamo model in 1954. The theoretical foundations draw on the earlier work of Joseph Larmor, who in 1919 suggested that the Sun's magnetic field could be maintained by convective motions of conducting fluid — the first published dynamo hypothesis. Rigorous mathematical proof that self-exciting dynamos can exist (the anti-dynamo theorems by Cowling ruling out simple geometries) and later the Braginsky and Busse models in the 1960s-70s put the theory on a firm footing.
The solar dynamo drives the 11-year sunspot cycle, coronal mass ejections, and space weather events that affect satellite operations and power grids on Earth. Magnetars are neutron stars with extraordinarily strong magnetic fields generated by dynamo action in their dense, rapidly rotating interiors shortly after formation. Accretion disks around black holes sustain magnetic fields via the magnetorotational instability, a dynamo-adjacent process that drives turbulence and angular-momentum transport. In the laboratory, liquid-metal experiments such as the VKS (von Karman Sodium) experiment in France achieved the first experimental demonstration of a self-excited fluid dynamo in 2006.
The word dynamo itself comes from the electrical generator, and the rotating-conductor-in-a-magnetic-field principle underlies every electromagnetic generator from bicycle dynamos to multi-gigawatt power-station alternators. In geophysics, understanding the dynamo informs satellite constellation design (GPS, communication) because the geomagnetic field determines radiation belt structure and influences satellite drag. Paleomagnetic dating techniques based on field reversals are standard tools in stratigraphy. Magneto-hydrodynamic (MHD) simulations of the core are also used to forecast geomagnetic field evolution decades ahead, which matters for navigation systems that depend on accurate pole positions.
Several major questions remain open: Why are geomagnetic reversals irregular — occurring every few thousand to tens of millions of years — rather than periodic? What determines whether a reversal excursion (a partial flip) becomes a full reversal? How does the growing solid inner core change the dynamo's long-term behaviour? High-performance numerical simulations (such as those from the Johns Hopkins dynamo group and the ETH Zurich group) are beginning to reach more Earth-like parameter regimes, but the ratio of magnetic to viscous diffusivity (the magnetic Prandtl number) in real planetary cores is many orders of magnitude smaller than any current simulation can resolve, leaving a fundamental gap between models and nature.