Is a miniature version of Earth's magnetic field too big for scientists to handle?

In "Too Hard For Science?" I interview scientists about ideas they would love to explore that they don't think could be investigated. For instance, they might involve machines beyond the realm of possibility, such as devices as big as galaxies, or they might be completely unethical, such as experimenting on children like lab rats. This feature aims to look at the impossible dreams, the seemingly intractable problems in science. However, the question mark at the end of "Too Hard For Science?" suggests that nothing might be impossible.

The scientist:Eric King, Miller Research Fellow in earth and planetary science at the University of California, Berkeley.

The idea: Earth's magnetic field was likely vital to the evolution of life, protecting our planet from solar output that might otherwise have stripped away our atmosphere and left early organisms vulnerable to dangerous radiation from the sun. Indeed, Mars' loss of its magnetic field is probably why its atmosphere dwindled away, apparently leaving the red planet a dead world. But how Earth's magnetic field came to be and why that of Mars vanished remains largely a mystery, "because we aren't really sure about the details of planetary magnetic field generation," King says.

Earth's global magnetic field or magnetosphere comes from its dynamo — electrically conducting fluids in the planet's liquid metallic core that flow turbulently due to convection of heat left over from the birth of the world. To learn more about Earth's dynamo, scientists would ideally like to create a model version of it.

The problem: The difficulty in developing a miniature version of Earth's dynamo comes mostly from the immense size of the planet's core. Shrinking it down to model size requires that the other factors, such as heat or the speed at which it spins become impossibly extreme.

"Let's say we had a 100-meter sphere filled with liquid metal," King says. "That's twice the size of the spherical icon of the Epcot Center, and this would already be a serious technical achievement. But, with enough money, it is not impossible."

"The first problem that arises after this is the fact that gravity is all wrong in the sphere — a sphere on the surface of the Earth feels a downward gravity, but gravitational acceleration in a planet is radially inward," he continues. "We could overcome this, in part, by rotating the sphere. Rotating fast enough, centrifugal acceleration would overcome gravity."

"You might then point out that centrifugal acceleration points outward," he says. In contrast, Earth's core has gravity that points inward and heat that radiates outward. To compensate, "our core model could be designed with outward gravity and inward heat flux — technically difficult with large amounts of heat, but mathematically identical."

However, "this is where it starts to become too hard for science," King explains. To achieve true dynamic similarity with Earth's core, to start with, "our sphere would have to rotate insanely fast to match core dynamics — more than 100,000 revolutions per minute. This means our 100-meter sphere would be moving about 100,000 miles per hour at its equator — that's 3,000 times the speed of sound." Still, if this were possible, only about 100 kilowatts of thermal power would be needed to drive the kind of turbulent flow we expect in Earth's core, due to the extreme strength of this artificial gravity.

"Let's say we restrict the speed of rotation such that the sphere doesn't break the sound barrier — in a 100-meter sphere, this limits the rotation rate to less than about 1 hertz, or about 10 revolutions per minute," he says. "Rotating slower, though, means we need much more heat to drive the necessary amount of convection ... in this case, we would need about a gigawatt of heat power, roughly the output of a nuclear reactor."

"It's even worse if we try to reduce the size of the container," King adds.

The solution? There are nevertheless a handful of teams worldwide that seek to simulate at least some aspects of Earth's dynamo using liquid metals.

"Notably, a French team in Cadarache was able to generate a dynamo in a roughly 1-meter cylindrical-ish container of liquid sodium driven by iron propellors. This is an important step, but in many ways is still far from Earth-like," King says. "Future plans include a 3-meter rotating spherical shell of sodium in Dan Lathrop's lab Maryland. The liquid metal will be driven to turbulence by rotating the inner and outer spherical surfaces at different rates. This isn't exactly how flow is driven in the core, but the experiment should generate its own field, which is notoriously difficult in experimental fluid dynamics."

Moving away from liquid metals, "Cary Forest's group in Wisconsin is developing a 3-meter plasma dynamo experiment, which should generate magnetic fields rather easily, and will permit them to examine dynamos for a broad range of fluid properties and flow fields," he notes. "Alternatively, computer simulations of rotating convection in spherical shells can successfully generate Earth-like magnetic fields. They do this by reducing the severity of turbulence for computational tractability and increasing the fluid's electrical conductivity — essentially, these simulations are like rotating convection in superconducting honey. Attacking the problem from this direction nonetheless illuminates the physics of magnetic field generation in planets."


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