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The original title: "geomagnetic field → low EQ: a bar magnet; high EQ: wonderful MHD ~"

Why does the earth have a magnetic field? That's a good question. The earth is indeed a magnet, though it is weak. A good refrigerator sticker is 200 times stronger than it. As a very rough approximation, you can think of the earth's magnetic field as formed by a strip magnet located in the center of the earth, which is roughly consistent with the earth's axis of rotation, but tilts about 11 degrees. The point at which the north-south axis of this bar magnet intersects the earth's surface is called the geomagnetic (north-south) pole. Due to the tilt of the magnet axis, the geomagnetic north and south poles are not in the same position as the geographical north and south poles.

This picture shows how the magnetic field of the earth is approximately represented by the magnetic field of a bar magnet. The blue line represents the earth's axis of rotation, with the geographical north and south poles at the top and bottom. The powder line represents the direction of the strip magnet with north and south magnetic poles. Photo: JrPole, CC BY-SA 3. 0.

We imagine that the south pole of the strip magnet points to the north of the earth, while its north pole points to the south. This is why the geomagnetic poles in the north of the earth actually correspond to the magnetic south pole, while the geomagnetic poles in the south of the earth correspond to the magnetic north pole.

For the poles, that's not all. Because the image of the bar magnet is only an approximation, the image of the north and south poles of the geomagnetism is only an approximation of the real magnetic poles of the earth's magnetic field. The real magnetic pole is the point where the line of magnetic force points vertically down on the earth. Unlike the geographical north and south poles and the geomagnetic north and south poles, the real magnetic poles are not facing each other, they also move independently of each other. At present, the magnetic poles of the Arctic seem to be moving northwest at a speed of 45 kilometers a year. In addition, geological records show that the earth's magnetic field can even be reversed. The last time this happened was about 780000 years ago.

The location of the magnetic north pole and the geomagnetic north pole in 2017 is shown on the map together with the geographical north pole. Figure: Cavit, CC BY-SA 4.0.

Where does the magnetic field come from? No one knows the exact answer, but the accepted theory is that the earth operates like a generator. To understand how this works, you must first remember some physics that you may have learned at school. When you move a conductive material in a magnetic field, an electric current is generated in the material, a process called electromagnetic induction. This process also takes place in generators that power bicycle lights. In contrast, electric current can also produce a magnetic field.

The earth has a strong core, which is about the size of the moon, but as hot as the surface of the sun. The core is surrounded by a liquid outer core, which is mainly composed of molten hot metal that can conduct electricity. Various processes taking place in the deep layer of the earth lead to the continuous movement of the liquid outer core (liquid convection).

Pictures of the internal structure of the earth: Kelvinsong, CC BY-SA 3.0. In order to understand the generator theory, we can assume that there is a magnetic field in the beginning. Don't worry about where the magnetic field comes from (for example, it may be caused by the solar wind), because all we need is it to start the geodynamo. Due to the movement of the conductive liquid outer core in the magnetic field, an electric current is generated. Due to the rotation of the earth, these currents are arranged in a spiral.

This chart shows the relationship between the motion of a conductive fluid (arranged in a row by the rotation of the earth) and the magnetic field produced by its motion. Photo: Andrew Z. Colvin, CC BY-SA 4.0. These currents in turn produce their own magnetic fields and enhance the original magnetic field, which makes the geomagnetic field evolve into what we see today. Due to the continuous convection of the liquid outer core and the continuous generation of electric current, the magnetic field can maintain itself for a long time. Because the motion of the liquid outer core is complex and changeable, the behavior of the magnetic field is also very complex.

A computer-simulated magnetic field of the earth. These lines represent magnetic field lines, blue indicates that the magnetic field points to the center, and yellow indicates that it is far away from the center. Dense groups of lines are located in the earth's core. Photo Source: NASA Old Earth, New Science the above discussion gives a (extremely rough) outline of the generator theory, but the details are far from simple. In order to really understand what is happening, to calculate the exact shape of the earth's magnetic field and to predict how it will evolve, you need to combine mathematics that describes fluid motion (Navid-Stokes equation) with mathematics that describes electromagnetism (Maxwell equation). People have done it, and have come up with a theory with a beautiful name-magnetohydrodynamics (Magnetohydrodynamics).

This theory can be used not only to describe the Earth's magnetic field, but also to describe the magnetic fields produced by other planets and stars. Understanding these magnetic fields can tell us a lot of information, such as the composition of celestial bodies and how they interact with the environment. Magnetohydrodynamics is also useful on Earth: it can help us make liquid metal batteries and cleaner power plants, and even help clinicians use magnetic fields to direct cancer drugs to tumors.

However, there is a problem. The central equation of magnetohydrodynamics is usually difficult to solve. To solve these problems, you either need to simplify them or rely on complex methods that provide approximate solutions, which usually require a lot of computing resources. At present, a large number of active research directions focus on the propulsion theory and improving the solution method, and the results of experimental observations are also taken into account in this process, such as the observation of the magnetic fields of planets and stars outside the earth.

Ulrich Ulrich Christensen, who works with Dom at the Newton Institute of Mathematics and Science (Isaac Newton Institute, INI), said: "of course, we all know about technical generators, but they only work because of the complex combination of components such as wires, sliding contacts, and so on." The iron core of the earth is an unstructured fluid ball, and it is more difficult to understand how a magnetic field is generated in such a system. "

Why do we care? The earth is not the only celestial body that has the behavior of "generator". Other planets in the solar system also have magnetic fields, just like the sun and other more distant stars. The sun's magnetic field determines the space weather our planet feels-including beautiful phenomena such as the aurora borealis and aurora borealis, but also dangerous phenomena such as solar flares. " Solar flares are bursts of particles emitted by the sun, which may pose a threat to low-orbit satellites because their electronic devices are very sensitive, "Christensen said." if you can better understand the causes of solar flares, and may one day be able to predict them, a lot of money can be saved. "

These applications are only speculative, but for other reasons, the magnetic field is also very interesting. "the magnetic field comes from deep inside the planet," explained Christopher Jones, another co-organizer of the INI project. "by studying these magnetic fields, we want to know more about the interior of the planet and the interior of the Earth, which is very difficult when you can only see the surface."

Excitedly, the aliens even played a role in the story. Because the magnetic field of a star can often determine the conditions of some of the planets orbiting it, it can be expected that the magnetic field will help us find life in other parts of the universe in the future.

Now is the time. First of all, the study of the magnetic fields of planets and stars is part of basic science and an attempt to unravel the mysteries of the universe. Now is a good time to focus on this area of research. In the past few decades, new technologies, such as the Juno spacecraft currently orbiting Jupiter, have provided an unprecedented wealth of information about the magnetic field, and more information is expected in the near future.

A computer model of the solar magnetic field. Photo: NASA Goddard Space Flight Center / Duberstein. These data not only provide important statistics on the magnetic fields of planets and stars-their strength and overall shape-but also provide a basis for the theories behind them. Take an example of the sun's magnetic field, which reverses its direction every 11 years. "We still don't have a detailed theoretical understanding of why this happened on this time scale and why it's not 20, 100 or five years," said Matthew Browning, another co-organizer of the INI project.

"the sun is an excellent laboratory for studying the theory of generators, but it is a laboratory that you can't control, for example, we can't make the sun spin faster." Observations of other stars can to some extent make up for this deficiency and reveal the similarities and differences between different rotation speeds or light and dark degrees of star magnetic fields. " Over the past decade or so, vast amounts of data have provided strong constraints on how people build different types of magnetic field models on different stars, which also provides some guidance for us to understand how the sun builds its own magnetic field. "

In general, observations have shown that the magnetic field properties of planets and stars can be very different. One of the key challenges that the INI project is trying to address is trying to explain these differences.

Models and simulations, like any physical theory, the theory that describes the "generator" models of celestial bodies and the earth is based on mathematical equations. This is the magnetohydrodynamics mentioned above. The behavior of conductive fluids, such as the liquid iron that forms the outer core of the earth, and the magnetic field they produce, need to be described by this theory.

A class of theories such as magnetohydrodynamics allow people to build mathematical models and describe the "generator" behavior of the earth or other planets and stars. Then, these models can be used to establish the computer simulation of the magnetic field, thus providing a method for people to compare the theory with observation. If the model has a good grasp of the relevant physical processes, then the simulated magnetic field should be similar to what we observe in reality. If the simulation results are not consistent with the observations, then you can know that there is something missing in the model. If the simulation produces a phenomenon observed in reality, it is possible to find out which part of the model is responsible for the phenomenon, thus providing clues about the physical processes that are at work.

"We have seen great progress in large-scale simulation [of the generator process] over the past decade or two," Christensen said. "" Through such simulations, we can explain many of the properties of the Earth's magnetic field-not only why it looks like a bar magnet at first glance, but also about how it changes over time and what its appropriate scale is. And why it occasionally reverses direction. Our understanding of stellar magnetism is not very deep, but what is certain is that we can expect more progress in this direction. With the help of direct numerical simulations and new observations, this is a rapidly developing field. "

Although chaos Challenge has made these progress, there are still many problems to be solved. " As far as we know, in the core of Earth and other planets, the motion is extremely complex, extremely chaotic, highly three-dimensional, and many events are driven by different sources, "explained Peter Davidson, another co-organizer of the INI project." But when you look at the magnetic field of Saturn, Jupiter or Earth from a distance, all you see is the magnetic field of a stable, occasionally reversed bar magnet. " The question is how such a complex and chaotic process can create something so stable, simple and ubiquitous.

A schematic diagram of Jupiter's magnetic field. Source: NASA / JPL-Caltech / Harvard / Moore, etc. The chaotic nature of the processes that occur inside planets and stars also hinders computer simulations. When there is chaos in a system, even things that occur in a very small range (such as the size of a room inside a star as big as the sun) can affect the overall behavior of the system. No supercomputer in the world can do all the necessary calculations to ensure that processes of different scales are reflected in the simulation.

This calculation problem also leads to a mathematical problem: generally speaking, there is no concise formula to give the solution of the magnetohydrodynamic equation. In fact, we are not even sure whether all the equations presented in this paper have solutions. This is why theoretical mathematics is very important in this field. "the development of mathematics is necessary," Dom said. "Measurement, observation or numerical models are not enough. People need to have a theoretical understanding of what is happening, which depends on the development of technical mathematics."

Original text link:

Https://plus.maths.org/content/why-earth-magnet

Https://plus.maths.org/content/mysterious-magnetism

The content of the translation only represents the author's point of view, not the position of the Institute of Physics of the Chinese Academy of Sciences.

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Marianne Freiberger, translator: Crunc, revision: Callo, Editor: Tibetan idiot

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