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What is a magnetic multipole?
July 7, 2008

Mathematically, a pole is any geometric singularity. For example, the Earth’s north and south poles are places where lines of longitude meet in singularities. In other words, the longitudes of these poles are undefined. Actual, physical poles don't seem to exist. Black holes are theoretical singularities, but are saved by having an event horizon. (They may be singularities, but not in this Universe!) Electrons are saved from being singularities by wave-particle duality.

In electromagnetism, the term “pole” refers to a point where field lines meet. Electric field lines, for example, meet at point charges. One point charge is called a monopole. Two charges form a dipole. Three form a tripole, and so forth. Of course, real charges are spread out over the surfaces of physical objects, so they aren't really singularities.

Magnetic fields never have actual poles, either. They do, however, have regions of “magnetic concentration” that may appear like poles when observed from the outside. For example, the ends of a long solenoidal coil of wire carrying a current appear to be magnetic poles. In actual fact, these solenoid ends really only form approximately spherical concentrations with diameters equal to that of the coil. Inside the coil, the field is fairly uniform. Outside the coil, it appears to have two poles, so it is a dipole. It is useful to classify magnetic field geometries as if there really were poles.

Physicists have found experimentally that, unlike electric fields, magnetic fields can only form shapes with even numbers of poles. That is, there are magnetic dipoles (2), quadrupoles (4), hexapoles, (6), and so forth, but there are no magnetic monopoles. This fact annoys some theoretical physicists no end.

Magnetic fields take on only geometries with an even number of poles.

Some years ago, I was involved in a series of development projects making useful multipoles out of anisotropic permanent magnet material. The term “anisotropic” simply means the material has a grain, like wood. It is easy to magnetize anisotropic magnetic material parallel to the grain (which is called the “easy axis”), but impossible to magnetize it perpendicular. I know because we tried it. We cut a piece of anisotropic barium ferrite into a cube one inch to a side with the easy axis parallel to the sides. Then, we clamped it into a very large electromagnet with the electromagnet’s field perpendicular to the easy axis.

Anisotropic magnetic material has a grain direction called the easy axis.

We had to clamp it because unclamped, the cube spun to point its easy axis parallel to the field. A technician almost lost a finger trying to hold it by hand.

Turning the electromagnet current up to several times what it would take to fully magnetize the magnetic material parallel to its easy axis had no discernible magnetizing effect across the easy axis. It just did not magnetize. The technicians continued to turn up the juice until finally the sample simply exploded! The pieces then spun to reorient their easy axes parallel to the electromagnet field, magnetized completely and flew to the electromagnet’s pole pieces.

We used this material, as well as other anisotropic materials, such as samarium cobalt, to create a number of ring-shaped multipole structures. For example, we built magnetic quadrupole lenses to focus proton beams in the world’s first privately owned linear accelerator. We also designed dipoles to steer charged particle beams around corners.

Anisotropic material was important for these devices because it has the unique property of steering magnetic field lines. The figure below shows a structure we designed and built for magnetic resonance imaging (MRI). Unlike conventional dipole magnets, this device concentrates all of the magnetic force lines into the ring’s interior, greatly increasing the field’s strength and uniformity. The field outside of the structure is almost non-existent.

Carefully designing structures made of anisotropic permanent magnet material makes it possible to have exquisite control of the magnetic field shape.

Also read: Magnetic RAM rockets into space

Posted by Charlie Masi on July 7, 2008 | Comments (0)