In the ideal case, shown above, this superposition would produce a field above the plane which is twice as large as if the structure were uniformly magnetized, and no field below the plane. However, in reality the ideal case is never observed and a very small field is produced on the underside. This arrangement can be continued indefinitely to produce large arrays.

These “one-sided flux” structures were first discovered by John C. Mallinson in 1973, who described them as “curiosities” with the potential to improve magnetic tape recording technology. However, their true potential wasn’t realised until the 1980s, when Berkley physicist Klaus Halbach independently rediscovered this magnetic phenomenon and created Halbach arrays for use in particle accelerators.Halbach produced the arrays using the ferromagnetic material cobalt to generate strong magnetic fields for focusing and steering the particle accelerator beams.

Halbach arrays now have many applications and are used in a range of systems of varying complexity. One of the simplest applications of Halbach arrays is in refrigerator magnets. In this case the one-sided flux properties are exploited in order to boost the holding power of the magnet. Variable arrays of magnetics rods can also be combined to create simple locking systems. If the magnetizations of the rods are arranged so the field is maximised above the plane and minimised below it, the flux confinement can be flipped by rotating each rod 90 ^o.

A more advanced example of a Halbach array in action is in a Maglev train track or Inductrack, where magnetic levitation is used to support the carriage. The magnetic arrays lift the train a small distance above the track and can support a weight of up to 50 times that of the magnet. The operation is based on the principle of induction; as the array is passed over the metallic track coils, the variations in the magnetic field induces a voltage in the track. The track then creates its own magnetic field and, similarly to when you attempt to push the two like poles of bar magnets together, when this field aligns with the field produced by the Halbach array, repulsion causes the train to levitate. Maglev trains do not suffer from many of the frictional forces which slow down traditional wheeled trains and are able to provide high speed transportation. In fact, the Japanese SCMaglev train system, which reached 361 mph in 2003, currently holds the Guinness World Record for the fastest rail transportation.

Halbach arrays are also used in advanced scientific experiments such as synchrotrons and free electron lasers (FELs), where they are known as Halbach ‘wigglers’. FELs have a very wide and highly tunable frequency range, and are used in many applications ranging from medical to military. A Halbach wiggler is one of the core components of a FEL, where the array’s magnetic field is used to periodically ‘wiggle’ a beam of charged particles (usually electrons). The wiggling effect causes a change in the direction and therefore a change in the acceleration of the particles. This in turn leads to emission of high intensity synchrotron radiation (photons) when combined with an external laser source.

It is also possible to create Halbach cylinders and rings, where the magnetic field is strong inside the ring or cylinder but negligible outside, or vice versa depending on the arrangement of magnets. These structures are typically used for brushless AC motors, where traditionally stray fields can reduce torque and efficiency. However, because Halbach cylinders are intrinsically shielded by their structure, with almost all flux contained within the centre, they are able to avoid this problem and produce higher torques.