Firstly, let us know where the halbach array usually applied:

Data security

Transportation

Motor design  

Permanent magnetic bearings

Magnetic refrigeration equipment

Magnetic resonance equipment.

The Halbach array is named for its inventorKlaus Halbach, a Berkley Labs physicist in the engineering division. The array was originally designed to help focus the beams in particle accelerators.

In 1973, “one-sided flux” structures were initially described by John C. Mallinson while he do an experiment of permanent magnet assembly and found this peculiar permanent magnetic structure, he called it “Magnetic Curiosity”.

In 1979, the American Dr. Klaus Halbach discovered this special permanent magnet structure during electron acceleration experiment and gradually improved it, and finally formed the so-called “Halbach” magnet.

The principle behind his innovative work is superposition. The superposition theorem states that the components of force at a point in space contributed by several independent objects will add algebraically. Applying the theorem to permanent magnets is possible only when using materials with coercivity nearly equal to residual induction. While ferrite magnets have this characteristic, it was not practical to use the material this way because simple Alnico magnets provided more intense fields at a lower cost.

The advent of high residual induction “rare earth” magnets SmCo and NdFeB(or permanent neodymium magnet) made the use of superposition practical and affordable. The rare earth permanent magnets allow developing intense magnetic fields in small volumes without the energy requirements of electromagnets. The disadvantage for electromagnets is the space occupied by electrical windings, and necessary to dissipate the heat generated by the coil windings.