Halbach Arrays

Ι What Are Halbach Arrays?

Halbach arrays are special arrangements of multiple permanent magnets that concentrate the magnetic field on one side of the array while keeping the field on the opposite side very weak. This effect is achieved by placing the magnets in a specific pattern, where the magnetization direction of each adjacent magnet is rotated by a fixed angle.

The “one-sided flux” behavior of Halbach arrays was first noted by John C. Mallinson in 1973. In the 1980s, Klaus Halbach at Lawrence Berkeley National Laboratory independently developed and applied this concept to devices such as lasers, traveling wave tubes, and particle accelerator beams.

Thanks to their ability to enhance magnetic fields efficiently and the precise assembly they require, Halbach arrays have become one of the most representative and widely discussed forms of magnetic assemblies in modern engineering.

Advantages of Halbach Arrays

Halbach arrays offer a major advantage: they can generate significantly stronger magnetic fields than conventional magnet arrangements using the same amount of permanent magnet material. In some cases, the magnetic field produced by Halbach arrays can even exceed the remanence of the magnet material itself, effectively improving the efficiency of the magnetic circuit. A key feature of this design is the one-sided flux effect: the working face of the array concentrates most of the magnetic strength, while the opposite face has minimal leakage. This strong, single-sided field makes Halbach arrays especially useful in applications where a powerful, focused magnetic field is required on only one side.

Types of Halbach Arrays

Halbach arrays can be designed in several main types based on how the permanent magnets are arranged. The most common are linear (planar) Halbach arrays, circular (cylindrical) Halbach arrays, and curve-edged (segmented) Halbach rings. Circular Halbach arrays are further divided into outside diameter (O.D.) and inside diameter (I.D.) types, depending on whether the magnetic field is concentrated on the outer or inner surface. In practice, cylindrical Halbach arrays are built in various multipole configurations—such as dipole, quadrupole, hexapole, and octupole—to meet different field strength and field distribution requirements.

Linear Type

Curve-Edged (Segmented) Type

Circular Type with Inside Diameter (I.D.) Configuration (Dipolar)

Circular Type with Inside Diameter (I.D.) Configuration (Quadrupole)

Circular Type with Outside Diameter (O.D.) Configuration (Quadrupole)

Circular Type with Inside Diameter (I.D.) Configuration (Hexapole)

Circular Type with Outside Diameter (O.D.) Configuration (Hexapole)

Understanding Halbach Array Magnets

Circular Halbach arrays and linear Halbach arrays are composed of multiple magnet segments, usually with the same dimensions within each array. Circular arrays typically use arc-shaped or trapezoidal pieces, while linear Halbach arrays are assembled from rectangular blocks. These segments are magnetized in different directions to concentrate the magnetic field on one side, and the individual pieces are often referred to as Halbach array magnets.

In general, the smaller the change in magnetization direction between neighboring segments and the greater the number of segments, the more efficient the magnetic circuit becomes, producing a stronger and more uniform magnetic output. However, finer magnetization steps increase machining complexity and assembly costs, and beyond a certain point the added manufacturing difficulty outweighs the extra gain in magnetic strength.

Unlocking the Power of Halbach Array Motors

Halbach array motors are permanent magnet motors that use a Halbach array to significantly improve magnetic and overall performance. By arranging the magnets so that the Halbach array strengthens the air-gap field while minimizing flux in the rotor yoke, these motors are especially well suited to internal or external rotor designs with surface-mounted magnets. The result is higher magnetic flux density in the air gap, allowing the motor to be made smaller and lighter while increasing power density and efficiency. Because the rotor yoke carries less flux, it can be made with less ferromagnetic material, reducing rotor weight and inertia.

In a Halbach array, magnets with different magnetization directions can operate at an effective working point above 0.9 on the demagnetization curve, improving magnet utilization. At the same time, the air gap flux is close to sinusoidal, which reduces cogging torque and torque ripple.

This makes it possible to use fractional-slot concentrated windings without skewing the stator slots, helping Halbach array motors achieve smoother operation with low harmonic content in applications that demand high precision.