tools — field visualization

Interactive Halbach Array Visualizer

A Halbach array rotates the magnetization direction from one element to the next, so each magnet's field reinforces its neighbors on one side and cancels them on the other. The result: nearly all the flux on one face, almost none on the back. Drag the controls — the field map below is computed live from the array you build.

interactive — live field map

Brightness shows field magnitude |B|; small arrows show field direction. The large arrows on each magnet show its magnetization. Switch to circular mode to see the configuration used in couplings and motor rotors.

number of elements

10 magnets

rotation per element

flip strong side / invert field

show field direction arrows

strong side vs. weak side — mean |B| ratio — a conventional magnet of the same size measures ≈ 1 : 1

what to try — flip the strong side and watch the flux jump to the other face with no change to the magnets themselves — only their rotation order. Switch 90° to 45° rotation: more elements per wavelength smooths the field and strengthens the working side. In circular mode, note how the dipole ring traps a nearly uniform field in the bore while the outside stays quiet.

the physics — why one side cancels

Think of each magnet as contributing two field patterns: one from its magnetization pointing through the array's thickness, one from magnetization pointing along its length. Rotating the magnetization 90° per element phases these two patterns a quarter-wavelength apart — on one face they add, on the other they subtract.

field boost	The working face of an ideal linear Halbach array carries up to √2 ≈ 1.4× the field of the same magnets all oriented conventionally — while the back face drops toward zero.
no back iron needed	Because the array self-shields, it delivers a strong one-sided field without a steel backing plate — saving weight in motors, actuators and levitation systems.
finer rotation, better field	45° steps (8 elements per wavelength) approach the ideal continuously rotating magnetization more closely than 90° steps (4 per wavelength): stronger fundamental, weaker harmonics.
circular arrays	Wrapping the pattern into a ring with magnetization angle rotating at (k+1)× the position angle creates a 2k-pole field: k=1 gives a uniform dipole field across the bore (magnetic couplings, NMR, beam optics); k=2 gives a quadrupole gradient.

where they're used — applications

brushless & linear motors	Halbach rotors raise air-gap flux and delete rotor back-iron, improving torque density and efficiency — the same reason they appear in flywheel energy storage.
magnetic couplings	Circular dipole arrays transmit torque through sealed barriers (pumps, mixers) with higher torque per volume than conventional pole arrangements.
levitation & transport	Inductrack-style maglev and conveyor levitation exploit the strong one-sided traveling field.
sensors & holding	One-sided flux keeps stray field away from nearby electronics, and doubles usable holding force per magnet weight in fixturing.

we stock halbach arrays — pre-assembled linear and circular Halbach configurations are available off the shelf in our halbach array category, and custom arrays — element count, wavelength, grade and carrier — are built to print through custom magnets & assemblies.

practical — specifying a halbach array

wavelength vs. reach	The field decays as e^(−2πz/λ): a longer wavelength (larger elements) throws field farther; a shorter one concentrates it near the surface. Match λ to roughly 2–4× your working gap.
assembly forces	Adjacent elements repel hard in a Halbach order. Arrays must be fixtured and bonded — never assume press-fit assembly. This is the main reason to buy them assembled.
grade & temperature	Element interactions push working points down; use one grade-suffix step more temperature margin than a lone magnet would need. Check with the temperature derating calculator.
tolerances	Angular placement error converts directly into harmonic content and back-side leakage. Specify magnetization-direction tolerance (typically ±3°) on drawings, not just dimensional tolerance.

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