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Dipoles: Halbach & Stelter Arrays


Halbach/Stelter dipoles are specialized dipoles that can produce large and/or uniform magnetic fields over large areas.  Magnetic field strength can exceed the remanence of the magnetic material.  We have manufactured dipoles that produced fields as large as 3.0 Tesla (30,000 Gauss).

Klaus Halbach, a professor with the University of California’s Lawrence Berkeley Labs, was an innovator in the application of permanent magnets to accelerator and synchrotron light projects around the world. 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 such as Sm-Co and Nd-Fe-B made the use of superposition practical and affordable. These materials 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 the need to dissipate the heat generated by the coils.

While Dr. Halbach pursued "high end" applications of superposition, Dexter’s Dick Stelter used the theorem in commercial applications. Halbach taught the use of "magic ring" dipoles to develop intense fields in a circular aperture. In this device trapezoidal magnets are assembled to form a ring. The orientation of each trapezoidal magnet is such that there is a continuous rotation of the magnetic vector in each half of the ring, and for an infinitely long ring, field strength in the aperture is proportional to the natural log of the ratio of OD to ID.

Stelter Arrays use the minimum number of rectangular magnet shapes to reach the desired results in a rectangular aperture. For a "Stelter Array", the relationships are similar, and the internal field is proportional to the natural log of the outer periphery to inner periphery ratio. Using rectangular shapes also permits "flux bottling" to shape the internal field. Highly uniform magnetic fields of over 2-3T can be routinely generated in a range of air gaps, and Dexter applications based on the patented Stelter Array include dipoles for NMR/MRI, "open" NMR, mass spectrometers, sputtering magnetrons, hard disk erasers, miniature rotary actuators, bulk erase tools and many more.

Hallbach and Stelter array dipoles are used where very high magnetic fields are required.  Halbachs are used when performance/uniformity are key requirements.  Stelter dipoles are cost effective, but do not produce as uniform fields.

Magnetic sensors indirectly measure properties such as direction, position, rotation, angle and current by detecting the magnetic field and its changes. The first application of permanent magnet was a third century BC Chinese compass, which is a direction sensor. Compared to other direct methods, such as optical or mechanical sensor, most magnetic sensors require some signal processing to get the property of interest. However, they provide reliable data without physical contact even in adverse conditions such as dirt, vibration, moisture, hazardous gas and oil, etc.

The most widely used magnetic sensors are:

  • variable reluctance,
  • Hall effect, and
  • reed switch.

Automotive crash safety systems use sensors based on a holding mechanism that can be closed or open using electrical current.  Hall effect sensors vary the output voltage in response to the changes in magnetic field. Reed switches have two overlapping ferromagnetic blades (reeds) hermetically sealed in a glass tube. When a magnetic field comes to the vicinity of a reed switch, the reeds are magnetized and attract each other, therefore close an electric circuit.

Sensor magnets can be simple as a bar or ring magnet for reed sensors, but can also be intricate and precise as those used in high definition measurements. Such examples are high resolution magnetic encoder magnets. austriamicrosystems makes high performance absolute and incremental linear magnetic encoder ICs, ranging from 8- to 12-bit resolution. One of the encoders require multipole strip or ring magnets, with 1mm±0.024mm pole width!.  We are proud to be a partner and magnet supplier for a wide range of austriamicrosystem sensor products.

Dexter_Sensor_Ring_Magnet Dexter_Sensor_ Strip_Magnet
Click on images to enlarge to see the following pieces labeled:

  • Magnet Bonding Surface
  • Magnetic Field Seen By Encoder
  • Magnetic Encoder
  • Motion Direction
  • Magnet

With the rapid development of GMR in the past decade, a new family of magnetic sensors has emerged - magnetoresistive sensors. Similar to Hall effect sensors, the major difference is that MR sensors detect current change instead of voltage. Permanent magnets can also be used in MEM sensor and CMOS magnetic sensor arrays to supply the magnetic field.

Dexter offers a variety of permanent magnet materials to suit your applications. Material selection depends on the field requirement, temperature, environment and cost. Please contact Dexter for assistance if you have special requirements on the sensor magnet.

When working with our engineering group, you might be asked:

1.  What is the minimum magnetic field strength requirement?

2.  How large a volume for the magnetic field do you need?

3.  Are there any limits to the external size of the dipole?

4.  Are there any uniformity specifications?

5.  Will it be in any harsh environments (temperature, humidity, etc.)?

Neodymium Iron Boron and Samarium Cobalt are typically used.  Hard ferrite materials can also be used but magnetic field output is reduced.  Because of the large internal demagnetization fields, Alnico is rarely used for Halbach/Stelter dipoles.

Aluminum is used for round Hallbach dipoles, whereas steel is used for square dipoles.


  1. What is the strongest magnetic field you can create?
  2. How large can the magnet be?
  3. I need a dipole to work in an oven, is this possible?
  4. I need to use this in a vacuum, is this possible?

1.  To date, the strongest magnetic field we have created is 3 Tesla (30,000 Gauss) across a 5mm air gap.

2.  Our largest magnet to date is cube shaped, approximately 2 meters per side.

3.  One typically uses Alnico materials for high temperature applications.  If Alnico material is not strong enough, then the dipole should be designed around the exterior of the oven.

4.  Yes, although the assembly should be sealed to prevent adhesive from outgassing.  Depending on the vacuum levels, there are some low outgassing adhesive that might work.

Because of the large number of variables, we do not have a standard Halbach/Stelter dipole design.  Each one is custom designed for a specific level of performance.  The design process can be completed within 1-2 weeks.  Generally prototypes are not needed and therefore turnaround time is typically 8 to 10 weeks.