I recently had an inquiry from a company that creates magnetic shielding for MRI facilities. In the past, the company installed iron sheets in response to customer specifications. The company's current goal is to assume more design responsibilities by developing an in-house computational capability. Figure 1 shows a typical MRI facility along with calculated contours of |B| supplied by the one of company's customers. A requirement is that |B| must be less than 5 gauss (0.0005 tesla) everywhere outside the central treatment room.
![](images/mri_shield_01.jpg)
Figure 1. Example of an MRI facility.
The complicating factor is that the inner workings of the MRI magnet are proprietary, so my contact would not know the geometry of the drive currents and iron poles that generate the field. He would have to base his shielding calculations entirely on fringing field patterns supplied by his customer (like that of Fig. 1). Everything inside the inner line would be a mystery. My contact was being pursued by a sales rep for a well-known alternative to Magnum. I won't name names, but for the sake of discussion let's refer to the program as Lucia di Lammermoor (LDL). The sales rep felt he had the perfect solution. On top of the high price of LDL, my contact could buy a special inverse-solution add-on that would determine the unknown magnet configuration from the fringing-field pattern. There are two drawbacks to this approach:
- James Clerk Maxwell says it's impossible.
- It's totally unnecessary.
The critical insight is that the fringing fields of any solenoid assembly (no matter how complex) approach those of a simple magnetic dipole in the region outside the assembly. This tutorial reviews the theory:
Magnetic Dipole Moment of a Coil Assembly
To emphasize the point, Figure 2 shows contours of |B| calculated by Magnum for a current loop of radius R = 0.5 m carrying current I = 1000.0 A (the plot plane includes the magnet z axis). The line shapes clearly resemble those of Fig. 1. Complicating the comparison is the fact that the lines and intervals of Fig. 1 (supplied by my contact's customer) are physically impossible. There are three possible explanations:
- LDL gave the wrong answer.
- The LDL user at the magnet manufacturer did not pay attention to the potentially large effects of computation boundaries on the weak fringing fields.
- The magnet manufacturer was reluctant to send actual data to my contact, so they had a draftsman create them.
![](images/mri_shield_02.jpg)
Figure 2. Fringing fields of a circular coil calculated by Magnum.
Supposing that some day my contact receives a PDF document with real data, here's how the analysis would proceed.
1) Use the Universal Scale (shown in Fig. 1) to measure the locations (zi) of contours |Bi| along the z axis and an axis normal to z passing through the magnet center (xi).
2) Calculate estimates of the magnet dipole moment from the equations
mi = Bi*zi^3/(µ0/2*p), mi = 2*Bi*xi^3/(µ0/2*p).
For a valid field distribution, all of the estimated values should be close, giving an average value m.
3) Set up a Magnum solution volume (large compared to the diagnostic room to minimize boundary effects). For the applied field, define a circular coil normal to z at the origin with a radius R comparable to that of the magnet assembly. Assign the coil current according to I = m/(p*R^2) to replicate the fringing field pattern.
4) Add shielding walls as needed, and run a standard Magnum calculation. Analyze the 5 gauss contour to make sure it is everywhere within the diagnostic room.
In the calculation, scaling relationships may be applied to deal with thin sheets of iron following the discussion in this tutorial:
Designing Magnetic Shields with PerMag and Magnum
To facilitate the application, we added two features to Magnum:
- We have modified the contour-line plot routines in MagView to enable users to enter a set of specific values (e.g., the 5 gauss limit).
- We have doubled the number of entries in the library of soft magnetic materials supplied with the code to include common shielding materials like M36.
Magnetic material data are available at http://www.fieldp.com/magneticproperties.html.
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