Field Precision title

Reflection of Magnum solutions

We can reduce computation time for three-dimensional magnetic-field solutions in Magnum through the use of symmetry planes. The application of symmetry conditions on boundaries makes it possible to cut the size of solution volumes to a half, a quarter and even an eighth of their original size. The speed increase follows from two effects: 1) a reduced number of nodes and 2) faster convergence with a smaller mesh.

A symmetry plane can cause problems if the magnetic field solution will be used for charged-particle beam simulations in OmniTrak because the plane often contains the main beam axis. A solution that covers only a fraction of the beam propagation volume degrades accuracy for two reasons:

  • Reflection conditions must be applied when particles reach the plane, with attendant interpolation errors.
  • The collection of points for second-order field interpolations is skewed.

For this reason, we introduced a reflection capability in MagView to generate field solutions that cover the full beam volume. Although the feature is described in Magnum manual, users often miss it because the program has so many capabilities. In this article, I will discuss an example to demonstrate the feature and to illustrate the choice of reflection parameters.


Figure 1. Reflected magnetic field solution cmagr.gou showing the symmetry boundary.

Figure 1 shows the geometry — the top half represents the CMAG example supplied with Magnum. The iron pole has the shape of the letter C. The coil on the right-hand side (light blue and pick rectangles) creates a dipole field in the air gap at the left. The original CMAG solution covers the region y ≥ 0.0 cm with a condition of fixed reduced potential in the plane y = 0.0 cm:

φ = 0.0 A-m2 [1].

If the applied field Hs (created by the coils) is normal to the plane, then Eq. 1 implies that the magnetic flux density B is also normal to the plane. This is the desired symmetry condition for a dipole magnet. The condition on applied field is ensured by including the full drive coil set, above and below the plane y = 0.0 cm.

The first step is to run MetaMesh and then Magnum to create the solution file CMAG.GOU. To create a solution file that covers both positive and negative regions along y, we load the original solution in MagView and click on File operations/Save reflected solution. Supply the output file name CMAGR.GOU. The dialog of Fig. 2 appears — the values are appropriate for this example:

  1. The reflection plane is YDn (y = 0.0 cm)
  2. Inversion of the values of φ and ψ means that the field generated by magnetic materials (proportional to the gradient) is normal to the boundary.
  3. The applied field component Hy should have the same value on each side of the boundary, while the components parallel to the symmetry plane (Hx and Hz) reverse.


Figure 2. Reflection properties dialog.

Clicking OK saves the new solution file. Figure 1 shows the magnitude and direction of the magnetic flux density (B). Figure 3 shows a plot of By(x,0,0) along a scan line from x = -3.0 cm to 3.0 cm. The line shows interpolated values using the full solution (CMAGR.GOU) and the cicrcles are values calculated from CMAG.GOU. There is a slight difference, and other tests confirm that values from the full solution are more accurate. You might ask: how could a bit of mathematical trickery(copying field values to a symmetric location on the other side of a reflection plane) increase the accuracy of the solution? Actually, the procedure does affect the solution accuracy, but rather the accuracy of interpolations. The method in MagView involves collecting node values in the vicinity of a test point. If the collection volume extends above and below the point, the symmetry conditions on field components are rigidly enforced.


Figure 3. Scan of By(x,0,0). Line: full solution. Circles: half solution.

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