Summary

When there is translational periodicity and then the external magnetic field is provided by an external current source such as LOOP, GCE, ARC, etc., the external magnetic field must have the same periodicity, so in principle, an infinite number of current elements must be input periodically. However, this is not practically possible. This section describes how to deal with such cases.

Explanation

As an example, consider a two-dimensional axisymmetric magnetostatic field analysis as shown in Fig. 1. There is an iron core in the center, which is excited by an axisymmetric coil (LOOP). Suppose such a structure is arranged with equal spacing in the z-direction. The blue and light blue areas are air. The analysis is assumed to be vertically symmetric and also symmetric on the upper side of the domain. These are the planes with Ht=0. The air part (including the coil part) is assumed to be the reduced potential region. Since it is impossible to define an infinite number of LOOPs in practice, a finite number of LOOPs are arranged as shown in Fig. 2, so that the magnetic field is similar to that of the periodic LOOPs in the analysis domain. In this example, 5 LOOPs are arranged. The analytical results are shown in Fig. 3. Good results are obtained.

Fig.1 Analysis model

Fig.2 Computation Model with five LOOPs are placed

Fig.3 Magnetic flux distribution in case of approximation with 5 coils

There is another possible method of analysis for such cases. Only the coil and the air region around it (light blue area in Fig. 1) are considered as the reduced potential region, and the other air region (dark blue area) is changed to the total potential region. In this case, only one LOOP input is needed as shown in Fig. 1. The boundary surface must be a total potential region, including the outer boundary. However, the bottom surface of Fig. 1 can be a reduced potential region since a single LOOP field satisfies the symmetry.

In this way, the symmetry condition is imposed on the total potential, so asymmetry of the source magnetic field is not an issue. This result is shown in Fig. 4, which shows little difference from Fig. 3. This method cannot be used when the coil crosses the symmetry plane. Also, the coil must be contained within the mesh region. When there is rotational periodicity, it is possible to do the same and only define the coil for one period.

Fig.4 Magnetic flux distribution for a model with one coil and a total potential region around the coil.

Download

1 coil 　　Sample data DL

・ input
・ pre_geom2D.neu ：Mesh data

5 coils 　　Sample data DL

・ input
・ pre_geom2D.neu ：Mesh data