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1 MeV strongly saturated objective lens |
The data show a similar study for 1 MeV lens (paper of Tsuno and Honda in Optik in 1982), and it also demonstrates the way the meshes were defined in the past (just around 6000 mesh points were used, piecewise constant step, sudden change of mesh step at the coarse mesh position) and in which way they are recommended now.
For more discussion on this lens see B. Lencova, NIM-a 519 (Proc CPO6) or the accuracy plot, or even Munro and Tsuno chapters in the 1997 Handbook (again with incorrect statement that the problem is in the first order FEM, whereas the real problem lies in the small number of mesh points). At 1996 EUREM in Dublin in a joint paper with Mulvey and Tsuno it was clearly shown that already with 15000 mesh points and a more careful selection of mesh step the results are already correct. The results are given in the EOD flier.
Geometry
Original fine mesh
Piecewise constant mesh step
Graded fine mesh
Graded fine mesh automatically generated by EOD. New mesh has 40 points in gap instead of 20, lines more parallel with z-axis and it has expanding mesh step (graded mesh, max. 2.5%)
Field accuracy
The computation of magnetic field in a mesh of 85 thousand mesh points with highly saturated magnetic materials takes just 17 seconds on a PC.
In original mesh (red line) the error is 10x larger than in the improved mesh with graded step.
The B(z) even in the original mesh does not have the “hump” causing 10 % error of Cs computed by Tsuno!
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