Hybrid high gradient permanent magnet quadrupole

This paper presents an innovative compact permanent magnet quadrupole with a strong gradient for potential use in future light source lattices. Its magnetic structure includes simple mechanical parts, rectangular permanent magnet blocks and soft iron poles. It has a wide aperture in the horizontal plane to accommodate an x-ray beam port, a common constraint in storage ring-based light sources. This specificity introduces field quality deterioration because of the resulting truncation of the poles; a suitable field quality can be restored with an optimized pole shape. A $82\mathrm{T}/\mathrm{m}$ prototype with a bore radius of 12 mm and a 10 mm vertical gap between poles has been constructed and magnetically characterized. Gradient inhomogeneities better than ${10}^{-3}$ in the good field region were obtained after the installation of special shims.

Figure 1

H-type hybrid PM quadrupole design.

Figure 2

Hybrid quadrupole geometrical dimensions. The contour integral for Ampere’s theorem computation is shown. All PM have the same dimension for simplicity. PM can be placed on poles top to increase the gradient.

Figure 3

3D view of the Radia quadrupole model including the mesh. The mesh is based on multiple polyhedrons. The model is divided into ten longitudinal slices concentrated on the edge. The pole tip has a higher mesh density because the field computation accuracy mainly depends on this area. Several simulations with different mesh refinements on the pole shape are done to check the stability of the results.

Figure 4

Gradient reduction with PM vertical displacement.

Figure 5

Integrated gradient simulation, computed with RADIA.

Figure 6

Hybrid quadrupole pole shape before and after optimization.

Figure 7

PM sensitivity to magnetic errors. Errors are in percent and angle errors are in degrees. Initial position: PM blocks without vertical translation; translated: PM blocks with 5 mm translation. Six blocks with independent magnetic errors are installed in each slot.

Figure 8

Simulations of magnet sensitivity to mechanical errors.

Figure 9

Hybrid PM prototype CAD model. Dimensions of the prototype are indicated (left). The upper mechanical parts of the quadrupole are removed to show the PM arrangement in slots (right). The total mass of this prototype is 45 kg and the weight of PM material is 12 kg.

Figure 10

Characteristics of the 36 NdFeB PMs used in the prototype. The average remanent field is $\mathrm{BR}=1.137\mathrm{T}$. These PM are recycled from an old undulator.

Figure 11

Quadrupole prototype installed on a stretched wire measurement bench.

Figure 12

Homogeneity of the integrated gradient along the horizontal and vertical axes. Simulation and measurement results are plotted. Results after correction shim implementation are shown.

Figure 13

Correction shim profile. The machined shape is composed of six slots with different thickness. The shim material is steel AISI 1006.