Design of Comb Fabricated Halbach Undulators

Abstract

An approach to fabricating Halbach array undulators using “combs” machined from single magnets is introduced. This technique is especially relevant to the fabrication of short period micro-undulators with period lengths considerably less than the few-centimeter-scale typical of current undulators. Manual, magnet-by-magnet assembly of micro-undulators would require the manipulation and alignment of thousands of magnets smaller than a grain of rice: comb fabrication dramatically increases the size of the basic unit cell of assembly with no increase in undulator period by creating many periods from a single piece, in a single machining modality. Further, as these comb teeth are intrinsically indexed to each other, tolerances are dictated by a single manufacturing step rather than accumulating errors by assembling many tiny magnets relative to each other. Different Halbach geometries, including M ′ = 2 , M ′ = 4 , isosceles triangle, and hybrid, are examined both from a theoretical perspective and with 3D magnetostatic simulations.

Permanent Helical Undulators with Strong Fields

“…We propose an alternative version of a permanent micro-undulator, which can be used to create an ultracompact X-ray FEL, the design of which is presented in [1]. To manufacture a planar micro-undulator assembled from magnetized NdFeB combs, in [1,3] it is pro-posed, in particular, to use the Wire Electric Discharge Machining. The same technology makes it possible to manufacture the proposed helical micro-undulator consisting of magnetized NdFeB helices with a micron accuracy.…”

“…One of the key elements in all projects of compact XFELs and IFELs are high-field micro-undulators. For example, in the XFEL-UC concept [1], this is a micro-undulator with a period of down to 3 mm and a field of 1 T. To do this, it is supposed to use a planar structure of Halbach lattices [2], assembled from solid combs of equally magnetized elements [3]. For the same purpose, we consider Halbach-type helical undulators of helices, each of which, like the combs in [1], is made of a single piece of ferromagnetic material [4].…”

“…Making the helix from one piece can also reduce the effect of possible deviations of the undulator field caused by the inhomogeneities of a rare-earth material and the directions of magnetization of its numerous individual elements. By analogy with a planar system of magnetized combs [3], to weaken the strong repulsion of oppositely magnetized and brittle NdFeB helices, when assembling the proposed design, a system of four combs but with spiral elements can be used (Fig. 3).…”

“…Let us compare the proposed hybrid Halbach-type helical system as a micro-undulator for a compact Xray FEL with a planar Halbach micro-undulator from comb elements considered in [1,3]. Table 1 lists several key parameters of electron bunches and a planar Halbach micro-undulator considered in the design of an ultra-compact XFEL with an electron energy of 1.6 GeV, an undulator period of 3 mm, and a radiation wavelength of 1.6 Å [1].…”

Towards an ultra-compact x-ray free-electron laser (Conference Presentation)

“…The HXR case examines the generation of x-rays near 1.6 Å using a U e = 1.6 GeV electron beam and a more ambitious undulator design; combining the concepts of cryogenically cooled, hybrid Halbach undulators with comb fabrication [78] to produce a 1 T peak field in a 3 mm period undulator. Below this period, the feasibility of the undulator faces challenges attendant with use of MEMS fabrication techniques [14,79].…”