Transverse gradient in Apple-type undulators

Abstract

Apple-type undulators are globally recognized as the most flexible devices for the production of variable polarized light in the soft X-ray regime, both at synchrotron and free-electron laser facilities. Recently, the implementation of transverse gradient undulators has been proposed to enhance the performance of new generation light sources. In this paper it is demonstrated that Apple undulators do not only generate linear and elliptical polarized light but also variable transverse gradient under certain conditions. A general theoretical framework is introduced to evaluate the K-value and its transverse gradient for an Apple undulator, and formulas for all regular operational modes and different Apple types (including the most recent Delta type and Apple X) are calculated and critically discussed.

Cryogenic permanent magnet and superconducting undulators

“…New APPLE designs: Variably polarizing devices in FELs and DLSRs with on-axis injection can be realized with APPLE III [135], Delta [136], or APPLE-X [137] magnet arrangement. The field boost vs. an APPLE II is at least factor of 1.4, depending upon the vertical gap needed for the chamber support.…”

“…Once, the technology is mature, the choice of the appropriate magnet structure is free, e.g. APPLE II [32] and APPLE III [135] including a gap drive; Delta [136] with a fixed gap and adjustable phases; APPLE X [137] and Delta II [H.-D. Nuhn, private communication, 2017] with four transverse degrees of freedom (e.g. realization of a transverse gradient undulator).…”

X-Ray Sources at Large-Scale Facilities

“…Instead of the two Halbach magnet arrays found in 'normal' undulators discussed thus far, APPLE undulators consist of four arrays (two above, two below) that can be longitudinally shifted relative to each other [A1-A4, Fig. 1.15a] [9]. Each array consists of a periodic repetition of four different orientations [down (blue ⊗); reverse (green arrow); up (yellow ); and forward (red arrow), see Fig.…”

SwissFEL: The Swiss X-ray Free Electron Laser

“…With an undulator periodicity of 38 mm it is not required to place the magnet array in vacuum. This in turn opens up the possibility of a more advanced design of the undulator, with better control and tunability of polarization, on-axis field and transverse gradient [37] as compared to the Aramis hard X-ray undulator, which is strictly planar. Another important distinction with respect to Aramis is the shorter length of the undulator modules and the inclusion of delaying chicanes between modules.…”