Development and operation of a ${\mathrm{Pr}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ based cryogenic permanent magnet undulator for a high spatial resolution x-ray beam line

Short period, high field undulators are used to produce hard x-rays on synchrotron radiation based storage ring facilities of intermediate energy and enable short wavelength free electron laser. Cryogenic permanent magnet undulators take benefit from improved magnetic properties of ${\mathrm{RE}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ (Rare Earth based magnets) at low temperatures for achieving short period, high magnetic field and high coercivity. Using ${\mathrm{Pr}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ instead of ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$, which is generally employed for undulators, avoids the limitation caused by the spin reorientation transition phenomenon, and simplifies the cooling system by allowing the working temperature of the undulator to be directly at the liquid nitrogen one (77 K). We describe here the development of a full scale (2 m), 18 mm period ${\mathrm{Pr}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ cryogenic permanent magnet undulator (U18). The design, construction and optimization, as well as magnetic measurements and shimming at low temperature are presented. The commissioning and operation of the undulator with the electron beam and spectrum measurement using the Nanoscopmium beamline at SOLEIL are also reported.

Figure 1

Magnetic design using RADIA [34]. (a) Seven period undulator: permanent magnet (green) of the main undulator part ($50\times 30\times 6.5{\mathrm{mm}}^3$), Poles of the main undulator part (red) ($33\times 22\times 2.5{\mathrm{mm}}^3$), permanent magnet (yellow) of the extremity part of the undulator(80% and 35% of the main magnet width) [35]. Pole of the extremity part (blue) of the undulator (50% of the main polewidth). (b) Extremity part of the magnetic design.

Figure 2

On-axis magnetic peak field calculated with RADIA. (Filled circle) U18 ${\mathrm{Pr}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ cryogenic undulator at 77 K, $B_r=1.57\mathrm{T}$ at 77 K, magnet dimensions $50\mathrm{mm}\times 30\mathrm{mm}\times 6.5\mathrm{mm}$, pole dimensions $33\mathrm{mm}\times 22\mathrm{mm}\times 2.5\mathrm{mm}$. (Filled square) U20 ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ in-vacuum undulator at 293 K, $B_r=1.25\mathrm{T}$ at 293 K, magnet dimensions $50\mathrm{mm}\times 30\mathrm{mm}\times 7.5\mathrm{mm}$, pole dimensions $33\mathrm{mm}\times 22\mathrm{mm}\times 2.5\mathrm{mm}$. (Filled triangle) U20 ${\mathrm{Sm}}_2{\mathrm{Co}}_{17}$ in-vacuum undulator at 293 K, $B_r=1.05\mathrm{T}$ at 293 K, magnet dimensions $50\mathrm{mm}\times 30\mathrm{mm}\times 7.5\mathrm{mm}$, pole dimensions $33\mathrm{mm}\times 22\mathrm{mm}\times 2.5\mathrm{mm}$.

Figure 3

Brilliance in logarithmic scale with $\mathrm{gap}=5.5\mathrm{mm}$ calculated with SRW [36] for three different undulators: (Black) U20 ${\mathrm{Sm}}_2{\mathrm{Co}}_{17}$ (100 periods) with peak field of 0.971 T, (Red) ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ (100 periods) with peak field of 1.053 T, and (Green) ${\mathrm{Pr}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ (110 periods) with peak field of 1.152 T at cryogenic temperature. Electron beam characteristics of Table 2, with ${\beta }_x=5.577\mathrm{m}$, ${\beta }_z=8.034\mathrm{m}$, ${\alpha }_x=0$, ${\alpha }_z=0.001\mathrm{rad}$), through a window aperture of $0.1\mathrm{mm}\times 0.1\mathrm{mm}$ placed at a distance of 11.7 m.

Figure 4

Spectra calculated (using SRW) with beam and undulator parameters of Fig. 3. (Green) U18 ${\mathrm{Pr}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ cryogenic undulator at 77 K, with $K=1.937$. (Red) U20 ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ in-vacuum undulator at 293 K with $K=1.967$. (Black) U20 ${\mathrm{Sm}}_2{\mathrm{Co}}_{17}$ in-vacuum undulator at 293 K $K=1.812$. H with the index represents the harmonic number at photon energy $\sim 29\mathrm{keV}$.

Figure 5

Mechanical design of the cryogenic undulator using 3D CATIA (http://www.3ds.com/fr/).

Figure 6

Field integrals versus horizontal position at minimum gap of 5.5 mm at room temperature. (Filled square) Vertical field integral (Iz) after magic finger corrections. (Filled circle) Horizontal field integral (Ix) after magic finger corrections. (Open square) Vertical field integral (Iz) before magic finger corrections (Open circle) Horizontal field integral (Ix) before magic finger corrections. Field integrals precision is $\sim 0.05\mathrm{G}\mathrm{m}$.

Figure 7

Electron beam trajectory in the cryogenic undulator at room temperature calculated with B2E code from Hall probe magnetic measurement at SOLEIL ($E=2.75\mathrm{GeV}$), with a precision of 0.5 Gauss. (Solid line) Horizontal and vertical trajectories after the assembly and corrections. (Dashed line) Horizontal and vertical trajectories after the assembly and before shimming.

Figure 8

SOLEIL dedicated magnetic measurement bench inside the vacuum chamber of the cryogenic undulator.

Figure 9

Hall probe rotation angle versus longitudinal position. (Filled circle) ${\theta }_s$ after corrections, (filled square) ${\theta }_z$ after corrections, (filled right triangle) ${\theta }_x$ after corrections, (open circle) ${\theta }_s$ before corrections, (open square) ${\theta }_z$ before corrections (open right triangle) ${\theta }_x$ before corrections.

Figure 10

Hall probe translation versus longitudinal position. (Filled circle) Translation in the vertical z axis direction, (triangle) translation in the horizontal x axis direction.

Figure 11

Cooling down of the cryogenic undulator. (Normal line) Undulator vacuum pressure, (dashed line) permanent magnets temperature.

Figure 12

Warming up the undulator to room temperature. (Blue) Undulator vacuum pressure, (Red) permanent magnets temperature.

Figure 13

Electron beam trajectory calculated from the measured magnetic field. (Line) At room temperature 293 K, (dashed) at cryogenic temperature 77 K after rod length correction.

Figure 14

(a) Phase error corrections with rod vertical displacement at minimum gap of 5.5 mm. (b) Phase error variation versus gap after correction.

Figure 15

U18 spectrum calculated with SRW code at a distance of 17 m from the source point through a slit of $0.1\mathrm{mm}\times 0.1\mathrm{mm}$ at minimum gap of 5.5 mm. (Solid line) At room temperature of 293 K, (dashed line) at cryogenic temperature of 77 K. Beam characteristics shown in Table 2.

Figure 16

The cryogenic undulator installed in the SOLEIL storage ring straight section.

Figure 17

Vertical betatron tune versus offset: (filled circle): experimental vertical tune measurement, (line): fitting curve.

Figure 18

Undulator vacuum pressure variation versus gap at high electron beam current of 400 mA.

Figure 19

Permanent magnet temperature variation versus gap at high electron beam current of 400 mA.

Figure 20

Variation of the measured horizontal (white diamonds) and vertical (black diamonds) tune variation as a function of gap. The vertical tune variation is compared to the expected one from measured vertical field scaling (dashed line).

Figure 21

Normalized spectra measured on the beam line (nonabsolute) and calculated from magnetic measurements at 5.5 mm gap through a $0.05\mathrm{mm}\times 0.05\mathrm{mm}$ aperture at a distance of 20.3 m from the undulator. Electron beam parameters of table 2, with ${\beta }_x=8.906\mathrm{m}$, ${\beta }_z=7.216\mathrm{m}$, ${\alpha }_x=-1.296\mathrm{rad}$, ${\alpha }_z=-1.477\mathrm{rad}$. (a): 9th harmonic, (b): 11th, and (c): 13th harmonic.

Figure 22

(Green) spectra computed by an ideal undulator using SRWE with beam characteristics as Fig. 21. (Blue) spectra from the beam line normalized to H9 of ideal undulator.

Figure 23

Spectra measured (uncalibrated energy monochromator) on the NANOSCOPIUM beam line through a window aperture of $0.2\mathrm{mm}\times 0.8\mathrm{mm}$ placed at a distance of 77 m from the undulator with electron beam parameters shown in Table 2, but with current $I=17\mathrm{mA}$, ${\beta }_x=7.507\mathrm{m}$, ${\beta }_z=2.343\mathrm{m}$, ${\alpha }_x=-0.846\mathrm{rad}$, ${\alpha }_z=0.03\mathrm{rad}$.

Figure 24

Intensity and Full Width Half Maximum (FWHM) of the 11th harmonic as a function of the offset that varied from 0.3 mm up to 0.8 mm.

Figure 25

Intensity and Full Width Half Maximum (FWHM) of the 11th harmonic as a function of the taper offset.