610 j.b. Bahrdt et al. / Proceedings of the 2004 FEL Conference, 610-613

UNDULATORS FOR THE BESSY SOFT-X-RAY FEL

J. Bahrdt #, W. Frentrup, A. Gaupp, B. Kuske, A. Meseck, M. Scheer, BESSY, Berlin, Germany Abstract variations are small compared to a SASE FEL scheme. BESSY plans to build a linac based Soft-X-ray FEL The three FELs will be operated at energies of facility. Three FEL lines will cover the energy range 1GeV (LE-FEL) and 2.3GeV (ME-FEL and HE-FEL), between 24eV and 1000 eV. The FELs are operated in a respectively. They consist of 2, 3, and 4 stages with a high gain harmonic generation scheme providing short modulator, a dispersive section and a radiator each pulses and stable operation. This paper describes the followed by a final amplifier (table 1). undulator systems for the FELs. The photon energy tuning will be done via gap motion. For the HE-FEL the electron beam energy has to be INTRODUCTION modified additionally to provide the full tuning range. The last radiators and the final amplifiers will be devices The time structure of a high gain harmonic generation with full polarization control. The other modules which FEL is determined by the time structure of the Laser are responsible for the electron beam bunching are planar system. The FWHM of the FEL radiation is expected to undulators. be below 30 fs. Furthermore, the shot to shot intensity

Table 1: Parameters of the BESSY Soft-X-Ray FEL. Period lengths (1st number) and section lengths (2nd number) are given in mm and m, respectively [1].

Device LE-FEL ME-FEL HE-FEL Energy range 24-120 eV 100-600 eV 500-1000 eV Modulator Radiator Modulator Radiator Modulator Radiator Stage 1 80 / 1.60 62 / 3.47 122 / 2.56 92 / 3.86 122 / 2.20 92 / 3.86 Stage 2 62 / 1.61 50 / 3.45 92 / 2.21 70 / 2x3.78 92 / 2.01 70 / 3x3.80 Stage 3 70 / 2.31 50 2x3.75 70 / 2.1 50 / 3x 3.1 Stage 4 50 / 2x2.65 28.5 / 2x 3.28 Final amplifier 50 / 3x3.85 50 / 3x3.85 28.5 / 5x3.65 Total length / m 21.68 37.55 60.98

beam pipe can be used and more magnetic material can be LAYOUT OF THE UNDULATORS located close to the electron beam. Side access to the Since all gaps are variable a separated function magnetic structure is needed only for Hall probe focussing scheme has been adopted. The quadrupoles of measurements and for the chamber support. A minimum the FODO structure are located between the undulator magnetic gap at the side of only 5.4mm can be realized segments. Permanent magnet phase shifters with still providing the space for a 10.4mm diameter tube. The adjustable magnetic gaps provide the correct phase magnetic field can be further enhanced by tilting the adaption between the undulator segments. Correction magnetization direction to 45 degrees. The reverse fields coils, and diagnostic systems are located in the in an APPLE III structure require a more stable material intersections as well. compared to an APPLE II undulator and as a consequence A dogleg collimator with a spatial and an energy the remanence of the material is about 6% lower. collimation stage protects the magnets from being hit by Nevertheless, the effective magnetic field is a factor of dark current . 1.4 higher than for an APPLE II with a gap of 10.4mm.

MAGNETIC DESIGN The modulators and the first radiators will be pure permanent magnet structures. The last radiator and the final amplifier are of the APPLE III type (see figure 1) [2]. An APPLE III provides the same flexibility concerning the polarization control as an APPLE II but the maximum field is larger at the expense of a reduced access from the side. In a linac driven FEL a circular

______Figure 1: Magnetic structure of an APPLE III (left) #bahrdt@.de compared to an APPLE II design (right).

THPOS03 Available online at http://www.JACoW.org j.b. Bahrdt et al. / Proceedings of the 2004 FEL Conference, 610-613 611

∞ ∞ r r−r The magnetic field of an APPLE III undulator can be r 1 r eik (r r ') parametrized with: E(x', y') = E(x, y) cos(β ) ⋅ dx ⋅ dy λ ∫∫ r − r = ⋅ ⋅ λ + ⋅ λ 2 −∞−∞ | r r '| B(T ) a exp(b (gap / 0 ) c (gap / 0 ) ) useing the parameters of table 2. 2: Application of Fourier optic methods. A FFT yields the angle distribution of the FEL output The parameters of table 2 have been evaluated with the ∞ ∞ 3D-code RADIA [3] for remanence = 1.13T and 1.19T r r −2πi(ν x+ν y) E (ν ,ν ) = E(x, y) ⋅ e x y dx ⋅ dy (longitudinally and 45° magnetized blocks), block 0 x y ∫∫ dimensions = 40x40mm2, minimum vertical distance = −∞−∞ 5.4mm, free aperture = 10.4mm. The parameters are valid This distribution is multiplied by a factor which for period lengths of 20mm ≤ λ0 ≤ 50mm. represents a longitudinal drift of ∆z. π ⋅∆ ⋅ λ2 −ν 2 −ν 2 r r 2 i z 1/ x y E(ν ,ν ) = E (ν ,ν ) ⋅ e Table 2: Field parameters of the APPLE III design x y 0 x y hor. lin. vert. lin. circular lin. 45° An inverse FFT provides the spatial distribution at A 2.481 2.035 2.209 1.569 z=z0+∆z. B -6.258 -6.576 -6.400 -6.392 ∞ ∞ r r 2πi⋅(ν x+ν y) E(x', y') = E(ν ,ν ) ⋅ e x y ⋅ dν ⋅ dν C 0.112 0.602 0.285 0.231 ∫∫ x y x y −∞−∞ The horizontal roll off of the vertical field component is The second method is much faster in cases where the larger for an APPLE III than for an APPLE II whereas the transverse dimension of the photon beam size does not roll off of the horizontal field component is smaller change too much within ∆z. The following results are (figure 2). For the HE-FEL a relative alignment accuracy derived with this method. of the undulator modules of ±20µm is required. The To study the development of the radiation properties undulator segments will be mounted onto remote within the final amplifier time dependent GENESIS controlled transversely movable stages in order to meet simulations [4] have been performed for various lengths L this tight tolerance. The indication for a correct alignment of the LE-FEL final amplifier of L=L0-81λ0, L0-60λ0, L0- will be the FEL output. 40λ0, L0-20λ0 and L0, where L0 is the length of the final amplifier given in table 1.The power distributions are 1.2 plotted in figure 3. The corresponding electric fields have HE-FEL 1 been propagated by amounts of ∆z with -30m ≤ ∆z ≤ +20m and the intensities have been projected onto the

field / Tesla 0.8 vertical field horizontal and the vertical plane. The first and second 0.6 moments of these projections have been evaluated and the results for slice 4 are plotted in figure 4. Similar numbers 0.4 horizontal field have been obtained for slices 2,3 and 5.

0.2 t 10

9 LE-FEL 0 APPLE III L=L0 APPLE II 8 124 eV -0.2 λ L=L0-20 0 -20 -15 -10 -5 0 5 10 15 20 power / GWat 7

x / mm 6 λ L=L0-40 0 Figure 2: Comparison of the transverse field profiles of 5 the APPLE II and the APPLE III design evaluated for the λ 4 L=L0-60 0 λ HE-FEL. L=L0-81 0 3

SOURCE CHARACTERIZATION 2 slice 3 slice 5 1 Three dimensional FEL codes provide information slice 1 0 about the electric field distribution at the end of the final 0.04 0.05 0.06 0.07 0.08 0.09 time / ps amplifier, z=z0. This point is not the location of the photon beam waist. The designer needs to know Figure 3: GENESIS simulations for different lengths L the exact location and the size of the photon beam waist of the final amplifier. The electric fields of five slices in order to maximize the brightness at the sample. This (black circles) have been propagated. information can be derived from the results of a longitudinal propagation of the electric field distribution. The photon beam waist is located several meters There are two ways to proceed: upstream from the FEL end and this distance increases 1: Integration of the diffraction equation of Fresnel and with L. As a consequence the brightness at the sample can Kirchhoff:. be increased by a factor of two if the waist is focussed instead of the FEL end.

New Concepts 612 j.b. Bahrdt et al. / Proceedings of the 2004 FEL Conference, 610-613

The photon beam size increases with the length of the design. The question has to be answered whether the final amplifier (figure 4). This might be partly due to the location of the waist moves with photon energy which increasing electron beam size which varies between 115 would imply the necessity of a variably focussing and 127µm horizontally and between 105 to 130µm beamline optic. Further studies for more photon energies vertically for L0-81λ0 ≤ L ≤ L0. and also for the ME-FEL and the HE-FEL are in progress.

0.15 0.15 σ 0.14 σ 0.14 x L=L x

L=L / mm / mm 0 0 σ σ x/y 0.13 x/y 0.13 y y σ σ 0.12 0.12 0.11 0.11 0.1 0.1 λ 0.09 L=L0-81 0 0.09 L=L -81λ 0.08 0.08 0 0 0.07 0.07 -30 -20 -10 0 10 20 -30 -20 -10 0 10 20 ∆z / m ∆z / m 0.3 1 hor. projection hor. projection 0.9 0.25 vert. projection 0.8 vert. projection L=L 0.7 0.2 0 L=L0 0.6 0.15 0.5 0.4 0.1 0.3 L=L -81λ 0.05 λ 0 0 L=L0-81 0

0.2 maximum intensity / a.u. maximum intensity / a.u. 0.1 0 0 -30 -20 -10 0 10 20 -30 -20 -10 0 10 20 ∆z / m ∆z / m Figure 6: Photon beam size (top) and maxima of the Figure 4: Photon beam size (top) and maxima of the projected intensity (bottom) versus longitudinal distance projected intensity (bottom) versus longitudinal distance to the final amplifier end. The data of slice 1 are plotted. to the final amplifier end. The data of slice 4 are plotted.

The photon beam divergence decreases with L and the FIELD OPTIMIZATION phase space product σσ’ is nearly independent of L for The field tuning for the planar modulators and the slice 4 (figure 5) and also for slices 2, 3 and 5. For a radiators of the first stages is straight forward [5]. diffraction limited beam we expect a product of σσ’ = Shimming of the last radiator and the final amplifier is λ/4π = 0.8nm (124eV). Based on the GENESIS more complicated due to several reasons: i) Iron shims simulations we obtain for each of the slices 2, 3, 4 and 5 a can not be used as usual because the signature changes product of about 1.25nm which is close to the theoretical with magnet row shift. ii) the shims do not stick by limit. magnetic forces. iii) The shims can not be applied directly above or below the electron beam because the magnet m -9 2.25 rows are separated by a slit of 1mm. iv) The field

2

σσ p / 10 integrals depend on the shift of the magnet rows which is slice 1 1.75 due to the non unity of the magnetic permeability. 1.5 slice 4 Magnet sorting techniques based on detailed field data 1.25 of individual magnets are essential for these devices to 1 reduce the work on shimming after assembly. At BESSY 0.75 diffraction limit for 124eV

0.5 a precise set-up for the characterization of magnet block

0.25 inhomogeneities has been developed [6]. Using the

0 inhomogeneity data together with the Helmholtz coil data -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 ∆L / λ 0 in a simulated annealing code the best magnet Figure 5: Phase space volume of the LE_FEL radiation configuration is evaluated. It has been demonstrated at for various lengths of the final amplifier. BESSY that even for devices consisting of more than 1000 individual blocks the field integrals can be predicted For L= L0-81λ0 slice 1 is far below saturation. The with an accuracy of ± 1.5Gm [6]. The prediction is based waist is located close to the FEL end and moves further only on single block data and no further field upstream for increasing L (figure 6). The phase space measurement and resorting has been performed during product of slice 1 is a factor of 2.5 above the diffraction magnet assembly. The remaining field errors can be limit for L= L0-81λ0 and approaches the value of the slices removed in three steps: 2-5 for increasing L (figure 5). 1: Trajectory and phase errors are minimized with The specific case of the LE-FEL at 124eV indicates transverse block movements (virtual shimming). that the location of the waist moves upstream relative to 2: The endpoles can be designed such that the field the FEL end when the FEL goes into saturation. A integral variation with gap is small [1] [7]. The remaining distance of 10m between the FEL end and the waist is significant and has to be regarded in a monochromator

THPOS03 j.b. Bahrdt et al. / Proceedings of the 2004 FEL Conference, 610-613 613 shift dependent terms are minimized with iron shims which are glued onto the magnets. 54 3: Shift independent field integrals are removed with permanent magnet arrays at both ends of the device. 53 These techniques have been applied to several APPLE II undulators at BESSY and they are documented in detail

reduced gap / µ m 52 in [6].

SUPPORT AND DRIVE SYSTEM 51

The support structure (cast iron) consists of a base 50 frame carrying two C-frames. The magnetic structures will have a length of up to 4m. The magnet girders will be 0.62 0.64 0.66 0.68 0.7 0.72 0.74 made from aluminum. The deflection is minimized with field / Tesla four supports (instead of two) using two cross bars. This design has already been implemented successfully at Figure 8: Measured gaps versus magnetic field for BESSY. several cycles of gap opening and closing. A 4th order Four longitudinal drive systems give the flexibility to polynomial has been subtracted from the raw data to show move each row individually. This provides full the residual error. polarization control for the user. Parallel motion of two rows changes the polarization from horizontal linear to REFERENCES circular and to vertical linear. Anti-parallel motion tilts the [1] The BESSY Soft-X-Ray Free Electron Laser, linear polarization vector continuously from 0° to 90°. Technical Design Report, Berlin, Germany, March, Sometimes, the orientation of the sample is not well 2004. known. In these cases it is useful to rotate the polarization [2] J. Bahrdt, W. Frentrup, A. Gaupp, B. Kuske, A. vector by more than 90°. With 4 motors a rotation of 180° Meseck, M. Scheer, “Undulators for the BESSY is possible. SASE-FEL Project”, 8th International Conference on

Synchrotron Radiation Instrumentation, San Francisco, Cal., 2003, AIP 0-7354-0180-2/04, p215. [3] P. Elleaume, O. Chubar, J. Chavanne, ''Computing 3D magnetic fields from insertion devices'', Proc. of the 1997 PAC, Vancouver, Canada (1997) 3509- 3511. O. Chubar, P. Elleaume, J. Chavanne, ''A three- dimensional magnetostatics computer code for insertion devices'', J. Synchr. Rad. 5 (1998) 481-484. [4] A. Meseck, B. Kuske, these proceedings [5] D.C. Quimby, S.C. Gottschalk, F.E. James, K.E. Robinson, J.M. Slater, A.S. Valla, ''Development of a 10-meter wedged-pole undulator'', Nucl. Instr. and Meth., A285 (1989) 281-289. S.C. Gottschalk, D.C. Quimby, K.E. Robinson, J.M. Slater, '' error Figure 7: The new gap measurement system as reduction through shim tuning'', Nucl. Instr. and implemented at the BESSY UE49 undulator. Meth., A296 (1990) 579-587. B. Diviacco, R.P.

Walker, ''Recent advances in undulator performance Two servo motors provide the gap tunability. The gaps optimization'', Nucl. Instr. and Meth., A368 (1996) of the individual undulator sections have to be adjusted 522-532. J. Chavanne, P. Elleaume, ''Undulator and with a relative accuracy better than 3µm. This tight wiggler shimming'', Synchr. Rad. News, Vol.8 No.1 tolerance can not be achieved with measurement systems (1995) 18-22. used so far. Rotary encoders suffer from backlash of [6] J. Bahrdt, W. Frentrup, A. Gaupp, M. Scheer, gearboxes and linear encoders coupled to the upper and “Magnetic field optimization of permanent magnet the lower I-beam do not follow Abbe’s comparator undulators for arbitrary polarization”, Nucl. Instr. and principle. We have developed a new measurement system Meth. A, 516 (2004) 575-585. where the linear encoder is located directly above the [7] J. Chavanne, P. Elleaume, P. Van Vaerenbergh, ''End electron beam thus following Abbe’s comparator field structures for linear/helical insertion devices'', principle. The system recently installed at the BESSY Proc. of the PAC, New York, NY, USA (1999) 2665- APPLE II undulator UE49 (figure 7) demonstrated a gap 2667. reproducibility of ±1µm independent of the gap history (figure 8).

New Concepts