Design study of the bending sections between harmonic cascade FEL stages - eScholarship

Design Study of the Bending Sections between Harmonic Cascade FEL Stages W. Wan, J. Corlett, W. Fawley, A. Zholents, LBNL, Berkeley, CA 94720, USA Abstract The present design of LUX (linac based ultra-fast X-ray facility) includes a harmonic cascade FEL chain to gener- ate coherent EUV and soft X-ray radiation. Four cascade stages, each consisting of two undulators acting as a mod- ulator and a radiator, respectively, are envisioned to pro- duce photons of approximate wavelengths 48 nm, 12 nm, 4 nm and 1 nm. Bending sections may be placed between the modulator and the radiator of each stage to adjust and maintain bunching of the electrons, to separate, in space, photons of different wavelengths and to optimize the use of real estate. In this note, the conceptual design of such a bending section, which may be used at all four stages, is presented. Preliminary tracking results show that it is possible to maintain bunch structure of nm length scale in the presence of errors, provided that there is adequate orbit correction and there are 2 families of trim quads and trim skew quads, respectively, in each bending section. β (m) β x β y D x s (m) δ E / p 0 c = 0 . Table name = TWISS Figure 1: Plots of the lattice functions using MAD [8] least, is to take full advantage of the four cell achromat first systematically studied and applied in realistic design by K. Brown ([5]). The basic result is that a beamline is an achro- mat if it consists of 4 identical FODO cells with 90 degree phase advance in both planes. To the first order, time-of- 0). If 2 families flight depends on momentum only ( of sextupoles are added to correct chromaticity, to the sec- ond order, time-of-flight depends on momentum only ( 0). To maintain bunch structure at the 1 nm level, both and have to be under control, which means that one extra knob each on the first and second order optics. It is certain that at 2.5 GeV, the knob to adjust has to be a sextupole. Yet there are at least two options to cancel and adjust . To cancel , or to make very small, which is the case here, either negative dispersion has to be created or reverse bends have to be used. Generally speak- ing, using reverse bends requires weaker quadrupoles. It was found that third order aberrations are too large if neg- ative dispersion is used to cancel . To adjust , one option is to use an additional family of quads, which was not adopted due to the concern of the cost and the length of the beamline. The scheme used here is the redistribution of bending (keeping the total bending fixed). As a result, the bending section consists of 4 identical cells. Each cell contains 2 dipole, 2 quadrupole and 3 sextupole magnets. The total bending angle of the beamline is 5 degrees. It turns out that, at sub-micron level, adjusting does not affect focusing, making it an independent knob. To shorten the length further, two families of sextupoles are placed in- side the quads. The spacing between magnets is 10 cm, except that, after each quad, an extra 10 cm is reserved for BPM and correct/skew quad coils. The characteristics of the electron beam are summarized in Table 1, the key pa- rameters of all main magnets are listed in Table 2 and the INTRODUCTION The present design of LUX ([1, 2, 3, 4]) includes a har- monic cascade FEL chain to generate coherent EUV and soft X-ray radiation. Four cascade stages, each consist- ing of two undulators acting as a modulator and a radiator, respectively, are envisioned to produce photons of wave- lengths 48 nm, 12 nm, 4 nm and 1 nm ([3, 4]). Four bend- ing sections are placed between the modulator and the ra- diator of each stage to adjust and maintain bunching of the electrons, to separate, in space, photons of different wave- lengths and to optimize the use of real estate. In this note, the conceptual design of such a bending section, which can be used at all four stages, is presented. Preliminary tracking results show that it is possible to maintain bunch structure of the length 1 nm with the presence of errors, provided that there is adequate orbit correction and there are 2 fami- lies of trim quads and trim skew quads, respectively, in the bending section. LAYOUT First of all, maintaining bunch structure at the scale of 1 nm over a bending section is at least an order of magnitude shorter than any study that has appeared before ([6, 7]). There is no doubt that all second order aberrations in time- of-flight have to be corrected. It remains to be seen whether higher order aberrations are small enough. The most effi- cient way of achieving this goal, to the mind of the author at Work supported by the Director, Office of Energy Research, Office of Basic Energy Science, Material Sciences Division, U.S. Department of Energy, under Contract No. DE-AC03-76SF00098 D x (m) Win32 version 8.51/07