New Tweaker Quadrupole Magnets for the LCLS LTU April 24 2010 P. Emma Introduction In order to allow remote control of the bunch compression properties (R 56 ) of the dog-leg-2 (DL2) within the LCLS Linac-to-Undulator (LTU) beamline two new weak quadrupole magnets (CQ31 and CQ32) are needed in the area of the QDL33 magnet. The new quadrupole magnets should be copies of the 10.8-cm long ( 1.259Q3.5 ) Everson-Tesla LCLS-injector quadrupoles of which there are seven already located in the LTU (QE31-QE36 and QEM3V). At least two spares should already be available. These magnets require no water cooling. Each of the new quadrupoles will require its own bipolar power supply (±12 A or an MCOR12 supply). Their exact locations as well as detailed analysis of their use in the LCLS are listed in the sections to follow. Installation Details The center of the new CQ31 and CQ32 quadrupoles should be located in the DL2 beamline exactly 7.0 m either side of the center of the existing QDL33 quadrupole magnet (with CQ31 upbeam of CQ32 by 14 m). These magnets will require simple support stands with reasonable vibration tolerances (<1 m). The final transverse alignment is only required to be accurate at the level of <0.5 mm the longitudinal alignment tolerance is <50 mm and the roll angle tolerance is 40 mrad. Each new magnet requires its own bipolar MCOR12 power supply and appropriate cabling connections to the above service building. The magnets should be measured (unless already done) and B vs. I polynomials determined. The installation and operations parameters are listed in Table 1. Table 1: Quadrupole installation and operation parameters. Parameter value unit Maximum excitation current ±12 A Maximum length-integrated gradient of each quad (BMAX) ±20 kg Transverse alignment tolerance 0.5 mm Longitudinal alignment tolerance 50 mm Roll angle tolerance 40 mrad Magnet transverse vibration tolerance (rms) 1 m Location of CQ31 center with respect to QDL33 center 7.0 m Location of CQ32 center with respect to QDL33 center +7.0 m Effective magnetic length of each new quadrupole 0.108 m Power supply type MCOR12 Suggested EPICS controls name for CQ31 QUAD:LTU1:440 Suggested EPICS controls name for CQ32 QUAD:LTU1:460
Use of the New Quadrupole Magnets The nominal compression factor of the DL2 beamline is R 56 = 0.10 mm (MAD sign convention where a chicane produces R 56 > 0). To better control the 1-micron long electron bunch at low-charge (20 pc) there is a growing motivation to control this compression factor to the level of ±0.5 mm in a smooth continuum including R 56 = 0. In order to adjust the compression characteristics of the DL2 beamline there are three parameters which need to be controlled: R 56 R 16 and R 26. Therefore we require three independent control knobs: 1) the QDL31-QDL34 quadrupole magnet string [4 magnets in series on one power supply] 2) a new weak quadrupole magnet (CQ31) 7 meters upbeam of the QDL33 quadrupole magnet and 3) a second new weak quadrupole magnet (CQ32) 7 meters downbeam of QDL33. These three independent controls can be used in three different linear combinations each to orthogonally control R 56 R 16 and R 26. To determine the strength needed for the CQ31 and CQ32 we calculate the spatial (R 16 ) and angular (R 26 ) dispersion needed to increase the projected emittance by 10%. If the point for evaluation of the R 16 and R 26 values is BPMDL4 at the end of DL2 where nominally = 5.0 m and = 0 then the remaining parameters are taken as: 0 = 0.5 m mc 2 = 13.6 GeV and = 0.1% (worst case rms energy spread). The 10%-emittance-growth-values are R 16 = ±4.4 mm and R 26 = ±0.89 mrad taken one at a time. We would like the new quads to be strong enough to reach twice these values. We find by using MAD that the maximum quadrupole k value needed is then ±0.32 m 2 for a 10.8-cm long quadrupole magnet. At 13.6 GeV this corresponds to a length-integrated quadrupole field gradient of ±16 kg which is achieved in the 1.259Q3.5 Everson-Tesla LCLS-injector quadrupole magnets at about ±10 A. To determine the set of three multi-knobs to orthogonally control R 56 R 16 and R 26 we use MAD and apply small changes to each quadrupole magnet (or magnet string) in order to find the 9 partial derivatives which can be used to form the control matrix where k 1 represents the differential strength of QDL31-QDL34 magnet string (with respect to its nominal value of k 1 = 0.4427 m 2 and with an effective length of each magnet within the string of L eff = 0.316 m) k 2 is CQ31 and k 3 is CQ32. Units are m 2 for k 1 k 2 and k 3 and m rad and m for R 16 R 26
and R 56 respectively). This matrix can be inverted in order to predict the k i settings needed for any prescribed values of R 16 R 26 and R 56 within the range of linearity (see below) or three orthogonal linear combinations can be formed as. Again the units are m 2 for k 1 k 2 and k 3 and m radians and m for R 16 R 26 and R 56 respectively. These are then tested in MAD to ensure that they give reasonable results within the linearity of their behavior (which ultimately limits the linear control to R 56 = ±0.5 mm R 16 = ±8 mm and R 26 = ±2 mrad at BPMDL4 although nonlinear MAD calculations can be used to apply larger settings but not beyond the quadrupole strengths: ±0.4 m 2 for CQ31 and CQ32 at ±12 A). Figures 1-4 show the x and y functions including the dispersion function D x for nominal conditions with R 56 = 0.10 mm (Fig. 1) isochronous conditions with R 56 = 0 (Fig. 2) more compression with R 56 = 0.50 mm (Fig. 3) and reversed compression with R 56 = 0.50 mm (Fig. 4). Fig. 1: Nominal optics functions ( x y D x ) in the dog-leg-2 (DL2) with R 56 = 0.10 mm (MAD sign convention).
Fig. 2: Optics functions ( x y D x ) in the dog-leg-2 (DL2) with R 56 = 0. The dispersion (position and angle) is completely suppressed but the beta functions may need to be rematched. Fig. 3: Optics functions ( x y D x ) in the dog-leg-2 (DL2) with R 56 = 0.5 mm. The dispersion (position and angle) is completely suppressed but the beta matching needs to be rematched.
Fig. 4: Optics functions ( x y D x ) in the dog-leg-2 (DL2) with R 56 = +0.5 mm. The dispersion (position and angle) is completely suppressed but the beta matching needs to be rematched.