Beam-Based Alignment of the LCLS Undulator Paul Emma, SLAC April 24, 2002 Motivation Technique Simulations LCLS LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Undulator Design planar hybrid type 3.42 m undulator line length 122 m undulator period, u 3 cm undulator parameter, K 3.71 1-mm BPM  cavity and button-type in compact package (G. Decker, ANL) planar hybrid type QF QD BPM 3.42 m undulator section vacuum pump Quad-magnets and undulator sections on independent movers LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

b-functions through undulator Undulator Optics 33 undulator sections, L = 3.4 m ~4000 undulator periods (3 cm) Permanent magnet quadrupoles ~13º b-phase adv./cell, 18 m Magnet movers on each quad (x,y) Movers on each undulator section 1-mm BPM at each quad (x,y) Quads aligned w.r.t. adjacent undulator sections to <50 mm b-functions through undulator 18 m LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Alignment Motivation Need good overlap of e-/photon beam (30 mm rms) 1.5-Å phase slippage between photons and e- sensitive to trajectory e- undulator trajectory must be straight to <5 mm over 10-m gain length difficult to achieve with survey methods rely on beam-based alignment… e- with large b-osc. amplitudes will ‘slip’ w.r.t. photon beam… LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Basic Strategy Save BPM readings as a function of large, deliberate changes in e- energy (e.g., 15, 10, and 5 GeV) Calculate and correct quad & BPM misalignments and adjust ‘launch’ Repeat ~3 times with first application Re-apply one iteration per ~1 month (?) LCLS LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

The Method BPM readings, mi, written as sum of upstream kicks + offset, bi Kicks are sensitive to momentum, pk, while offsets, bi, are not j ith BPM bi > 0 DE < 0 DE = 0 s quad offsets and/or pole errors LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

The Method Reference line defined by incoming x0, x0 launch conditions mi linear only if Cij independent of p offset = -bi 1/p p (15 GeV/c)-1 (10 GeV/c)-1 (5 GeV/c)-1 LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

The Method Define… then solve the linear system… BPM readings at p1 BPM offsets BPM readings at p2 quad offsets known optical functions at each pk LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Constraints Solve with ‘soft-constraints’* on resulting BPM and quad offsets ~1 mm Without this ‘reasonability’ weighting, resulting BPM and quad offsets can stray out to large values at low frequencies Scanning beam energy gives sensitivity to (and ~correction of) all field errors, including undulator poles, Earth’s field, etc… * C. Adolphsen, 1989 PAC LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

permanent magnet quadrupoles and undulator poles Schematic layout Undulator misaligned w.r.t. linac axis with uncorrelated and correlated* (‘random walk’) component original incoming launch error BPMs quads ~300 mm x0 LINAC best final trajectory x0 steering elements UNDULATOR (120 m) permanent magnet quadrupoles and undulator poles * suggested by C. Adolphsen LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Beam-based alignment steps ×3 LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Input errors used for simulation LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Initial BPM and quad misalignments (w.r.t. linac axis) + Quadrupole positions o BPM readback quad positions BPM offsets Now launch beam through undulator LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Initial trajectory before any correction applied + Quadrupole positions o BPM readback e trajectory ‘real’ trajectory fit used to smooth launch quad positions BPM readings Note, all trajectory plots are w.r.t. linac axis (except last two) LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Trajectory after initial rough steering (14.3 GeV) + Quadrupole positions o BPM readback e trajectory Save as 1st set of BPM readings LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Energy now reduced to 10 GeV + Quadrupole positions o BPM readback e trajectory Save as 2nd set of BPM readings LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Energy reduced again to 5 GeV + Quadrupole positions o BPM readback e trajectory Save as 3rd set of BPM readings Now analyze BPM data… LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Fitted quadrupole offsets Fit results Actual offsets ‘real’ offsets fitted offsets results differ by straight line… similar plot for BPM offsets (not shown) Now correct quad and BPM positions… use linear component of fitted offsets to re-adjust launch LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Absolute trajectory after 1st pass of BBA (14.3 GeV) + Quadrupole positions o BPM readback e trajectory LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Possible Absolute Trajectory Beam is launched straight down undulator, with possible inconsequential kink at boundary LINAC dispersion generated is insignificant Now look at trajectory w.r.t. undulator axis  LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

After 1st pass of BBA (now w.r.t. undulator line) + Quadrupole positions o BPM readback e trajectory sx  48 mm Now repeat procedure of energy changes two more times… sy  24 mm LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

After 3rd pass of BBA (14.3 GeV) + Quadrupole positions o BPM readback e trajectory sx  1.7 mm Dj  100° rms beam size: 30 mm RON (FEL-code) simulation shows Lsat increased by <1 gain-length; R. Dejus, N.Vinokurov sy  2.7 mm LCLS DOE Review, April 24, 2002 Paul Emma, SLAC

Summary BPMs resolve trajectory to ~1 mm rms BPM readings ‘drift’ <1 mm over 1-2 hr (temperature) Magnet movers are settable to within 1 mm (or use coils) BPM readings are not sensitive to variable beam size, etc. Trajectory is stable enough to <20% of beam size (already demonstrated in FFTB) Alignment can be achieved at adequate level using beam-based technique, given that… LCLS LCLS DOE Review, April 24, 2002 Paul Emma, SLAC