BBA Related Issues Heinz-Dieter Nuhn, SLAC / LCLS June 28, 2004

Undulator Meeting, June 28 - 29, 2004Undulator Meeting, June 28 - 29, 2004 Heinz-Dieter Nuhn, SLAC / LCLSHeinz-Dieter Nuhn, SLAC / LCLS

BBA Related IssuesBBA Related Issues [email protected]@slac.stanford.edu

Linac Coherent Light Source Stanford Synchrotron Radiation LaboratoryStanford Linear Accelerator Center

BBA Related IssuesHeinz-Dieter Nuhn, SLAC / LCLS

June 28, 2004

BBA Related IssuesHeinz-Dieter Nuhn, SLAC / LCLS

June 28, 2004

TechniqueTechnique

SimulationsSimulations

Earth Field ConsiderationsEarth Field Considerations

TechniqueTechnique

SimulationsSimulations

Earth Field ConsiderationsEarth Field Considerations LCLSLCLS




Basic StrategyBasic Strategy

Save BPM readings as a function of large, deliberate changes in Save BPM readings as a function of large, deliberate changes in ee energy (e.g., 14, 7, and 5 GeV) energy (e.g., 14, 7, and 5 GeV)

Save BPM readings as a function of large, deliberate changes in Save BPM readings as a function of large, deliberate changes in ee energy (e.g., 14, 7, and 5 GeV) energy (e.g., 14, 7, and 5 GeV)

LCLSLCLS

Calculate and correct quad & BPM misalignments and adjust ‘launch’

Repeat ~3 times with first application

Re-apply one iteration per ~1 month (?)

Courtesy of Paul EmmaCourtesy of Paul EmmaCourtesy of Paul EmmaCourtesy of Paul Emma




The MethodThe Method

BPM readings, BPM readings, mmii, written as sum of upstream kicks , written as sum of upstream kicks ++ offset, offset, bbii

Kicks are sensitive to momentum, Kicks are sensitive to momentum, ppkk, while offsets, , while offsets, bbii, are not, are not

Reference line defined by incoming Reference line defined by incoming xx00, , xx00 launch conditions launch conditions

BPM readings, BPM readings, mmii, written as sum of upstream kicks , written as sum of upstream kicks ++ offset, offset, bbii

Kicks are sensitive to momentum, Kicks are sensitive to momentum, ppkk, while offsets, , while offsets, bbii, are not, are not

Reference line defined by incoming Reference line defined by incoming xx00, , xx00 launch conditions launch conditions

ss

bbii > 0 > 0

EE = 0 = 0

EE < 0 < 0quad offsets and/or pole errorsquad offsets and/or pole errors

iithth BPM BPM jj





Extrapolation to infinite momentum give BPM offsetsExtrapolation to infinite momentum give BPM offsetsExtrapolation to infinite momentum give BPM offsetsExtrapolation to infinite momentum give BPM offsets


1/1/pp

mmii

offset = bi

(15 GeV/c)(15 GeV/c)11 (10 GeV/c)(10 GeV/c)11 (5 GeV/c)(5 GeV/c)11pp

linear only if linear only if CCijij independent of independent of pp






Define…Define…

then solve the linear system…then solve the linear system…

Define…Define…

then solve the linear system…then solve the linear system…

BPM BPM readings readings at at pp11

BPM BPM readings readings at at pp22

BPM BPM offsetsoffsets

quad quad offsetsoffsets

known optical functions at each known optical functions at each ppkk





ConstraintsConstraints

Solve with ‘soft-constraints’Solve with ‘soft-constraints’** on resulting BPM and quad offsets on resulting BPM and quad offsetsSolve with ‘soft-constraints’Solve with ‘soft-constraints’** on resulting BPM and quad offsets on resulting BPM and quad offsets

* C. Adolphsen, 1989 PAC* C. Adolphsen, 1989 PAC

~1 mm~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) Scanning beam energy gives sensitivity to (and ~correction of) all field errors, including undulator poles, Earth’s field, etc…all field errors, including undulator poles, Earth’s field, etc…





Schematic layoutSchematic layout

~300 ~300 mm

UNDULATORUNDULATOR(120 m)(120 m)

LTULTUbest final trajectorybest final trajectory

steering elementssteering elements

xx00xx00

original incoming original incoming launch errorlaunch error

Undulator misaligned w.r.t. linac axis with uncorrelated Undulator misaligned w.r.t. linac axis with uncorrelated and correlatedand correlated** (‘random walk’) component (‘random walk’) component

permanent magnet quadrupoles permanent magnet quadrupoles and undulator polesand undulator poles

* suggested by C. Adolphsen* suggested by C. Adolphsen

BPMsBPMsquadsquads


130130




Beam-based alignment stepsBeam-based alignment steps

×3×3





Input Errors Used for SimulationInput Errors Used for Simulation

0.040.04

44

100100

100100

22





Initial BPM and quad misalignments (w.r.t. linac axis)Initial BPM and quad misalignments (w.r.t. linac axis)

++ Quadrupole Quadrupole positionspositions

oo BPM offsets BPM offsets

quad positionsquad positions

BPM offsetsBPM offsetsNow launch Now launch beam through beam through undulatorundulator


130130

130130




Initial trajectory before any correction appliedInitial trajectory before any correction applied


oo BPM readback BPM readback

ee trajectory trajectory

fit used to smooth launchfit used to smooth launch

Note, all Note, all trajectory plots are trajectory plots are w.r.t. linac axis w.r.t. linac axis ((except last twoexcept last two) )

‘‘real’ trajectoryreal’ trajectory

quad positionsquad positionsBPM readingsBPM readings


130130

130130




Trajectory after initial rough steering (14.3 GeV)Trajectory after initial rough steering (14.3 GeV)




Save as 1Save as 1stst set of BPM set of BPM readingsreadings


130130

130130




Energy now reduced to 10 GeVEnergy now reduced to 10 GeV




Save as 2Save as 2ndnd set of BPM set of BPM readingsreadings


130130

130130




Energy reduced again to 5 GeVEnergy reduced again to 5 GeV




Save as 3Save as 3rdrd set set of BPM of BPM readingsreadings

Now analyze Now analyze BPM data…BPM data…


130130

130130




Fitted quadrupole offsetsFitted quadrupole offsets

Fit resultsFit results

Actual offsetsActual offsets

similar plot for similar plot for BPM offsets BPM offsets (not shown)(not shown)

Now correct Now correct quad and BPM quad and BPM positions…positions…

results differ by straight line…results differ by straight line…

‘‘real’ offsetsreal’ offsets

fitted offsetsfitted offsets

use linear component of fitted use linear component of fitted offsets to re-adjust launchoffsets to re-adjust launch


130130

130130




Absolute trajectory after 1st pass of BBA (14.3 GeV)Absolute trajectory after 1st pass of BBA (14.3 GeV)





130130

130130




Possible Absolute TrajectoryPossible Absolute Trajectory

LTULTU

Beam is launched straight down undulator, with Beam is launched straight down undulator, with possible inconsequential kink at boundarypossible inconsequential kink at boundary

dispersion generated is insignificantdispersion generated is insignificant

Now look at trajectory w.r.t. undulator axis Now look at trajectory w.r.t. undulator axis





After 1st pass of BBA (now w.r.t. undulator line)After 1st pass of BBA (now w.r.t. undulator line)




Now repeat Now repeat procedure of procedure of energy changes energy changes two more times…two more times…

xx 48 48 mm

yy 24 24 mm


130130

130130




After 3rd pass of BBA (14.3 GeV)After 3rd pass of BBA (14.3 GeV)




RON RON (FEL-code) (FEL-code) simulation shows simulation shows LLsatsat increased by increased by

<1 gain-length;<1 gain-length;R. Dejus, R. Dejus, N.VinokurovN.Vinokurov

100°100° 100°100°

xx 1.7 1.7 mmxx 1.7 1.7 mm

yy 2.7 2.7 mmyy 2.7 2.7 mm

rms beam size: rms beam size: 30 30 mm


130130

130130

Was confirmed with Was confirmed with GENESIS simulationGENESIS simulation



Linac Coherent Light Source Stanford Synchrotron Radiation LaboratoryStanford Linear Accelerator CenterTrajectory After BBA ConvergenceTrajectory After BBA Convergence

Trajectory through undulator at 14 GeV after 3 passes of BBA procedure.Trajectory through undulator at 14 GeV after 3 passes of BBA procedure.

2-2-mm BPM BPM resolutionresolution50-50-mm initial initial BPM & quad BPM & quad offsetsoffsets1-1-mm mover mover backlashbacklash14-7-4.514-7-4.5 GeV GeV 204°204°

2-2-mm BPM BPM resolutionresolution50-50-mm initial initial BPM & quad BPM & quad offsetsoffsets1-1-mm mover mover backlashbacklash14-7-4.514-7-4.5 GeV GeV 204°204°








BPM read-backs through undulator at 14 GeV (top) and 4.5 GeV (bottom) after rough steering, but before BPM read-backs through undulator at 14 GeV (top) and 4.5 GeV (bottom) after rough steering, but before the BBA procedure. The energy is changed and the launch is re-established. Trajectory changes are the BBA procedure. The energy is changed and the launch is re-established. Trajectory changes are expected at the expected at the 500-500-mm level. level.

500 500 mm

Verify BBA Convergence by noting orbit change from 14 to 4.5 GeVVerify BBA Convergence by noting orbit change from 14 to 4.5 GeVBeforeBefore BBA procedure BBA procedureBeforeBefore BBA procedure BBA procedure

14.1 GeV14.1 GeV

4.5 GeV4.5 GeV

drop energy, drop energy, reset launch, reset launch, note changenote change





BPM read-backs through undulator (note scale change) at 14 GeV (top) and 4.5 GeV (bottom) after three BPM read-backs through undulator (note scale change) at 14 GeV (top) and 4.5 GeV (bottom) after three rounds of the BBA procedure, where trajectory changes with energy are expected at the rounds of the BBA procedure, where trajectory changes with energy are expected at the 20-20-mm level. level.

20 20 mm

Verifying BBA ConvergenceVerifying BBA Convergence

AfterAfter BBA procedure BBA procedureAfterAfter BBA procedure BBA procedure

drop energy, drop energy, reset launch, reset launch, note changenote change

14.1 GeV14.1 GeV

4.5 GeV4.5 GeV





0.1-Gauss Earth’s field in 0.1-Gauss Earth’s field in xx- direction – perfect system, quads on, no steering- direction – perfect system, quads on, no steering





0.1-Gauss Earth’s field in 0.1-Gauss Earth’s field in xx-direction – perfect system, after BBA-direction – perfect system, after BBA





0.1-Gauss Earth’s field in 0.1-Gauss Earth’s field in xx-direction – standard errors, after BBA-direction – standard errors, after BBA

no Earth’s field – standard errors, after BBAno Earth’s field – standard errors, after BBA





0.2-Gauss Earth’s field in 0.2-Gauss Earth’s field in xx-direction – standard errors, after BBA-direction – standard errors, after BBA

Courtesy of Paul Emma Courtesy of Paul Emma Courtesy of Paul Emma Courtesy of Paul Emma




SummarySummary

BPMs resolve trajectory to ~1 BPMs resolve trajectory to ~1 m rmsm rms

BPM readings ‘drift’ <1 BPM readings ‘drift’ <1 m over 1-2 hr (temperature)m over 1-2 hr (temperature)

Magnet movers are settable to within Magnet movers are settable to within 1 1 m (or use coils)m (or use coils)

BPM readings are not sensitive to variable beam size, etc.BPM readings are not sensitive to variable beam size, etc.

Trajectory is stable enough to <20% of beam size (already Trajectory is stable enough to <20% of beam size (already demonstrated in FFTB)demonstrated in FFTB)

Earth magnetic field needs to be compensatedEarth magnetic field needs to be compensated

BPMs resolve trajectory to ~1 BPMs resolve trajectory to ~1 m rmsm rms

BPM readings ‘drift’ <1 BPM readings ‘drift’ <1 m over 1-2 hr (temperature)m over 1-2 hr (temperature)

Magnet movers are settable to within Magnet movers are settable to within 1 1 m (or use coils)m (or use coils)

BPM readings are not sensitive to variable beam size, etc.BPM readings are not sensitive to variable beam size, etc.

Trajectory is stable enough to <20% of beam size (already Trajectory is stable enough to <20% of beam size (already demonstrated in FFTB)demonstrated in FFTB)

Earth magnetic field needs to be compensatedEarth magnetic field needs to be compensated

Alignment can be achieved at adequate level Alignment can be achieved at adequate level using beam-based technique, given that…using beam-based technique, given that…

LCLSLCLS

4 4




End of Presentation

Documents

BBA Related Issues Heinz-Dieter Nuhn, SLAC / LCLS June 28, 2004