The Quest for a Nanometer-Resolution Beam Position Monitor

1. The Quest for a Nanometer-ResolutionBeam Position Monitor Sean Walston N-Division Seminar 13 July 2005

2. The International Linear Collider • Searches for new physics • Origin of mass (Higgs Boson) • Supersymetry • Dark matter • Dark energy • Extra dimensions • Unification of fundamental forces • Precision measurements • Top quark • Higgs Boson (if it exists) • New accelerator physics will be required to achieve luminosity goals: • In particular, must be able to collide beams with very smallspot sizes of only a few nanometersby afew hundred nanometers • This is a very serious challenge for the beam delivery system • Can the magnets and support structures be stabilized to the required precision?

3. The Origin of the NanoBPM Project • Nanobeam 2002 Workshop • Talk by Tor Raubenheimer during Session 10 • Slide 8, Bullet 3: LINX was to run the old SLC for the purpose of testing the stabilization of final focus optics “Of course nobody can do nanometer resolution with a BPM.” – Tor Raubenheimer “Well, you didn’t ask...” – Joe Frisch and Steve Smith

4. Stability of ILC Beam Optics • ILC requires two sets of final focus magnets to be stabilized with respect to each other to within a few nanometers • No existing technology can provide nanometer resolution with respect to a reference line • We expect to develop this technology using a high energy electron beam and nanometer resolution BPMs • With nanometer resolution BPMs the beam can be used as a “mechanical device” to test component stability

5. Monopole Mode TM010 Dipole Mode TM110 • Monopole mode: Proportional to bunch charge • Dipole mode: • Amplitude has strong dependence on beam offset • Phase depends on direction of offset Theory of Cavity BPMs C-Band Cavity BPM Monopole Mode: ~4900 MHz Dipole Mode: 6429 MHz • The bunch excites the cavity’s eigenmodes as it passes through • Excitation decays exponentially: • Power coupled out as signal • Power lost in the cavity walls

6. Dipole mode comparatively small • Monopole mode has non-zero amplitude at dipole mode frequency due to finite Q • Cannot be filtered out • Mode selective coupling can reject monopole mode • Exploits difference in field structure of monopole and dipole modes Beam Pipe Coupling slot (somewhat exaggerated) Cavity Wave Guide Coupling Slots Dipole Mode Coupling • Monopole mode has highest excitation of all modes

7. Bunch Low - Amplitude Bunch Centered Zero Amplitude Bunch High + Amplitude Bunch High + Amplitude Bunch Low - Amplitude Bunch Centered Zero Amplitude Other Available Beam Information • Beam Trajectory: • Signal scales with cavity length • Signal out of phase by 90o relative to position signal • Can also be determined using position signals from 2 or more BPMS • Bunch Angle of Attack: • Signal scales with bunch length • Signal out of phase by 90o relative to position signal • Beam trajectory must be known a priori to determine this

8. Limits on Resolution • Resolution limited by signal/noise ratio • Thermal noise • Electronic noise • Slot misalignment causes contamination from other modes (principally TM010) • Theoretical resolution ~1 nm

9. 30 cm 30 cm • Want to measure the “residual” between three BPMs • Beam position in one BPM compared with the position determined from the other two BPMs • BPM Resolution sResidual Reference Cavity BPM 1 BPM 2 BPM 3 BPM 1 BPM 2 BPM 3 Residual “Hits” NanoBPM Setup at ATF • 3 Cavity BPMs with dipole mode couplers • Designed and built by BINP • 1 Reference Cavity for phase and beam charge normalization

10. Mechanical Stabilization • BPMs mounted on x, y, x’, y’ hexapod strut movers in rigid space frame • First vibrational mode at ~200 Hz • Entire space frame can also move in x, y, x’, y’ • System developed at LLNL

11. Hexapod Strut Movers • Solid piece of metal • Rigid body that still allows movement: • Calibration • Beam position and trajectory/bunch angle of attack • Cavity alignment • 4 degrees of freedom per BPM • Change in gap [ 1/12 change in axial length • 3000 microns [ 250 microns

12. NanoBPM Project ATF and the NanoBPM Experiment Extraction Line Damping Ring

13. Why ATF? • Ultra-low emittance • Highly stable beams • High precision beam instrumentation • We are counting on the beam to be uniform, stable, and straight

14. Exchange A and j for I and Q • Normalize A and j by Reference Cavity waveform BPM signals Saturation • Fit non-saturated part of each waveform to • V0, w and G known a priori for each cavity: Looking for A and j

15. Q Tilt Position Q IQ I QIQ and Getting Position and Tilt • Angle QIQ is a rotation which converts I, Q into Position, Tilt • Zero Amplitude [ Beam passed straight through the electrical center of the cavity This is calibration data where BPM 2 has undergone pure translations of 20 mm in addition to its nominal position. Each point is a beam pulse event. The axis labeled Position is a linear fit to the data points. The spread in the three clusters is due to beam jitter. +20 mm Nominal -20 mm

16. In events where none of the BPMs has been moved, we can calculate I and Q from the Is and Qs measured by the other two BPMs: Calculated vs. Measured DQ vs. DI • Compare calculated Is and Qs to measured Is and Qs for events including those where the BPM has been translated in x (or y); any difference is the result of a pure translation: • Finally, regress DQn against DIn: • Need to remove beam jitter and drift to isolate pure translations Calculating QIQ

17. A Quick Aside on Linear Regression • Let b be a column vector of the Is (or Qs) for BPM 2 • Let the Columns of A be Is and Qs for BPMs 1 and 3, and a column of 1s for the constant term. • Each row of A and b correspond to an event • Invert A to solve for x, the vector of coefficients

18. General m5 n matrix A • Factor A into product of two orthogonal matricies, m5 mU and n5 nVT, and the m 5n matrix S • Least squares solution that minimizes |Ax - b| Inverting a Matrix UsingSingular Value Decomposition • Square, non-singular matrix A • Factor A into product of two orthogonal matricies, U and UT, and the diagonal matrix S

19. BPM 2 BPM 2 BPM 2 Move Calibration BPM 1 BPM 3 • Coordinate system defined by the electrical centers of BPMs 1 and 3 • Assume beam is a by God! straight line • Trajectory of beam between BPMs 1 and 2 same as that between BPMs 2 and 3 • True even if a BPM is moved BPM 2 Offset Nominal electrical center of BPM x Position of electrical center of BPM after move Position of beam in BPM BPM 2 Response BPM 1 Response BPM 1 Response BPM 2 Move BPM 2 Offset z

20. Nominal electrical center of BPM x Position of electrical center of BPM after move Slope12 Position of beam in BPM Slope23 z12 s1P1 s2P2 z23 s3P3 m2 m1 m3 x2 z Calibrate All BPMs Simultaneously • Move each BPM in turn • Linear regression (using SVD again) to calculate scale constants sn and x2

21. Calibration Performance • After Scales sn and BPM 2 Offset x2 are determined, calculate BPM moves from BPM position signals: • Algorithm immune to beam jitter and beam drifts

22. BPM 1 BPM 2 BPM 3 Residual Calculating the Residual • Regress y2 against: • Nominally y1 and y3 • x1 and x3 in case BPMs are rotated with respect to one another • x1’, x3’, y1’, and y3’ for good measure • Can add BPM temperatures • Beam energy (coming soon…) • Additional parameters can be added as necessary…

23. Resolution (March Data) • RMS = 28.91 nm • Divide by geometric weight factor • Resolution = 23.6 nm (over ~20 minutes)

24. Residual vs. Time • Beam drift apparent as structure in position plot • Lack of structure in residual plot suggests BPMs are not moving differentially from one another

25. The Story So Far… • Resolution to date ~20 nm • Desire one more order of magnitude of resolution • We have assumed the beam to be by God! straight! Anything which weakens that assumption needs to be investigated… • Fluctuations in the earth’s magnetic field • Effect on resolution ~0.1 nm • Beam energy jitter interacting with magnetic fields • We estimated the effect on resolution at ~0.1 nm because Dpz/pz small at ATF • Analysis in progress using June data • “Mode leakage” (No payoff yet…) • Frequencies for x and y modes not quite degenerate • x[y and y[x • Temperature fluctuations of BPM mounts (in progress)

26. The NanoGrid Metrology System • Ultra-precise measurement of 2-dimensional planar displacements • 10 mm pitch diffraction grid [ 5 mm measurement period • 14 bits [ 0.3 nm resolution

27. Attachment points for the lasers Metrology • Reference frame with zero coefficient of thermal expansion • Carbon fiber is a known technology • Radial struts will reach from the metrology frame through the Livermore space frame to the laser attachment points • Nanogrids attach to these struts • Three struts per BPM to measure six degrees of freedom Carbon Fiber Metrology Frame Struts

28. Carbon Fiber Metrology Frame Carbon Metrology Frame Nanogrid mounting struts Installation at ATF planned for late September

29. “You know, I have one simple request... and that is to have BPMs with frickin' laser beams attached…” – Dr. Evil

30. a b a Welcome to Reality!

31. Mode Leakage: x[y and y[x • Frequencies for x and y slightly off • First fit waveforms in the usual way • Then refit the waveforms with a second decaying sine-wave and examine the frequency • Peak of second frequency matches the frequency for the opposite direction! Fishy waveforms: x and y beating? Frequency, second y sine-wave Frequency, second x sine-wave • Fish waveforms less pronounced since cavities were re-tuned: • Literally squeeze the cavity with a C-clamp while watching a network analyzer • Can only increase the resonant frequency wx1 wy1 wx1 wy1 Don’t understand these other peaks wx2 wy2 wy2 wx2

32. Dipole Magnet Dipole Magnet Dipole Magnet Dipole Magnet High Energy Insert BPM Here Nominal Energy Low Energy How to Measure Energy with BPMs • Chicanes exploit this property: • Bunch compression and other beam manipulations • Beam energy measurement • Dispersion: Correlation of Beam Energy with Transverse Beam Position • In a dipole magnetic field, low-energy particles get deflected more than high-energy particles New physics at the International Linear Collider expected to require beam energy measurements with a resolution of ~100 parts per million!