1. Matching Injector To Linac

2. Caveats • This is all loose and fuzzy – sort of religion • We don’t have real tight control over and knowledge of the machine • “functional modularity”, “beam based methods”, etc => dial it in, rather than lock it down • We have gotten it to work well enough to lase hard and reliably • Y’all are a test sample – we’ll all try to figure out how to tell people what we’ve done and how it works • Ask questions • Give advice

3. Issues Inaccuracies/ambiguities in model-based predictions • Drive laser variations • Cathode model approximations • Injector, accelerator magnets not well characterized • Field calibrations, current control • Field inhomogenieties • Simplified field models in cavities • 3-d field details needed for accuracy • Gradient calibrations “loose” Can model trends very well, and values well - but only with extremely tight configuration control Must provide beam-based tuning algorithms

4. Methodology • Set phases (spectrometer, miniphase) • “Calibrate” model • Quads don’t set with good precision • Use “difference orbits” to check focusing • Modify model to produce agreement with observation • Change magnet (usually quad) set-points to make model match reality • Perform multi-monitor emittance measurement • Gives notional beam properties at front end of machine • Rematch • Resets beam properties to fit within downstream acceptance

5. Machine Model • Analysis of beam and accelerator properties requires a means of evaluating transfer matrix elements, beam envelopes, etc • Typical machine models are home-brewed, machine specific, but generally are • based on matrix-multipliers • Read parameters directly from the machine • Run fast • Have a high degree of interactivity • Can modify easily • Pull in/push out data • Optimize optics solutions, orbit corrections, etc

6. Difference Orbits • When we phased, we “zeroed” the BPMs and looked at the effect of changing phase • The signature was the change in position at the spectrometer observation point • Method works for other parameters: zero the BPMs and see what happens when we kick beam • Can be used to establish transfer matrix elements (esp. M12, M34, M62, …) • Twiss parameter representions (betatron amplitudes) • Phase advance • Momentum compactions M55,T555, … • Basic method: • Zero BPMs • Change “something” and look at response • Corrector (M12, M34) • Beam energy (M16) • Injection phase (M55, T555,…) • Analysis of data can • Set BPM scale factors • Trap focusing errors (quad, dipole, screwdrivers, allen wrenches…) • Measure/correct compactions This measurement characterizes the lattice - and helps you use the lattice to measure the beam

7. Multi-monitor Emittance Measurements • Beam envelopes at an observation point are defined by their value at some upstream reference + the transfer matrix • If the transfer matrix (matrices) are known, can measure spot sizes at several (more than three) places and determine beam envelopes and emittance • Form sum of square deviations between projection & observation, and minimize by varying “injected” betas

8. Rematch • After fitting “initial” beam envelopes to reproduce in model observed spot sizes, you can see the propagated Twiss parameters • Adjust quads to make “real” betas match design acceptance values • Iterate: • Remeasure, check propagated envelopes, see if agreement improves

9. The Dread “Matchathon” • Wailing, cursing, gnashing of teeth… • Apply same process to • linac-to-arc match, • dispersion management in arc(s), • arc-to-wiggler match, • momentum compaction (M55, T555) for bunch length compression, • wiggler-to-arc match, • arc-to-linac (reinjection) match, • energy compression (M56, T566, W5666), • Iterate • Then trim for loss suppression as you boot-strap lasing

10. To Consider • Beam is very irregular – must consider just what you match on • Full beam size (stuff all the electrons through tight apertures) • Sigmas – fit to gaussian • Rms beam size • Usually worry about the 1st • Hard to associate “which gaussian goes with which other” when you march down the line