Bench-top Transverse Impedance Measurements with Phase I Graphite Collimator

1. Bench-top Transverse Impedance Measurements with Phase I Graphite Collimator Jeff Smith SLAC September 2, 2008

2. Theory • New resistive wall impedance regime discovered when • wall radius < wall thickness • skin depth ≥ wall radius • Referred to as Inductive By-Pass • Critical frequency for transverse beam stability in LHC dependent on fractional part of the betatron tune • For the design operating point of 0.3 => ~8 kHz • Complementary tune point of 0.7 => ~3 kHz • At 8 kHz • Nominal collimator half-gap is 1 mm • So, Inductive By-Pass regime for both Copper and Graphite collimators (and pretty much any other LHC collimator for that matter) • For more information on theory: • “Transverse Resistive Wall Impedance and Wake Function with ‘Inductive Bypass’” A. Koschik et al., EPAC04

3. Theory • Note that at low frequencies below 200 kHz graphite has lower real part impedance than copper! 3

4. Theoretical Impedance of Rotatable Collimator • This graph includes • Resistive Wall with inductive by-pass • Geometric using Yukowa Formula • Contact Resistance using classical contact resistance transverse impedance formula (this over-estimates effect) • Resistive wall dominates 4

5. Experimental Method • Method adapted from • “Bench Measurements of Low Frequency Transverse Impedance,” A. Mostacci, F. Caspers and U. Uriso PAC03 • Performed in conjunction with recent CERN measurements: • “Bench Measurements of the Low Frequency Transverse Impedance of the CERN LHC Beam Vacuum Interconnects with RF Contacts,” B. Salvant, F. Caspers, E. Metral and F Roncarolo, EPAC08 • “Comparison Between Laboratory Measurements, Simulations and Analytical Predictions of the Resistive Wall Transverse Beam Impedance at Low Frequencies,” F. Roncarolo, F. Caspers and B. Salvant, EPAC08 5

6. Experimental Method • Measure the complex Impedance of a coil. • Coil introduces dipole field in Device Under Test (DUT) • Transverse Impedance can then be found from • However, a reference should be used to remove impedance of coil not due to DUT, so • If the impedance of the reference can be determined independently then data can be processed to find impedance of DUT Imp. measured on coil Coil width Number of turns

7. Measurement Equipment • Coil considerations: • Greater the coil width the stronger the signal • But, the wider the coil the greater the DUT radius must be from the beam • Greater number of turns the stronger the signal • But, more turns results in lower resonance frequency of the coil • Ideal coil is a trade-off of these parameters • From my experience • 10 turns seems to work well • Make coil as wide as possible but still fit in DUT • Measurement device • In principle, can use any device that can measure complex impedance of the coil. • Vector Network Analyzer and LCR meter are two examples and recommended to me to use • From my experience • VNA works better at higher frequencies above 50 kHz since the measurement is based on measuring the reflected signal (poor at low frequencies) • LCR meter (Using an Auto-Balancing Bridge OpAmp) works well down to 500 Hz or even below but will only go to a couple Mhz (2 Mhz for mine).

8. Part I: Simple Plates • Measure impedance from ten turn coil within two copper and graphite plates of similar dimensions • Use LCR meter and Kelvin clips to precisely measure coil impedance • Tried different coils but will only summarize results here with best coil • VNA also works but only at high frequencies above 50 kHz. • We are more concerned with 1-10 kHz range

9. Raw Data • Real data clearly distinct between copper and graphite • Imaginary also has clean distinct curves just difficult to see the difference in the plots even when plotting log scale!

10. Results • In addition to the data, also plotted are: the theoretical Inductive By-Pass curves and the theoretical curve if there was no inductive by-pass (thick wall) • Inductive By-Pass clearly evident • Not complete agreement with theory but close • Note that graphite has smaller real impedance than copper at low frequency

11. Part II: Phase I Graphite Collimator • Want to compare the resistive wall versus geometric impedance • Standard setup with silver coated BeCu fingers • Remove fingers, just look at graphite jaws • Insert foil transitions similar to our Phase II rotatable collimator setup • My Expectations: • Restive wall impedance much greater than geometric • Greatest impedance with no transition pieces (sharp right angle at beginning and end of jaw) • Little difference between BeCu fingers and copper foil in its stead 11

12. Measurements • Coil Parameters: • Lucite core: 0.95cmx4cmx1.53m • Coil: 10 turns 24 gauge magnet wire (0.53 mm diameter) • Second thinner coil with 1.57mm thick lucite core also constructed but not used (explained below) • Measured several configurations • Coil in air (reference) • In two copper plates (reference) • Copper plates: 1.27cm thick x 6.7cm tall x 1.2m long • 13.9 cm total gap • In graphite collimator at various gap widths • With fingers • Without fingers • With foil transition pieces 12

13. In Air

14. In Copper

15. In Collimator

16. Measurement Considerations • Due to miscommunication, coil support bars made out of aluminum. • Ideally would be some plastic • But as is, resulted in small perturbation. • Copper and air measurements performed with support bars attached so that perturbation removed in reference (but effect small enough that can be ignored) • Our graphite collimator was purchased from CERN as a damaged but operation model. • Actually one of the jaws would not move completely toward the center, not sure what it’s hitting but presumably due to the damaged vacuum chamber => Minimum full gap width of about 12 mm • With this in mind, there was little use in using the thinner coil. So, only thicker coil was used and minimum half gap of 13.9 mm was used (same as copper plates). 16

17. In Collimator with Fingers

18. Without Fingers Fingers removed

19. Raw Data • Raw data looks about right. • ‘w/trans’ means with transition pieces (fingers) • With jaws fully retracted raw data very similar to coil in air • Little difference when removing transitions • At high frequency data starts to go wild (can see better in processed data below)

20. Use Air as Reference • Here we can begin to see the frequency limits of the measurement. • At low frequency huge fluctuations occur probably due mainly to slight temperature fluctuations (as also found by CERN measurements) • At high frequency hit a coil resonance. Can use less turns to pull resonance higher but risk too small of signal to noise ratio. • Practical limits to measurement: ~500 Hz - 500 kHz Frequency limitsof measurement

21. Use Air as Reference, cont... • Real curves fairly close to theory. • Imaginary quite a bit off. Due to Imaginary impedance measured on coil in air is large whereas theory assumes it’s zero. • Best to use copper as the reference. Note that both copper and graphite curves are off from theory by same offset => difference between curves will eliminate the offset!

22. Graphite - Copper • Agreement with theory OK but a bit off • Effects of transition are in agreement with expectation • Geometric only effects imaginary part and is roughly constant (real curves are the same, almost) • Worse (greater impedance) without transition -- effectively right angle transitions at collimator ends which is worse than smooth transition • Small compared to resistive wall component

23. Different collimator gaps, air as reference • Measured at full gap 13.9, 15.9, 17.9, 22.0, 26.0, 34.0, 42.0 and 55.0 (fully open) • Below plotted with air as reference • As gap increases approaches air measurements

24. Different Collimator Gaps, copper as reference • As gap increases, with/without transition curves merge. • Resistive wall goes as r^-2, geometric as r^-1 • Below plotted with Copper (fixed gap size) as reference

25. Couple more notes on measurements • Silver coated fingers have been in air for a long time, so plenty of oxidation. • Also looked a little worn, but that may be a good thing, actually rubbing off the oxidation. But in some places along the contact silver coating looked completely rubbed off! • I don’t think this will effect results by much because contacts are far away from beam near flange. Would have greater effect if contacts were on other side of fingers near graphite jaws 25

26. Phase II foil transitions • Look at effects of using copper foils for transition pieces • ~250 microns thick copper foil attached to graphite jaws replacing the silver fingers • Similar to the foils in our rotatable collimator design

27. Phase II foil transitions • Only one pair of foils manufactured so effect should be multiplied by two to get effect of both sides • Very little difference with or without foils. • Resistive wall of jaw surface completely dominates Frequency limitsof measurement

28. Conclusions • Inductive by-pass resistive wall component clearly dominates at relevant frequencies. • True for both Graphite and Copper. • Below 300 kHz graphite actually has a lower real impedance than copper. • Although transition pieces are required to carry the image current, their geometry are of little consequence. • The Yukowa formulas for round collimators predict this but it is still important to make the physical measurement, especially since our geometry is far from round. • This doesn’t address impedance contributions due to trapped modes (which is at much higher frequencies). • See results by Liling Xiao for trapped mode analysis. 28

29. Special Thanks Goes to: • CERN experts and students for collaboration and great advice: • Fritz Caspers, E. Metral, F. Roncarolo, B. Salvant • SLAC RF experts for helping set up experiment: • Dan Van Winkle, Jim Lewandowski • SLAC LHC research group • Lew Keller, Steve Lundgren, Tom Markiewicz, Reggie Rogers, Eric Doyle 29