in the Tevatron Budker Seminar Fermilab Village Users

β* in the Tevatron + α Budker Seminar @ Fermilab Village Users Center 10/25/2005 Ryoichi Miyamoto (UT Austin) Supervisors: Sacha Kopp (UT Austin) Mike Syphers (Fermilab) Also Thank: Andreas Jansson (Fermilab)

List of Topics: AC Dipole I. 1. 2. β* Measurement in the Tevatron II. 1. 2. 3. 4. III. Introduction From Now Theory Let’s Try! Issues Conclusions and Future Projects Appendix

I. AC Dipole

I. AC Dipole – 1. Introduction q AC Dipole Is… § An oscillating dipole with controlled f and Bmax Used in AGS & RHIC @ BNL to avoid spin resonance. § Remember forced harmonic oscillators and resonance. § The phase space position can be “controlled”. “Nondestructive Controllable Kicker”. q Here, Now @ FNAL… § To study linear and nonlinear dynamics of Tevatron with Better BPM’s and IPM. q In Future… § One for LHC? ?

I. AC Dipole - 2. From Now q It’s just started! § From now, study, simulation, design, construction, measurements, analysis and write up… q Accelerator Physics and Technology Seminar § 11/17/2005 “TBA (About AC Dipole)” by Mei Bai (BNL)

II. β* Measurements in the Tevatron

II. β* Measurements in Tevatron - 1. Theory q Motivation: • It is not easy to directly measure beta functions. • With resolutions of new BPM system in Tevatron, beta around IP can be measured in the following way: q Two BPM’s at IP w/ no magnetic fields in-between. Particles drift. (x 1, x’ 1) can be measured TBT. L*=7. 5 m BPM 1 (x 1) L*=7. 5 m IP s BPM 2 (x 2)

II. β* Measurements in Tevatron - 1. Theory q If we know (x, x’)… [Based on Syphers’ Beam. Docs] § Betatron Oscillation: § TBT Average: § Similarly:

II. β* Measurements in Tevatron - 1. Theory q CS Parameters: qβ around IP and etc:

II. β* Measurements in Tevatron 2. Let’s Try! q A data set and results: Data by Yuri

II. β* Measurements in Tevatron – 3. Issues a. Decoherence q How Many Turns to Take the Average? (= How Fast Decoherence Messes Data? )

II. β* Measurements in Tevatron – 3. Issues a. Decoherence q Another data set. Depends on how beams decohere but only a few 100 seems to be the safe. q Why AC Dipole maybe good! q Data by Eliana

II. β* Measurements in Tevatron - 3. Issues b. Nonlinearity in BPM Signals q Huge x-offset @ CDF: Data by Yuri q Nonlinearity in BPM Signals:

II. β* Measurements in Tevatron - 3. Issues b. Nonlinearity in BPM Signals q How amplitudes change? q Before & After Filtering.

II. β* Measurements in Tevatron - 3. Issues b. Nonlinearity in BPM Signals q Other Type of Nonlinearity q Effects on β* and Etc: • β*=69. 9 cm → 38. 2 cm • βmin=31. 6 cm → 32. 2 cm • Δs*=34. 8 cm → -13. 9 cm

II. β* Measurements in Tevatron 4. Conclusions and Future Projects q Conclusions: § The analysis seems working OK. § For the average, only a few hundred turns seems safe. q From now… Apply to study couplings. Install the system into MCR. A “REAL” beam study (take data for this analysis) to control couplings, chromaticity, and beam-beam. § A little more (personal) studies about decoherence and BPM. § § §

III. Appendix: Geometry of BPM Signals

III. Appendix: • Geometry of BPM: B Beam Position: A Tevatron:

III. Appendix: • In infinite order… • After a little bit of manipulation… Looks complicated…

III. Appendix: • They have simple geometrical meanings! • Let’s see the 1 st term: A x • Also introduce θu. A, θu. B, and θd. B similarly. Then…

III. Appendix: • Measuring IA/I 0 (IB/I 0) is equivalent to specify the circle passing points PCD (PEF). • The beam is at one of intersections. • By solving the intersection problem… Infinite order!

III. Appendix

III. Appendix • Remarks: – The approximation (IA+IB)/I 0≈2φ/2π recovers the linear relation of x and (IA-IB)/(IA+IB). – For practical purposes, need to measure I 0 (and it is not easy). – If possible, how δI 0 affects δx? (Proceeding) – What happens if φ=π/2? (Proceeding)

References AC Dipole I. q Search “Mei Bai & AC Dipole”. β* Measurements in the Tevatron II. q M. Syphers, Beams-doc-1088 and 1880. Appendix III. q R. Kutschke, Beams-doc-1893 -v 3 Web Page: q q /home. fnal. gov/~ryoichi/

The End Thank you!