# Presentation: 812097

## 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
- Introduction
- From Now
- β* Measurement in the Tevatron
- Theory
- Let’s Try!
- Issues
- Conclusions and Future Projects
- Appendix

## AC Dipole

## I. AC Dipole – 1. Introduction

- 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”.
- Here, Now @ FNAL...
- To study linear and nonlinear dynamics of Tevatron with Better BPM’s and IPM.
- In Future...
- One for LHC??

## I. AC Dipole - 2. From Now

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

## β* Measurements in the Tevatron

## II. β* Measurements in Tevatron - 1. Theory

- 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:
- Two BPM’s at IP w/ no magnetic fields in-between.
-       Particles drift.      (x1,x’1) can be measured TBT.

- IP

- BPM2
- (x2)

- BPM1
- (x1)

- L*=7.5m

- L*=7.5m

- s

## II. β* Measurements in Tevatron - 1. Theory

- If we know (x,x’)... [Based on Syphers’ BeamDocs]
- Betatron Oscillation:
- TBT Average:
- Similarly:

## II. β* Measurements in Tevatron - 1. Theory

-  CS Parameters:

- β around IP and etc:

## II. β* Measurements in Tevatron2. Let’s Try!

- A data set and results:

- Data by Yuri

## II. β* Measurements in Tevatron – 3. Issuesa. Decoherence

- How Many Turns to Take the Average?
-      (= How Fast Decoherence Messes Data?)

## II. β* Measurements in Tevatron – 3. Issuesa. Decoherence

- Depends on how beams decohere but only a few 100 seems to be the safe.
- Why AC Dipole maybe good!

-  Another data set.

- Data by Eliana

## II. β* Measurements in Tevatron - 3. Issuesb. Nonlinearity in BPM Signals

- Huge x-offset @ CDF:
- Data by Yuri

- Nonlinearity in BPM Signals:

## II. β* Measurements in Tevatron - 3. Issuesb. Nonlinearity in BPM Signals

- How amplitudes change?

- Before & After Filtering.

## II. β* Measurements in Tevatron - 3. Issuesb. Nonlinearity in BPM Signals

- Other Type of Nonlinearity

- Effects on β* and Etc:
- β*=69.9cm → 38.2cm
- βmin=31.6cm → 32.2cm
- Δs*=34.8cm → -13.9cm

## II. β* Measurements in Tevatron4. Conclusions and Future Projects

- Conclusions:
- The analysis seems working OK.
- For the average, only a few hundred turns seems safe.
- 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.

## Appendix:Geometry of BPM Signals

## III. Appendix:

- Geometry of BPM:

- A

- B

- Beam Position:

- 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 1st term:
- Also introduce *θ**u**A**, **θ**u**B**, and **θ**d**B **similarly.*
*Then...*

- A

- x

## III. Appendix:

- Measuring IA/I0 (IB/I0) 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)/I0≈2φ/2π recovers the linear relation of x and (IA-IB)/(IA+IB).
- For practical purposes, need to measure I0 (and it is not easy).
- If possible, how δI0 affects δx? (Proceeding)
- What happens if φ=π/2? (Proceeding)

## References

- AC Dipole
- Search “Mei Bai & AC Dipole”.
- β* Measurements in the Tevatron
- M. Syphers, Beams-doc-1088 and 1880.
- Appendix
- R. Kutschke, Beams-doc-1893-v3
- Web Page:
- /home.fnal.gov/~ryoichi/

**The End**
**Thank you!**