# Presentation: 404821

## Driving Term Experments at CERN

- References
- List of Possibilities
- General Overview
- Theory
- New Developments
- List of Limits

- Linear Coupling    Compensation
- Sextupole Resonances
- Exotic Applications
- Commissioning of the LHC

**Notes:**
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## Reference

- 1988 - J. Bengtsson, “Non-linear transverse dynamics for storage rings with applications to the Low-Energy  Antiproton Ring (LEAR) at CERN”, Cern Yellow Report 88-05.
- 1992 - J. Laskar, C. Froeschlé and A. Celletti, “The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping” , Physica D **56**, pp. 253—269.
- 1998 - R. Bartolini and F. Schmidt, “Normal Form via Tracking or Beam Data”, Part. Accel. 59, pp. 93-106.
- 2003 - R. Tomás, “Direct Measurement of Resonance Driving Terms in the Super Proton Synchrotron (SPS) of CERN using Beam Position Monitors”, Cern PhD Thesis.
- 2004 – P. Urschütz, “Measurement and Compensation of Betatron Resonances at the CERN PS Booster Synchrotron”, Cern PhD Thesis.

- Driving Term Experiments at CERN

- 8 November, 2005

## List of Possibilities

**List of Possibilities**

- Driving Term Experiments at CERN

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## Slide 4

- Driving Term Experiments at CERN

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## Slide 5

- Driving Term Experiments at CERN

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## Slide 6

- Driving Term Experiments at CERN

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## Slide 7

- Driving Term Experiments at CERN

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## Theory – General Overview

- II. Term Comparison and Sextupole Resonances                                                 

**Theory – General Overview**

- I. Equivalence of Spectral Lines and Terms in the Generating Function                            

**Resonance-Line Definition                           **_**[](resline2.ppt)**_

- Driving Term Experiments at CERN

- 8 November, 2005

## Recent Developments

**Recent Developments**

- Effect of Particle Distribution  Signal reduces by **1/(m-1)** ( derivation Rogelio’s thesis)
- AC-Dipole instead of Kicker  (non-destructive!!)                       R. Tomás, “Normal Form of Particle Motion under the Influence of an AC Dipole”,  Phys. Rev. ST Accel. Beams, **5**, 54001 (2002).

- Driving Term Experiments at CERN

- 8 November, 2005

## List of Limits

**List of Limits**

- Pairs of 90 ̊ pick-ups needed
- Method does not work near chaos (no surprise!)
- Detuning Terms are not directly accessible
- Higher order Terms need large Kicks, in particular due to **1/(m-1)** reduction due to decoherence ( AC-Dipole)
- High resolution pick-up System needed each Turn! Did not work at DESY, BNL & FERMILAB! ( a PhD student made it work for PS booster)

- Driving Term Experiments at CERN

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## Slide 11

- Driving Term Experiments at CERN

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## Linear Coupling Compensation

**Linear Coupling Compensation**

- PS Booster          _[](PS_booster_coup.ppt)_

- Driving Term Experiments at CERN

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## SPS
Polarity Problem                                 
Sextupole Failure                                
Measure Coefficient                            

PS Booster                                       

**Sextupole Resonances**

- SPS
- Polarity Problem                                 _[](SPS_pol.ppt)_
- Sextupole Failure                                _[](sexfail.ppt)_
- Measure Coefficient                            _[](sexcoef.ppt)_
- PS Booster                                       _[](PS_boost_sex.ppt)_

- Driving Term Experiments at CERN

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## Single 4ơ Kick does everything!!                    

AC-Dipole idea great  positive indications at BNL 

Chromaticity Measurement (sign also!)                                  In simulation works with simultaneous transverse and longitudinal kick  experiment remains sketchy

- Single 4ơ Kick does everything!!                    _[](dist.ppt)_
- AC-Dipole idea great  positive indications at BNL
- Chromaticity Measurement (sign also!)                                  In simulation works with simultaneous transverse and longitudinal kick  experiment remains sketchy

**Exotic Applications**

- Driving Term Experiments at CERN

- 8 November, 2005

## Polarity Checks & Correction Steering  both Beam-based

Mostly for Injection and b3 Spool Piece Correction

Higher Orders and Top Energy not excluded

Need turn-by-turn BPM System on Day 1, which means low Failure Rate for all BPMs each Turn!!

**Commissioning of the LHC**

**Polarity Checks & Correction Steering  both**** ****Beam-based**
**Mostly for Injection and b****3 ****Spool Piece Correction**
**Higher Orders and Top Energy**** *****not***** ****excluded**
**Need turn-by-turn BPM System on**** *****Day 1*****, which means low Failure Rate for all BPMs each Turn!!**

- Driving Term Experiments at CERN

- 8 November, 2005