# Presentation: 854628

## Use of Head-Tail Chromaticity Measurement in the TevatronV. H. Ranjbar (FNAL)

## Overview

*Introduction to Head-Tail Phase Shift method to measure chromaticity*
*Advantages of H-T method*
*Set-up of H-T monitor in the Tevatron*
*Limitation of system in Tevatron.*
*Measurement issues in the LHC*
*Other possible uses of the H-T monitor:*
*Fitting Wake fields, 2**nd** order Chromaticity*

## Longitudinal Beam Dynamics

## Chromaticity Measurement Using Head-Tail Phase Shift

## Advantages of Head-Tail method

*Allows a single point measurement (no-need to vary rf frequency)*
*Fast: especially important in LHC during snap-back. Traditional methods you are limited by the speed which you can cycle the rf frequency.*
*Can allow for other parasitic measurements: (i.e. coupling, optics, maybe even impedance and 2**nd** order chromaticity)*

## Extracting Transverse position

** **

## Vertical turn by turn position after vertical 1.6 mm kick. Head and Tail are separated by .8 nsecs

## Head Tail Phase Evolution for Chromaticity =  5 units

- Average 40 points

## Comparison of Head-Tail with RF at 150 GeV for Horizontal

- Chromaticity

## Comparison of Head-Tail with RF at 150 GeV for Vertical

- Chromaticity

## Results from test during Acceleration ramp

## 2.5 GHz Scope running Lab View program

- C100 vax Console Program

- F17 Horizontal kicker: Voltage, Event Trigger and Delay settings

- E17 vertical kicker: Voltage, Event Trigger and Delay settings

- Beam Synch scope trigger: Event, #triggers, Timing

- C100 Head-Tail Chromaticity measurement program
- layout

- Acnet

- Acnet

- Acnet

- Acnet

- Cx,Cy
- Qx,Qy

- Datalogger

## C100 Program screen shots

## Limitations of current set-up 

*Destructive measurements*
*Emittance blow up, aperture limitations*
*Extracting usable signal*
*Phase contamination: coupling*
*Decoherence time: Tune spread*
*Linear chrom.*
*2**nd** order chrom*
*Octupoles*
* **Impedance*
* **beam intensity*
* **rms bunch length*
* **synchrotron tune.*

## Emittance Blow up after 5 kicks in Horizontal and 

- Emittance Blow up after 5 kicks in Horizontal and
- 5 kicks vertically

## Decoherence time

- Octupoles at Injection:
- Damping time can be less than 100 turns
- Effected by
- bunch intensity ( need > 280E+9) to get signal at 300 turns.
-  transverse emittance.
-  Flat-top
-  high chromaticities
-  longer synchrotron periods

## Head and Tail turn-by-turn vertical motion with strong Coupling

- and Octupoles on.

## Less usable signal with faster decoherence time.

## Synchrotron Period: 
 182  - 525 turns in LHC 
 564 – 1412 turns in Tev
Chromaticity Range 
 (2 to +/-50 units) in LHC initially later (+/- 15 units) need control to 0.5 units tolerance 5 units [3]
(0 to 25 units) in Tev
2nd Order Chromaticity Range 2
 11,000 uncorrected in LHC [3]
 ~1500 in Tev
Damping Time (LHC) [3]
 8 turns at 50 units of Chrom, 130 turns at 10 units.
250 turns at collisions 

* **182  - 525 turns in LHC *
* **564 – 1412 turns in Tev*
*Chromaticity Range ***
* **(2 to +/-50 units) in LHC initially later (+/- 15 units) need control to 0.5 units tolerance 5 units [3]*
*(0 to 25 units) in Tev*
*2**nd** Order Chromaticity Range ****2*
* **11,000 uncorrected in LHC [3]*
* **~1500 in Tev*
*Damping Time (LHC) [3]*
* **8 turns at 50 units of Chrom, 130 turns at 10 units.*
*250 turns at collisions *

**Differences between LHC and Tevatron**

## Measurement Issues in LHC

*Larger swings in Chromaticity in the LHC *
*( > 50 unit swing during 30 sec snap back with only 80% control from feed forward). [4]*
*Decoherence Time*
*High 2**nd** order chromaticity *
*Helped by a shorter synchrotron period..*
*With Chrom > 20 units becomes a problem*
*Emittance blow-up*
* **Use current current method of kicking beam ~ 1 mm will allow only ~ 10 kicks. *
*Longitudinal Bunch Motion ?*
*This currently makes HT measurements in Tevatron with uncoalesced bunches very difficult.*

## Possible Solutions and Plans for HT use in the LHC

*Large Chromaticities*
*  **damping time *
* **Tracking phases > 360 degrees*
* **Solution: Measure damping time or frequency width to grossly estimate large chromaticities. *
*Damping Time and Emittance Blow up *
*Solution: Improve S/N by taking out the closed orbit offset in the signal*
*Auto-zeroing using variable attenuators*
*Zero crossing *
*Using diodes : R. Jones?*

## Other Possible Measurements with HT monitor

*Measure Wake field strength?*
*Measure 2**nd** Order Chromaticity?*
*Evolution of Beam Envelope over Bunch *
*Compare with multiparticle simulations*

## The Results of multi-particle simulation N=1000 particles with Resistive wall wake field 4.4E+5cm-1  (Zeff=7 Mm) =3.733 total charge equal 2.6E+11 e .  We did not include 2nd order chromaticity. The behavior is almost identical. Especially you can see larger re-coherence followed preceded by smaller one.

## The tail of the bunch also displays a structure  almost identical to the actual data. In fitting the data we found we could specify the strength of the resistive wall wake from 7E+5 cm-1 to 4.4E+5cm-1 (Zeff=7-10 M/m)

- The tail of the bunch also displays a structure  almost identical to the actual data. In fitting the data we found we could specify the strength of the resistive wall wake from 7E+5 cm-1 to 4.4E+5cm-1 (Zeff=7-10 M/m)

## Now adding 2nd Order Chromaticity for a better fit.

## Conclusion

*Applying the HT Chromaticity in LHC will involve overcoming several issues*
*Emittance blow-up*
*Decoherence time*
*Tracking large Chromaticity swings*
*Coupling issues*
*Perhaps issues with longitudinal bunch motion?*
*The information we get from the HT monitor can be mined to extract in addition to linear chromaticity, wake field strength, 2**nd** Order chromaticity and perhaps other effects at this stage these fits must be done offline but with more experience and perhaps using empirical model based on simulation.*

## References:

- [1] S. Fartoukh and R. Jones, LHC Project Report 602
- [2] LHC Beam parameters and definitions (Vol 1. Chapter 2.)
- [3] S. Fartoukh and J.P. Koutchouk,, LHC-B-ES-0004 rev 2.0 (2004)
- [4] R. Jones,  Beam measurement capabilities for controlling dynamic effects in the LHC (LHC Reference Magnetic System Review July 27th and 28th  2004)