Development of a Chromaticity measurement application using

Head-Tail phase shift technique.

Overview

• Discussion of measurement needs in the Tevatron

• Introduction to Theory of Head-Tail Phase Shift

• Results from initial tests in the Tevatron• Coupling and Bunch Amplitude profiles• Limitations of current set-up• Conclusion

Measurement needs in the Tevatron

• Moving from uncoalesced to coalesced protons during machine tune-up

• Measurement during Acceleration ramp.

- Chromaticity, Tune, and Coupling.

• Current RF chromaticity system draw-backs

- Requires uncoalesced protons

- Requires three acceleration ramps.

H T

P/P

s

Longitudinal ‘phase-space’ Graph

Longitudinal Beam Dynamics

Chromaticity Measurement Using Head-Tail Phase Shift In the presence of non-zero chromaticity the betatron equation of motion becomes:

Thus from phase difference between two locations in a bunch the chromaticity can be calculated:

)1)2(cos(2cos so nqnY

)1)2(cos(

so nq

Using the vertical and horizontal strip-line detectors installed in the Tevatron at the F0 location we extract a profile of the transverse behavior of the beam over a single longitudinal bunch. 

Extracting Transverse position

Difference Signal (A-plate – B-plate)

Reflected Signal

Reconstructed Signal

Sum Signal (A-plate + B-plate)

The Raw Signal is Processed to remove the Reflected Signal

0 10 20 30 40 50 60 70 80 900.4

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Sj

RSj

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Turn by Turn Sum(A+B) Profile from Strip-line monitor

S

From the Sum and Difference (A-plate B-plate) Signals the Transverse position can be calculated using:    Here G is the ratio of the A-B gain over the A+B gain.Once the Transverse Position as a function of longitudinal bunch position is known () we can use this to analyze the phase shift between the Head and the Tail to Calculate Chromaticity.

,,

,,27,nBnASumnBnADifferenceGnX

Vertical and Horizontal turn by turn position after horizontal 1.6 mm kick

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Vertical and Horizontal turn by turn position after vertical 1.75 mm kick

Difference in Head Tail Phase EvolutionQ'=7.49

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Turn Number

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ase

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Chromaticity CalculationQ'=7.49

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Q'

Take Average Across 40 Turns around 1/2 Synchrotron Period Q' = 7.49

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Horizontal Chrom. Set point

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Head Tail

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Vertical Chrom. Set point

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Head Tail

Other measurements

• Coupling

• Bunch Amplitude

max

21maxmin

||||

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XQ

Aj mm

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4 sin 2X

j 1 mm Xj 1 mm 2 X

j mm 2 tan 2 Xj 1 mm X

j 1 mm 2

A

Ay

Color Contour Plot of Bunch Amplitude after 1.6 mm Horizontal kick after first 2.5 sec of ramp.

Cv=-0.93 Ch=5.1

A

Instability Studies Performed Last Spring: (Jim Crisp, Peter Ivanov)

Cv= -2.1 Ch = 6.2

A

A

Cv = -5.1 Ch = 6.2

A

Cv =-6.43 Ch =6.3

Tunes up the ramp

0.568

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Results from most recent tests during ramp:

Coupling up the ramp

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Chromaticity up the ramp

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E17 kicker delay vs. Voltage

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Timing of E17 vertical kicker

Screen Shots of Software

Limitations of current set-up

• The major drawback of this system of measurement is its destructiveness. For measurement during tune up current system is ok. For a store we need more work.

• In addition both the kickers and scope have limitations which restrict operations.

F17 and E17 kickers

• The Horizontal kicker requires a ramp up time of 2.5 secs. (~30 possible horiz. Meas.)

• The E17 kicker produces a half sinusoid current pulse with a base width of 10 micro secs. The F17 kicker produces a square current pulse with a width of 1.8 micro secs.

• Thus the E17 kicker is too slow hit only one bunch during 36x36 store. But the F17 kicker could accomplish this if fired at the right time in the abort gap.

Scope

• With all four channels Scope can store only 12048 turns which means the max number of measurements possible is 23 (every-other-turn).

• The scope resolution is limited by the bit size and closed-orbit offset which set our minimum resolution to .1 mm.

Moving towards less destructive measurements

• By removing the closed-orbit current offset we should be able to reduce this resolution down to the signal noise floor from the beam and cables. Thus we could increase effective scope resolution and possibly reduce the required kick amplitude.

• Excite beam adiabatically (ac dipole technique)• Run the damper kickers resonantly. This method

of chirp excitation has been tested successfully at HERA . Can be gated to hit only one bunch.

Conclusion

• This system is nearing completion – Last major issue: E17 kicker timing– Rigrous comparison with RF technique on ramp.

• Now time for beam physics studies:– Study chromaticity and coupling changes during ramp.– Study of Bunch amplitude using color contour plots

• Possible future improvements– Minimally destructive measurements – Measure beam-beam effects on chromaticity and coupling.– Measure Pbars?