Development of a Chromaticity measurement application using ...

Development of a Chromaticity measurement application using ...

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, 2nd order Chromaticity Longitudinal Beam Dynamics P/P s H T Longitudinal phase-space Graph (s)

2qs r sin( 2qs s / C ) C z ( s ) r cos(2qs s / C ) Chromaticity Measurement Using Head-Tail Phase Shift Y ( , , n) e 0 2 2 2 2 sin ( 2q s n ) 2 2 0 sin 2Qn (1 cos(2qs n)) o (cos(2nqs ) 1) Advantages of Head-Tail method Allows a single point measurement (no-need to vary rf frequency)

Fast: especially important in LHC during snapback. 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 2nd order chromaticity) Extracting Transverse position 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. Vertical turn by turn position after vertical 1.6 mm kick. Head and Tail are separated by .8 nsecs Xtail i 0 0 100 200 300 400 500

600 700 600 700 800 900 1000 i Xheadi 0 0 100 200 300 400 500 i

800 900 1000 Head Tail Phase Evolution for Chromaticity = 5 units Head Tail Phase difference 136 136 PhaseD ifferenceinD egrees Average 40 points 180 1 k 68 0 0 50 40 100

150 200 250 k Turn number 300 350 400 450 500 500 Comparison of Head-Tail with RF at 150 GeV for Horizontal Chromaticity 14 Horizontal Measured Chrom. 12 10 8 RF

Head Tail 6 4 2 0 30 32 34 36 38 Horizontal Chrom. Set point 40 42 Comparison of Head-Tail with RF at 150 GeV for Vertical Chromaticity 10 9 8 Vertical Measured Chrom. 7

6 RF 5 Head Tail 4 3 2 1 0 25 27 29 31 Vertical Chrom. Set point 33 35 Results from test during Acceleration ramp Chromaticity at start of ramp 16 14

Chromaticity 12 10 Cx 8 Cy 6 4 2 0 150 155 160 165 170 Energy (GeV) 175 180

185 190 C100 Head-Tail Chromaticity measurement program layout F17 Horizontal kicker: Voltage, Event Trigger and Delay settings Beam Synch scope trigger: Event, #triggers, Timing Acnet Cx,Cy Qx,Qy Acnet C100 vax Console Program Acnet Acnet 2.5 GHz Scope running Lab View program

Datalogger E17 vertical kicker: Voltage, Event Trigger and Delay settings 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. 2nd order chrom Octupoles Impedance beam intensity rms bunch length synchrotron tune. 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. 2 Xtaili 0 2 0 100 200 300 400 500 600

700 800 900 1000 i Xheadi 0 0 100 200 300 400 500 i 600 700 800

900 1000 Less usable signal with faster decoherence time. Head Tail Phase difference PhaseDifferenceinDegrees 136 136 180 1 k 68 0 0 50 40 100 150 200 250

k Turn number 300 350 400 450 500 500 Differences between LHC and Tevatron 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

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 2nd 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 2nd 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 Mm) =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. Head of bunch (Actual Data) mm 1 X n t 0 1 0

100 200 300 400 500 600 700 800 900 1000 n turn number Head of Bunch (Simulation) mm 1

RY n t 0 1 0 100 200 300 400 500 n turn number 600 700 800 900 1000

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) Tail of bunch (Actual Data) mm 1 Xn t 0 1 0 100 200 300 400 500 600

700 800 900 1000 n turn number Tail of Bunch (Simulation) mm 1 RY n t 0 1 0 100 200 300

400 500 n turn number 600 700 800 900 1000 Now adding 2 Order Chromaticity for a better fit. nd 2 X Amp i bbc A2i bb 1

A3i bb 0 0 100 200 300 400 500 600 bb 13 700 800 900 1000 1100

i 2 X Amp i bbc A2i bb 1 A3i bb 0 0 100 200 300 400 500 600

700 800 900 1000 1100 i bb 3 2 X Amp i bbc A2i bb 1 A3i bb 0 0 100

200 300 400 500 600 i 700 800 900 1000 1100 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, 2nd 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)

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