Elias Métral, APC meeting, 02/02/2006 1/35 E. Métral, G. Arduini and G. Rumolo u Observations of...

Elias Métral, APC meeting, 02/02/2006 1/35

E. Métral, G. Arduini and G. RumoloE. Métral, G. Arduini and G. Rumolo

Observations of fast instabilities in the SPS (1988 and 2002/3) and PS (2000)

Intensity threshold vs. beam/machine parameters

Analysis of the evolution in time of the instability

Measurements in the V- and H-planes (SPS - 2003)

Theories: BBU and HT&TMC

Simulations with the HEADTAIL code

The case of the PS instability

Conclusions and future work

Appendices: BB impedance model, FFT, spectrum analyzer, linear HT phase shift

FAST VERTICAL SINGLE-BUNCH INSTABILITY

AT SPS INJECTION


Fast instability of Fast instability of positronpositron bunches in the bunches in the SPSSPS Gareyte & Brandt in Gareyte & Brandt in 19881988 (BBU analysis) (BBU analysis)

cm16zGeV/c3.5p

turns76periodn Synchrotro


0.8y0y

Instability suppressed Instability suppressed by increasing by increasing

the chromaticitythe chromaticity

ms7periodn Synchrotro

Fast vertical single-bunch instability with Fast vertical single-bunch instability with protonsprotons at at the the SPSSPS injection in injection in 20032003

eVs35.0eVs 0.2 LHC ll

p/b10 1.2 11bNGeV/c26p


Fast vertical single-bunch instability with Fast vertical single-bunch instability with protonsprotons at at the the PSPS near transition in near transition in 20002000

, R, V signals

Time (10 ns/div)~ 700 MHz

Instability suppressed by increasing the longitudinal emittanceInstability suppressed by increasing the longitudinal emittance

GeV6E p/b10 4 12bN

Head stableTail unstable


BBr

lthb f

fN y 1

Scaling of the intensity threshold with beam&machine Scaling of the intensity threshold with beam&machine parametersparameters

The farther the transition energy the better

(confirmed by the HEADTAIL code)

As in the PS As in the SPS

It is not the energy which matters!!


MEASUREMENTS IN THE VERTICAL PLANE (1/5)MEASUREMENTS IN THE VERTICAL PLANE (1/5)

1st trace (in red) = turn 2 Last trace = turn 150 Every turn shown

0.14y

Head Tail

Travelling-wave pattern along the bunch




0.54y




2.04y


Turn 99 shown

Δt 1.25 ns f 800 MHz

Δt 1 ns f 1 GHz

Δt 1.1 ns f 900 MHz


0.14y



Betatron phase difference between different temporal slices

with respect to the central slice (=centre of the bunch)

Slice preceding the central one by 1 ns

Slice following the central one by 1 ns

Every 250 ps shown

0.14y

~ Time of beam loss

The phases are arranged for a coherent

instability (the centre of mass changes along the

bunch)


MEASUREMENTS IN THE HORIZONTAL PLANE (1/2)MEASUREMENTS IN THE HORIZONTAL PLANE (1/2)


0.09x

0.14y


MEASUREMENTS IN THE HORIZONTAL PLANE (2/2)MEASUREMENTS IN THE HORIZONTAL PLANE (2/2)

Betatron phase difference between different temporal slices

with respect to the central slice (=centre of the bunch)

Slice preceding the central one by 1 ns

Slice following the central one by 1 ns

Every 250 ps shown

The phases are not arranged for a

coherent instability


BBU THEORYBBU THEORY

1st trace = turn 1 Last trace = turn 115 Every turn shown

ns7.0t

/mM10 yR

GHz1rf

1Q

BB resonatorimpedance

Travelling-wave pattern

along the bunch

Head Tail


The spectrum of mode mq (σmq) is peaked at and

extend

2 modes with same q are peaked at the same frequency (same line

density), and therefore have ~ the same sensitivity in the same

frequency range. They however correspond to entirely different

patterns in phase space

In the next 2 slides, the same plots as Laclare (CERN 87-03) are

shown for a single (Head-Tail) mode, i.e. no TMC

bq

qf

2

1

1 b

HT&TMC THEORY (1/10)HT&TMC THEORY (1/10)

kmq 2 k0with


f

00

S00

X00

f

02

S02

X02

f

04

S04

X04

f

11

S11

X11

S00

S02

S04

S1110 b

13.xQ

0

HT&TMC THEORY (2/10)HT&TMC THEORY (2/10)22bb

2/ˆ0 b

revfQf


f

13

S13

X13

f

22

S22

X22

f

24

S24

X24

f

33

S33

X33

S13

S22

S24

S33




Observations in the PS in 1999 (20 revolutions superimposed)

7qm5qm4qm

8qm 10qm6qm

Time (20 ns/div)




0yTime evolution for HT Time evolution for HT

mode -24 alone mode -24 alone (no rise-time)(no rise-time)

Standing-wave pattern




0.14y


Time evolution for HT Time evolution for HT mode -24 alone mode -24 alone (no rise-time)(no rise-time)




0y






0.14y






ns8.24 tb

turns SPS 55MOSESTMC

TMC between TMC between modes -24 and -35modes -24 and -35 Complete theory Complete theory

not yet finishednot yet finished

Travelling-wave pattern along the bunch

0y


/mM10 yR

GHz1rf

1Q

BB resonatorimpedance

p102.7

mA5.010

thb

thb

N

I

mA83.0

p102.1 11

b

b

I

N

turnsSPS552TMC

sT

9.0

mA5.0thbI

mA83.0bI


Instability rise-time from MOSES


HEADTAIL SIMULATIONS (1/5)HEADTAIL SIMULATIONS (1/5)

GHz1rf


p/b102.1 11bN

Flat chamber

ns7.0t/mM20 yR

1Q


along the bunch

Head Tail



Turn 38 shown

Δz/2 16 cm f 0.94 GHz




Round chamber GHz1rfp/b102.1 11bN

ns7.0t/mM20 yR

1Q


along the bunch



b / p108.2 10,, ythb

xthb NN Round chamber

b / p108 10, xthbN

Flat chamber

b / p105.3 10, ythbN

4.312

2.82

8.624

2.82

The intensity threshold is increased in a flat chamber by

- The vertical Yokoya factor in the y-plane

- Slightly more than the horizontal Yokoya factor in the x-plane (it is not suppressed! and the effect of the detuning impedance, if any, seems small and in the plane of higher threshold)

This is the starting point for our study on the effect of linear coupling

y-Yokoya factor

x-Yokoya factor


HEADTAIL SIMULATIONS (5/5)HEADTAIL SIMULATIONS (5/5) The role of space charge and

longitudinal mismatch has also been

studied in detail in a recently published

paper “Simulations of the fast

transverse instability in the SPS”, G.

Rumolo, V. G. Vaccaro and E.

Shaposhnikova (CERN-AB-2005-088-RF)

Emittance blow-up in space

charge regime below TMCI threshold!

LHC beam

!


THE CASE OF THE PS INSTABILITY (1/4)THE CASE OF THE PS INSTABILITY (1/4)

, R, V signals


MEASUREMENTS IN 2000MEASUREMENTS IN 2000 BBU THEORY BBU THEORY AFTER 90 TURNS (~ 200 AFTER 90 TURNS (~ 200 μμss))

Seem very close except head and tail exchanged!!! It may start only

for the maximum peak intensity, i.e. in the middle…

Try to produce the same movie with measurements next year (as we

did for the SPS fast instability at injection)

Slide from APC 08/12/05Slide from APC 08/12/05


THE CASE OF THE PS INSTABILITY (2/4)THE CASE OF THE PS INSTABILITY (2/4)HEADTAIL SIMULATIONHEADTAIL SIMULATION


GHz1rf

/mM3 yR

1Qns5.7t

p/b104 12bN

Flat chamber

bunch thealong

slices 500

Head Tail


THE CASE OF THE PS INSTABILITY (3/4)THE CASE OF THE PS INSTABILITY (3/4)

Turn 130 shown

Δz 40 cm f 750 MHz

Δz 120 cm f 250 MHz

HEADTAIL SIMULATIONHEADTAIL SIMULATION


THE CASE OF THE PS INSTABILITY (4/4)THE CASE OF THE PS INSTABILITY (4/4)HEADTAIL SIMULATIONHEADTAIL SIMULATION

Same simulation for a flat bunch Same simulation for a flat bunch (same density as the Gaussian peak density)(same density as the Gaussian peak density)


p/b104.62

4p/b104 1212

bN

bunch thealong

slices 150


Using the classical BB impedance model of the SPS machine (Q~1,

~1 GHz, ~10-20 MΩ/m), the evolution in time of the instability can be

reasonably reproduced ( Travelling-wave pattern along the bunch)

using either the BBU or TMC formalism

The instability starts near the middle of the bunch, i.e. at the

maximum of the peak intensity (and even on flat bunches)

Local phenomenon

This is why the intensity threshold is the same as the one for

coasting beams with peak values Transverse microwave instability

CONCLUSIONS AND FUTURE WORK (1/3)CONCLUSIONS AND FUTURE WORK (1/3)


Measured pictures very close to the simulated ones

HeadHEADTAIL SIMULATIONHEADTAIL SIMULATIONMEASUREMENTMEASUREMENT


, R, V signals


HeadTail

Tail

Head Tail

SPSSPS

PSPS

Tail Head



Future work: Try to better estimate the impedance (and aperture) of

the machine

Produce the movies of the evolution in time of the coherent motion

(instability) AND the beam intensity AND the transverse beam

sizes (measurements and HEADTAIL code) At which turn do we

lose and where (BLM) and how?

Repeat the same measurements with larger transverse emittances

to see the effect of space charge

Analysis of the relative difference between 2003/2004 and 2006

(4 new MKE kickers installed)

We proposed to measure the transverse impedances of these MKE

kickers (without and with coating) as was done in the PS for new

kickers to be installed for the new CT (the resonance frequency

seems to be lower than predicted by 2D theory Worse for TMCI)

Simulations with MAFIA by Bruno Spataro (Frascatti) of the BPM

impedances (108 BPH and 108 BPV) Ongoing


APPENDIX 1 : THE BB IMPEDANCE MODELAPPENDIX 1 : THE BB IMPEDANCE MODEL

It is a single-bunch instability Short-range wake field BB

impedance

Measured impedances of the PS kickers for the new CT very close

to BB impedances. Predictions for the MKE also

BB impedance model deduced from Head-Tail growth/decay rate

Intensity threshold vs. quality factor (from MOSES)

y = 4.207x + 0.0356

R2 = 0.9966

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5 6 7 8 9 10

Quality factor Q

Nb

th [

1e

10

]

/mM20 yR

GHz3.1rf

Resonator impedance


APPENDIX 2 : MEASURED FFT IN APPENDIX 2 : MEASURED FFT IN V- & H-PLANEV- & H-PLANE

FFT of the HT monitor signals applied over the full acquisition depth (372 turns ~ 8.6 ms). The peaks at 40 MHz are due to the fact that at each turn only 25 ns out of the full revolution period of 23.1 μs are acquired


APPENDIX 3 : SPECTRUM ANALYZER IN APPENDIX 3 : SPECTRUM ANALYZER IN V- & H-PLANEV- & H-PLANETransverse pick-ups (BPWA31901 for V and BPWB32101 for H) in the Faraday Cage have been connected to a Spectrum Analyzer Wide-band directional couplers with exponential coupling, optimized for the studies of instabilities in the frequency domain

MHz 600 ~

GHz 1.1 ~

GHz 1.4 ~

GHz 2.1-1.5

GHz 2.3-1.7

GHz 1.5 ~


APPENDIX 4 : Time evolution for the linear HT phase shift (1/4) APPENDIX 4 : Time evolution for the linear HT phase shift (1/4)

1st trace = turn 1

Last trace = turn 308

Every turn shown

ns8.24 tb

turnsSPS308sT

0y

Head and Tail remain in phase

LHC Project

Report 602

(Fartoukh&Jones)


ns8.24 tb

turnsSPS308sT

05.0y

1st trace = turn 1

Last trace = turn 308

Every turn shown

LHC Project

Report 602

(Fartoukh&Jones)

APPENDIX 4 : Time evolution for the linear HT phase shift (2/4)APPENDIX 4 : Time evolution for the linear HT phase shift (2/4)


turn 2

Head and Tail in phase



turn 150

~ Maximum phase difference between

Head and Tail


Elias Métral, APC meeting, 02/02/2006 1/35 E. Métral, G. Arduini and G. Rumolo u Observations of...

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Transcript of Elias Métral, APC meeting, 02/02/2006 1/35 E. Métral, G. Arduini and G. Rumolo u Observations of...