ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004F. Zimmermann Review of Single-Bunch...

ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann

Review of Single-Bunch Instabilities Driven by an Electron Cloud

• experimental evidence• simulation approaches• analytical treatments • similarities & differences to

impedance-driven instabilities

• synergetic effects• countermeasures• open issues

Napa ValleyApril 2004


concerns

• beam loss • emittance growth• trajectory change (turn-by-turn or pulse-to-pulse)


single-bunch instability

• but in multibunch or multi-turn operation (in all/most cases e- are already present when bunch arrives)• for long proton bunches as in PSR, e- density increases towards tail of the bunch due to ‘trailing-edge multipacting’ tail becomes unstable first• e- cloud can as well drive coupled-bunch instabilities (talk by K. Ohmi)• also strong possibility of combined coupled-bunch head-tail instabilities! (talk by D. Schulte)


(1) observations


INP Novosibirsk, 1965, bunched beam

‘first observation of an e- driven instability? coherent betatron oscillations & beam loss with bunched proton beam; threshold ~1-1.5x1010, circumference 2.5 m, stabilized by feedback (G. Budker, G. Dimov, V. Dudnikov, 1965).

other INP PSR 1967:coastingbeam instability suppressed byincreasing beamcurrent;fast accumulation ofsecondary plasmais essential forstabilization;1.8x1012 in 6 m

V. Dudnikov, PAC2001


Argonne ZGS,1965 bunched beam, h=8(J.H. Martin, R.A. Winje, R.H. Hilden, F.E. Mills)

oscilloscope tracesshowing coherentvertical instability. Sweep rate is 0.2 sec/cm;top: signal fromvertical pick up;bottom: beam current.

growth time 5-100 ms,threshold 2-8x1011 protons distributed over 8 bunches,largest bunches are most unstable; bunches moveindependently from each other; threshold varies withhorizontal position; range or memory of the blow up does notextend for more than 70 feet around the machine;instability suppressed by wideband (100 MHz) transverse damper


BNL AGS, 1965(E.C. Raka)

coherent verticalbetatron oscillationsand beam loss

caused by a poor vacuum (>10-5 mm Hg) in a small portion (1/12)of the ring

threshold showedweak dependenceon pressure; but rise time stronglypressure dependent

threshold around 4x1011 protons per pulse;growth rates 20-500 ms for n=8, 9 modes, slow compared with 8 ms synchrotron period,instability suppressed by sextupoles; narrow-band feedback studied

10 ms/cm, 0.2 cm amplitude growth at 1.15x1012 protons, bunched beam

also at Orsay pressure dependent instabilities were observed, and attributedto nonlinear fields introduced by electrons (H. Bruck, 1965)


Bevatron, 1971, coasting beam(H.A. Grunder, G.R. Lambertson)

MHz 455.2 ,)( 00 ffQnf yn

n=3-10

mode number changedtowardssmaller valuesas instabilityprogressed;electronoscillationfrequency decreased as beam sizegrew

for 1012 protons/pulse, beam size doubled in 200 ms;clearing field at pick ups decreased oscillation signal by factor 2;instability not very sensitive to octupoles; gas pressure 2x10-6 Torr;feedback stopped growth


extensive system of electrostatic clearing electrodes

ISR, coasting proton beam, ~1972 (R. Calder, E. Fischer, O. Grobner, E. Jones)

excitation of nonlinearresonances; gradualbeam blow up similarto multiple scattering

beam induced signalfrom a pick up showingcoupled e-p oscillation;beam current is 12 A andbeam energy 26 GeV

2x10-11 Torr,3.5% neutralization,Q=0.015


PSR instability, 1988(D. Neuffer et al, R. Macek et al.)

beam loss on time scale of 10-100 s above threshold bunch charge of 1.5x1013, circumference 90 m,

transverse oscillationsat 100 MHz frequency

beam current and vertical oscillations;hor. scale is 200 s/div.


PSR instability cont’d(D. Neuffer et al, R. Macek et al.)

beginning ofinstability,=0

=100 s

=300 safterbeam loss

0 1 GHz

frequency spectrum of oscillation

log. y scale

lower frequencies associatedwith lower intensities,

If


PSR instability cont’d(R. Macek et al., M. Blaskiewicz et al.)

• maximum number of protons scales linearly with rf voltage & depends only weakly on bunch length!

• conditioning over time• increases in pressure & losses have marginal effect • sustained coherent oscillations below loss threshold• intense e- flux on the wall during bunch passage

• instability starts at bunch tail

instability & e- production combined process!

brf NV


AGS Booster, 1998/99(M. Blaskiewicz)

coasting beamvertical instabilitygrowth time ~3 s

~100 MHz downward shift as instability progresses

beam current [A]

500 s-500 s

5

y power density

0.2 GHz

time


KEKB e+ beam blow up, 2000(H. Fukuma, et al.)

threshold of fastvertical blow up

slow growthbelow threshold?

beam current

IP spot size


KEKB witness bunch experiment: bunch size depends on its charge; current of preceding bunches was kept constant. Blow up has single-bunch characteristics!

KEKB e+ beam blow up, 1999(H. Fukuma, E. Perevedentsev, et al.)


centroid motion & bunch size &tilt by KEKBstreak camera – preliminary,October 2002

[J. Flanagan,H. Fukuma,S. Hiramatsu,H. Ikeda,T. Mitsuhashi]

tail bunches blown up,slight evidence for tilt


PEP-II e+ beam blow up, 2000 (F.-J. Decker, R. Holtzapple)

single beamcolliding beam

specific lumi

oldnew

blow up due to combined effectof e-cloud andbeam-beam

x blow updisappeared afterchange inworking point


CERN SPS with LHC beam, 2000

Intensity of 72-bunch LHC beam in the SPS vs. time. batch intensity (top) and bunchintensity for the first 4 bunches and last 4 bunches (where losses are visibleafter about 5 ms) of the batch (bottom)

(G. Arduini)


CERN SPS with LHC beam, since 2000

x: coupled bunch instability; y: single-bunch instability; ~50 turns

• suppressed by damper and high chromaticity (x&y), possibly by linear coupling• much improved after scrubbing, but residual blow up may occur• interaction e- cloud & impedance

(K. Cornelis, G. Arduini,…)


tune vs oscillation amplitude for a bunch in the tail of a train, sliding average over 32 turns; evidencing positive and negativedetuning with amplitude and sort of hysteresis; indication ofnonlinear coupling between bunches in the tail due to e- cloud

[G. Arduini]


calculated & measured head-tail phase differencefor an LHC bunch train inthe SPS

start of train

end of train

additional e- cloud wake field with wavelength of0.3-0.5 bunch length canreproduce measurement

[K. Cornelis, 2002]


CERN PS, 2001with LHC beam(R. Cappi, et al.)

adiabatic rf gymnasticsfor shorten the bunch:horizontal instabilityleading to persistent oscillations w/o loss

threshold Nb~4.6x1010

rise time 3-4 ms almost constant abovethreshold; but onset in time depends on intensity

for highest intensity bunches are longer (z is constant only over last 100 ms)

central frequency 357 kHz, zero span


CERN PS, 2001with LHC beam(R. Cappi, et al.)

instability rise time independent of (up to ~0.5)marginal effect of octupoles introducing HWHM tune spread of 0.5x10-4.

Nb~5.5x1010signal at 357 kHz vs. time Fourier spectrum up to 10 MHz

PS pickup before extraction pickup in transfer line to SPS

instabilityvisible onlyin the horizontalplane(due to combinedfunctionmagnets!?)

no regular patternalong the bunch train


BEPC e+ beam sizeblow up study (ZY. Guo et al, APAC04;talk by J.Q. Wang)

0 600 V

BPM bias-18%

y y

y

y

Q’-46%

solenoid-27%

octupole-34%

2.00.2

1.0 A0.0

0 30

tailhead

tailheadw/o BPM bias

with BPM bias


90 consecutive bunches + 30 bucket gap

Bunches 25, 50, 70, 90 Bunches at the train end:75, 80, 85,90

DAFNE e+ ring, 2004(M. Zobov, C. Vaccarezza, et al.)

horizontal instability

positive x tune shift

probably linked to electron cloud but several open questions


what is new after 40 years?

similar cures: chromaticity, octupoles, wide-band and/ornarrow-band feedback, clearing electrodes,better pumping

new cures:TiN or getter coating

clear identification as e-cloud, better diagnostics, improved models, computer simulations

still lots of questions


(2) simulations


simulation approaches• Microbunches (K. Ohmi, PEHT; Y. Cai, ECI)• Soft-Gaussian approximation (G. Rumolo,

HEADTAIL v.0)• discrete PIC codes (K. Ohmi, PEHTS; HEADTAIL,

G. Rumolo; IHEP program)• quasi- continuous PIC codes (QUICKPIC, USC)• codes by M. Blaskiewicz, T.-S. Wang (centroids)• f method for solving Vlasov-Maxwell equations

(BEST code, H. Qin, R. Davidson)


no synchrotron motion with synchrotron motion

after 100 turns

no synchr. motion with synchr. motion

Q’x,y=4,8Q’x,y=0,0

densities2, 4, and 10x1011

m-3

microbunches, multiple air bag model

BBU

TMCI& HT

TMCI

(K. Ohmi, F.Z., PRL 85, 2000 )

PEHT


ECI microbunch simulation for PEP-II (Y. Cai, ECLOUD’02)

slow emittance growthalong bunchtrain below TMCI threshold

e-cloud density for each bunch was obtained by fit toindependent simulation (M. Pivi)


(G. Rumolo)

d2 x p,i(s)

ds2K(s)x p,i(s)

e

mpc2

E e x p,i(s); fe (x,y,t) (s nsel )

n0

N int 1

d2 x e, j

dt 2

e

me

E p x e, j; f p,SL (x,y) dx e, j

dtBext

simulation scheme for discrete PIC code


e- TMCI instability in PIC code:effect of synchrotron tune & e- density

instability is suppressed by higher synchrotron tune;synchrotron tune required scales ~linearly with density

(K. Ohmi, et al., PAC 2003)PEHTS


this scaling works well for moderate e- densities;for largest densities there is a different type of emittance growth (2 regimes, see talk by E. Benedetto)

(K. Ohmi, et al., PAC 2003)

scaling with Qs

PEHTS


PEHTS (K. Ohmi) HEADTAIL (G. Rumolo)

code comparison: chromaticity dependence for KEKB

(G. Rumolo, F.Z.,PRST-AB 5, 121002, 2002)

in PIC code Q’ acts stabilizing, HT-inst. not seen (different from microbunch codes)


e-cloud instability simulations using the plasma code QUICKPICCERN-USC collaboration [T. Katsouleas, A. Ghalam, G. Rumolo,…]

e- density beam density

quasi-static plasma code


Contacts Persons for the Comparison of Electron-Cloud Simulations

Identified at ECLOUD02

Mike Blaskiewicz BNL

Yunhai Cai SLAC

Miguel A. Furman LBNL

Tom Katsouleas USC

Kazuhito Ohmi KEK

Mauro Pivi LBNL

Lanfa Wang KEK

Hong Qin PPPL

Giovanni Rumolo GSI/CERN

Tai-Sen Wang LANL

Frank Zimmermann CERN

Build-up simulations highly successful; 5 results – Mike Blaskiewicz,ECLOUD (F.Z./G. Rumolo), PEI (Ohmi), POSINST (Pivi/Furman), CLOUDLAND (L. Wang); less results for instability simulations!

& G. Bellodi, RAL!

detailed comparisonsbetween ECLOUD andPOSINST


http://wwwslap.cern.ch/collective/ecloud02/ecsim/instresults.html

Code Comparison after ECLOUD02

benchmark case for instability simulationsround bunch in a round pipe: 1e11 protons uniform electron cloud with density 1e12 m^-3 each bunch passage starts with a uniform cloud chamber radius 2 cm uniform transverse focusing for beam propagation zero chromaticity, zero energy spread no synchotron motion energy 20 GeV beta function 100 m ring circumference 5 km betatron tunes 26.19, 26.24 rms transverse beam sizes 2 mm (Gaussian profile) rms bunch length 30 cm (Gaussian profile, truncated at +/- 2 sigma_z) no magnetic field for electron motion elastic reflection of electrons when they hit the wall


5 ms 5 ms

4 ms

0.06 mx,y

x,y

x,y

1 m 1.4 m

HEADTAIL1 IP, G.Rumolo

PEHTS1 IP, K. Ohmi

quasi-continuous QUICKPICA. Ghalam, T. Katsouleas

Post-ECLOUD02 Instability Code Comparison -below TMCI threshold;QUICKPIC gives a ratherdifferent result!

need several/many IPs!?

http://wwwslap.cern.ch/collective/ecloud02/ecsim/instresults.html


HEADTAILwith 1 IP

discretizedQUICKPICwith 1 IP

another comparison of QUICKPIC-HEADTAIL for the emittance growth in LHC; here QUICKPIC was discretizedto model 1 IP for benchmarking purposes; both codes consider conducting boundary conditions for rectangular pipe.

(E. Benedetto, A. Ghalam)no explanation for difference yet.

discretizedQUICKPICwith 1 IP

HEADTAILwith 1 IP


change from incoherent to coherent emittance growth as # IPs is increased; no clear convergence;example HEADTAIL simulation for LHC at injection; e=6x1011 m-3 (E. Benedetto, 2003)

transitionbetween2 regimes? HEAD-

TAIL


effect of space charge

Simulated bunch shape after 0, 250 and 500 turns (centroid and rms beamsize shown) in the SPS with an e- cloud density of e=1012 m-3 without (left) and with (right) proton space charge

(G. Rumolo, 2001)


Evolution of centroid vertical position of an SPS bunch over 500 turns for three cases:e- cloud & broadband impedance,broadband impedance & tune spread,broadband impedance alone

Vertical emittance versus time for three chromaticities.e-cloud, broad-band impedance & space charge.

y [m]

(G. Rumolo, F.Z.,PRST-AB 5, 121002, 2002)

simulation results including effects of space charge, broadband impedance and chromaticity

e-cloud &broadbandimpedance& tune spread

suppression bychromaticity –no HT in PIC

<y>


e- cloud effects in single-passsystem (LC beam delivery)

• e- can build up along bunch train and reach densities up to 1014 m-3

• blow up of IP spot size for densities above

threshold of 1011 m-3

• two effects: breakdown of –I in CCS and

direct focusing effect at IP

Cr ee

C

yey

y dss0

2 )(sin4

phase advance change direct focusing effect

(D. Chen, et al., 2003)


IP beam size and central electrondensity 100 m upstream of IP,vs. position along the bunch

IP beam size vs electrondensity, revealing thresholdat 1011 m-3

(D. Chen, A. Chang, M. Pivi, T. Raubenheimer, 2003)

e- cloud effect in NLC beam delivery


(3) analytical treatments


interaction of beam and electron cloud

electrons accumulate near beam center (‘pinch’)• tune spread, nonlinear fields, dynamic beta • incoherent growthelectrons follow transverse perturbations in bunch shape with delay • wake field resulting net cloud response can drive instabilities • beam break up (<< Ts) • TMCI or strong head-tail (~Ts)• head-tail instability (>>Ts) • exotic plasma instability? (e.g., monopole type)• ‘incoherent growth’?


e- density due to charge neutralization[F.Z., LHC Project Report 95, 1997]

e- density due to space charge andthermal energy [after S. Heifets, ECLOUD’02]

SB and CB wake of e- cloud[K. Ohmi + F.Z., PRL 85, 3821, 2000,G. Rumolo + F.Z., APAC 2001, Beijing]

coherent tune shift due to e- cloud[K.O. +S.H. + F.Z., APAC2001, Beijing]

ee

sate rbcm

E22

0 1

sep

bsate Lb

N2

b

e

N

CW

)8...4(0

Cr

Q ee 2

analytical estimates of equilibrium electron density, wake field and coherent tune shift


(1)adapt FBII theory (F.Z., CERN-SL-Note-2000-004)

2/12/1

2/12/12/34

1

yx

zbee

Ncr

2

cfor

2

cfor 2

1

ez2

ez

yx

zbee

ee

BBUN

cr

cr

0

2

T

Q

crs

ethr

(2) 2 particle model with length (K. Ohmi & F.Z.,PRL 85, 3821, 2000)

0

'

)1( 3

641

T

Qr yzee

BBU

BBU

Head-Tail instability

TMCI threshold

analytical estimates for single-bunch instability


(3) approximate wake by broadband resonator (K. Ohmi, F.Z., E. Perevedentsev, PRE 65, 016502, 2001)

z

beR

Ncr

22 2

2

C

N

r

CN

rH

Q

cR

b

zeezR

b

zeeenh

R

s

2/1

2/12/14/52

2/1

2/12/14/5

2241

2

z

ccQ

z

Q

Q

RczW R

R

R

R

R

s sin

2exp

4

11

1

2

51 RQlow Q: nonlinear force,variation of lattice,variation of beam linedensity

resonator frequency ~ electron oscillation frequency

shunt impedance

Greenfunctionwake ~damped oscillation


cQRcr

QQ

cN z

Rse

sRzRthrb

R

2

, for /

3.5

|Re|

||/44

max032,

eff

zRrmsthrb Z

Epp

Zce

CN

(applying conventional formalism by R.D. Ruth & Wang, IEEE Tr. NS-28 no. 3, 1981; P. Kernel, et al., EPAC 2000 Vienna; D. Pestrikov, KEK Report 90-21, p. 118, 1991)

(applying conventional formula from B. Zotter, CERN/ISR-TH/82-10, 1982)

then apply standard instability analysis

(3a) TMCI threshold ‘for long’ bunches(G. Rumolo et al, PAC2001)

(3b) threshold of ‘fast blow up’ (K. Ohmi, F.Z., E. Perevedentsev, PRE 65, 016502, 2001)

implicit equation since Rs/QR and R dependon Nb!

implicit equation since Zeff and R dependon Nb!


(3c) coasting beam instability threshold(E. Perevedentsev, ECLOUD02; K. Ohmi, ECLOUD02, A. Chao)

(1) 12ln222

32

0

2

Rz

R

R

R

sbp Q

Q

cRN

T

cr

for mode near peak of resistive e-cloud impedance c

l zR

no Landau damping for R

ebzb

z NaN

2

2/1

2/3

1left side of (1) scales as

(4) multiparticle models for combined effect of e-cloudand beam-beam and/or space charge(weak-strong: G. Rumolo & F. Zimmermann, TWOSTREAM01 KEK; strong-strong: K. Ohmi & A. Chao, ECLOUD02)


• centroid equations, transverse uniform distribution, one-pass two stream effect, Lorentzian energy distribution, instability always grows quasi-exponentially, growth rate is a function of both space and time; eventual damping by proton frequency spread; electron oscillation frequency spread causes spatial damping but not temporal damping [T.S-. Wang et al, PRST-AB 6, 014204 (2003)]• semi-analytical model: linear proton space charge, longitudinal dynamicsby a square well potential (‘boxcar distribution’) to reduce dimensionof eigenvalue problem; coasting-beam estimate; simulations including space charge; prediction that SNS will be stable [M. Blaskiewicz et al., PRST-AB 6, 014203 (2003)]• electron oscillation amplitude much larger than proton amplitude (factor20-50), phenomenological theory for the nonlinear regime, e- give driving force, slower linear or logarithmic growth in time, head of bunch carries memory; possible cure: drive head at frequency different from sideband[P. Channel, PRST-AB 5, 114401 (2002); c.f. S. Heifets, SLAC-PUB-7411]•nonlinear Vlasov-Maxwell equations, 3D perturbative f particle simulation, noise much treduced (f/f)2, noninear space charge, nonlinear growth phase [H. Qin et al., PRST-AB 6, 014401 (2003)]

)'(exp zf

various approaches to instability in PSR and/or SNS


characteristic features of e-cloud for intense long p bunches

(see M. Blaskiewicz, next ICFA newsletter)

• [nonlinear] space charge is important – ‘varied opinion exists’

• e- oscillation frequency depends on local beam current and local e- density which strongly increases near bunch tail

• self-consistent treatment of instability and e- generation likely necessary


2/1

2 )(

2

2

2

yyx

ezbez rZN

cn

no. of oscillations over 2z

n>>1: long; n<<1: short bunch

Ring Type of particles Typical z/c (ns) n Z/(A

DANE Positrons 0.083 0.6 1.88

SPS (LHC) Protons 1 1.1 0.036

LHC (inj) Protons 0.45 1.4 0.0021

KEKB LER Positrons 0.013 1.4 0.27

LHC (coll.) Protons 0.25 1.6 1.3x10-4

RHIC Au79+ ions 2.5 2.7 0.0037

PS (store) Protons 2.5 2.7 0.036

SIS18 U73+ ions 17 6.5 0.25

ISIS Protons 23 13.3 0.54

PSR Protons 54 48 0.54

(G. Rumolo, ICFA NewsL4/2004)

long vs. short bunches


0.5 1 1.5 2

thbN ,

n

cf zr

4

/8

Transverse wake-field

Time

rft

2

1

TMCI threshold vs n

n=1/4

Transverse Green f. wake

if n<1/4, wake has same sign over 4 z

(E. Metral, ECLOUD’02, for conventional resonator wake field)

according to this definition, all our bunches are ‘long’!


rbr fffmy

/121

yZRe yZImr

s/rad

mmh , 1,1 mmh

1, mmh

yf

yf0,0h1,1 h

0,1hr yZRe

yZIm

s/rad

power spectra and real & imaginarybroadband impedance

long bunch

short bunch

(E. Metral, ECLOUD’02, for conventional broadband impedance)

TMCI thresholdincreases as R /1

)/(where

‘threshold slowly increases with chromaticity’


one difference between e-cloud and a conventionalimpedance is the evolution of the e-cloud densityduring the bunch passage (“pinch”)

see Monday’s talk by E. Benedetto


snapshot of horizontal and vertical e- phase space (top) and theirprojections onto the position axes [G. Rumolo]

simulated e- distributionduring bunch passage

electron pinch


Simulated electron distribution after bunch passage in PEP-II (left) and e- densityenhancement alongthe bunch (right)

(M. Furman, A. Zholents, PAC 99)

electron pinch


density enhancement at beam center during LHC bunch passage

(E. Benedetto, 2003)

modulation reflects linear rotation in phase space

electron pinch


incoherent vertical tune spread at KEKB

solenoids off(e- cloud)

solenoids on(less e- cloud)

(T. Ieiri, H. Fukuma, 2001)


tune footprintobtained byapplying frequencymap analysison HEADTAIL simulation withfrozen-fieldapproximationfor LHC at injection(E. Benedetto,Y. Papaphilippou,PAC 2001)

a tune spread of only 0.002 is expected for unperturbed uniform cloud

nonlinear tune spread and resonance excitation in simulation

multitude of excited resonances (0,3) (1,-4), 10th order,… less emittance growth thanfor dynamic 2-stream case!


no incoherent tune shiftQ=0

incoherent tune shiftQ(+/-z)=+/-2.5Qs

in TMCI calculation pinch effect acts stabilizing!

head-tail mode tunes in units of synchrotron tunevs. the cloud density in units of 1012 m-3 at Nb=1011

real part imaginary part

(E. Perevedentsev,ECLOUD02; see also V. Danilov et al.,PRST-AB, 1998)


Wake Field Calculation

(G. Rumolo)

displace 1 slice & calculate either field on axis or average force onsubsequent slices; normalize to charge and offset of displaced slice


average wake wake on axis

(G. Rumolo, F.Z., PRST-AB 5, 121002, 2002)

factor 20 difference!dependence on z!


different e- distributionsyield different wakesfor the sameaveragedensity

(G. Rumolo,EPAC2002)


electron-cloud ‘wake’ & impedance1) wake not strictly linear (nonlinear force)2) wake depends on intensity, beam size &

bunch length 3) no translational invariance

(pinch, varying beam line density)4) superposition principle does not apply

(nonlinear forces, e- memory)5) wake depends on transverse position6) dependence on #IPs (different from conv. wake)conventional formalism must be applied with great care and cross-checked with simulations!

only Point 3) addressed so far; tune change was included in 3 and 4 particle models [G. Rumolo, F.Z., 2-Stream 2001]; in ECLOUD02 Proc.exact analytical treatment by E. Perevedentsev using generalized impedance


generalization of transverse impedance

• must consider wake W1(z,z’), not W1(z-z’)

czzieZi

ddzzW /)''(

11 )',(ˆ1

2

'

2)',(

2-dimensional Fourier transform

(E. Perevedentsev, ECLOUD’02)

• the wake W1(z,z’) can be obtained from simulations


(E. Perevedentsev, ECLOUD’02; G. Rumolo)

standardTMCI


(E. Perevedentsev, ECLOUD’02; G. Rumolo)

generalizedTMCI


(G. Rumolo)

extracting the 2-dimensional wake


2-dimensional impedance for SPS & SIS

(G. Rumolo)


(4) some questions


is there a monopole instability?axisymmetric instabilitymode found in plasmasimulations with cylindrical symmetry inquasi-static approximation

strong emittance growth if arrival point is in front of the beam center

36.32

r

zebrN

(V. Lotov, G. Stupakov,EPAC 2002)


increasing # IPs

w/o bunch centroid motion

w/o slice centroid motion

symmetrized positionof macroparticles(1 per quadrant)

Simulations by HEADTAIL

emittance growth driven only by dipolar motion! (E. Benedetto, D. Schulte, et al., PAC2003)

for LHC


two types of instability (see talk byE. Benedetto) - slow emittance growth??

effect of lattice? more realististic electron distributions,e.g., longitudinal discontinuities?

better approaches than PIC?(‘PIC is for the birds’ – R. Talman)


longitudinal plasma waves?


longitudinal e- plasma waves- observed & calculated

measured calculated

Tevatron Electron Lens (V. Parkhomchuk)


FNAL TEL experiment 1 April 2004

transverse position of TEL vs. p & pbar location during the scan

loss rates on 2D grid

(P. Lebrun, T. Sen, V. Shiltsev, X.-L. Zhang, F. Zimmermann)


FNAL TEL experiment 1 April 2004

losses decrease 1/(distance)^3

proton lossesdue to longitudinalshaving

note: sometimes longitudinal shaving was observed for LHC beam in the SPS when e-cloud was present

(P. Lebrun, T. Sen, V. Shiltsev, X.-L. Zhang, F. Zimmermann)

(1) scattering off plasma fluctuations(2) longitudinal coherent waves excitedat entry and exit of p bunch


Thanks toG. Arduini, V. Baglin, E. Benedetto, M. Blaskiewicz, K. Cornelis, V. Danilov, V. Dudnikov, H. Fukuma, Y. Funakoshi, M. Furman, A. Ghalam, Z.Y. Guo, S. Heifets, T. Ieiri, D. Kaltchev, T. Katsouleas, R. Macek, E. Metral, K. Ohmi, K. Oide, E. Perevedentsev, M. Pivi, T. Raubenheimer, B. Richter,

F. Ruggiero, G. Rumolo, D. Schulte, V. Shiltsev, C. Vaccarezza, J. Wang, R. Wanzenberg, A. Wolski, M. Zobov …!

ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004F. Zimmermann Review of Single-Bunch...

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