ecloud04, review of single-bunch instabilities, napa, april 2004f. zimmermann review of single-bunch...
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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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
concerns
• beam loss • emittance growth• trajectory change (turn-by-turn or pulse-to-pulse)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(1) observations
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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.
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
KEKB e+ beam blow up, 2000(H. Fukuma, et al.)
threshold of fastvertical blow up
slow growthbelow threshold?
beam current
IP spot size
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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.)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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,…)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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]
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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]
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(2) simulations
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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>
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(3) analytical treatments
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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’?
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
cQRcr
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!
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
• 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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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’!
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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’
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
snapshot of horizontal and vertical e- phase space (top) and theirprojections onto the position axes [G. Rumolo]
simulated e- distributionduring bunch passage
electron pinch
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
Simulated electron distribution after bunch passage in PEP-II (left) and e- densityenhancement alongthe bunch (right)
(M. Furman, A. Zholents, PAC 99)
electron pinch
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
density enhancement at beam center during LHC bunch passage
(E. Benedetto, 2003)
modulation reflects linear rotation in phase space
electron pinch
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
incoherent vertical tune spread at KEKB
solenoids off(e- cloud)
solenoids on(less e- cloud)
(T. Ieiri, H. Fukuma, 2001)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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!
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
average wake wake on axis
(G. Rumolo, F.Z., PRST-AB 5, 121002, 2002)
factor 20 difference!dependence on z!
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
different e- distributionsyield different wakesfor the sameaveragedensity
(G. Rumolo,EPAC2002)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(E. Perevedentsev, ECLOUD’02; G. Rumolo)
standardTMCI
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(E. Perevedentsev, ECLOUD’02; G. Rumolo)
generalizedTMCI
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(G. Rumolo)
extracting the 2-dimensional wake
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
2-dimensional impedance for SPS & SIS
(G. Rumolo)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
(4) some questions
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
longitudinal plasma waves?
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
longitudinal e- plasma waves- observed & calculated
measured calculated
Tevatron Electron Lens (V. Parkhomchuk)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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)
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 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
ECLOUD04, Review of Single-Bunch Instabilities, Napa, April 2004 F. Zimmermann
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 …!