Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam...
-
Upload
randall-day -
Category
Documents
-
view
218 -
download
4
Transcript of Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam...
![Page 1: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/1.jpg)
Beam observation and
Introduction to Collective Beam Instabilities
Observation of collective beam instability
Collective modes
Wake fields and coupling impedances
Head-tail instability
Microwave instability
Beyond
T. Toyama KEK
![Page 2: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/2.jpg)
Observation of collective beam instability
Example: KEK-PS 12 GeV Main Ring
At 500 MeV injection plat bottom
a beam loss occurs (red curve).
Amount and timing of the loss => random.
Proton number NB
(Feedback CT)
Magnetic field
![Page 3: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/3.jpg)
Example: KEK-PS 12 GeV Main Ring
At phase transition energy~5.4 GeV (in kinetic energy)
a large beam loss occurs (red curve).
Amount of the loss is at random.
Proton number NB
(Feedback CT)
Magnetic field
![Page 4: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/4.jpg)
Observation
NB
Multi-trace of horizontal betatron oscillation
NB
Amplitude of betatron oscillationMagnetic field
![Page 5: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/5.jpg)
Observation horizontal betatron tune during acceleration
t
f
frev 2frev
frev-ffrev-f
2frev-f 2frevf
Without external kick, coherent oscillation emerged
![Page 6: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/6.jpg)
Measurement by a wall current monitor
Real signals may be attenuatedby the loss in the cable > 100 mand limited band width of the WCM.
![Page 7: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/7.jpg)
Beam loss: collective instabilities --- at random, a kind of
positive feedback starting from a random seed direct space charge effects --- regular
some mistake in parameterrs --- regular(B, fRF, tune, …)
![Page 8: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/8.jpg)
Collective modes
Coasting beam / longitudinal
n=3
Beam
![Page 9: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/9.jpg)
Coasting beam / transverse
Collective modes
n=3
Beam
betattonoscillation
x or y
![Page 10: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/10.jpg)
Bunched beam / logitudinal
Collective modes
l=1 l=2 l=3dipole quadrupole sextupole
zz z
charge density
Phase space
…..
no momopole mode
![Page 11: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/11.jpg)
Bunched beam / transverse
Collective modes
dipole mode density zx
zzz
l=0 l=1 l=2monopole dipole quadrupole …..
superimposed
![Page 12: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/12.jpg)
Wake fields and coupling impedance
Electromagnetic fields is produced by the beam passed by.
+ + +++++++ + +
− − − − − − −
− − − − − − −
IB
Wall Current −IB
![Page 13: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/13.jpg)
−
−
v
Wall Current
++e qF//
s
F⊥
€
Wake functions (W//, W⊥) : "Green function"
Force acting on a test particle (charge e)
produced by the delta-function beam (charge q, dipole moment qy)
Longitudinal component:
F // = F//ds−L /2
L /2
∫ =−eqW//(s)
Transverse component:
F ⊥ = F⊥ds−L /2
L /2
∫ =−eqyW⊥(s)
[W//]=[V /C]
[W⊥]=[V /Cm]
![Page 14: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/14.jpg)
Wake fields and coupling impedance
€
Wake functions (W//, W⊥) of a resistive wall
Force acting on a test particle (charge e)
![Page 15: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/15.jpg)
Wake fields and coupling impedance
€
Longitudinal impedance Z// :
Sinusoidal current J 0(s,t)= ˆ J 0ei(ks−ωt) produces
longitudinal wake potential across the section:
V(s,t) =−1v
d ′ s J 0(s,t−′ s −sc
) s∞∫ W//(s− ′ s )
=−J 0(s,t) Z//(ω)
longitudinal impedance:
Z// =dzc
e−iωz/c −∞∞∫ W//(s)
[Z//]=[Ω]
![Page 16: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/16.jpg)
Wake fields and coupling impedance
€
Transverse impedance Z⊥ :
Sinusoidal dipole moment J1(s,t) =
Current J 0(s,t)× dipole displacement y(s,t)
J1(s,t)=y(s,t) J 0(s,t) = ˆ J 1ei(ks−ωt) produces
transverse wake potential across the section:
V⊥ =i J1(s,t) Z⊥(ω)
transverse impedance:
Z⊥ =iβ
dzc
e−iωz/c −∞∞∫ W⊥(s)
[Z⊥]=[Ω/m]
![Page 17: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/17.jpg)
Wake fields and coupling impedance
Wake fields due to a Gaussian beam in a resistive pipe
Longitudinal wake potential Transverse wake potential
Acc
eler
atio
nD
ecce
lera
tion
Dam
pen
defl
ecti
onF
urth
er
defl
ecti
on
![Page 18: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/18.jpg)
Wake fields and coupling impedance
Impedance of a resistive pipe
![Page 19: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/19.jpg)
Wake fields and coupling impedance
Wake fields by cavities
Q=1 Q=10
![Page 20: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/20.jpg)
Wake fields and coupling impedance
Impedance of cavities
Q=1 Q=10
![Page 21: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/21.jpg)
Head-Tail InstabilityTransverse bunched beam instability
Time domain picture
![Page 22: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/22.jpg)
Head-Tail InstabilityChromaticity = 0
Red full line: (z)x(z)Red dushed line: (z)x’(z)Blue: kick due to resistive wall
x
x’
Growth
Damp No effect
~Totally no effect
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
headtail
![Page 23: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/23.jpg)
Head-Tail Instability
Head-tail phase
z
p/p
€
ˆ z
€
−̂ z 0
€
χ =ξωβˆ z
cη
€
Δνβ
νβ=ξ
Δpp
phase of betatron oscillation
phase space of synchrotron oscillation
![Page 24: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/24.jpg)
Head-Tail Instability
x
x’
Damp
~ 1
Red full line: (z)x(z)Red dushed line: (z)x’(z)Blue: kick due to resistive wall
(1)
(2)
(1)
(2)
~Totally damping
headtail
![Page 25: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/25.jpg)
Head-Tail Instability
x
x’
Growth
~Totally growing
(1)
(2)
~
Red full line: (z)x(z)Red dushed line: (z)x’(z)Blue: kick due to resistive wall
(1)
(2)
headtail
![Page 26: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/26.jpg)
Head-Tail Instability
Summary of Growth rate vs. Chromaticity
Head-tail phase
Gro
wth
rat
e
Chao’s text book
mode = 0
mode = 1mode =2
mode =3
€
χ =ξωβˆ z
cη
Stab
le
Un
stable
![Page 27: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/27.jpg)
Head-Tail InstabilityKEK-PS 12 GeV Main Ring
T. Toyama et al., PAC97, APAC98, PAC99
mode=0
mode=1 mode=2
NB
amplitude of dipole oscillation
![Page 28: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/28.jpg)
Head-Tail InstabilityCERN PS higher order head-tail mode
R. Cappi, NIM
![Page 29: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/29.jpg)
Head-Tail Instability
KEK-PS12GeV MR
Frequencydomainanalysis
growth rate∝Re[Z()] F()
Re[
ZT]
For
m f
a ct o
r F
(f
req.
spe
ctru
m
o f t h
e b e
a m)
m=0
m=1
m=2
€
ωξ =ξωβ
η
![Page 30: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/30.jpg)
Head-Tail Instability
ObservationGrowth ratemode=0
![Page 31: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/31.jpg)
Head-Tail Instability
Cure
Chromaticity control
Landau damping by octupole magnets …
![Page 32: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/32.jpg)
Beam response and Landau dampingCoasting beamTransverse motion
€
Single particle oscillating at ω.
External driving force is on at t=0.
˙ ̇ x +ωx=AcosΩt
x(t >0) =−A
Ω2−ω2(cosΩt−cosωt), ω≠Ω
x(t >0) =−AtΩ
(cosΩt−cosωt), ω=Ω
![Page 33: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/33.jpg)
Beam response and Landau damping
€
Magenta: x(t)=−A
Ω2 −ω2(cosΩt−cosωt),
Ω =1.1ω
Driving force
Response
€
Blue: x(t)=−AtΩ
SinΩt,
Ω =ω
€
Red: f(t)=AcosΩt
![Page 34: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/34.jpg)
Driving force
Response of the beam
Absorbed power by the beam
The beam: ensemble of the particlesFrequency distribution:
The beam motionapproaches steady oscillation.
Velocity d<x>/dt: in phase with the forceWork is done on the beam
Absorbed power by the beam: constantStored energy in the beam:
Macroscopic aspect: a beam driven by a force approaches steady oscillation.
Microscopic aspect: Small amount of resonant particles grows infinitely large.
€
∝ tResponse of particles
![Page 35: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/35.jpg)
Longitudinal instabilityMicrowave Instability uniform distribution
Wake: V=Z (z)The seed of density modulation is produced
V1= Z (z), slippage,
![Page 36: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/36.jpg)
Landau damping by the spread of rev =p/p phase slippage factor = 1/t
21/2
t phase transition energy
p/p
p/p
p/p
p/p
Density modulation reduced! Larger p/p more stable
![Page 37: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/37.jpg)
Microwave Instability
Observation & simulation
K. Takayama et al., Phys. Rev. Lett. 78 (1997) 871
![Page 38: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/38.jpg)
Microwave Instability
Sources: Narrow-band resonances
res ~ 1GHz
![Page 39: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/39.jpg)
Cures
Reducing Impedance
Landau dampingReducing local beam chaege line density
Artificial increasing momentum spread
p/p > rev
MethodsHigher harmonic rf cavity
Voltage modulation of foundamental rf cavity
…
![Page 40: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/40.jpg)
Cures
Reducing Impedance Exchange ~ 2/3 BPMs new ESM BPM
~2/3 Pump port new one with slits
Growth rate reduction
![Page 41: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/41.jpg)
Reducing local beam chaege line density
Increasing momentum spread > rev
Voltage modulation of foundamental rf cavity
T. Toyama, NIM A447 (2000) 317
![Page 42: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/42.jpg)
BeyondImpedance calculationImpedance measurements
Beam transfer function
Vlasov equationCoupled bunch instability
Mode-coupling instability
Electron-cloud instabilityfeedback system
feedback in RF control system
feedback damper = pick-up & kicker
![Page 43: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/43.jpg)
“… every increase in machine performance has accompanied by the discovery of new types of instabilities.” - J. Gareyte (CERN)
![Page 44: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/44.jpg)
References
Schools:CAS, USPAS, and OHO (Japanese)
Conferences proceedings:APAC, EPAC, and PAC
Textbook etc.:• A. W. Chao, PHYSICS OF COLLECTIVE BEAM
INSTABILITIES IN HIGH ENERGY ACCELERATORS• Editors: A. Chao and M. Tigner, Handbook OF
ACCELERATOR PHISICS AND ENGINEERING
![Page 45: Beam observation and Introduction to Collective Beam Instabilities Observation of collective beam instability Collective modes Wake fields and coupling.](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f1c5503460f94c32ba5/html5/thumbnails/45.jpg)
Good Luck!