Transcript Document

Impedance and Collective
Effects in BAPS
Na Wang
Institute of High Energy Physics
USR workshop, Huairou, China, Oct. 30, 2012
Contents
•
•
•
•
Introduction
Impedance
Collective effects
Conclusions
Introduction
• The electromagnetic fields generated by the beam will be
deformed by the interaction with the surroundings.
• The deformed field, which is known as the wake field, will
disturb the beam dynamics, and under certain conditions,
lead to collective instabilities.
• The impedance and collective effects should be well
estimated during the design stage.
• A thorough evaluation of the impedance is necessary in
controlling the total impedance of the ring, which can
accordingly prevent the occurrence of the beam instability.
Main parameters of BAPS
Parameter
Symbol, unit
Value
Beam energy
E, GeV
5
Circumference
C, m
1364.8
Beam current
I0, mA
100
Bunch number
nb
1836
Number of particles per bunch
Nb
1.55109
Natural bunch length
l0, mm
2.9
RF frequency
frf, MHz
500
Harmonic number
h
2276
Natural energy spread
e0
1.5103
Momentum compaction factor
p
4105
Betatron tune
x/y
113.4/39.3
Synchrotron tune
s
0.004
Damping time (H/V/s)
x/y/z, ms
28, 43, 29
Emittance (horz./vert.)
x/y, pmrad
10/10
Trans. beam size (horz./vert.)
x/y, m
4.4/7.4
What might be important in BAPS
• Short bunch of l = 2.9 mm 
– Large loss factor and high beam power loss
– Coherent Synchrotron radiation (CSR)
• Small beam pipe aperture b = 11 mm  High resistive
wall impedance  Transverse resistive wall instability
• High filling factor nb/h = 1836/2276 with small transverse
emittance 
– Coupled bunch instability due to HOMs
– Fast Beam Ion Instability
– Intra-beam Scattering (IBS)
Impedance
• Main impedance components in BAPS
– Resistive wall, vacuum transitions, RF cavities, BPMs,
vacuum flanges, injection kickers, bellows, vacuum pump, etc.
Objects
Description
Insertion devices
inside vacuum
Stainless steel + TiN coating, b = 2.5mm
Resistive wall, 72 taper transitions
Insertion devices
outside vacuum
Stainless steel, b = 5mm
Resistive wall, 72 taper transitions
Other part of the ring
Stainless steel, b = 11mm, Resistive wall
RF cavities
7
1. Resistive wall
• For cylindrical beam pipe, the longitudinal and transverse
resistive wall impedance are estimated by
Z //
(1  i )  L
 Z0
n
2 b 2R
Z   Z 0 (1  i )
 L
b 3 2
• 1) Longitudinal impedance
Z //
 18.4(1  i ) / n 
n
– With natural bunch length of 2.9 mm, kl = 101.7 V/pC (Ploss = 2.5kW).
• 2) Transverse impedance
Z  278(1  i) / n M / m
– Transverse resistive wall impedance can induce coupled bunch
instability.
2. Taper transitions
• Main contribution is from the transition of the insertion device.
• The impedance and loss factor are calculated by the code ABCI.
• A slope angle of 5 is suggested as a compromise between the
impedance and the longitudinal space occupied.
0.8
0.07
Power loss, kW
0.05
||
Z /n, 
0.06
0.04
0.03
0.02
0
Longitudinal wake potential
(b = 11mm,  = 5,  = 2.9mm)
10
20
Slope angle, degree
30
0.6
0.4
0.2
0
0
10
20
Slope angle, degree
Longitudinal impedance and power loss with different
slope angle.
30
3. RF cavities
• The BEPCII superconducting RF cavity will be used in BAPS.
• With bunch length of l = 2.9 mm, the calculated loss factor for
single cavity is kl = 6.4 V/pC (Ploss = 0.2 kW)
• Inductive impedance Z///n=i0.05 
Summary of the impedance study
Components
Z///n, 
Z, M/m
Loss factor kl
(V/pC) (l0=2.9
mm)
power P (kW)
(54.5A, 1836)
Resistive wall
(b=11mm)
18.4(1i)/n
278(1i)/n
101.7
2.5
Taper transitions
(b=11mm, =5)
0.03i
0.14i
1.0
0.03
RF cavities
0.36i
1.55i
45
1.1
• Resistive wall impedance is dominated in both longitudinal and
transverse impedances, and RF cavities contribute high inductive
impedance.
• Further studies are needed with more vacuum components are
designed.
Collective effects
• Single bunch effects
– Longitudinal microwave instability
– Transverse mode coupling instability (TMCI)
– Coherent synchrotron radiation (CSR)
• Multi bunch effects
– Transverse resistive wall instability
– Longitudinal/transverse HOMs of RF cavities
• Ion effects
– Ion trapping
– Fast beam-ion instability (FBII)
• Intra-beam scattering effects (IBS)
1. Single bunch effects
• Longitudinal microwave instability
E
 e 0 2 l
e
I th 
Z
R | |eff
n
– According to the Keil-Schnell criterion, the threshold of
longitudinal impedance is |Z///n| < 0.28 .
– This will induce bunch lengthening and energy spread increase.
2  p
• Transverse mode coupling instability (TMCI)
Z 
4 s Eb
eI b R    
– The threshold of transverse impedance is |Z| < 12 M/m.
– The equivalent longitudinal impedance is 2.7 , which is much
larger than that of the longitudinal instability.
• Coherent synchrotron radiation
– The threshold of bunch population for coherent synchrotron
radiation is
N 0,Th
3 22 I A z C

 3 / 2bec
– The CSR threshold in BAPS is N0,Th = 4.31010 >> Nb = 1.55109.
– CSR is supposed not to be a problem in BAPS.
2. Multi bunch effects
• Transverse resistive wall instability
nb I bc

  4 ( E / e) x, y
1

e
(w pn w0 /  p )2 2
Re Z  (w pn )
p 
with wpn = 2frev  (pnb + n + x,y)
The growth rates are much higher than the
transverse radiation damping rate.
An efficient transverse feedback system is
necessary!
With Cu beam pipe and Cu coating on the
ID, the growth time will increase to 0.6 ms.
6000
4000
(1797, 6158)
y
1/ 
 The growth rate for the most dangerous
instability mode is 6 kHz in the vertical plane
with mode number of  = 1797.
8000
2000
0
-2000
-4000
-6000
0
500
1000

1500
2000
Growth rate vs. mode
number in the vertical plane
4
2
x 10
6500
6250
1.5
y
1/ 
1/ 
y
6000
1
5750
5500
0.5
5250
0
39
39.2
39.4
y
39.6
39.8
40
Instability growth rate vs. vertical
tune
5000
-1
-0.5
0

0.5
1
Instability growth rate vs. chromaticity
Larger decimal tune are preferred to alleviate the transverse
resistive wall instability.
Nonzero chromaticity will also help to damp the instability.
• Longitudinal/transverse HOMs of RF cavities
– The main longitudinal and transverse HOMs’ data of the BEPCII
superconducting cavity is used in the calculations.
– The instability rising time for the fastest growing longitudinal
mode is z = 1.7 s and for the transverse mode is y = 0.5 s.
– The instabilities will not be driven by the HOMs of the RF cavities.
0.8
2.5
0.6
2
0.2
1/  , Hz
0
1.5
y
z
1/  , Hz
0.4
-0.2
-0.4
1
0.5
-0.6
-0.8
0
500
1000

1500
2000
0
0
500
1000

1500
2000
3. Ion effects
• Ion trapping
The condition of ion trapping for the beam with a gap Tg is
1
cos(wiltrain / c)  wiTg sin(wiltrain / c)  1
2
– The oscillation frequency of the ion is wi = 540 MHz (CO+).
– Including a gap of Tg = 0.9 s (~ 20% of the ring
circumference), the left side of the equation gives 211.
– The ion trapping is not supposed to happen in BAPS.
• Fast beam-ion instability (FBII)
The growth rate for the trailing bunches can be expressed as
1
 inst
[ s 1 ]  5 p[Torr]
/2
Nb3 / 2 nb2 re rp1 / 2 L1sep
c
 y3 / 2 ( x   y )3 / 2 A1 / 2w
– Taking into account the bunch gap, the instability growth time is
about 0.02ms.
– With multi-trains, the growth time is 0.04 ms for two bunch trains,
0.07 ms for four bunch trains, and 0.1 ms for eight bunch trains.
– Feedback system is needed.
– The nonlinear effects will introduce spread in the effective ion
frequency, which will help to damp the instability.
– Detailed simulations should be done to estimate the instability.
Summary of collective effects
• The growth time of the FBII is too fast to be damped
effectively by feedback systems even with a long beam gap.
Multi-train scheme should be used along with the feedback
system to damp the instability.
• The coupled bunch instability induced by the transverse
resistive wall impedance need to be damped with feedback
systems.
• The longitudinal microwave instability is expected to
happen, which will induce bunch lengthening and energy
spread increase.
• TMCI and CSR are not supposed to be problems in BAPS.
Thank you for your attention!