Download PowerPoint プレゼンテーション

Electron cloud and ion effects in SuperKEKB
H. Fukuma, KEK
SuperB2008
2008.05.31, Elba, Italy
I. Introduction
II. Electron cloud effects
III. Ion effects
IV. Summary
I. Introduction
•SuperKEKB is an upgrade plan of KEKB.
Parameters
LER / HER
Luminosity
5 - 10 1035 cm-2 sec-1
Beam energy
3.5 / 8.0 GeV
Beam current
9.4 / 4.1 A
Number of bunches
5018
Circumference
3016 m
Bunch spacing
0.6 m
Emittance
24 nm
•In SuperKEKB, the electron/positron beam may be stored in LER/HER after
LINAC upgrade in order to mitigate the electron cloud effects ("charge switch").
•The ion effects would be stronger and the electron cloud effects be weaker
than those before the charge switch.
•So far two effects were studied mainly assuming the charge switch.
•This talk also assumes it.
II. Electron cloud effects
•Photoelectrons produced by synchrotron radiation and secondary
electrons produced by impinging electrons on a chamber wall
form an electron cloud in positron storage rings.
•The interaction between the electron cloud and a beam leads to the
electron cloud effects such as single- and multi-bunch instability, the tune
shift, the increase of pressure and so on.
•Above all a beam blowup caused by the strong head-tail instability is one
of the issues in KEKB though it is largely mitigated by solenoid winding
in field free regions.
• In SuperKEKB, TiN coated ante-chambers and solenoids will be
installed to reduce the number of electrons.
1. Buildup of electron cloud
•Cloud buildup was calculated by 3D PIC code “CLOUDLAND”
developed by L.F. Wang.
•Assumption
a) Round chamber
b) Uniform production of primary electrons on chamber wall.
c) Effect of ante-chamber
Primary electron yield of 0.01 is artificially used in order to
take into account of the reduction of electron yield by the
ante-chamber.
•Parameters used in a simulation of electron cloud buildup
Beam energy(GeV)
Bunch spacing(ns)
Number of particles in a bunch
Chamber radius(mm)
Maximum secondary emission yield
Energy of maximum secondary yield
Number of bunches
Number of train
Primary electron yield
rms bunch length(mm)
Horizontal emittance(m)
Vertical emittance(m)
Average horizontal beta function (m)
Average vertical beta function (m)
8
2
5.2 1010
37
1.5
250eV
200
1
0.01
3
2.4 10-8
4.8 10-10
10
10
•Distribution of electron cloud
a) Drift space without solenoid
Central density of electrons is very high.
H. Fukuma and L. Wang, PAC2005.
b) Quadrupole magnet
No saturation
Trapping
At the end of bunch train
Trapped electrons
At a bunch gap (40ns after the last bunch in the train)
Trapping of electrons is seen.
c) Dipole magnet
Two stripes of electrons appear.
d) Uniform solenoid field of 60G
Trapping
60 G is enough to suppress the electron cloud near the beam.
•Average electron volume density and electron volume density
at a pipe center in various magnetic fields
Drift space
Dipole
Quadrupole
Solenoid
Field strength average (1012m-3)
1.0
0.25(T)
20.0
10.3(T/m)
8.4
60(G)
0.61
at pipe center (1012m-3)
10
0.6
0.46
0.0
Solenoid field of 60G is very effective.
Electron cloud remains inside
bending and quadrupole magnets.
Integrated electron density along the ring

L
0
  ds
= 0.6 x 1015m-2
2. Strong head-tail instability
•According to the theory K. Ohmi and F. Zimmermann,
instability occurs if
2 s
   ds  r0  y
0.6 x 1015m-2
(from simulation)
:density of electrons, s:orbit length
y:beta function, s:synchrotron tune
4.5 x 1015m-2
•Left side is smaller than right side, which indicates the electron
density is below threshold of the instability.
3. Tune shift
•A betatron tune shift by the electric field of the electron cloud is
L
 x , y 
re   x , y     ds
2
0
= 0.0005
4. Coupled bunch instability
•Coupled bunch instability(CBI)
by the electron cloud was studied
by PEI code developed by K.
Ohmi.
•Comparison between positron
storage in LER and HER was
done.
S. S. Win et al., APAC2004.
a) Cloud buildup
without solenoid
with 60G solenoid
• Electron density is almost same in HER and LER.
b) Bunch oscillation by CBI by a tracking
Damping time of bunchby-bunch FB system at
KEKB is 0.2 ms (20
turns).
•Growth rate in LER is larger than that in HER.
•Large growth rate might be caused by a trapping of electrons in solenoid.
Needs further study.
5. Summary of electron cloud effects
• Electron cloud effects are estimated in the positron storage in HER.
a) Solenoid field of 60G is very effective to reduce the electron density
around the center of a chamber.
b) Simulated electron density is below the threshold of the strong
head-tail instability.
c) Substantial electron cloud stays inside bending and quadrupole
magnets.
d) Growth rate of the coupled bunch instability should be studied more.
• Remaining works are,
a) Refinement of input parameters for simulations
i) final design of a size and shape of the chamber
ii) secondary emission coefficient etc.
b) Positron storage in LER
III. Ion effects
•After the charge switch,
◊Beam energy : 8
3.5 GeV
◊Beam current :4.1
9.4A
•Larger vacuum pressure than KEKB : 5 nTorr (CO)
Ion instability would be strong enough to degrade
the luminosity.
•Requirements from operation
◊Residual centroid oscillation by the instability should be small.
◊Tune shift along the train by the ions should be small.
◊Number of bunches should be maximized if train gaps are
introduced to mitigate the ion effects.
Small number of train gaps is desirable.
1. Ion trapping
•Ions are trapped for a long time in a beam potential.
•A bunch interacts with an ion again and again in many turns.
•Ion motion
 y
 y
   M   
 y  n 1
 y  n
 1    1
  
M  
0
1
  K

y : ion coordinate
n : turn of a bunch train
0 

1 
2 N b re mc
K
M ion y ( x   y )
•Stability condition
p
 1 (h  p) 


0
1


kick by a bunch
Tr M  2
p bunches
c
ion
h-p gaps
Nb : number of electrons / bunch,
m, Mion : electron and ion mass,
x,y : beam size of electron bunch
•Trace |M|/2 in SuperKEKB is the same order of magnitude as that in
KEKB.
•According to the linear theory, ion trapping would be avoided with a
train gap of 2 % RF buckets in SuperKEKB.
2. Fast ion instability (FII)
•The ions created by the head of the bunch train affect to the tail.
•The FII is a single pass coupled-bunch instability (possibly seen at
a ring but also a linac or a beam transport line).
•The instability is transient.
◊If damping such as radiation damping exists, the oscillation is
damped from the head to the tail in the train then the oscillation of
all bunches is finally damped (A. W. Chao and G. V. Stupakov).
◊Actually an equilibrium amplitude is determined by the balance
of the excitation of the instability by the noises and the damping.
bunch
ion
1) Linear theory (G. V. Stupakov et al., P.R.E. 52, 5499)
z
•The offset of the centroid of the beam y(s,z) is given by
z
 2
2
y ( s , z ' )
y
(
s
,
z
)

y
(
s
,
z
)



z
'
D( z  z ' )dz '
2
2

0
s
c
z '
.
D(t  t ' )   d i cos  i (t  t ' ) f ( i ) : decoherenc e function
s
f (i ) : distributi on function of ions
4ionre
4 N b rp c 2
(ion frequency)

i 0 
,
3sb y ( x   y )
3 Asb y ( x   y )
0
ion  N b ionizationngas : ion line density / bunch , ngas: gas density
b: bunch population , : Atomic mass number of ions , sb: bunch spacing
•Assuming a solution of y ( s, z )  Re A( s, z )  e
s
A( s, z )  A0 ( z )  exp( )
 ec
1
e

 i  s / c  i i 0 z / c
,
2cre ion
Q z
3 sb y ( x   y )
Q : quality factor of ion oscillations
•Behavior of the amplitude growth
◊Linear regime without decoherence
of the ions
log (amplitude)
y (t )  exp( a t )
◊Linear regime with decoherence
of the ions
y (t )  exp( bt )
nonlinear regime (linear growth)
1 y
◊Nonlinear regime (S. Heifets)
y (t )  ct
linear regime (exponential growth)
turns
•Numerical example in SuperKEKB (a long train)
Energy 3.5 GeV
Bunch spacing : 2ns (=0.6m)
   2.72 107 sec 1
 i  1.23 108 sec 1
Number of bunch : 5120
ion  806 m 1 (per bunch)
Bunch current : 1.9 mA
ion  i  sB / c  0.246
Pressure : 1 nTorr (CO)
  8.53 10-9 m 3
Emittance (H/V) : 24 nm/0.96 nm
Beam size (H/V) : 0.6 mm/0.12 mm
Beta function (H/V) : 15 m/15 m
Tune(V) : 43.545
Q : 10
(revolution time : 10 s)

i
2Qc
 0.0205
 e  2  2.3 s
less than one turn
2) Mitigation method
A) Decrease the ion density
a) Better vacuum pressure
•This might be an ultimate cure, but may be
difficult.
b) Clearing electrode
•A condition where an ion is not trapped in a
potential well by a dc beam,
U ce
I
 E (a) 
2rc
20 c  a
+
electrode
2a r
c
ion
(A. Poncet)
-
U ce  280kV for SuperKEKB. It looks very high.
•Introducing gaps makes motion of ions unstable.
•Ions might be collected on electrodes with smaller voltage.
A simulation is necessary for studying the effectiveness
of the electrodes.
c) Gaps in a bunch train (J. Seeman)
•Growth rate
 g1  nb2
nb : the number of bunches
•If a train is divided by ten gaps
g
=10 turns
 g1
0.01 g
1
1000 turns
•Very effective, but loose luminosity because the number of bunches
decreases due to the gaps.
d) Beam shaking (9th KEKB Accelerator Review Committee(ARC))
•Shaking the beam may resonantly excite the ion motion,
then ions will be lost.
•Most effective shaking frequency
i (ion tune) +/- fractional betatron tune )0 ≈ 24MHz
•Amplitude of the excitation should be small so as not to loose the luminosity.
Experiment or simulation will be interesting.
B) Damp the bunch oscillation
a) Transverse bunch-by-bunch feedback system
•A damping time of the bunch-by-bunch feedback in KEKB is
20 turns.
•It could not suppress the beam oscillation in rapid growth
region if full buckets are occupied.
•Possibility to increase gain limit by multiple
feed back systems (9th KEKB ARC)
kicker
•4 systems with feedback delays of a quarter
of a turn
4 times faster damping time
•Straight signal paths cutting across the arcs
must be provided to match the beam flight
time.
•A feasibility study is necessary.
signal
pick up
b) Tune spread among bunches
•It is well known that tune spread among bunches stabilize the
coupled bunch instability.
Tune spread  1 /( g / T0 )  0.1 , if g is 10 turns.
 g : growth time of a mode
•According to the experience of KEKB, stable operation will be
impossible.
c) Octupoles
•Non-linear, amplitude depended tune shift by octupoles
will damp the coherent oscillation of a bunch due to
filamentation in a phase space.
1
1 B '''
2


 
 a
d

32 B
 d  10turns   0.1  y  20m a y   y  60m
B '''
 108 m 3 too strong.
B
d) Lower vertical emittance or beam size (K. Oide)
•Amplitude saturates at about y.
•A reduction of the vertical emittance by a factor 2 will give a design
beam size.
0.5% coupling. (KEKB 5% @collision)
e) Beam-beam detuning
(Actually this is not a cure, but a mitigation effect.)
 x , y
(A. Chao, "NONLINEAR BEAM-BEAM
RESONANCES", AIP Proceedings No. ?)
H 00 ( x , y )
 
 x , y

0.93
beam-beam parameter
H 00  

0
1  exp[ 
 x 1 a

y/x=0.012
x=0
 y 1 a
]
2 1  at 2 a  t I (  x 1  a ) I ( y 1  a )dt
0
0
2 1  at
2 at
1
(  t )( a  t )
a
a   y /  x  x , y  J x , y /( x   y )
tune shift @1y =0.015 for 
=0.0036 for 
d=67 turns
y/y
Hereafter we discuss the gaps in a bunch train for mitigation method
because it seems simplest way among above mentioned methods.
3) Estimation of growth time
•Conditions to be taken into account
a) Train gap should be less than 200 ns to avoid the effect of the
transient beam loading on the RF system (K. Akai).
b) The vacuum pressure is 5 nTorr for CO and 10 nTorr for H2 to
get a lifetime of 10 hr (Y. Suetsugu).
c) Typical damping time of the bunch-by-bunch feedback system
is 0.2 ms from the experience of KEKB.
•A code developed by L. F. Wang was used in simulations.
◊Features
1) 2D space charge
2) Tracking through elements
3) Realistic vacuum model
(various pressure and multigas species)
4) Any beam fill pattern
5) Bunch-by-bunch feedback
6) Wake of ion-cloud
…
A) Growth time from the tracking
50 trains; train Gap=20 buckets
Number of bunch per train=82
Total number of bunch=50*82= 4100
Pressure=1nTorr
Growth time=35turns=0.35 ms
H. Fukuma and L. Wang, ECLOUD07.
B) Growth rate from the ion density
number of train =50
number of bunch per train=82
gap=40ns (20 missing bunch)
emittancex=2.4E-8, emittancey=4.8E-10
pressure : 0.75 nTorr
•Estimated growth rate
1
e

cre  y
1
3 2  i /  i rms
i / i rms  0.3
 e  0.38 ms
 e1 (tracking @1nTorr )
  e1 (estimation from ion density @ 0.75Torr
and i / i of 0.3 )
•This relation in our calculation is
valid even if the gap is changed.
•We estimated the growth rate@1nTorr from the ion
density @0.75 Torr .
Train length vs. estimated growth rate
•From the growth rate and the damping rate
of the feedback system the storable total
number of bunches is determined, then we
can get the relation between the luminosity
loss and the growth rate.
•If the pressure of CO is 5 nTorr and the
growth rate should be less than 5 ms-1, which
is the damping rate of the feedback, the
bunches in a train should be less than 35,
which leads to the luminosity loss of about
40%.
•If the pressure of CO is 1 nTorr and the
growth rate should be less than 5 ms-1, 150
bunches in a train would be possible,
which leads to the luminosity loss of about
15%.
gap 15
gap 10
gap 20
damping rate of
the feedback
4) Tune shift
•Beam-ion force changes the tune of the bunches.
•As the ion density changes along the train, the tune also changes along the train.
50 trains; train Gap=20
Number of bunch per train=82
Total number of bunch=50*82= 4100
P=1nTorr
Growth time=35turns; tune
shift=0.0035
•The vertical tune shift of the last bunch in the train was estimated
using the ion density from the simulation as,
y
r
 y  e i
ds , i : line density of ions

6 trapped region  y ( x   y )
Tune shift of the last bunch
•In KEKB,
◊Tune change of 0.001 affects to the
luminosity.
5 nTorr (gap 20)
1 nTorr (gap 15)
1 nTorr (gap 10)
◊Vertical tune in LER changes 0.0018
along the train due to the electron
cloud.
Tune change of 0.002 along the train
would be a good reference which is
acceptable in SuperKEKB.
1 nTorr (gap 20)
•From the pressure and the allowable tune shift the storable total number of
bunches is determined, then we can get the relation between the luminosity loss
and the pressure.
•If the pressure of CO is 5 nTorr and the tune shift along the train should be
less than 0.002, the bunches in the train should be less than 25, which leads to
the luminosity loss of 45 %.
•If the pressure of CO is 1 nTorr, 135 bunches in a train would be
possible, which leads to the luminosity loss of 15 %.
3. Summary of ion effects
•The train length to mitigate the FII and the tune shift was discussed when
electrons are stored in LER at SuperKEKB.
•When the pressure of CO is 5 nTorr,
assuming the damping rate of the feedback system of 5 ms-1, length
of the train would be limited to 35, which leads to the luminosity
loss of about 40%.
if the tune shift due to the ions should be less than 0.002, length of
the train would be limited to 25, which leads to the luminosity loss
of about 45%.
•If the pressure of CO is 1 nTorr, the luminosity loss due to the
growth rate and the tune shift will be 15 % and 15 %, respectively.
•The CO pressure of 1 nTorr will be necessary for SuperKEKB if
electrons are stored in LER.
•The tune shift would be as much serious as the amplitude growth by
the FII.