Design of Positron Damping Ring for SuperKEKB!

TUPEB054

M. Kikuchi, T. Abe, K. Egawa, H. Fukuma, K. Furukawa, N. Iida, H.Ikeda, T. Kamitani, K. Kanazawa, K. Ohmi, K. Oide,
K. Shibata, M. Tawada, M. Tobiyama, D. Zhou,!
KEK, High Energy Accelerator Research Organization!
Abstract: Super-KEKB, an upgrade plan of the present KEKB collider, has recently
changed its baseline-design from “high current” option to “nano-beam” scheme. The
current is relatively low(4A/2.3A for LER/HER ring) compared to that of the highcurrent option(9.4A/4.1A), while the vertical beam size is squeezed to 60 nm at theinteraction point to get the high luminosity. Since the Tousheck lifetime of LER is very
short(600 sec), the intensity of the positron beam is as high as 8 nC/pulse. Theemittance of the injected positron beam should be small enough to be accepted in theaperture of the LER. A damping ring has been proposed for the high-current option[1].
In this paper an updated design optimized to the nano-beam scheme is presented.

1.1
50
1.7
1.67
2.6729880.50
11.7GeVHzµm%mmnsnC† defined as extension that contains 99.7% divided by 6.

Layout of the System
CSR induced instability• Coherent Synchrotron Radiation wake
dominates the longitudinal impedance• CSR induced microwave
instability occurs: the onset isconsistent with 1-D theory ofStupakov – Heifets:!
⌅ 1/6 1 r ⇥Nb,th ⇥ ⇤ C
2 1 + |r| ⇧1/3

2p ⌃ ⌃z

Vacuum chamber

CSR12/3⇤cb3 /⇥, ⇤z 1 )c = min( 2Tracking simulation
Table 4: Ring parameters for simulation
E(GeV)
ασz (mm)σδτ" (ms)
(a)
(b)
(c)
(d)

1.0
1.1
1.1
1.1

0.00360.00610.01410.0141

5.03
7.30
11.0
7.75

5.25×10−4
5.57×10−4
5.50×10−4
5.50×10−4

6.3
6.9
5.4
5.4

σz /σz0 , σδ /σδ0EnergyRepetition frequency
Emittance
Energy spread†
Bunch length†
Number of bunches
Bunch spacing
Bunch charge

Table 2: Parameters of the Damping Ring
Energy1.1
GeV
No. of bunch trains
2
No. of bunches / train
2
Circumference
135.50207
mMax. stored current
70.8mAEnergy loss / turn
0.091
MV
Hor. damping time
10.87
ms
Inj.-beam emittance
1700nm
Emittance (h/v)
41.4 / 2.07
nm
Energy spread
5.5×10−4Coupling5%
Extracted emittance (h/v)
42.5 / 3.15
nm
Cavity voltage
0.5
1.0MV
Bucket height
0.81
1.24 %
Synchrotron tune
0.0152 0.0216
Bunch-length
11.01
7.74 mmPhase advance/cell (h/v)
64.39 / 64.64 deg
Momentum compaction
0.0141
Bend-angle ratio
0.35
No. of normal-cells
40RF frequency
509
MHz
Chamber diameter
34mm

Nb,th
0.35 × 1010
1.1 × 1010
2.9 × 1010
2.6 × 1010

74;

• Optics optimization!

3T03
⇤
1 r
=C
re 3 J x I 2
2⇥c re Jx 3 1 + |r|⇥1 r
3⇤
2⇥⇤ +=L1
2⇥c re Jx 3
1 + |r|

748

749
747

748

7748

r = 0.35,8<96!"#748

747
7436

378

<96'%()*"+,-./.&01"2.

1/2

r: Bend ratio = B1/B2

2 ⇥ = 17 m

(Normal FODO ⇥ r = 1)
L1 : Total length except bend length

B = 1.35 T<96::3456

378<96:'%()*"+,-./.&01"2.

B 11/6V = 1.0 M V, B = 1.35 T

Ver. 1210= 2.7 m, L1 = 100 m

Bh = 1.24 %2600

Bh = 0.8 %

8743

743

Ver. 1210

s = 0.008

7!$#

7476

7477436

V = 0.5 M V, B = 1.35 Tr)/(1 + |r|) = 0.48

3:

7476

3456

2600

(17Nb,th = F ( , ⇥, V, B) = C0 ( L)3/2 ⇥ 8/3 V• Short damping time with lower field!

⌅=!&#

74<74:

Maximize the function!

Solution: FODO with Reversed Bend749!%#3

Linear Optics

Optics requirements !
• Large acceptance!
• Fast Damping

87σz /σz0 , σδ /σδ0

Table 1: Parameters of the injected beam
before ECS after ECS units = 0.008

2400

2400(c)2200

2000(d)

2200

2000

0.000

0.005

0.010

0.015

0.000

0.005

p

0.010

0.015

p

Electron cloud instability
2010年5月21日金曜日• Threshold of electron density!
⇧e,th =2 ln 2⌅ ⇥ ⇤s ⌥e ⌃z /c⌃y(1 +)⌃x
3 2 KQ re L

⇤e2 =2+ re c /⇥y (⇥x + ⇥y )Q = min(5, ⇥e z /c)

K=3• For case [c]! e,th = 0.52 1013 m 3
Non-linear Optics
No errors• DA is limited by systematic multipole errors• Simulation of photo-electron formation!

Table 5: Electron density for various conditions
Condition
Drift Bend Q+Sx

• Integrated electron density = !

δmax = 2, SR=1
1.3
δmax = 1, SR=10.4
δmax = 1, SR=0.1 0.15

0.511014 m 2 ⇥e,th L = 7.01014 m 2

0.6
0.5
0.11

0.5
0.15
0.03

1012 m−3
1012 m−3
1012 m−3

SR: photon flux ratio to the design flux

Conclusion
with errors (a)Injected beamwith (a) + multipole errors

MagnetErrors (a):K/K = 0.1 % for quads
K/K = 0.2 % for sexts= 0.3 mrad for quads and sexts
Misalignments =0.15 mm for quads sexts, and BPM

Bend
QuadSext

Table 3: Systematic multipole errors∆B/B
K2 /K02.5
K4 /K0 2.3 × 105
K5 /K1 3.1 × 105
K9 /K1 1.5 × 1016
K8 /K2 1.1 × 1011
K14 /K2 7.6 × 1016

m−2m−4m−4m−8m−6m−12

6.0 × 10−42.3 × 10−3
6.0 × 10−4
2.3 × 10−3
6.0 × 10−4
2.3 × 10−3

• Positron damping ring has been designed based on the Reverse-bendFODO.!
• Dynamic aperture is limited by the systematic multipole errors.!
• CSR dominates the longitudinal impedance.!
• Ring parameter was optimized to increase the threshold of the CSR
induced instability. !
• Proposed ring parameters satisfy the requirements!