Estimation of Impedances & Lossfactors of SuperKEKB LER
16/Feb/2010
K ShibataK.
Shib(KEKB Vacuum Group)Introduction•

Beam duct of SKEKB is quite different from that of KEKB.
– Cross‐section : Circular duct
beam duct with antechambers– Diameter of beam channel (LER): 94 mm
90 mm– Material : Cu
Al or Cu•

Designs
g of manyy componentspwere changed
g and theloss factors and impedances of them have been
estimated by using GdfidL. (LER only. HER is not yet.)–––––––••

Bellows chamber
SR maskFlange connection
Movable mask (Collimator)
Pumping port
BPM, BxB FB BPM
IP chamber

Bunch (q=1 C) went through the center of the beam
channel, and the wake potentials were monitored.
Loss factor and impedance (longitudinal) were
estimated from the wake potential.
potential– Bunch length : 3 ∼ 10 mm– Length of wake potential : 0.1 m (for loss factor calculation)
5.0 m (for impedance calculation)– Mesh size : ∼00.2
2 mm

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Beam duct with antechambers
NEG strip

BeamSR

Beam channel

SR channel2Bellows• Bellows chamber with comb‐type RF shield will be used in SKEKBSKEKB.
– There is no radial step on the inner surface.
(There is a small step (∼1 mm) in a conventional bellows chamber.)– RF is shielded by nested comb teeth.
length : 10 mmradial thickness : 10 mm

SKEKB

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KEKB

KEKB Review

3BellowsKEKB

SKEKB

•

cut‐off
cut
off
frequency

Loss factor (σz = 6 mm)
k = 2.2×10‐3 V/pC
1000 pieces in one ringk_total = 2.2 V/pC

•Impedance
It was found that there are trapped modes at 7.5 GHz and 25 GHz (over cut‐off frequency (2.5GHz)).
Effects of these trapped modes on the beams will be investigated.
2010/2/16

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4SR mask•SR mask is located at the side wall of the SR
channel (antechamber).

SKEKB– The height of the SR mask is ∼8 mm– Compared to KEKBKEKB, the effect of the SR maskon the beam will be very small.

110 mmSKEKBKEKBSR Mask
φ90 mm

47 mm

KEKB

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5SR mask
KEKB

SKEKB

•Loss factor (σz = 6 mm)
k = 1.8×10
1 8×10‐15 V/pC (much smaller than KEKB)
1000 pieces in one ringk_total = 1.8×10‐12 V/pC (much smaller than other components)•Impedance
Negligible small.

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Pumping port
• NEG strips are installed into the antechamber.
antechamber– The antechamber for pump is isolated by using a screen with small holes(φ4mm).
– GdfidL modeld l with
ith a llength
th off 00.247
247 m was maded ffor calculation.
l l tiKEKB
SKEKB

screenscreen

NEG strips(3 layers)

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KEKB Review7Pumping port
KEKB (1 ring)SKEKB (1 ring)•Loss factor (σz = 6 mm)
k_0.247 m = 90.2 V/C
2200 m for 1 ringk_total = 4.5×10‐7 V/pC•

(much smaller than the conventional pumping port)

I
Impedanced– No trapped mode is found.
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8Flange connection• MO‐type
MO type flange will be used instead of theconventional one (Helicoflex gasket).
– Inner surface is much smoother than theconventional one.

SKEKB_type2(0.5mm step)

KEKB• Loss factor (σz = 6 mm, type1)– k = 1.28×10‐5 V/pC x2000 k_total =0.03 V/pC
– Calculations for other bunch length are now inprogress.

SKEKB_type1(0.2mm step)• Impedance– Calculations are now in progress.

SKEKB

CopperGasketFlange

r=45 mmbunch

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1 mm

Step size
ype 1 : 00.2 mm
TypeType 2 : 0.5 mm

9Movable mask & Taper•

Basic design
g of the movable mask will be as sameas the conventional one in the commissioning
stage.
– Cross‐section of the mask chamber is circular with adiameter of 90 mm.
(no antechambers)– The lengths of a ramp and a mask head are 200 mm
and 20 mm, respectively.
– The distance between a beam and the mask head is10 mm.
– The transition ducts (taper ducts) between themovable mask and the duct with antechambers arenecessary at the both side of the movable mask.

Mask chamber
φ90 mm
10 mm

beam
200 mm20 mm

Taper duct

Bellows Chamber
Mask Chamber
Bellows Chamber
Beam
Mask Head

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10Movable mask & Taper

KEKB

SKEKB

•Loss factor (σz = 6 mm)

k = 2.31×10
2 31×10‐1 V/pC (movable mask : 22.31
31 ×10‐1, taper duct : 3.83
3 83 ×10‐4)
16 pieces in one ringk_total = 3.7 V/pC (larger than other vacuum components)•

Impedance
Effect on the beam will be studied.
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11Resistive wall
• Wake fields were calculated from the following formulas
formulas.
Impedance :Z m// ω Z m⊥==Lc L

Circular duct

4 b2m
2πσib 2
imc 2(1 + δ m 0 )bc[1 + sgn (ω )i ] −ω+ωm +1ω∞
Wake function : Wm' (z < 0) = 2 ∫0 dω Re Z m// (ω ) cos ωzπcbCu or Al(A. Chao, “Physics of Collective Beam Instabilities in High Energy Accelerators”)– The beam duct does not have antechambers.
(circular duct)– The diameter of the duct is 90 mm.
(b = 4.5 cm)– The beam duct is made of Cu or Al.
(Conductivity [s‐1]: Cu=5.4×1017, Al= Cu=3.2×1017)– The total duct length is 2200 m.

• Loss factor (σz = 6 mm)

SKEKB(Al, φ90)

KEKB(Cu, φ94)

k _2200m = 1.7 V/pC (Cu)
2 3 V/pC
2.3
V/ C (Al)2010/2/16SKEKB(Cu, φ90)

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12BPM & BxB FB BPM (M. Tobiyama)•BPMs for high beam current were developed for SKEKB.
– Reduction of the button electrode size (BPM), duct radius (BxB FB BPM), etc.

•Loss factor (σz = 6 mm)

BxB FB BPM

×440–k_total = 7.2 ×10‐2 V/pC×10– FB BMP : k = 5.9×10
5 9 10‐44 V/pC
V/ C
kk_totalt t l = 5.9
5 9 ×10
10‐33 V/pC
V/ CBMP : k = 1.6×10‐4 V/pC

•Impedance– Growth rate of coupled bunch instability was estimated from this result,g gsmall.
and it was confirmed that it is negligible

BxB FB BPM(SKEKB)BPM(SKEKB)

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ReZ_BPM(SKEKB)BPM (KEKB)KEKB Review

ImZ_BPM(SKEKB)

ReZ_FB BPM(SKEKB)ImZ_FB BPM(SKEKB)13

IP chamber• Two types of IP chambers were designed for SKEKB.
SKEKB– Both chambers are same in design except for the diameter of IP duct.
– IP duct is connected to beam ducts for QCS‐magnets (φ20 mm) via crotch duct.
(crossing angle is 83 mrad)• Loss factor (σz = 6 mm)
k_type1 = 8.72×10‐4 V/pC
k type2 = 7.98×10
k_type2
7 98×10‐4 V/pC
Type B

Type A
φ20 mmType B (φ30 mm)

Beam

φ20 mmType A (φ20 mm)

φ20 mm

φ30 mmbeam
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beam
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IP chamber• Impedancep

Result of Eigenmode solver– No longitudinally trapped mode is found.
– Vertical deviation of beam from the center of IP
duct excites manyy TE modes which are trapped
pp inthe crotch.
– Effect of these trapped modes on the beam andIP duct will be investigated.
longitudinalImaginary part :TTypeA (φ20 mm))
Type B (φ30 mm)

2010/2/16ytransverseyBeam(x,y)=(0,0mm)

Rs = 3.9e+05 Ω/m
Q = 4.9e+03
fr = 4.8e+05 Hz

Real part :Type A (φ20 mm)
Type B (φ30 mm)

xReal part :Type A (φ20 mm)
Type B (φ30 mm)

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Imaginary part :Type A (φ20 mm)
Type B (φ30 mm)

Beam(x y)=(0 2mm)(x,y)=(0,2mm)

Cut‐off
frequency(φ20 mm)15x

Total loss factor & Power loss (LER)
Component
Resistive wall

Loss factor [V/C]
AlCu

Pumping port
Flange connection
Bellows
Gate valve
SR maskMovable mask
Taper
BPM
BxB FB BPM
FB kicker
IP chamber
Cavity (ARES)
AlTotal kCu•

Number of items

1.03E+09
7.89E+08
3.65E+02
1.28E+07
3.00E+09
3.00E+09
1.82E-03
2.31E+11
3 83E+08
3.83E+08
1.63E+08
5.90E+08
5.01E+11
8.00E+08
4.35E+112200 [m]2200 [m]2200 [m]2000
1000
3010001616440
101118Loss factor (total) [V/pC]
2.26
1.74
8.04E-07
0.03
3.00
0.09
1.82E-12
3.70
6 13E-03
6.13E-03
0.07
5.90E-03
0.50
8.00E-04
7.83
17.5 +α17.0 +αPower Loss : PHOM––––Beam current I: 3.6 A
Number of bunch : 2503
Circumference : 3016.26 mBunch spacing Tb: 4 ns

2010/2/16

PHOM = I2kTb = 910 + α kW (Al duct)
883 + α kW (Cu duct)

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16Summary• Loss factors and impedances of the components of SKEKB LER werecalculated by GdfidL.
– Pumping port
– Flange connection– Bellowsll((Gate Valve)l )– SR mask– Movable mask
– Taperp– BPMs
– IP duct• Total loss factor is ∼18 V/pC, and the corresponding power loss is ∼ 900 kW.
• Next step:– Estimation of other components such as injection section, interaction
region etc
region,etc.
– Investigation of the effects of the high‐impedance components at highfrequency on the beam. (bellows, movable mask, etc)
– Calculation of loss factors and impedances of the components of HER.

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