Impedance estimation ofSuperKEKB components

Samo Stanic/KEKB RF GroupKEKB Accelerator review 2003/02/11

KEKB
Due to high design currents (2.6A LER, 1.1A HER), effects ofbeam interactions with its surroundings were an importantconcern already in the design of KEKB collider (KEK Report 95-7).
Resulting effects include:•Coupled-bunch instabilities due to high-Q resonant structures(i.e. RF cavities)•Power deposition generated by the beam in the form of HOM
losses•short bunches, needed to achieve high luminosity, can pickup impedance at very high frequency à enormous heatdeposition•Heat likely to be localized where wake fields can be trapped(IR beampipe, masks, fingers, etc.)

2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group2

Goal•Reduce impedance of various beam-line
components•Eliminate structures which can trap higher ordermodes (HOM) of the generated wake fields
Due to complex geometries of beam-line components, theproblem was mostly approached at by numerical computation ofwakes and loss factors using ABCI and MAFIA simulation codes•ABCI is a 2D code exploiting rotational symmetryin φ (r,φ,z) to reduce number of mesh points•MAFIA is a 3D code, can use mirror symmetries
over (x,y,z) to reduce number of mesh points –slow, needed for asymmetric problems
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KEKB Accelerator Review
S.Stanic/KEKB RF Group3

Impedance estimation for KEKB

Many items not yet estimatedEstimate of the Loss Factorof LER (94φduct), as in theKEKB design report
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KEKB Accelerator Review
S.Stanic/KEKB RF Group4

Major remaining problems•Measured longitudinal loss factor of the KEKBstorage ring differs from the one obtained fromnumerical calculation for a factor of 2-3•IR chamber within Belle (version for SVD1.x detector)
is resonant to HOM generated at certain bunch
patterns (5 bucket spacing) and due to overheating
poses a constraint on KEKB operation

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KEKB Accelerator Review
S.Stanic/KEKB RF Group5

Total loss factor measurement
Total loss factor of the ringcan be related to a shift insynchronous phase:

Phase (deg)Which can be measured as a function of bunch current:
91

HER BL=5mm Vc=8MV 1999/04/15-5290-5489-56(Ieiri)

8800.5

11.5

LER BL=5.1mm Vc=4MV 1999/04/15(Ieiri)-58
20

Bunch current (mA)
2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group

0.5

11.5

2

Bunch current (mA)6

Results
HER H/4/15/99

LER L/4/15/99

80(Ieiri)

Loss Factor (V/pC)

Loss Factor (V/pC)

80
60
4020(Ieiri)

60
40
20
0045678
Bunch Length (mm)91045678
Bunch Length (mm)9•In both rings loss factor is 20-30 V/pC for 6-7mm long bunches•Hard to estimate for 4mm or 3mm, exponential extrapolation
gives much more than the estimated values!
New experiment is scheduled where we will be able to measure theloss factor dependence down to 3mm (SuperKEKB design) bychanging the beam optics
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KEKB Accelerator Review
S.Stanic/KEKB RF Group

710

Present IP chamber was found to be resonant to HOM
generated in 5 bucket spacing operation
Be central part with He cooling

SVD 1.X beampipe design

SR masks

Sawtooth structure in SVD1.4 chamber(in SVD1.6 IR chamber not present)2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group8

Resonant mode identified
Multi-bunch resonanceoccurred since the eigenfrequency of the IR chamber
was integer multiple of KEKB
bunch frequency

Observed resonance waspredicted to be due to TM-01
mode by multi-bunch
simulation, with f=5.81GHz,
and was seen for 5 bucket
spacing for both beams, aswell as HER and LER alone
2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group9And experimentally confirmed

By tuning the RF phase difference between HER and LER it waspossible to achieve destructive interference between HOMs fromthe two beams, where temperature rise dissapears
Measured phase shift of 31.75 deg agrees nicely with thepredicted 31.54 deg
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KEKB Accelerator Review
S.Stanic/KEKB RF Group10

Remedy
The problem will be solved in the upgraded version of IRchamber (for SVD2.0), by removing one of the SR masks andthus prevent HOM trapping

No SR mask here

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KEKB Accelerator Review
S.Stanic/KEKB RF Group11

SuperKEKB
Physics processes of interest require further increaseof luminosity and vertex precision:•Smaller radius of IR chamber (1-1.5cm)•Shorther beam bunches (design KEKB 4mm, current
6mm à design SuperKEKB 3mm!)•Resonance free design of beamline components forall (or at least most) bunch patterns, especiallydesign of the IP
All KEKB HOM considerations remain, plus a necessity
to increase the number of RF stations to compensate
for larger beam energy loss.
2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group

12Estimate of required no. of RF stations in LER
Total RF power needed
To compensate for energy loss:

Contrib. to the loss factor fromRF cavities separated from thosefor rest of the ring:

No. of RF cavities as afunction of kother:
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KEKB Accelerator Review
S.Stanic/KEKB RF Group13

Required No. of RF stations in LER(Akai)

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KEKB Accelerator Review
S.Stanic/KEKB RF Group14

Smaller number of RF stations highly desired•Due to limited available space in the KEKB
tunnel for cavity installation•Larger number of cavities present a larger
threat for beam instabilities•Due to limited funding we wish to minimize
construction (200MYen/ARES station) andrunning costs (1.2MW/ARES station)

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KEKB Accelerator Review
S.Stanic/KEKB RF Group15

ABCI vs. MAFIA comparison at NC RF (ARES) cavity
beam

Shape of the accelerating
part of ARES cavity as
used by the ABCI code
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S.Stanic/KEKB RF Group16

Long. Loss factor of ARES

Good agreement between ABCI and MAFIA simulation
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KEKB Accelerator Review
S.Stanic/KEKB RF Group

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HOM power estimation in ARES

3mm
4mm5mm

HOM Power (kW)

Bunch length dependence
on total beam current (fitto measurement)

HOM power in ARES as a function of beamcurrent:

GBP HOM Pwr /Cavity (kW)WG HOM Pwr /Cavity (kW)HOM
Data(D7C2020219)
Total
HOMPwr/Cavity(kW)BL=7mm assumed (ABCI)

51224 bunches (4-bucket spacing)(Kageyama)

43Agrees!
Blue line accounts for bunch
length change with current

10mm

210

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KEKB Accelerator Review
S.Stanic/KEKB RF Group

0500

1000
1500
LER Beam Current (mA)

18

Reducing the impedance beam-line components
using small-angle tapers•Long. loss factor at locations where beampipe radius changes can bereduced using tapered structure•Change in radius contributes a log(R/r) term – comparing to step,
taper can reduce the loss factor for up to 50 %•Reasonable taper length is

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KEKB Accelerator Review
S.Stanic/KEKB RF Group19

Accuracy criterion for a numerical mesh computationof tapered structure

Field surrounding beam almost plane wave, diffracted at edge withand diffraction angle
In a mesh with given dz largest wave number that can be seen is

Smallest taper that can be calculated is 1/kmax a, limited by the givenmesh size dz.
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KEKB Accelerator Review
S.Stanic/KEKB RF Group

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For convergence we must require:

Critical wave number – here the difraction angle
equals the taper angle“frequency range” a mesh can represent, inunits of σz
Optimization parameter, guaranteeing
convergence above certain ηminAnsatz

Empyricallygives

For shallow tapers and short bunches we need a very fine mesh dz!
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KEKB Accelerator Review
S.Stanic/KEKB RF Group21

Example: Symmetric
tapered structure (ABCI)

Cavity shape

η=117

Step-out

W/o log terms

Taper lengthdependence of loss
factor. Squares: logterms for step-in andstep-out included

Step-in2003/2/11

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S.Stanic/KEKB RF Group22

Example:
Result stability w.r.t.
calculation parameters

Bunch length dependence of long. Loss factor

ABCI with log terms

ABCI vs. MAFIA
comparison for rot.
symmetric step
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KEKB Accelerator Review
S.Stanic/KEKB RF Group23

Example: Finger inbellows (ABCI)

Cavity shape

Bunch length dependenceof long. Loss factor

2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group24Example:
Gate valve (ABCI)(RF shield that covers the valve
entrance enters into the duct)
Cavity shape

Bunch length dependence
for various finger heights
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Finger heigth dependence
for various configurations
KEKB Accelerator Review
S.Stanic/KEKB RF Group25

Impedance estimation for SuperKEKB

More work needed!

Preliminary estimate of theLoss Factor of LER (94φduct)
for SuperKEKB

2003/2/11

KEKB Accelerator Review
S.Stanic/KEKB RF Group26

Summary•Combining computer simulation and experiment
we are striving to reduce discrepancy between
estimated and measured loss factor of KEKB rings•“Tuning” the design parameters of various
beam-line components we are trying to decrease
the overall loss factor of the rings and to avoid
dangerous resonances, especially in the IR•Success of these endeavors is of particularinterest for SuperKEKB, where from the viewpointof RF systems smaller loss factor means lessproblems and smaller financial burden
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