Crab cavities for high currents

K. Akai (KEK)
16 Feb. 2004
for KEKB Review Committee

Crab crossing
crab cavity

crab cavity

KickKickele
ctr
onsonsitrposcrossing angle
head-on collision

Palmer for LC (1988)
Oide and Yokoya for storage rings (1989)

Recent simulations by Ohmi showed significant increase ofluminosity by several times by the crab crossing.

Crab cavities for high currents (K. Akai, KEK)

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Parameters for the crab crossing
KEKB

Super-KEKB

StrategyBackup scheme

Adopted as baseline

RingLER

HER

LER

HER

Beam energy (GeV)

3.5

8.0

3.5

8.0

Beam current (A)

2.6

1.1

9.4

4.1

RF frequency (MHz)508.887508.887

Crossing angle (mrad)±11±15βx* (m)

0.33

0.33

0.2

0.2βx, crab (m)

20

100

100~200

300~400

Required kick (MV)

1.41

1.44

1.10 ~ 0.78 1.45 ~ 1.26

Crab cavities for high currents (K. Akai, KEK)3

Damping parasitic modes• Accelerating cavities– Operating mode (TM010) is
the lowest frequency mode.
– Any parasitic mode (HOM)
has higher frequency than theoperating mode.
– Wave guides or beam pipewith cut-off frequency higher
than the operating mode candamp all HOM’s. (ARES,SCC, PEP-II cavity, etc)

• Crab cavity– Operating mode (usuallyTM110) is NOT the lowest
frequency mode.
– Frequency of several parasitic
modes can be lower than (orclose to) the crabbing mode.
– Special cure is needed for thedamping of parasitic modes.

Crab cavities for high currents (K. Akai, KEK)

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Original crab cavity• Squashed cell operating in TM2-1-0 (x-y-z)• Coaxial coupler is used as a beam pipe• Designed for B-factories (1~2A)(axial view)

Absorbingmaterial

Notch filter

Coaxial beam pipe

Absorbingmaterial

inner conductor
Cooling for
inner conductor"Squashed cell"

Squashed Crab cavity for B-factories(K. Akai et al., Proc. B-factories, SLAC-400 p.181 (1992).)

Crab cavities for high currents (K. Akai, KEK)

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Analogy with rectangular cavity" n %2 " m %2 " l %2
f n,m,l = c $ ' + $ ' + $ '# 2a & # 2b & # 2d &bad

Rectangular(n-m-l)

CylindricalBeam couplingMode

TM1-1-0TM010

monopole-like

Accelerating mode

TM2-1-0

TM110(H)dipole-like

Crabbing mode

TM1-2-0

TM110(V)dipole-like

Unwanted crabbing

TE0-1-1

TE111(H)dipole-likeLowest TE-like

TE1-0-1

TE111(V)dipole-likeLowest TE-like

TM3-1-0-monopole-like

TM4-1-0-

dipole-like

TE0-2-1

TE211

quadrupole-like!

Crab cavities for high currents (K. Akai, KEK)

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Squashed cell• Extremely polarized cell
– Large eccentricity where horizontal size is about twice the vertical size.
– Frequency of the unwanted crabbing mode increases.

• Relatively short cell length– The frequencies of lowest TE-like parasitic modes increase.

• Frequencies of all parasitic modes except the accelerating
mode can be made higher than the crabbing mode.

Crab cavities for high currents (K. Akai, KEK)

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Coaxial coupler with notch filter• Monopole mode (including the Lower Freq. Mode)– Couples strongly and propagate in the coaxial line as TEM wave.

• Crabbing mode
– Couples as dipole-like, but does not propagate in the coaxial line, if thecut-off frequency of TE11 mode is higher than the crabbing frequency.
– Possible asymmetry or misalignment causes monopole-like coupling,which propagates in the coaxial line as TEM. A notch filter is attached toreject the TEM-coupled crabbing mode back to the cavity.
notch filter
absorberPossible location to attach coaxial coupler
Crab cavities for high currents (K. Akai, KEK)

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Original crab cavity (1/4 cell)

Crab cavities for high currents (K. Akai, KEK)

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10A beam in Super-KEKB• The original cavity is designed for 1 ~ 2A beam
– Suitable for SC → High kick voltage obtained by one cavity.
– Sufficient damping of parasitic modes.

• Possible problems for 10A beam
– Large HOM power (200kW)• Loss factor is not very small, because beam pipe radius can not be
widely opened due to the coaxial beam pipe.
• Additional loss factor comes from the absorber on wide beam pipe.

– Much heavier damping of HOM’s may be needed, particularly forhorizontal polarization of transverse modes.

Crab cavities for high currents (K. Akai, KEK)

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Impedance requirement• Longitudinal" #1 =e$% z Ib' (( f + Re Z + # f # Re Z # )CE%&– Growth rate (@9.4A, σz=3mm) ≦ radiation damping rate
– → #cav x freq [GHz] x Re Z [Ω] ≦ 4230!

• Transverse

ef rev Ib$ % crab $ &(ImZT+ # ImZT# )2E– Large βcrab → required kick reduces, but growth rate increases.
– Although the number of cavities is small, the impedance should be
reduced even lower than that of the ARES.
-1– 9.4A, β!
crab=200m → τ = 0.0267 x #cav x Im ZT– #cav=4, τ≧1ms (bunch feedback) → ImZT ≦ 9.4 kΩ/m

" #1 =Crab cavities for high currents (K. Akai, KEK)

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Design concept of new crab cavity
K. Akai and Y. Morita,
submitted to PRST-AB.

• Squashed cell operating in TM2-1-0 (same).
• Waveguide dampers are attached.
– Much heavier damping of parasitic modes can be obtained.
– Larger HOM power is allowed for the dampers.

• Coaxial dampers are used, but not as a beam pipe.
– The TM1-1-0 is well damped.
– Loss factor is reduced since widely opened beam pipes can beused.

• Optimization has been carried out for both the SCand NC versions.
Crab cavities for high currents (K. Akai, KEK)

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Schematic drawing of new crab cavity
coaxial damperY(cross section at Y-Y')

absorbercross-shaped
waveguide dampers••

Y'(Left) The cross-shaped waveguide dampers and coaxial dampers areattached at the squashed-cell.
(Right) Cross section of the coaxial damper at the cut plane of Y-Y’.
Crab cavities for high currents (K. Akai, KEK)

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Beam pipe radius
Bunch length = 3mm
1.680

1.475
R/Q (ohm/m)

70

165

0.8

60

0.655

0.4

50
Loss factor (V/pC)

0.2045020

4060

80

100

120

R/Q (ohm/m)

Loss factor (V/pC)

1.2– Loss factor is calculatedusing analytical form.
– R/Q is calculated using
MAFIA without wave
guides– Radius of 70~90mm
gives sufficiently highR/Q and relatively low
loss factor.

40140

Beam pipe radius (mm)Crab cavities for high currents (K. Akai, KEK)

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Damping of the Lower Freq. Mode120

Qext for the LFM

1008060
r0=2040r0=25r0=30r0=40

200100120140160180200220• Inner and outer radii of thecoaxial damper are chosen
10mm and 30mm.
• The external Q value ofthe LFM is sufficiently
reduced to 25.
• The effect of the coaxial
damper on the crabbing
mode is small; the R/Q isdecreased by only 1%.

Vertical position, y_0 (mm)Crab cavities for high currents (K. Akai, KEK)

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3-D drawing of new crab cavity

NC version

SC version

Crab cavities for high currents (K. Akai, KEK)

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Coupling impedance of parasitic modes
Ohm/m

Ohm

Crabbing mode

Lower frequency mode

Horizontal

Longitudinal

Original

New(SC)

New(NC)

unit

Highest value of ZT (H)

25.0

5.64.4kΩ/mHighest value of ZT (V)

15.0

3.2

10.1kΩ/mHighest (Z// x freq./GHz)

2070

1020

760

Ω GHz

Kloss@3mm

0.73

0.56

0.56

V/pC

Crab cavities for high currents (K. Akai, KEK)

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Crabbing mode property• SC: 1.5 MV kick can be obtained.
• NC: 0.4 MV kick @Pwall=70kW.
SCNC

unit

Frequency

508.9

508.9

MHz

R/Q

5860.8Ω/m

Q0 (Copper)-36000

Epeak/Vkick

11.7(MV/m)/MV

Hpeak/Vkick

424

Gauss/MV

Crab cavities for high currents (K. Akai, KEK)

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Crab crossing experiment in KEKB
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<KR

The crab crossing experiment in KEKB is planned in FY 2005.
The original crab cavity will be used for the experiment.

Crab cavities for high currents (K. Akai, KEK)

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Crab crossing in Super-KEKB.CG)"H I H J<KIL >
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P Q#3Q O?1ABR P.CG)"H I H J<TI L>
M3"&NOFV?;P Q#3Q O61FBR P(01+02+3&4#5#)9 "0* 5:+5#;)+<:0"#=0%5&'>
9 "0* 5:+5#;)+<'0%$#5C,#%&'>
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9 "0* 5:+5#;)+<'0%$#5C,#%&'>
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New crab cavity has advantages for Super-KEKB, especially in LER.
Original crab cavity could also be used in HER, if HOM absorber is OK with 44kW.

Crab cavities for high currents (K. Akai, KEK)

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Summary• We have designed a new crab cavity for high-current
accelerators.
• Parasitic modes are sufficiently damped.
– The lower frequency mode is also damped.
– Instability can be suppressed with the present FB system, even at a beam
current of 10A.

• The problem for the dampers due to a large parasitic poweris greatly eased:– Loss factor of the cell is reduced.
– The absorbers do not contribute to the loss factor.
– The parasitic power to each damper is further reduced since it is divided
into the waveguide and coaxial dampers.

• The new crab cavity is promising in Super-KEKB.
Crab cavities for high currents (K. Akai, KEK)

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