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Sasha NovokhatskiSLAC, Stanford

University

Accelerator Session April 20, 2005

Low R/Q Cavitiesfor Super B-

factory

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”Why Low R/Q Cavities for

Super B?

Because we need high currents to achieve super high luminosity

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”Low R/Q cavities are:

• To damp multi-bunch instability• To avoid single-bunch instability• To decrease HOM power

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”How we can make low

R/Q?• By decreasing cavity gap

– in this case HOM power goes down – but surface fields go up and bring limit

very soon

• By increasing beam pipe radius– smaller R/Q -

- closer to cut-off frequency

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”Varying cavity gap length

cavity gap cavity gap

35.5 Ohm R/Q 24.3 Ohm

0.39 V/pC HOM loss factor 0.24 V/pC

12.77 MV/m Max surface electric field* 31.12 MV/m

30.16 A/m Max surface magnetic field* 58.78 A/m

*for 1 MeV energy gain, f=952 MHz, bore radius 70 mm

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”Varying beam pipe radius

“Wakefield” calculations

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”Wakefield spectrum

“Wakefield” calculations

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”Electric Field Distribution

Rb=110mm

Rb=90mm

Rb=70mm

“SUPERFISH” calculations

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”Surface fields distribution**1 MeV energy gain. Electric field – Green. Magnetic field - pink

“SUPERFISH” calculations

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”Cavity parameters

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”R/Q and HOM Power

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”Transient time factor and stored

Energy

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”Maximum surface fields

magnetic

electric

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Periodic Structure. Main mode coupling

Distance between cavities 787.5 mm (5)

Zero mode

mode

Coupling: 0.55/952=5.8E-04

TM01

Cut-off

1.04276 GHz

Rb=110mm

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”Trapped TM11 modes

Zero mode

mode

TM11

Cut-off

1.6621 GHz

“MAFIA” calculations

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”Trapped TE11 modes

Zero mode

mode

TE11

Cut-off

798.55 MHz

“MAFIA” calculations

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”Checking single–bunch

stabilityWe need to know:

• Wake potentials

• Number of cavities

• Total voltage

• Momentum compaction

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”Cavity wake Potential

Bunch shortening ?

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”Yes, cavity wake produces shorter

bunches

Bunch Current 3.300 mA Bunch Charge 24.21 nC Zero bunchlength 1.80 mm Moment. compact. 9.400E-04 Ring Energy 3500.0 MeV Energy Spread 2.400 MeV SR Energy loss 0.970 MeV per turn RF Voltage: 52.50 MV Number of cavities 42 Phase Angle 1.059 degree (0.926 mm) Harmonic Number 6984 Rev. frequency 136.2707 kHz Synchrotron freq. 17.045 kHz (7.995 Turns) Damping turns 4100.000

1.8 mm 1.75 mm

1.25MV/cav

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”Resistive-Wall Wake (bunch lengthening)

PowerSS: 39.44 MW Al: 7.88 MWCu: 6.06 MW

SR: 22.3 MW

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”IP wake (large additional

part)PowerIP HOMs: 4.0 MW

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”All wakes included

Bunch Current 3.300 mA Bunch Charge 24.21 nC Zero bunchlength 1.80 mm Moment. compact. 9.400E-04 Ring Energy 3500.0 MeV Energy Spread 2.400 MeV SR Energy loss 0.970 MeV per turn RF Voltage: 52.50 MV Number of cavities 42 Phase Angle 1.059 degree (0.926 mm) Harmonic Number 6984 Rev. frequency 136.2707 kHz Synchrotron freq. 17.045 kHz (7.995 Turns) Damping turns 4100.000

1.83 mm

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”Bunch length in the ring

IP

cavities

1

3 2

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IP

1.83 mm

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2.00 mm

Before cavities

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2.00 mm

after cavities

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IP

1.83 mm

IP

Cavities

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”More Voltage

• 1.5 MV/cavity * 42 = 63 MV

• Momentum compaction goes to 1.128E-03 to have the same bunchlength

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IP

1.77 mm

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2.02 mm

Before cavities

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2.02 mm

after cavities

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IP

1.77 mm

IP

Cavities

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”More focusing

• We can increase momentum compaction more to bring bunch length to 1.8mm at IP

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IP

1.816 mm

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2.085 mm

Before cavities

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2.085 mm

after cavities

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IP

1.816 mm

IP

Cavities

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”Conclusions

• Low R/Q cavities are needed for super high luminosity factories. These cavities are superconducting cavities.

• Low R/Q is achieved by using large beam pipe. Cut-off frequency is very closer to the working frequency.

• Trapped transverse modes must be damped using external loads.

• High voltage and correspondent momentum compaction give additional bunch shortening at interaction point.