A New TEM-Type

Deflecting/Crabbing Cavity

Jean Delayen

18 February 2009

Genesis

• LHC Upgrade would

need a small, low

frequency (400 MHz)

crabbing cavity

• Low velocity ion

accelerators need

deflecting cavities at

~150 MHz, β~0.2

Genesis

• ELIC

– 24 MV for protons

– 1.2 MV for electrons (KEK is 1.4 MV)

• 11 GeV separator

• Generation of subpicosecond light pulses

Existing Solutions

• TM110 cavity (à la KEK) 509 MHz

Existing Solutions

• CEBAF Deflecting cavity, 499 MHz

Parallel-Bar Cavity

• Basic cell is made of 2 TEM resonant lines, of length

/2 , operating in opposite phase

Electromagnetic Fields

TEM Modes

• If no beam aperture, no rounded corners

• Translational Invariance

– No z component

• Multiply connected

Analytical Model

2 circular cylinders between 2

infinite planes

Pure TEM mode

Electrostatic problem of 2

infinitely long, parallel cylinders

Analytical Model

• If side wall are sufficiently

far from the parallel bars,

the electromagnetic

properties can be obtained

analytically

• Since the electromagnetic

mode is TEM, it is an

electrostatic problem

• If the cross section of the

bars is circular, they can be

modeled by 2 parallel,

infinitely long, uniformly

charged lines

Potential and Fields

Equipotentials

Capacitance and Inductance

• Capacitance per unit length

• Inductance per unit length

• Transmission line impedance

Energy Content

• Energy content

Losses in Bars

• Power dissipation in the bars

Losses in Planes

• Power dissipation in the planes

• Total power dissipation

Transverse Voltage and Gradient

• Transverse voltage and gradient

Surface Fields

0

1

2

3

4

5

6

7

8

9

10

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

R/

Ep/Et

A/R= 1.6

A/R= 1.8

A/R= 2.0

A/R= 2.2

A/R= 2.4

0

5

10

15

20

25

30

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14m

T/(

MV

/m)

R/

Bp/Et

A/R= 1.6

A/R= 1.8

A/R= 2.0

A/R= 2.2

A/R= 2.4

Energy Content and Geometrical Factor

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

J

R/

U/(E2 λ3)

A/R= 1.6

A/R= 1.8

A/R= 2.0

A/R= 2.2

A/R= 2.4

0

20

40

60

80

100

120

140

160

180

200

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

R/

Geometrical Factor

A/R= 1.6

A/R= 1.8

A/R= 2.0

A/R= 2.2

A/R= 2.4

R/Q and Shunt Impedance

0

100

200

300

400

500

600

700

800

900

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

R/

Rt/Q

A/R= 1.6

A/R= 1.8

A/R= 2.0

A/R= 2.2

A/R= 2.4

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

2

R/

RtRs=G*Rt/Q

A/R= 1.6

A/R= 1.8

A/R= 2.0

A/R= 2.2

A/R= 2.4

Microwave Studio and Model

0

1

2

3

4

5

6

7

8

9

20 25 30 35 40 45 50 55 60 65 70

Rod Radius (mm)

Ep/Et

A/R= 1.6

A/R= 1.8

A/R= 2

A/R= 2.2

A/R= 2.4

0

1

2

3

4

5

6

7

8

9

20 25 30 35 40 45 50 55 60 65 70

Rod Radius (mm)

Ep/Et

A/R= 1.6

A/R= 1.8

A/R= 2

A/R= 2.2

A/R= 2.4

Microwave Studio and Model

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

20 25 30 35 40 45 50 55 60 65 70

2

Rod Radius (mm)

G*Rt/Q

A/R=1.6

A/R=1.8

A/R=2.0

A/R=2.2

A/R=2.4

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

20 25 30 35 40 45 50 55 60 65 70

2

Rod Radius (mm)

G*Rt/Q

A/R=1.6

A/R=1.8

A/R=2.0

A/R=2.2

A/R=2.4

Omega3P and Model

Multicell

Other Cross-section

Parallel Bar vs. TM110

400

615

1101

305

0.375

4.25

12.24

220

46.7

10274

Other Possible Improvements

• Variable cross-section

• Curved resonant lines

Some Numbers (Superconducting)

2 2 129

/ 8.8

80 9.1

(9.1)(2.9) 26.4

500 / 2 30 2.73

2.73248

11000

(2.73) 1015 10 3.6

/ (92.6)(336)

p t

t

p

c s

B E

E

E

VP R

G R Q

P

mT/(MV/m)

Should be able to achieve mT MV/m

MV/m

At MV/m, = cm MV

At 11 GeV, = rad

W

6 6(2.73 10 )(400 10 ) 1.1

42 1

rf VI kW

CEBAF deflecting cavity produces rad at kW

Next

• Optimize bar geometry

• Multicell

• Higher order modes

• Coupling

– Fundamental

– HOM