a new tem-type deflecting/crabbing...
TRANSCRIPT
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