Page 1
Jean Delayen
Center for Accelerator Science
Old Dominion University
and
Thomas Jefferson National Accelerator Facility
TEM-CLASS CAVITY DESIGN
USPAS@Rutgers
June 2015
Page 2
• There have been increased needs for reduced-beta (b<1) SRF cavity especially in CW machine (or high duty pulsed machine; duty >10 %)
• Accelerator driven system (ADS)
Nuclear transmutation of long-lived radio active waste
Energy amplifier
Intense spallation neutron source
• Nuclear physics
Radioactive ion acceleration
Muon/neutrino production
• Defense applications
• SRF technology Critical path !!
Introduction
Page 3
• SRF cavity for CW application or long pulse application
• efforts for expanding their application regions down to b~0.1,
• Reduced beta Elliptical multi-cell SRF cavity
• for CW, prototyping by several R&D groups have demonstrated
as low as b=0.47
• for pulsed, SNS b=0.61, 0.81 cavities & ESS
• Elliptical cavity has intrinsic problem as b goes down
• mechanical problem, multipacting, low RF efficiency
• Spoke cavity; supposed to cover ranges b=0.1~0.5(6), f=300~900 MHz
• design & prototype efforts in RIA, AAA, EURISOL, XADS, ESS, etc.
For proton b=0.12 corresponds ~7 MeV all the accelerating structures
(except RFQ)
Introduction
Page 4
Low and Medium β Superconducting Accelerators
Accelerator driven systems
waste transmutation
energy production
Production of radioactive ions
Nuclear Structure
Pulsed spallation sources
High Current Medium/Low Current
CW
Pulsed
Page 5
High-current cw accelerators
• Beam: p, H-, d
• Technical issues and challenges
– Beam losses (~ 1 W/m)
– Activation
– High cw rf power
– Higher order modes
– Cryogenics losses
• Implications for SRF technology
– Cavities with high acceptance
– Development of high cw power couplers
– Extraction of HOM power
– Cavities with high shunt impedance
Page 6
High-current pulsed accelerators
• Beam: p, H-
• Technical issues and challenges
– Beam losses (~ 1 W/m)
– Activation
– Higher order modes
– High peak rf power
– Dynamic Lorentz detuning
• Implications for SRF technology
– Cavities with high acceptance
– Development of high peak power couplers
– Extraction of HOM power
– Development of active compensation of dynamic Lorentz
detuning
Page 7
Medium to low current cw accelerators
• Beam; p to U
• Technical issues and challenges
– Microphonics, frequency control
– Cryogenic losses
– Wide charge to mass ratio
– Multicharged state acceleration
– Activation
• Implications for SRF technology
– Cavities with low sensitivity to vibration
– Development of microphonics compensation
– Cavities with high shunt impedance
– Cavities with large velocity acceptance (few cells)
– Cavities with large beam acceptance (low frequency, small frequency transitions)
Page 8
Common considerations (I)
• Intermediate velocity applications usually do not require (or cannot
afford) very high gradients
• Operational and practical gradients are limited by
– Cryogenics losses (cw applications)
– Rf power to control microphonics (low current applications)
– Rf power couplers (high-current applications)
• High shunt impedance is often more important
• To various degrees, beam losses and activation are a consideration
Page 9
Common considerations (II)
• Superconducting accelerators in the medium velocity range
are mostly used for the production of secondary species
– Neutrons (spallation sources)
– Exotic ions (radioactive beam facilities)
• Medium power (100s kW) to high power (~MW) primary
impinging on a target
• Thermal properties and dynamics of the target are important
considerations in the design of the accelerator (frequency,
duration, recovery from beam trips)
• Some implications:
– Operate cavities sufficiently far from the edge
– Provide an ample frequency control window
Page 10
Design considerations
• Low cryogenics losses
– High QRs * Rsh/Q
– Low frequency
• High gradient
– Low Ep/Eacc
– Low Bp/Eacc
• Large velocity acceptance
– Small number of cells
– Low frequency
• Frequency control
– Low sensitivity to microphonics
– Low energy content
– Low Lorentz coefficient
• Large beam acceptance
– Large aperture (transverse acceptance)
– Low frequency (longitudinal acceptance)
Page 11
A Few Obvious Statements
Low and medium b
b<1
Particle velocity will change
The lower the velocity of the particle or cavity b
The faster the velocity of the particle will change
The narrower the velocity range of a particular cavity
The smaller the number of cavities of that b
The more important it is that the particle achieve design velocity
Be conservative at lower b
Be more aggressive at higher b
Page 12
Two main types of structure geometries
TEM class (QW, HW, Spoke)
TM class (elliptical)
Design criteria for elliptical cavities
Pagani, Barni, Bosotti, Pierini, Ciovati, SRF 2001.
Challenges and the future of reduced beta srf cavity design
Sang-ho Kim, LINAC 2002.
Low and intermediate β cavity design
Jean Delayen, SRF 2003
High-energy ion linacs based on superconducting spoke cavities
K. W. Shepard, P. N. Ostroumov, J. R. Delayen, PRSTAB 6, 080101 (2003)
A Few More Statements
Page 13
Superconducting Structures – Circa 1987
Page 14
β<1 Superconducting Structures – Circa 1989
Page 15
β<1 Superconducting Structures – 2002..
0.1
1
100 1000
Frequency (MHz)
Be
ta
Prior to 1989
1989 to 2002
Page 16
Basic Structure Geometries
Resonant Transmission Lines
– l/4
• Quarter-wave
• Split-ring
• Twin quarter-wave
• Lollipop
– l/2
• Coaxial half-wave
• Spoke
• H-types
– TM
• Elliptical
• Reentrant
– Other
• Alvarez
• Slotted-iris
Page 17
A Word on Design Tools
TEM-class cavities are essentially 3D geometries
3D electromagnetic software is available
MAFIA, Microwave Studio, HFSS, etc.
3D software is usually very good at calculating frequencies
Not quite as good at calculating surface fields
Use caution, vary mesh size
Remember Electromagnetism 101
Page 18
Design Tradeoffs
Number of cells
Voltage gain
Velocity acceptance
Frequency
Size
Voltage gain
Rf losses
Energy content, microphonics, rf control
Acceptance, beam quality and losses
Page 19
Energy Gain
Transit Time Factor - Velocity Acceptance
Assumption: constant velocity
( ) cos( )W q E z t dzw f+¥
-¥
D = +ò
0 0cos ( ) ( )
( ) cos
( )
( ) cos
( )
( ) cos
Max
Transit Time Factor
Velocity Acceptance
Max
W q W T W E z dz
zE z dz
c
E z dz
zE z dz
cT
zE z dz
c
f b
w
b
w
bb
w
b
+¥
-¥
+¥
-¥
+¥
-¥
+¥
-¥
+¥
-¥
D = D D = Q
æ öç ÷è ø
Q =
æ öç ÷è ø
=æ öç ÷è ø
ò
ò
ò
ò
ò
Page 20
Transit Time Factor
(a)
(b)
Page 21
Velocity Acceptance for 2-Gap Structures
0 0
0 0
0
0 0
sin sin2 2
( )
sin sin2 2
x xT
x x
b bpa p
b bbb
b pa p
æ ö æ öç ÷ ç ÷è ø è ø
=æ ö æ öç ÷ ç ÷è ø è ø
0
02
xl
b l=
Page 22
Velocity Acceptance for 3-Gap Structures
0 0 0
0 0 0
0
0 0 0
sin cos cos3 3
( )
sin cos cos3 3
x x xT
x x x
b b bpa pa p
b b bbb
b pa pa p
é ùæ ö æ ö æ ö-ê úç ÷ ç ÷ ç ÷è ø è ø è øë û
=é ùæ ö æ ö æ ö
-ê úç ÷ ç ÷ ç ÷è ø è ø è øë û
0
02
xl
b l=
Page 23
Higher-Order Effects
( )2
0 (2) (2)
0
(2)
(2)
2
0
cos ( ) ( ) sin 2 ( )
( ) ( ) ( ) /4
( ) ( ) ( ) ( )( )
4
s
s
q WW q W T T T
W
k dT k T k T k k c
dk
k T k k T k k T k T kT k dk
k
f b b f b
w b
p
¥
Dé ùD = D + +ë û
= - =
+ - -¢ ¢= - ¢
¢ò
Page 24
If characteristic length <<l (b<0.5), separate the problem in two parts:
Electrostatic model of high voltage region
Transmission line
A Simple Model:
Loaded Quarter-wavelength Resonant Line
Page 25
Basic Electrostatics
a: concentric spheres
b: sphere in cylinder
c: sphere between 2 planes
d: coaxial cylinders
e: cylinder between 2 planes
Vp : Voltage on center conductor
Outer conductor at ground
Ep: Peak field on center conductor
Page 26
Loaded Quarter-wavelength Resonant Line
Capacitance per unit length
Inductance per unit length
0 0
0 0
2 2
1ln ln
Cb
r
pe pe
r
= =æ ö æ öç ÷ ç ÷è ø è ø
0 0
0 0
1ln ln
2 2
bL
r
m m
p p r
æ ö æ ö= =ç ÷ ç ÷è ø è ø
Page 27
Center conductor voltage
Center conductor current
Line impedance
Loaded Quarter-wavelength Resonant Line
0
2( ) sinV z V z
p
l
æ ö= ç ÷è ø
0
2( ) cosI z I z
p
l
æ ö= ç ÷è ø
0 0
0
0 0 0
1ln , 377
2
VZ
I
mhh
p r e
æ ö= = = Wç ÷è ø
Page 28
Loading capacitance
Loaded Quarter-wavelength Resonant Line
( ) ( )
( )
0 0
0
2cotan cotan
2( )
ln 1/ ln 1/
Arctan2 ln 1/
z
zr
l
p pz
lle le
r
l le
p r
æ ö æ öç ÷ ç ÷è ø è ø
G = =
é ù= ê ú
Gë û
Page 29
Peak magnetic field
Loaded Quarter-wavelength Resonant Line
0
0
1ln sin
2300
9
m, A/m
m, T
cm, G
: Voltage across loading capacitance
mT at 1 MV/m
p
p
HV
c Bb
B
V
B
hp
r zr
ì ü ì üæ öï ï ï ïæ ö
= í ý í ýç ÷ç ÷ è øè øï ï ï ïî þ î þ
Page 30
Power dissipation (ignore losses in the shorting plate)
Loaded Quarter-wavelength Resonant Line
2 0
2 220
2 2
2
1sin
1 1/
8 lnsin
2
sp
s
RP V
b
RP E
z pzrp l p
ph rz
b lh
++
=
µ
Page 31
Energy content
Loaded Quarter-wavelength Resonant Line
( )2 0
20
2 2 3
0
1sin
1
8 ln 1/sin
2
pU V
U E
z pzpe pl
prz
e b l
+
=
µ
Page 32
Geometrical factor
Loaded Quarter-wavelength Resonant Line
( )0
0
ln 1/2
1 1/s
bG QR
G
rp h
l r
h b
= =+
µ
Page 33
Shunt impedance
Loaded Quarter-wavelength Resonant Line
222
0
0
2
sinln32 2
11 1/sin
sh
s
sh s
bR
R
R R
pz
rh
p l rz pz
p
h b
=+
+
µ
( )24 /pV P
Page 34
R/Q
Loaded Quarter-wavelength Resonant Line
( )
2
02
sin16 2ln 1/
1sin
sh
sh
R
Q
R
Q
pz
h rp
z pzp
h
=
+
µ
Page 35
Loaded Quarter-wavelength Resonant Line
Page 36
Loaded Quarter-wavelength Resonant Line
MKS units, lines of constant normalized loading capacitance G/le0
Page 37
More Complicated Center Conductor Geometries
2 2
2
2 2
2
10
ln 4
10
ln 4
( )( ) ( )
/
d v d dvv
d dd
d i d dii
d dd
i zz C z
di dz
r p
r r z zz
r p
r r z zz
- + =
+ + =
G = -
Page 38
Constant logarithmic derivative of line capacitance
Good model for linear taper
Constant surface magnetic field
exp( / )
01 1( )
z drdC
r z bC dz d b
æ ö= - = ç ÷è ø
( ) ( )i z r zµ
22 2
2 2
1 40
ln( / )
d r drr
r b r dzdz
p
l
æ ö- + =ç ÷è ø
More Complicated Center Conductor Geometries
Page 39
Profile of Constant Surface Magnetic Field
Page 40
Profile of Constant Surface Magnetic Field
MKS units, lines of constant normalized loading capacitance G/le0
Page 41
Another Simple Model:
Coaxial Half-wave Resonator
2b
2a
L
Page 42
Coaxial Half-wave Resonator
Capacitance per unit length
Inductance per unit length
0 0
0
2 2
1ln ln
Cb
a
pe pe
r
= =æ ö æ öç ÷ ç ÷è ø è ø
0 0
0 0
1ln ln
2 2
bL
r
m m
p p r
æ ö æ ö= =ç ÷ ç ÷è ø è ø
2b
2a
L
Page 43
Center conductor voltage
Center conductor current
Line impedance
Coaxial Half-wave Resonator
0
2( ) cosV z V z
p
l
æ ö= ç ÷è ø
0
2( ) sinI z I z
p
l
æ ö= ç ÷è ø
0 0
0
0 0 0
1ln , 377
2
VZ
I
mhh
p r e
æ ö= = = Wç ÷è ø
2b
2a
L
Page 44
Coaxial Half-wave Resonator
d: coaxial cylinders
Vp : Voltage on center conductor
Outer conductor at ground
Ep: Peak field on center conductor
Peak Electric Field
Page 45
Peak magnetic field
Coaxial Half-wave Resonator
0
0
1ln
300
9
m, A/m
m, T
cm, G
: Voltage across loading capacitance
mT at 1 MV/m
p
p
HV
c Bb
B
V
B
h
rr
ì ü ì üæ öï ï ï ï
= í ý í ýç ÷è øï ï ï ïî þ î þ
2b
2a
L
Page 46
Power dissipation (ignore losses in the shorting plate)
Coaxial Half-wave Resonator
2 0
2 2
0
2 2
2
1 1/
4 ln
sp
s
RP V
b
RP E
rp l
h r
b lh
+=
µ
2b
2a
L
Page 47
Energy content
Coaxial Half-wave Resonator
( )2 0
0
2 2 3
0
1
4 ln 1/pU V
U E
pel
r
e b l
=
µ
2b
2a
L
Page 48
Geometrical factor
Coaxial Half-wave Resonator
( )0
0
ln 1/2
1 1/s
bG QR
G
rp h
l r
h b
= =+
µ
2b
2a
L
Page 49
Shunt impedance
Coaxial Half-wave Resonator
22
0
0
2
ln16
1 1/sh
s
sh s
bR
R
R R
rh
p l r
h b
=+
µ
( )24 /pV P
2b
2a
L
Page 50
R/Q
Coaxial Half-wave Resonator
( )02
8ln 1/sh
sh
R
Q
R
Q
h rp
h
=
µ
2b
2a
L
Page 51
Some Real Geometries (l/4)
Page 52
Some Real Geometries (l/4)
Page 53
l/4 Resonant Lines
Page 54
l/2 Resonant Lines
Page 55
l/2 Resonant Lines – Single-Spoke
Page 56
l/2 Resonant Lines – Double and Triple-Spoke
Page 57
l/2 Resonant Lines – Multi-Spoke
Page 58
TM Modes
Page 59
Design Considerations
• Minimize the peak surface fields Bp; approaches to theoretical limit (190 mT) high RRR, defect control, better surface treatment (~170 mT) Ep; fields exceed 80 MV/m improved surface cleaning tech. • Reasonable Inter-cell coupling between cells in Elliptical cavity • Spoke cavity intrinsically has big coupling constant • Provide required external Q • In CW, higher shunt impedance (mainly determined by the cavity
type) • Reasonable mechanical stiffness common; reasonable tuning force, mechanical stability under
vacuum pressure (test~2 atm), stable against microphonics pulsed; affordable dynamic Lorentz force detuning • Safe from Multipacting • Verify HOM and related issues • Coupled field problems are common between RF, mechanical,
thermal.. strong interfaces are needed
Page 60
RF Geometry Optimization (elliptical cavity)
Elliptical cell geometry and dependencies of RF parameters on the
ellipse aspect ratio (a/b) at the fixed slope angle, dome radius and bore
radius.
Page 61
RF Geometry Optimization (Spoke Cavity)
•There have been extensive efforts for design optimization especially to reduce the ratios of
Ep/Eacc and Bp/Eacc.
• Controlling A/B (Ep/Eacc) and C/D (Bp/Eacc) Shape optimization
• Flat contacting surface at spoke base will help in another minimization of Bp/Eacc
• For these cavities:
Calculations agree well Ep/Eacc~3, Bp/Eacc~(7~8) mT/(MV/m),
though it is tricky to obtain precise surface field information from the 3D
simulation.
Intrinsically have very strong RF coupling in multi-gap cavity.
Have rigid nature against static and dynamic vibrations.
Beta dependency is quite small.
Diameter~half of elliptical cavity.
Page 62
Velocity Acceptance
• Energy gain
Transit time factor for single cell
Depends on field profile in cell
Phasing factor in multicell cavities
Depends on cell spacing and field amplitude in cells
Does not depend on field profile in cells (assumed to
be identical)
2x
l
bl=
( )T x
( ) ( ) cosW q V T x x jD = F
( )xF
Page 63
Velocity Acceptance
Velocity Acceptance for Sinusoidal Field Profile
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0b/bg
Page 64
Voltage in Cells
Voltage in jth cell
N: Number of cells, M: Mode number
( )2 1sin
2
M
j
jM
NV p
æ ö-= ç ÷è ø
6 Cell, Mode 6
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
6 Cell, Mode 5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
6 Cell, Mode 4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
6 Cell, Mode 3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
6 Cell, Mode 2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
6 Cell, Mode 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
Page 65
Phasing Factor
For fundamental mode:
For all modes:
If M=N, recover previous formula
If x=1
1( 1) sin , 2
21( )
cos ( 1) cos , 2 12 2
n
n
NN n
xx
NN n
x x
p
p p
+ì æ ö- =ç ÷ï è øï
F = íæ ö æ öï - = +ç ÷ ç ÷è ø ï è øî
1
1 1sin sin
2 21( ) ( 1)
2 1 1sin sin
2 2
M
N M N M
N x N xx
M M
N x N x
p p
p p
+
æ öé ù é ùæ ö æ ö- +ç ÷ ç ÷ê ú ê úç ÷è ø è øë û ë û
ç ÷F = + -é ù é ùæ ö æ öç ÷
- +ç ÷ ç ÷ê ú ê úç ÷è ø è øè øë û ë û
( ) MNx NdF =
( )p
Page 66
Phasing Factor
6 Cells, Mode 6
-4
-3
-2
-1
0
1
2
3
4
5
6
7
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
x = b l / 2 l
(x)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
Page 67
Phasing Factor
6 Cells, Mode 5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
x = b l / 2 l
(x)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
Page 68
Phasing Factor
6 Cells, Mode 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
x = b l / 2 l
(x)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6
Page 69
Surface Electric Field
• TM010 elliptical structures
– Ep/Ea ~ 2 for b =1
– Increases slowly as b decreases
• l/2 structures:
– Sensitive to geometrical design
– Electrostatic model of an “shaped geometry” gives
Ep/Ea ~ 3.3, independent of b
Page 70
Surface Electric Field
• Lines: Elliptical Squares: Spoke
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Beta
Ep/E
a
Page 71
Surface Magnetic Field
• TM010 elliptical cavities:
– B/Ea ~ 4 mT/(MV/m) for b=1
– Increases slowly as b decreases
• l/2 structures:
– Sensitive to geometrical design
– Transmission line model gives B/Ea ~ 8 mT/(MV/m),
independent of b
Page 72
Surface Magnetic Field
• Lines: Elliptical Squares: Spoke
0
2
4
6
8
10
12
14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Beta
Bp/E
a (m
T/(
MV
/m))
Page 73
Geometrical Factor (QRs)
• TM010 elliptical cavities:
– Simple scaling: QRs ~ 275 b (W)
• l/2 structures:
– Transmission line model: QRs ~ 200 b (W)
Page 74
Geometrical Factor (QRs)
• Lines: Elliptical Squares: Spoke
0
50
100
150
200
250
300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Beta
QR
s (W
)
Page 75
Rsh/Q per Cell or Loading Element
• Rsh= V2/P
• TM010 elliptical cavities:
– Simple-minded argument, ignoring effect of beam line
aperture, gives:
– When cavity length becomes comparable to beam line
aperture :
– Rsh/Q ~ 120 b2 (W)
• l/2 structures:
– Transmission line model gives: Rsh/Q ~ 205 W
– Independent of b
/shR Q bµ
2/shR Q bµ
Page 76
Rsh/Q per Cell or Loading Element
Lines: Elliptical Squares: Spoke
0
50
100
150
200
250
300
350
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Beta
Rsh/Q
per
cell (
W)
Page 77
Shunt Impedance Rsh
(Rsh/Q QRs per Cell or Loading Element)
• TM010 elliptical cavities:
– Rsh Rs ~ 33000 b3 (W2)
• l/2 structures:
– Rsh Rs ~ 40000 b (W2)
Page 78
Shunt Impedance Rsh
(Rsh/Q QRs per cell or loading element)
0
5000
10000
15000
20000
25000
30000
35000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Beta
RshR
s p
er
cell
(W
2)
• Lines: Elliptical Squares: Spoke
Page 79
Energy Content per Cell or Loading Element
Proportional to E2l3
At 1 MV/m, normalized to 500 MHz:
• TM010 elliptical cavities: – Simple-minded model gives
– In practice: U/E2 ~ 200-250 mJ
– Independent of b (seems to increase when b <0.5 – 0.6)
• l/2 structures: – Sensitive to geometrical design
– Transmission line model gives U/E2 ~ 200 b2 (mJ)
2/U E bµ
Page 80
Energy Content per Cell or Loading Element
0
50
100
150
200
250
300
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Beta
U/E
2 p
er
cell (
mJ)
@ 1
MV
/m , 5
00 M
Hz
Page 81
Size & Cell-to-Cell Coupling
TM010 Structures
Dia ~ 0.88 – 0.92 l
Coupling ~ 2%
l /2 Structures
Dia~ 0.46 – 0.51 l
Coupling ~ 20 - 30%
Example : 350 MHz, b= 0.45
Page 82
Multipacting
• TM010 elliptical structures
– Can reasonably be modeled and
predicted/avoided
– Modeling tools exist
• l/2 Structures
– Much more difficult to model
– Reliable modeling tools do not exist
– Multipacting “always” occurs
– “Never” a show stopper
Page 83
TM Structures – Positive Features
• Geometrically simple
• Familiar
• Large knowledge base
• Good modeling tools
• Low surface fields at high b
• Small number of degrees of freedom
Page 84
l/2 Structures – Positive Features
• Compact, small size
• High shunt impedance
• Robust, stable field profile (high cell-to-cell
coupling)
• Mechanically stable, rigid (low Lorentz
coefficient, microphonics)
• Small energy content
• Low surface fields at low b
• Large number of degrees of freedom
Page 85
• Static Lorentz force detuning (LFD) at EoT(bg)=10 MV/m, 805 MHz
(Magnification; 50,000)
• In CW application LFD is not an issue, but static LFD coeff. provides
some indication of mechanical stability of structure
bg=0.35 bg=0.48 bg=0.61 bg=0.81
Suitable for all CW & pulsed applications
Recent test results of SNS prototype cryomodule,
bg=0.61;
quite positive; piezo compensation will work
Will work in CW
Pessimistic in
Pulsed application
Would be a
competing Region
with spoke cavity
RF efficiency; x
Mechanical
Stability; x
Multipacting;
Strong
possibility
How Low Can We Go with bg in TM Cavities ?
Page 86
How High Can We Go with bg in Spoke Cavities?
• What are their high-order modes
properties?
– Spectrum
– Impedances
– Beam stability issues
• Is there a place for spoke cavities in high-
b high-current applications?
– FELs, ERLs
– Higher order modes extraction
Page 87
Layout of the AEBL at ANL – 200 MeV/u, 400 kW
Color code:
Black = existing facility
Blue+ green = AEBL baseline
Red = Low-cost upgrade
Courtesy P. Ostroumov and K.
Shepard
Page 88
Driver linac
Courtesy P. Ostroumov and K.
Shepard
Page 89
AEBL Driver Linac - SC Resonator Configuration
• Input of uranium 33+ and 34+ at beta = .0254 Beta Type Freq Length Esurf Eacc # Cav
MHz cm MV/m MV/m
0.031 FORK 57.5 25 22.4 5.60 3
0.061 QWR 57.5 20 27.5 9.29 21
0.151 QWR 115.0 25 27.5 8.68 48
72
0.263 HWR 172.5 30 27.5 9.45 40
0.393 2SPOKE 345.0 38.1 27.5 9.17 16
0.500 3SPOKE 345.0 65.2 27.5 9.55 54
0.620 3SPOKE 345.0 80.9 27.5 9.26 24
134
Total Cavity Count = 206
Subtotal
STRIPPER Subtotal
Courtesy P. Ostroumov and K.
Shepard
Page 90
SC cavities covering the velocity range 0.12 < b < 0.8
developed for the RIA driver linac and will be used in AEBL
345 MHz b=0.5
Triple-spoke
345 MHz b=0.62
Triple-spoke
115 MHz b=0.15
Steering-
corrected QWR
172.5 MHz
b=0.28 HWR 345 MHz b=0.4
double-spoke
See publications by K.W. Shepard, et al. Courtesy P. Ostroumov and K.
Shepard
Page 91
Cavity Walk – Voltage Gain per Cavity for Uranium Beam
0 0.1 0.2 0.3 0.4 0.5 0.6
β = v/c
8
6
2
0
MV
4
Courtesy P. Ostroumov and K.
Shepard
Page 92
ANL extended to TEM-class SC cavities the very high-
performance techniques pioneered by TESLA
Courtesy P. Ostroumov and K.
Shepard
Page 93
Effects of interstitial hydrogen on triple-spoke cavity performance
Effects of Interstitial Hydrogen on
Triple-spoke Cavity Performance
1.E+08
1.E+09
1.E+10
1.E+11
0 2 4 6 8 10 12 14
Eacc - MV/m
Ca
vit
y Q
at 1.9Kat 1.9K after 600C bakeat 4.2 Kat 4.2K after 600C bake
Courtesy P. Ostroumov and K.
Shepard
Page 94
Features of Spoke Cavities
• Small Size
– About half of TM cavity of same frequency
• Allows low frequency at reasonable size
– Possibility of 4.2 K operation
– High longitudinal acceptance
• Fewer number of cells
– Wider velocity acceptance
350 MHz, b= 0.45
Page 95
Features of Spoke Cavities
• Strong cell-to-cell coupling in multi-spoke
– All the cells are linked by the magnetic field
– Field profile robust with respect to manufacturing inaccuracy
– No need for field flatness tuning
– Closest mode well separated
Magnetic Field Profile: 352 MHz, β=0.48 (FZJ)
Page 96
Features of Spoke Cavities
• Accelerating mode has lowest frequency
– No lower-order mode
– Easier HOM damping
M. Kelly (ANL)
Page 97
Features of Spoke Cavities
• Electromagnetic energy concentrated near the
spokes
– Low energy content
– High shunt impedance
– Low surface field on the outer surfaces
• Couplers (fundamental and HOM) can be located on outer conductor
• Couplers do not use beamline space
325 MHz, β=0.17 (FNAL) M. Sawamura et al. SRF 2011
Page 98
Features of Spoke Cavities
• Few mechanical modes, none at low
frequency
• Low microphonics and sensitivity to
helium pressure
345 MHz, β=0.5, triple-spoke
(Z. Conway, ANL)
df/dp= -0.4 Hz/mbar
Page 99
How High Can We Go with bg in Spoke Cavities?
• What are their high-order modes properties?
– Spectrum
– Impedances
– Beam stability issues
• Is there a place for spoke cavities in high-b
high-current applications?
– FELs, ERLs
– Higher order modes extraction
Page 100
Compact Light Sources
• Most existing SRF cavities require or benefit from 2K operation
– Too complex for a University or small institution-based accelerator
– Cryogenics is a strong cost driver for compact SRF linacs
• Spoke cavities can operate at lower frequency
– Lower frequency allows operation at 4K
– No sub-atmospheric cryogenic system
– Significant reduction in complexity
• Similar designs for accelerating low-velocity ions are close to
desired specifications
Page 101
Compact Light Sources
RF amp RF amp RF amp
Superconducting
RF photoinjector
operating at 300
MHz and 4K
RF amplifiers
1 MeV
30 kW
beam dump
30 MeV
Bunch compression
chicane
Coherent enhancement
cavity with Q=1000
giving 5 MW cavity
power
5 kW cryo-cooled
Yb:YAG drive
laser
Inverse Compton
scattering
X-ray
beamline
Electron beam of ~1 mA
average current at 10-30 MeV
8 m
SRF Linac Parameters
Energy gain [MeV] 25
RF frequency [MHz] 352
Average current [mA] 1
Operating temperature [K] 4.2
RF power [kW] 30
MIT proposal
Page 102
GeV-scale Proton LINAC
Page 103
Compact ERL (JAEA)
• ERL combined with laser Compton
scattering for non-destructive assay system
for nuclear materials in spent fuel
Page 104
JAEA Tokai (650 MHz)
Masaru Sawamura et al.
Page 105
• Goal is to maximize G*R/Q:
– C↓; L↑; B field broad distributed
– Longer and thinner spoke central part
– Smaller end-cone radius
– Larger spoke base in beam transverse direction
– Make field stronger in the end-gap (by making the re-entrant part
deeper)
Jlab: Double spoke cavity RF design
C L C C
L L L
Feisi He, JLab
Page 106
JLAB 352 MHz Cavity Design Spoke Elliptical
Frequency [MHz] 352 352
Aperture diameter[mm] 50 170
Lcavity (end-to-end) [mm] 1289 + 140 1277 + 300
Cavity inner diameter [mm] 578 730
Cavity weight (3mm wall) [kg] 111 99
Ep/Ea 4.3 ± 0.1 2.26 ± 0.1
Bp/Ea [mT/(MV/m)] 7.6 ± 0.2 3.42 ± 0.1
Geometry factor [Ω] 179 283
Ra/Q [Ω] 781 458
Ra*Rs (=G*Ra/Q) [Ω2] 1.40 x 105 1.29 x 105
At Vacc =
8.5 MV
and 4.5K.
So
Rbcs=48n
Ω, and
assume
Rres=20n
Ω
Ep [MV/m] 28.6 ± 0.9 15.0 ± 0.5
Bp [mT] 50.3 ± 1.5 22.8 ± 0.7
Max heat flux
[mW/cm^2] 4.6 1.4
Q0 2.6 x 109 4.2 x 109
Power loss [W] 35 42.6
Leff=1.5*β0*λ [m] 1.2768 1.2768
Jlab: Cavity RF design (2)
• Key is to maximize G*Ra/Q to
minimize dynamic heat load
Feisi He, JLab
Page 107
Old Dominion University
• 325 MHz, β= 0.82 and 1, single and double
– Collaboration with JLab
• 352 MHz, β= 0.82 and 1, single and double
– Collaboration with JLab
• 500 MHz, β= 1, double
– Collaboration with Niowave
– Collaboration with JLab
• 700 MHz, β= 1, single, double, and triple
– Collaboration with Niowave, Los Alamos and NPS
Designs by:
Chris Hopper
Suba De Silva
Rocio Olave
Page 108
Design Optimization (a small sample)
C. Hopper, ODU
Page 109
Double Spoke
Surface Electric Field Surface Magnetic Field
Electric Field On Axis Electric Field
C. Hopper, ODU
Page 110
Cavity properties
Cavity Parameters β0 = 0.82 β0 = 1.0 Units
Frequency of accelerating
mode
325 325 MHz
Frequency of nearest mode 333 329 MHz
Cavity diameter 627 640 mm
Iris-to-iris length 949 1148 mm
Cavity length 1149 1328 mm
Reference length 757 922 mm
Aperture diameter at spoke 60 60 mm
Cavity Parameters β0 = 0.82 β0 = 1.0 Units
Frequency of accelerating
mode
352 352 MHz
Frequency of nearest
mode
361 357 MHz
Cavity diameter 563 595 mm
Iris-to-iris length 869 1059 mm
Cavity length 1052 1224 mm
Reference length 699 852 mm
Aperture diameter at spoke 50 50 mm
Page 111
Cavity properties
RF properties 325 MHz,
β0 = 0.82
Low Ep,Bp
325 MHz,
β0 = 1.0
High R
352MHz,
β0 = 0.82
Low Ep,Bp
352 MHz,
β0 = 1.0
High R
Units
Energy gain at β0 757 922 699 852 kV
R/Q 625 744 630 754 Ω
QRs 168 195 169 193 Ω
(R/Q)*QRs 1.05x105 1.45x105 1.07x105 1.46x105 Ω2
Ep/Eacc 2.6 2.8 2.7 2.75 -
Bp/Eacc 4.97 5.6 4.9 5.82 mT/(MV/m)
Bp/Ep 1.9 2.0 1.8 2.12 mT/(MV/m)
Energy Content 0.45 0.56 0.35 0.43 J
Power Dissipation* 0.37* 0.43* 0.33** 0.36** W
At Eacc = 1 MV/m and reference length β0λ
*Rs = 68 nΩ
**Rs = 73 nΩ
Page 112
Mode types in two-spoke cavities
Accelerating
modes Deflecting
(degenerate)
modes
Longitudinal position along beam axis (mm)
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
Ma
gn
eti
c f
ield
(A
/m)
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Hz(z) - M18
TE-type
modes
Longitudinal position along beam axis (mm)
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
Ele
ctr
ic f
ield
(V
/m)
-6e+5
-4e+5
-2e+5
0
2e+5
4e+5
6e+5
8e+5
Ez(z) - M47
Ex(z) - M47
Ey(z) - M47
Hybrid
modes
Examples of modes
for the 325 MHz
cavity, b=1
C. Hopper, R. Olave, ODU
Page 113
R/Q values of HOMs
(R/Q) values for particles at design velocities
b0=1 and b0=0.82 for the 325 MHz two-spoke cavity
All HOMs have (R/Q)s significantly smaller
values than the fundamental mode C. Hopper, R. Olave, ODU
Page 114
Excitation of modes by a single bunch
Single Gaussian bunch, on-axis, σ = 1 cm
(bunch couples only to accelerating modes)
C. Hopper, ODU
ACE3P
F. Krawczyk, LANL
MAFIA
Page 115
Multipoles
Nonlinearities of field, 500 MHz cavity, racetrack spokes(symmetric tet [quarter] mesh)
x, y offset (mm)
-20 -10 0 10 20
Vtr
an
svers
e / V
ac
c
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
x offset vs Normalized Vx
y offset vs Normalized Vy
Nonlinearities of field, 500 MHz cavity, ring-shaped spokes(symmetric tet [quarter] mesh)
x, y offset
-20 -10 0 10 20
Vtr
an
svers
e / V
ac
c
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
x offset vs Normalized Vx
y offset vs Normalized Vy
500 MHz, β = 1
R. Olave, ODU
Page 116
Surviving MP after 40 RF periods
Prediction of multipacting (MP) level
1: 0.4-2.9 MV
5: 5-9 MV 4: 2.7-
4.6 MV
2: 0.5-2.6
MV
3: 0.6-4.1 MV
• No stable MP with impact energy between 60 to 1000 eV
• 0.5 – 4 MV and 5 – 9 MV is likely to have MP in the first high power RF test
• Some field levels are especially dangerous when the surface is not clean:
• 1.4 – 1.7 MV and 2.3 – 2.9 MV in zone 1
• 1.5 MV, and 2.4 – 2.6 MV in zone 2
• 1.4 – 2.2 MV and 2.8 – 4.1 MV in zone 3
• 6 – 7 MV in zone 4
• Plasma cleaning may be used to process away the MP
352 MHz, β=1
Feisi He, JLab
Page 117
Multipacting
325 MHz, β=0.82
ACE3P
C. Hopper, ODU
Page 118
Multipacting
700 MHz, β=1
ACE3P
R. Olave, ODU
Page 119
700 MHz, β=1, double-spoke
Collaboration between Niowave, ODU, Los Alamos, NPS
Designed By ODU
Fabricated by Niowave
Page 120
Parting Words
In the last 30+ years, the development of low and medium b
superconducting cavities has been one of the richest and
most imaginative area of srf
The field has been in perpetual evolution and progress
New geometries are constantly being developed
The final word has not been said
The parameter, tradeoff, and option space available to the
designer is large
The design process is not, and probably will never be, reduced to a
few simple rules or recipes
There will always be ample opportunities for imagination, originality,
and common sense