High gradient Superconducting Cavity
Development for FFAGs
Sergey V. Kutsaev, Zachary A. Conway, Peter N. Ostroumov
C. Johnstone and R. Ford
Cyclotrons’13
September 23, 2013
Vancouver, BC, Canada
FFAG is typically configured to accelerate a large
momentum admittance within a modest magnet
aperture.
1 GeV CW FFAG for C Therapy
C. Johnstone – Trinity College, 2011
3 to 10 GeV muon double beam FFAG
T. Planche - Nufact09
They are brilliant designs, as long as you don’t want too much beam current…
FFAG13 TRIUMF
P. McIntyre, FFAG13
Confusion about the new breed of nonlinear nsFFAGs with constant tune
(above and PAMELA, for example) and EMMA (swept tune)
2
Advanced design and simulation of an
Isochronous 250-1000 MeV Nonscaling FFAG
2m
v
DRad
3.0
0.07
2.5
0.06
cA
5.0
4.5
C
4.0
3.5
cD
E
F
3.0
2.5
cC
B
cE
D
G
cF H
cG
cH
0.5 1.0 1.5 2.0 2.5 3.0 3.5
0.05
2.0
cB
A
A 1. ,4.88616
B 2.674 ,4.20703
C 3.03267 ,3.85867
D 3.43662 ,3.43662
E 1. ,3.2672
F 2.00856 ,2.8764
G 2.2306 ,2.67393
H 2.45023 ,2.45023
0.04
1.5
0.03
0.02
1.0
0.01
cA 1. ,5.37477
cB 3.25798 ,5.37477
cC 3.31087 ,4.2696
cD 3.79024 ,3.79024
cE 1. ,2.58876
cF 1.86471 ,2.58876
cG 2.03113 ,2.37929
cH 2.20521 ,2.20521
P, MeV c
800
1000
1200
Cell  x / y (2 rad)
Ring.
Field F/D (T)
Magnet Size F/D Inj
•
250 MeV
3.419
0.380/0.237
1.520/0.948
1.62/-0.14
1.17/0.38
P, MeV c
1600
1000
1400
1600
5.0
585 MeV
4.307
1000 MeV
5.030
0.400/0.149
1.600/0.596
0.383/0.242
1.532/0.968
2.06/-0.31
2.35/-0.42
1.59/0.79
1.94/1.14
4.5
4.0
P , MeV c
1000
1200
1400
1600
Clockwise: Matematica: Ring tune, deviation from
isochronous orbit (%), and radius vs. momentum
Comments and further work
–
–
1200
Ravg
General Parameters of an initial 0. 250 – 1 GeV non-scaling, nearisochronous FFAG lattice design
Parameter
Avg. Radius (m)
1400
Tracking results indicate ~50-100 mm-mr; relatively insensitive to errors
Low losses
FFAG cavity
May 13, 2013
4
F-D quads control betatron motion
Uniform gradient in each channel: excellent linear dynamics.
5.5
5.0
4.5
4.0
0.0
0.5
1.0
1.5
2.0
2.5
We can lock x, y to any desired operating point.
BTC quads are tuned in 2 x 5 families.
Sextupole correctors at exit of each BTC are tuned
in 2 x 6 families.
First 2 turns each have dedicated families so that
they can be tuned first for rational commissioning.
FFAG13 TRIUMF
P. McIntyre, FFAG13, “ Strong-focusing cyclotron”
5
Now look at effects of synchrobetatron and
space charge with 10 mA at extraction:
Move tunes near integer fraction resonances to observe growth of islands
After two turns … bunch is lost by 20 MeV
1/3 order integer effect
1/5 order integer effect
1/5-order islands stay clumped, 1/3-order islands are being driven. Likely driving
term is edge fields of sectors (6-fold sector geometry). We are evaluating use of
sextupoles at sector edges to suppress growth.
FFAG13 TRIUMF
6
Synchrobetatron/space charge in longitudinal
phase space:
Tunes again moved to approach resonances, but retaining transmission through lattice
Injection
extraction
Phase width grows x5 at extraction
FFAG13 TRIUMF
7
Simulations of a proton FFAG with space
charge
FFAG’12, Osaka, Japan
14/11/2012
Dr. Suzie Sheehy, ASTeC/STFC
8
Overview
 Motivation
 4-cell 1GeV FFAG
– Single energy simulations
– Serpentine acceleration with SC
 6-cell 1GeV FFAG simulations
– Single energy simulations
– Serpentine acceleration with SC
 Two discussion points:
– Cost to build an FFAG vs linac
– Terminology
 Summary
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
9
4-cell Lattice design
F
Total tune variation = 0.12 (H) / 0.56 (V)
D
C. Johnstone et al, AIP conference proceedings 1299,
1, 682-687 (2010)
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
10
Serpentine channel acceleration



Using Carol’s 4-cell 1 GeV FFAG ring
330MeV-1GeV
Serpentine acceleration is possible due to 3%
time of flight variation
Using single particle tracking:
10 MV/turn
12 MV/turn
15 MV/turn
From
Dr. Suzie Sheehy, ASTeC/STFC
IPAC’11, S. L. Sheehy, WEPS088
14/11/2012
11
Setting up the simulation in OPAL
 Beam matching at 300 MeV
 Single energy tracking at realistic
intensities shows no emittance
growth.
 At very high intensities emittance
grows, as expected.
– (See HB2012 MOP258)
Dr. Suzie Sheehy, ASTeC/STFC
Single bunch
10 π mm mrad in horiz/vertical
Length ~ 4% of ring circumference
50 turns at 300 MeV with no acceleration
Current is average of full turn
14/11/2012
12
Setting up the simulation
Harmonic number = 1 (for now)
Space charge ‘off’ – track bunch of 2000 particles with parabolic profile
Energy (MeV)
•
•
Cavity phase (deg)
Issue: OPAL outputs after set num of tracking steps NOT azimuthal position ie. not a full ‘turn’
if not perfectly on phase! In the newer version of OPAL (1.1.9) I can use ‘probe’ element to
get ‘screen-like’ physical position readout (in process of updating on SCARF).
For now – the following simulations were run overnight on my quad core desktop!
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
13
Turn-by-turn orbit with bunch
Try a short & small 1 π mm mrad beam to see what happens
Using ‘probe’ element to get turn-by-turn at 0 degree position, 200 particles
Momentum [βγ]
•
•
Acceleration!
With VRF/turn= 22 MV
Dr. Suzie Sheehy, ASTeC/STFC
X Position [mm]
14/11/2012
14
With space charge ‘on’
• 1 pi mm mrad bunch
• Tracked for 30 turns in
serpentine channel
• Vary (average) beam current
up to 10 mA
• 10 MW beam at 1 GeV
• NOTE: VERY SHORT BEAM!
• Total beam length approx.
1cm so peak current = 22A!
• Lots of space charge!!
Acceleration with 3 cavities
VRF/turn= 22 MV
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
15
ΔE [MeV]
Longitudinal evolution
1
15
2
20
5
10
28
25
Δt [ns]
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
16
Δx [mm]
Horizontal pos vs time
1
2
5
10
15
20
25
26
Δt [ns]
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
17
Δz [mm]
Vertical pos vs time
1
2
5
10
15
20
25
26
Δt [ns]
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
18
(NB as discussed
before these are per
‘turn’ wrt time so not
‘real’ turns)
Emittance evolution
NOTE DIFFERENT SCALES!!
300 MeV – 30 turn serp. Accel.
300 MeV – no acceleration
horizontal
Question: why does
vertical emit grow even
with no space charge?
vertical
longitudinal
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
19
6-cell 1GeV Ring
 Initially I had issues modeling this ring as short magnets were not wellreproduced with the interpolation in OPAL
 I now have a much finer field map! (thanks to K. Makino)
 The main driver behind this design was to achieve better isochronicity but
the vertical tune variation also improved.
• Total tune variation = 0.42 (H) / 0.234 (V)
• Lower B field (cf 2.35T in 4-cell design)
• Larger radius
Dr. Suzie Sheehy, ASTeC/STFC
Field profiles from C. Johnstone, IPAC’12, THPPR063
14/11/2012
20
Single energy with space charge
• No acceleration, 10 pi beam
• 50 turns with space charge
• Short beam (0.04% ring)
• No acceleration, 10 pi beam
• 50 turns with space charge
• Longer beam (4% ring)
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
21
Serpentine channel
 Much smaller TOF variation than 4-cell
version
 Required RF frequency & energy gain
per turn to open up the serpentine
channel (δE) can be estimated by
4MV/turn !
total energy gain required is ΔE and ω =2πFRF
In this case, we expect δE ~ 3.7 MV/turn.
(A few quick simulations confirm this)
If we make it ‘isochronous enough’, perhaps we can use the
serpentine channel without superconducting cavities?
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
22
Acceleration & space charge
 Use ‘reasonable’ 8MV/turn (equiv. 4 PSI-type cavities)
 Beam matched at 330 MeV
 Same emittance & length beam as in 6-cell simulations
Dr. Suzie Sheehy, ASTeC/STFC
14/11/2012
23
Outline
 Motivation and Background
• Next generation ultra-compact, high-energy fixed field accelerators
• Medical, security, energy applications
• CW FFAGs ; i.e. strong-focusing cyclotrons
–
–
–
–
Relativistic energies: ~200 MeV – 1 GeV
Ultra-compact
Constant machine tunes (optimized gradients)
High mA currents (low losses)
 These machines require high gradient acceleration; SCRF
required for
• Compactness
• Low extraction losses
– Large horizontal aperture of the FFAG, like the cyclotron, is a
challenging problem for SCRF design
FFAG cavity
September 16, 2013
24
NEXT-generation CW high-energy Fixed-field
Compact Accelerators




Reverse gradient required for vertical envelope
Isochronous or CW (serpentine channel relaxes tolerances)
Stable tune, large energy range
The footprint of CW FFAG accelerators is decreasing rapidly
v
3.0
2.5
2.0
1.5
1.0
P, MeV c
800
1000
1200
1400
1600
Machine tunes:
r ~1.4
z ~0.8 – factor of ~4
> than compact cyclotron
September 16, 2013
MAGNETS and modeling
Parameter
Units
Number of magnets
6
Number of SC coils
12
Peak magnetic field on coils
T
7
Magnet Beam Pipe gap
mm
50
Superconductor type
NbTi
<3m
Operating Temperature
K
Superconducting cable
<5m
Value
4.0
Rutherford
Coil ampere-turns
MA
3.0
Magnet system height
M
~1
Total Weight
tons
~10
One straight section occupied by RF cavities and injection/extraction in the other
FFAG Horizontal / Vertical Stable beam area @200 MeV
cyclotron
80 mm x 293 mr
H = 23,440π mm-mr
norm = 16,059π mm-mr
FFAG Horizontal Stable beam area @1000 MeV vs. DA of
800 MeV Daealus cyclotron*
cyclotron
10 mm x 9 mr
V = 90π mm-mr
norm =62π mm-mr
Tracked: 130 mm x 165 mr
 = 21450π mm-mr
norm = 38820π mm-mr
Tracking: Horizontal – 1 cm steps, Vertical – 1 mm steps
F. Meot, et. al., Proc. IPAC2012
*FFAG vert. stable area at aperture limits.
September 16, 2013
26
Acceleration Gradient required for low-loss
extraction
Reference radius in center of straight for the energy orbits preceding extraction. For an
accelerating gradient of ~20 MV/m orbits are sufficiently separated for a “clean” (beam
size: 1.14 cm; =10 mm-mr normalized) or low-loss extraction through a septum magnet.
Kinetic Energy
(MeV)
Acc Gradient
per turn
(MV)
800
r
RS
Radius @center of
straight
(m)
1.1955
(cm)
785
15
1.1879
0.76
775
25
1.1816
1.39
765
35
1.1751
2.04
For 20 MV/turn, and a 2m straight section, we require 10 MV/m – implies a SCRF
cryomodule – in order to achieve extraction with manageable shielding, radiation levels,
and activation. This requirement drove the design of the high-energy stage.
Design specifications
 Large horizontal beam aperture of 50 cm
 Cavity should operate at 150 or 200 MHz (harmonic of the
revolution frequency)
 Should provide at least 5 MV for proton beam with energies
200 – 900 MeV
 Peak magnetic field should be no more than 160 mT
(preferably, 120 mT or less)
 Peak electric field should be minimized
 Cavity dimensions should be minimized
FFAG cavity
September 16, 2013
28
Cavity options
 Half-wave resonator
H-Resonators
Beam
trajectories
HWR is very dependent on particle velocity
Can’t be used efficiently for such a wide range
of particle energies
Dimensions are very large as is peak magnetic
field on the electrode edge
FFAG cavity
May 13, 2013
29
Rectangular Cavity
 Rectangular cavity operating at H101 mode has electric field
concentrated in the center of the wall
 To concentrate electric field at beam aperture, we introduced
tapers
 To reduce peak magnetic field the blending was introduced
Beam
direction
W
H
L
FFAG cavity
May 13, 2013
30
Gap and Frequency Optimization
 The voltage at 160 mT maximum field dependence on gap
length was calculated for cavities with different frequencies
and lengths
Beam Energy = 200 MeV
Voltage in the center of the aperture
Peak magnetic field = 160 mT
150 MHz 1.5 m structure has a potentially higher possible voltage or lower peak
magnetic field at 5 MV
200 MHz structure is more compact
FFAG cavity
May 13, 2013
31
Cavity shape optimization
 A taper was introduced to distribute the
magnetic field over a larger volume keeping
the electric field concentrated around the
beam aperture
 Such a cavity design has smaller dimensions for
the same volume
 All edges were rounded and improved
reentrant nose shape reduced the peak
magnetic field by more than 15% and the
transverse dimensions by more than 10 cm
 Final study was an elliptical cell shape where
the magnetic field varies along the cavity wall
such that there are no stable electron
trajectories and multipacting is inhibited
FFAG cavity
May 13, 2013
32
Comparison of different cavity geometries
Parameters of the different cavity designs.
Parameter
Frequency, MHz
Rectangular
top
200
Rectangular
middle
200
Elliptical
bottom
200
Length, cm
100
100
120
Height, cm
104.5
92.9
142
Voltage (β=0.56, edge), MV
4.67
4.66
4.68
Voltage (β=0.78, center) , MV
6.72
6.71
6.89
Voltage (β=0.86, edge) , MV
5.00
5.00
5.00
R/Q (β=0.86, edge), Ohms
82.8
89.7
75.0
G, Ohms
147.9
150.2
134.2
Peak magnetic field, mT
92.1
72.7
77.2
Peak electric field, MV/m
55.2
47.0
48.1
The RF performance degrades at higher frequencies.

Rectangular cavity is better than elliptical by all parameters except multipactor resistivity
FFAG cavity
May 13, 2013
33
RF input coupler design
 As 1 mA beam is accelerated by 4 cavities from 200 to 900
MeV, each cavity requires about 175 kW of power
 One of the options is to attach 2 100kW couplers to the
cavity
80K
126K
4K
300K
133K
Heat Flows:
To 4K = 9.8W
To 60K = 92.0W
From 300K = 18.8W
ANSYS estimations show no significant overheating
FFAG cavity
May 13, 2013
34
Magnetic power coupling and mechanical design
 External Q-factor should be ~ 1.9*106
 Preliminary results predict ~1.1mm Nb and ~0.6mm SS
deformation at magnetic field area
The complete mechanical design:
1 – niobium shell, 2 – RF ports, 3- extra ports,
4 – frequency tuning, 5 – steel jacket, 6 – rails
FFAG cavity
35
Summary
 Two options of 200 MHz cavities were studied: "rectangular"
and " elliptical". The "elliptical" option has been introduced to
avoid multipacting (MP) problem. The latter can be problem
for rectangular cavity
 However, the rectangular option provides better parameters
(peak fields, dimensions etc)
 100 kW RF coupler has been designed. More studies are
needed to minimize cryogenic load.
 Initial mechanical design was created and structural analysis
has been performed. Both cavities can be made structurally
stable.
FFAG cavity
May 13, 2013
36