FFAG
Hardware development for
EMMA
Electron Model with Many Applications
Electron Model with Muon Applications
C. Johnstone, Fermilab
NuFact05
INFN, Frascotti, Italy
June 21-26, 2005
FFAG
Design Information
• Background
– Scaling vs. nonscaling
• Ring components
– Rf
– magnets
• Diagnostics
– BPMs
– OTRs
– Single Wire Scanners
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Scaling
As a function of momentum
 Parallel orbits
 Constant optical properties
 Orbit change, r, linear
As a function of momentum
 Nonparallel orbits
 Varying optics
 resonance crossing
 Orbit change ~quadratic
 Smaller aperture requirements
 Simple magnets
vs. Linear Non-Scaling
  min
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Optical layouts of FFAGs
• Scaling and nonscaling lattices can have identical optical structures
– FODO
– Doublet
– Triplet
• The important difference is in the
TOF vs. p, which is of particular
importance for the linear non-scaling
lattice: the FODO is 1.5 x (T1 + T2)
as compared with the triplet (lower
T implies less phase slip, more
turns for fixed, high frequency rf)
Rf drifts
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Momentum Compaction of Orbits
• Momentum Compaction, 
– Measure of orbit similarity as a function of momentum (also
isochronicity for relativistic beams)
– Measure of the compactness of orbits -   0, aperture  0
C
p
  ring
C
p
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Momentum compaction in scaling FFAGs
• Scaling FFAGs:
p
C  r  
( is a constant)
p
• Pathlength or TOF always increases with p
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Momentum compaction in linear nonscaling
FFAGs
• Linear non-scaling FFAGs:
p0
cell
p
where p0 is a reference orbit defined as the 0 - gradient point -
F  cell 
CF magnet is a pure dipole, 0 - field point in F quad.
p  po ;  F  0
reverse bend at low energy
p  po ;  F  0
added bend at high energy
0.3
F 
B' lr
B' l are technical choices
p
r  pF  cell ( p  p0 )
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Cont….
F
l
• But, the transverse excursion cannot be ignored at low energy
rt  l  l   l
2
2
2
F
rt  l (1   )  l  l
2
F
• Eventually this transverse correction
overtakes the net decrease with low
momentum and C turns around
giving an approximate quadratic
dependence of C and TOF.
2
F
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What does this mean?
• Scaling FFAG can have only 1 fixed point, or orbit with is synchronous
with the rf (fixed points are “turning” points in the phase slip relative to
the rf waveform)
– 1 turning point implies the beam slips back and forth across the rf crest
twice
• Linear nonscaling FFAG can have 2 fixed points (or 1)
– Beam can optimally cross the rf crest 3 times
• By using two fixed points for maximal acceleration,
the ratio of extraction energy can be ~3:2
for nonscaling vs. scaling FFAGs
Fixed points
FFAG
Electron Model - Non-scaling Demonstration of New
Accelerator Physics
Momentum Compaction
Unprecedented compaction of momentum into a small aperture.
Gutter Acceleration
asynchronous acceleration within a
rotation manifold outside the rf bucket.
“Uncorrectable” Resonance Crossing
Rapid crossing of many resonances
including integer and ½ integer; multiresonance crossings in a single turn
Evolution of phase space
Under resonance conditions and gutter acceleration
Validate concept for muon acceleration
Characterize and optimize the complex parameter space for rapid
muon accelerators
FFAG
Electron Model - Construction
– similar to the KEK ATF without straight sections (scaled down from
1.5 GeV to 20 MeV). Host: Daresbury Laboratory U.K. downstream of
their 8-35 MeV Energy Recovery Linac Prototype (ERLP) of the 4th
Generation Light Source (4GLS).
6m
6m
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Radiofrequency system
Where possible adopt designs already existing at the host laboratory.
Adopt 1.3 GHz ELBE buncher cavity to be
used at Daresbury 4GLS
1.3 GHz preferred over 3 GHz:
reducing RF while magnet length
is fixed, implies magnets become
a smaller number of RF
wavelengths. This implies smaller
phase slip and more turns.
Frequency variation of few 10-4
to investigate 1 or 2 fixed points
operation.
Adopt TESLA-style linear RF
distribution scheme to reduce
number of waveguides
R=1M,
Q=1.4104
20 cm straight for installation
FFAG
Quadrupole Magnet
Fermilab Linac quad
General
requirements:
•Gradient: 7 T/m
•Slot length: 10 cm
•Aperture: 40 mm
wide, 25 mm high
•Rep rate <1Hz
The 5cm-long upgrade Fermilab linac quadrupole has peak pole-tip field
near 3.5 kG, and the bore is 5cm. This is ideal for the 3 cm orbit swing
envisioned for the ring. The gradient is stronger than required and will
likely require a different coil.
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Combined function magnet
Specifications
Dipole component of 0.15 – 0.2 T
Slot length: 10 cm
Magnetic length: 7cm
Quad component of ~4T/m
Magnet spacing: 5 cm
Aperture (good field): 50 mm wide, 25 mm high
Field uniformity  1% at pole tip
Space for internal BPM
1Hz operation or less
No cooling
No eddy current problems
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Dipole only field lines
Magnet Concept
(Vladimir Kashikhin,
FNAL)
Power
Dipole plus quad field lines
the dipole
component with permanent
magnets
Compact
No power issues
Thermally stable PM
material
Power the quadrupole
component with a
(modified) Panofsky coil
Compatible with
rectangular aperture
Relatively short ends
Permanent quad +
trim coil ±20%
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Advantage of variable quad and dipole fields?
• Variable quad was felt to be most important for phase advance and
resonance crossing controol
• Variable dipole allows exploration of acceleration with 1 fixed point
(1/2 synchrotron oscillation around “bucket”) or 2 (gutter acceleration
– Measure phase space and emittance dilution
• Both: different C /TOF parabolas
– Asymmetric vs. symmetric
– Correct for errors/end field
Potential
Fixed points
FFAG
CF magnet with independently variable
dipole and quad fields
FFAG Combined Function Magnet
V.S.Kashikhin, June 21, 2005
The proposed combined function magnet has C-type iron yoke and separate
dipole and quadrupole windings. Each winding powered from individual power
supply. They can be connected in series in accelerator ring. Dipole component
of magnetic field formed by parallel surfaces of iron poles. Quadrupole field
component formed by sectional quadrupole winding placed into the pole slots.
Such configuration provides independent regulation both field components.
Magnet parameters
Magnet configuration
Dipole field
Adjustable quadrupole gradient
Dipole winding ampere-turns
Quadrupole pole winding ampere-turns
Magnet body length
C- type
0.15 T
0 – 6.8 T/m
7600 A
11638 A
50 mm
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2D modeling of new CF magnet
Flux lines at maximum dipole and quadrupole currents. Dipole coil (blue),
Quadrupole (red).
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Diagnostics
• Diagnostic designs described here
– BPMs
• bunch train/single bunch operation
• Turn by turn data
– OTRs (Optical Transition Radiation)
• Foils + detection
• 108/bunch or lower for a bunch train
• 109/bunch for single bunch operation – will require closer
examination for 108/bunch, single bunch operation
• Other diagnostics
– Single Wire Scanners
• orbits are non-overlapping,
• step increment microns
– Pepperpot
• phase space measurements in extraction line
FFAG
BPM (Jim Crisp, FNAL)
BPM Specification - General
1.3GHz
button-type BPMs
(FNAL Main Injector)
1 set per magnet
3 to 5 cm aperture
20 micron resolution
 Internal mounting
Turn by turn for ~10 turns
109 electrons/bunch
~66 nsec rotation period
Hardware and Single Bunch
Operation
Digital receiver
210 MHz adc sample rate
12 bit resolution
 Single-bunch excitation of a
filter as shown
105 MHz center frequency
10 MHz bandwidth
Filters must be stable and
matched
adc must be synched to beam
1
0.5
0
-0.5
-1
FNAL MI BPM
0
20
40
60
80
100
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EXAMPLE: Profiles from an OTR foil in the 120 GeV AP-1
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proton line at Fermilab
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FFAG
Beam Profile Diagnostics for the Fermilab
Medium Energy Electron Cooler
Abstract—The Fermilab Recycler ring will employ an electron cooler
to store and cool 8.9-GeV antiprotons. The cooler will be based on a
Pelletron electrostatic accelerator working in an energy-recovery
regime. Several techniques for determining the characteristics of the
beam dynamics are being investigated. Beam profiles have been
measured as a function of the beam line optics at the energy of 3.5MeV in the current range of 10-4-1A, with a pulse duration of 2µs.
The profiles were measured using optical transition radiation
produced at the interface of a 250µm aluminum foil and also from
YAG crystal luminescence.
I=0.975 A, F=-4 kV. Horizont. profiles
80
SPA05=0 A
SPA05=9 A
SPA05=11 A
I(x), rel. units
60
SPA05=14 A
40
20
10.12 mm
Marks on the OTR
0
15
20
25
30
35
40
45
X, mm
. 3-D image of the electron beam obtained with
OTR monitor
Variation of the beam X-profile versus SPA05
lens current
FFAG
Electron Model - Demonstrates:
Unprecedented compaction of momentum
Asynchronous 2-fixed pt. gutter Acceleration
Resonance Crossing
Evolution of phase space and
comparison with simulation
Validate concept for muon acceleration
FFAG
Electron Model - Hardware and Measurements:
Magnetic components designed or under design; short: 5-6
cm and strengths appear technically reasonable
Full Complement of Diagnostics designed or available including
- Large aperture BPMs, OTR foils and detectors
- Single Wire Scanners, Pepperpots
Measure:
-orbits, orbit stability, injection stability
- probe injection phase space with a pencil beam
- tolerances : field, injection, contributions of end fields
-Evolution of phase space and comparison with simulation
under different conditions of acceleration and resonance
crossing
- optimization and operational stability of accelerator
conditions