Download Ultra-compact CW racetrack nsFFAGs - FFAG`13

Dr. C. Johnstone, Fermilab
FFAG13
13th International Workshop on
FFAGs
TRIUMF
Sept 21 2013
Vancouver, Canada

Motivation and Background
 Next generation ultra-compact, high-energy fixed field
accelerators
 Medical, security, energy applications
 CW FFAGs ; i.e. strong-focusing cyclotrons
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Relativistic energies: ~200 MeV – 1 GeV
Ultra-compact
Constant machine tunes (optimized gradients)
High mA currents (low losses)
These machines require high gradient acceleration;
and SCRF for high currents
 Compactness
 Low extraction losses

Large horizontal aperture of the FFAG, like the cyclotron, is a
challenging problem for SCRF design
2
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Cyclotrons are the highest current, most compact
solution, but only up ~200 MeV for protons
As the energy becomes relativistic, orbit separation
becomes smaller and smaller for CW operation
Higher energies require separated sectors (like the 590MeV PSI or 500-MeV TRIUMF machines) – in order to
insert strong accelerating (RF) systems.



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Stronger acceleration is required to minimize beam losses and
radioactivity particularly during beam extraction
Fewer acceleration turns and larger between different
acceleration orbits facilitate efficient extraction.
However, once space is inserted between the magnetic
sectors of the cyclotron, the footprint grows rapidly.
At relativistic energies, above 200 MeV, cyclotrons do
not scale. Field profile must be nonlinear at relativistic
energies for CW operation

One of the most important indicators of stability is called machine
tune; the no. of oscillations a particle makes about the energy-specific
reference orbit in one translation around the ring
Begin position  end


DA problems occur when the tune is an integer or fraction of an
integer (units of 2 rad) because particles retrace through
nonlinearities and imperfections
Begin position = end
The tune in a cyclotron must vary as it enters relativistic energies.
A gradient must be imposed to keep the beam CW
Predicted tune from an ultracompact medical cyclotron(left) and ZGOUBI (middle)
and COSY (right).. Predicted problems are marked with red arrows
A Fixed Field Alternating Gradient Accelerator is a ~ a
cyclotron with strong synchrotron-like focusing
•
The ns-FFAG combines all forms of transverse beam (envelope)
confinement in an arbitrary, optimized magnet field:
–
For the horizontal, the three terms are
synchrotron


1/ f F  kF l 

F F
cyclotron
with  is the sector bend angle,  the edge angle (edge angle is assume small
so tangent is approximat ed), length, l , is the F half - magnet length and
k F is the " local" gradient for an arbitrary order field.
–
The power of the FFAG is that the confinement terms can be varied independently
to optimize machine parameters such as footprint, aperture, and tune in a FFAG
AND DC beam can be supported to very high energies
Simplest Dynamical Definition:

FFAG is ~ a cyclotron with a gradient; beam confinement is via:

Strong alternating-gradient (AG) focusing, both planes: radial sector FFAG


normal/reversed gradients alternate (like a synchrotron)
Gradient focusing in horizontal, edge focusing in vertical: spiral sector FFAG


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vertical envelope control is through edge focusing (like a cyclotron)
the normal gradient increases edge focusing with radius /momentum (unlike a cyclotron)
A cyclotron can be considered the lowest-order FFAG

Types of FFAGs:

Scaling:


B field follows a scaling law as a function of radius - rk (k a constant;) presentday scaling FFAGs: Y. Mori, Kyoto University Research Reactor Institute
Nonscaling:



Linear (quadrupole) gradient; beam parameters generally vary with energy
(EMMA FFAG, Daresbury Laboratory, first nonscaling FFAG)
Nonlinear-gradient; beam parameters such as machine tune can be fixed (as in
a synchrotron)
FFAGs and their Variations
Scaling FFAGs (spiral or
radial-sector) are characterized
by geometrically similar orbits
of increasing radius, imposing
a constant tune (field and
derivative gradient scale
identically with r). Magnetic
field follows the law B  rk,
with r as the radius, and k as
the constant field index.
Spiral Sector: example: more
compact; positive bend field
only. Vertical focusing controlled
by edge crossing angle.
Field expansion: k determines multipole order;
Comments: the lower the k value, the more slowly field increases
with r and the larger the horizontal aperture, but the more linear
the field composition and dynamics.
F
Radial Sector: example: This is a
triplet DFD cell; there are also
FDF, FODO and doublets. In a
radial sector the D is the negative
of the F field profile, but shorter.
Linear nonscaling FFAGs
for rapid acceleration
Linear-field, nonscaling FFAGs.
Ultra-compact magnet aperture,
proposed and developed for High
Energy Physics (Neutrino
Factories and Muon Colliders),
relaxes optical parameters and
aims only for stable acceleration.
In general they are not suitable
for an accelerator with a modest
acceleration system and
accelerate only over a factor of 23 range in momentum.
EMMA – world’s first nonscaling
FFAG, @Daresbury Laboratory,
commissioning, late December, ‘09
Extraction
reference orbit
D
Injection
reference
orbit
Cartoon of orbit compaction: nonsimilar orbits,
nonconstant tune, resonance crossing
Characteristics– tune sweep/unit cell, parabolic pathlength on
momentum (small radial apertures); serpentine (rapid)
acceleration – beam “phase-slips”, crossing the peak 3 times,
accelerating between rf buckets
Linear-fields, constant gradient F and D magnets
Magnets are shaped with a linear edge contour with only tune
constrained
Dramatic improvement in tune stability – to over a factor of 6 in
Cells Tunes for 30-400 MeV Tune-stablized FFAG
30-400 MeV Linear-field "Muon" Accelerator
momentum



0.4
0.4
0.35
EMMA –like machine
tune/cell
0.3
0.25
Slow acceleration
0.3
nux/cell
nuy/cell
tune/cell
0.35
0.2
0.15
0.25
0.2
0.15
nux/cell-model
nuy/cell-model
nux/cell-approx
nuy/cell-approx
0.1
0.1
0.05
0.05
0
0
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
Momentum (GeV/c)
0.8
1
Momentum (GeV/c)
Control of tune variations in a nonscaling FFAG with a constant gradient
NEXT STEP IS NONLINEAR FIELD VARIATIONS REQUIRED FOR:
MORE CONSTANT TUNE, LESS RF AND ISOCHRONOUS OR CW OPERATION


Apply a “synchrotron” strong-focusing field profile to each “cyclotron”
orbit
Strong-focusing allows

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Long injection/extraction or synchrotron-like straights
Strong RF acceleration modules
Low –loss profile of the synchrotron
DC beam to high energies in compact structure
 400 MeV/nucleon: charge to mass of ½ (carbon)
 1.2 GeV protons

Avoidance of unstable beam regions

constant machine tune
straight
=
 or normalized path length
NS FFAG can maintain isochronous orbits at relativistic energies

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Pathlength of isochronous orbits are proportional to velocity
Orbits as a function of momentum follow, therefore the B field must scale
with velocity
At relativistic energies, momentum is an increasingly nonlinear function
of velocity; therefore B field transitions from a linear slope to nonlinear,
non-relativistic to relativistic as an approximate function of radius.
THIS HAS BEEN ACHIEVED IN RECENT NONLINEAR NS FFAG DESIGNS
Nonlinear field expansion + edge angle can constrain the tune
Nonlinear gradient provides very strong focusing at high energy in both
3500
planes relative to the cyclotron
FFAG limit
3000
Cyclotron limit
~ 1 GeV protons
P (MeV/c)

<Br>  p/β for isochronous orbits
≥2 GeV protons
2500
2000
1500
1000
500
 or normalized path length
0
0
0.5
1
1.5
1.
Centripetal (Cyclotrons + FFAGs) :

bend plane only, horizontally defocusing or focusing

2.
Edge focusing (Cyclotrons + FFAGs) :

Horizontally focusing / vertically defocusing, vice versa, or no focusing
depending on field at entrance and entrance angle

3.
Strength   (bend angle/bend radius of dipole field component on reference orbit)
Strength  tan  , (or ~  for reasonably small edge-crossing angles)
Gradient focusing (Synchrotrons + FFAGs) :

Body gradient, fields components > dipole:
B= a + bx +cx2 + dx3 + …
B’= b + 2cx + 3dx2 + …



Linear field expansion, constant gradient

Synchrotrons + linear-field nonscaling FFAGs (muon accelerators)
Nonlinear field expansion up to order k, magnitude of gradient increases with r or energy:

Scaling FFAGs
Arbitrary nonlinear field expansion, magnitude of gradient increases with r or energy:

Nonlinear Non-scaling FFAGs
Edge crossing angles are kept deliberately small in large multi-cell synchrotron rings. This term becomes increasingly important for and
causes problems in small synchrotron rings.
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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
Stable, ~identical tunes are maintained
With small straights, extraction and RF modules for high gradient
acceleration are now an issue.
Hard edge
and full fringe
fields

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Incorporate a 1-2 m opposing straight
Refit isochronous orbits and recover stable tunes
Periodicity of 2
Decreases footprint without compromising acceleration and
stability
Most compact design- with SCRF has the dynamics of a RLA
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
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
Supplied OPERA field data
Two approaches:

A highly accurate tracking through a high-order field map
using FACT/COSY
 Field maps are constructed by expressing the azimuthal fields
in Fourier modes and the radial in Gaussians wavelets for
accurate interpolation

Particle tracking in the code ZGOUBI using the OPERA
data directly and linear interpolation
Opera field data plotted in the midplane for one quadrant and showing spiral sectors.
Most accelerator codes provide

too-little flexibility in field
description and are limited to
low order in the dynamics, new
tools were developed for the
study and analysis of FFAG
dynamics based on transfer map
techniques unique to the code
COSY INFINITY.
Arbitrary shapes, field content, contours
HARD EDGE

Various methods of describing
complex fields and components
are now supported including
representation in radiusdependent Fourier modes,
complex magnet edge contours,
as well as the capability to
interject calculated or measured
field data from a magnet design
code or actual components.
FULL FRINGE FIELDS

Most advanced modeling, design, and optimization of
fixed-field accelerators – both FFAGs and cyclotrons 

production runs
advanced optimization
 The lowest order Fourier mode in the cyclotron, for example,
can be re-fit to correct dynamics

Simple user interface allows switching fixed-field
modes and rapid computation

Performance can be optimized and iterated with magnet design
Stable beam area
@injection (200 MeV)
Stable beam area
@500 MeV
Stable beam area
@1000 MeV
Tracked: 24 cm x 240 mr
 = 57,600π mm-mr
norm = 39,460π mm-mr
Tracked: 36 cm x 225 mr
 = 81000π mm-mr
norm = 94,132π mm-mr
Tracked: 39 cm x 150 mr
 = 58,500π mm-mr
norm = 105,824π mm-mr
300 mr
520 mm
Stable horizontal Beam size vs. Energy, tracked in 3cm steps
Stable beam area
@injection (200 MeV)
Stable beam area
@500 MeV
Stable beam area
@1000 MeV
Tracked: 30 mm x 8 mr
 = 240π mm-mr
norm =165π mm-mr
Tracked: 33 mm x 6 mr
 = 198π mm-mr
norm =229π mm-mr
Tracked: 30 mm x 4 mr
 = 120π mm-mr
norm =216π mm-mr
10100
mrmr
40 mm
Stable Vertical Beam size vs. Energy: tracking ends at ±1cm, vertical magnet gap, tracked in 3mm steps
Stable beam area
@injection (200 MeV)
Stable beam area
@500 MeV
Stable beam area
@1000 MeV
Tracked: 8 cm x 293 mr
 = 23440π mm-mr
norm = 16,059π mm-mr
Tracked: 12 cm x 220 mr
 = 26400π mm-mr
norm = 30680π mm-mr
Tracked: 13 cm x 165 mr
 = 21450π mm-mr
norm = 38802π mm-mr
330 mr
180 mm
Stable horizontal Beam size vs. Energy
Stable beam area
@injection (200 MeV)
Stable beam area
@500 MeV
Stable beam area
@1000 MeV
Tracked: 10 mm x 9 mr
 = 90π mm-mr
norm =62π mm-mr
Tracked: 11 mm x 7 mr
 = 77π mm-mr
norm =89π mm-mr
Tracked: 10 mm x 5 mr
 = 50π mm-mr
norm =90π mm-mr
10100
mrmr
15 mm
Stable Vertical Beam size vs. Energy: tracking ends at ±1cm, vertical magnet gap
FFAG Stable beam area @200 MeV vs DA of ultracompact 250 MeV cyclotron
cyclotron
cyclotron
80 mm x 293 mr
10 mm x 9 mr
V = 90π mm-mr
norm =62π mm-mr
H = 23,440π mm-mr
norm = 16,059π mm-mr
FFAG: Horizontal – 1 cm steps
FFAG: Vertical – 1 mm steps
FFAG Stable beam area @1000 MeV vs. DA of 800 MeV Daealus cyclotron*:
factor of 4 larger for ~ a factor of 4 smaller footprint
Tracked: 130 mm x 165 mr
 = 21450π mm-mr
norm = 38820π mm-mr
Tracked: 10 mm x 5 mr
 = 50π mm-mr
norm =90π mm-mr
*FFAG vert. stable area at aperture limits.
*F. Meot, et. al., Proc. IPAC2012
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
<3m
Operating Temperature
NbTi
K
Superconducting cable
<5m
One straight section occupied by RF cavities
and injection/extraction in the other
Value
4.0
Rutherfor
d
Coil ampere-turns
MA
3.0
Magnet system height
M
~1
Total Weight
tons
~10
The magnetic field is relatively flat under the F-pole but the angular field length strongly
depends on the radius providing the needed range from injection to extraction. The
return flux provides the D or reverse gradient but needs careful optimization
21
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.

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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
23

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
24



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
directio
n
W
H
L
FFAG cavity
25

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
26




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
27


As 1 mA beam is accelerated by 4 cavities from
200 to 900 MeV, each cavity requires about 175
kW of power
One of the80K
options is to attach 2 100kW
couplers
126K to the cavity
4K
133K
300K
Heat Flows:
To 4K = 9.8W
To 60K = 92.0W
From 300K = 18.8W
ANSYS estimations show no significant
overheating
28


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
29
1st stage: Cyclotron or FFAG

1st stage

18 – ~250-330 MeV H-
 Fixed or swept-frequency RF, DC beam
 Low intensity for pCT
 Stripping controls extraction energy and
intensity in addition to source modulation
OR

9-~70-90 MeV charge to mass ratio of ½
 Fixed-frequency RF, DC beam for all ions
 Variable energy extraction
 Upstream injector for high-energy ring

2nd stage: 70/90 – 430 MeV/nucleon ions
2nd stage (~4 m x 5-6 m long)



70/90 MeV – 430 MeV/nucleon
Variable energy extraction
Adjustable, fast orbit bump magnets/extraction
septum in long straight
 DC extracted beam
 Variable energy on scale of tens of microseconds
 Investigating extracted energy range
Variable energy selection:
Injection/extraction straight
Heidelberg Ion Therapy Synchrotron


principle collaborators
(PAC/ANL/BNL/RAL/U of Huddersfield)
Proton and Ion Therapy



Can you find the carbon FFAG?
Radioisotope Production

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A 0.33 – 1.2 GeV proton RLA
= 400 MeV/nucleon C6+
Imaging: proton CT (@330 MeV)
<30 MeV FFAGs
Hospital units (PET)
No nuclear waste(Moly99)
Nuclear Waste Transmutation
 At reactor site
 Legacy stockpile
 Accelerator Driven
Subcritical Reactor demo
0.3 - 1 GeV
@10mA
stable
Tracking with space charge
@300 MeV
A linac accelerator for nuclear waste transmutation
MYRHHA Mol, Belgium
PAC’s
FFAG
A FFAG 1 GeV high power accelerator
facility
• The nsFFAG has evolved to an isochronous, high
•
energy, high current application
With constant strong-focusing machine tunes and
optics that are independent of energy
•
•
No resonance crossing
The DA aperture is 10,000 – 100,000 mm-mr depending on
size and tunes
• In the relativistic regime, the FFAG becomes more
compact than the separated sector cyclotron and
more stable if designed properly
•
The racetrack is the most compact
• Large aperture high-gradient cavities including
•
SCRF have been designed
Ironless, self-supported coil SC magnets are also
being developed