Transcript Tune and time of flight - J-PARC

Introduction and overview of FFAG accelerators
S. Machida
CCLRC-ASTeC
7 February, 2006
http://hadron.kek.jp/~machida/doc/nufact/
ffag/machida_20060207.ppt & pdf
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Contents
1.
2.
3.
4.
5.
6.
Cyclotron, synchrotron, and FFAG (11)
Revival (6)
Recent activities (12)
Non-scaling FFAG for muon acceleration (13)
Non-scaling FFAG for other applications (1)
Summary (1)
2
1.
2.
3.
4.
5.
6.
Cyclotron, synchrotron, and FFAG (11)
Revival (6)
Recent activities (12)
Non-scaling FFAG for muon acceleration (13)
Non-scaling FFAG for other applications (1)
Summary (1)
3
Accelerators of medium energy (< GeV)
cyclotron
synchrotron
• In uniform and fixed field, revolution
frequency is constant.
• Cyclotron produces continuous beams,
but fixed energy.
• Magnetic fields increases
synchronized with beam momentum.
• Beams go through a fixed orbit.
Accelerated beams are available only
as a pulse.
• Focusing in longitudinal direction.
Strong focusing in transverse direction.
• Bunch current is limited by
transverse space charge.
• Energy frontier machine.
• No focusing in longitudinal direction.
Weak focusing in transverse direction.
• Bunch current is limited by longitudinal
space charge.
• 590 MeV is maximum.
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Cyclotron, synchrotron, and FFAG
FFAG (Fixed Field Alternating Gradient)
• Fixed field like cyclotron
– No feedback between magnet and RF. Operation is easier.
– Cost of power supply is low.
– Repetition can be higher and make high average current.
• (strong) Focusing in both longitudinal and transverse
direction like synchrotron
– More particles can be accelerated.
– Beam size is smaller and vacuum chamber is smaller.
• Variable energy like synchrotron
– Medium energy machine is usually multi-purpose.
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Cyclotron, synchrotron, and FFAG
strong point
weak point
Comparison
Cyclotron
Synchrotron
FFAG
Field
fixed
varied
fixed
Repetition
continuous
slow pulse
<50Hz
fast pulse
~1kHz
Focusing in
longitudinal
no
yes
yes
Focusing in
transverse
weak
strong
strong
Average
current
medium
low
high? (not
Acceptance
Large? in H
Small in V
Small in H
Small in V
Large in H
Large in V
Energy
fixed
variable
variable
demonstrated)
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Cyclotron, synchrotron, and FFAG
FFAG accelerator
• Invented in early 1950s.
– Ohkawa in Japan, Symon in US, and Kolomenski in USSR.
• Research program at MURA (Midwestern University
Research Associate) in US
– Construction of electron FFAG of 180, 400 keV, and
40 MeV.
– Proposal of 30 GeV proton FFAG
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Cyclotron, synchrotron, and FFAG
Good old days at MURA
Chandrasekhar
400 keV radial sector
40 MeV two beam
accelerator
Bohr
180 keV spiral sector
All are electron
FFAG.
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Cyclotron, synchrotron, and FFAG
How does FFAG work? (field profile)
• Bending radius cannot be constant for all momentum.
However, sharp rise of field makes orbit shift small.
• Focusing force can be constant if the field gradient
increases with radius.
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B
k1 
f

p /e
• Proposed field profile in radial direction is
 r k

Br,   B0  F  
r0 
k >1

Bz(r)
Orbit of
low p
Orbit of
high p
Gradient of
high p
Gradient of
low p
r
Cyclotron, synchrotron, and FFAG
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How does FFAG work? (transverse focusing)
• Alternating gradient can be realized by two ways.
 r k
Br,   B0  F  
r0 
Bz(r)
• F() has alternating sign.
radial sector
r

+

r
• Add edge focusing.
spiral sector

r 
F    F   h ln 
r0 

Bz(r)
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Cyclotron, synchrotron, and FFAG
How does FFAG work?
(radial and spiral sector)
Radial sector consists of
normal and reverse bends.
Spiral sector use edge
to have vertical focusing.

machine center
machine center
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Cyclotron, synchrotron, and FFAG
How does FFAG work? (cardinal conditions)
• Geometrical similarity
  r 
0
 
p r0   const .
r0 : average curvature
r : local curvature

 : generalized azimuth
• Constancy of k at corresponding orbit points
k
r B 
 0 k   
p   const .
B r 
k : index of the magnetic field
 r k
B
r,   B0  F  
r0 
 field
The
satisfies the scaling law.
Tune is constant independent of momentum: scaling FFAG
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
Cyclotron, synchrotron, and FFAG
A way to change output energy
• Change k value by trim coils.
• Low momentum particle will reach the outer
(extraction) orbit with low k.
k
Bz(r)
extraction momentum
with high k. (Bz(r)h*rex)

extraction momentum
with low k. (Bz(r)l*rex)
 r 
Br,   B0  F  
r0 
k (high)

k (low)
r
injection
radius
extraction
radius
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Cyclotron, synchrotron, and FFAG
Three reasons to stop development
Development is stopped in late 1960s because,
1. Magnet design was complicated. It was hard to get
desired 3-D fields profile in practice.
2. No material for RF cavity. It requires high shunt
impedance, high response time, and wide aperture.
3. Synchrotron was more compact and better choice
for accelerator of high energy frontier.
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Cyclotron, synchrotron, and FFAG
1.
2.
3.
4.
5.
6.
Cyclotron, synchrotron, and FFAG (11)
Revival (6)
Recent activities (12)
Non-scaling FFAG for muon acceleration (13)
Non-scaling FFAG for other applications (1)
Summary (1)
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Revival in late 1990s
Technology becomes ready and enough reason to restart development,
1. 3-D calculation code such as TOSCA becomes
available. Static fields can be modeled precisely.
2. RF cavity with Magnetic Alloy (FINEMET as an
example) has most suitable properties for FFAG.
3. Growing demands for fast cycling, large acceptance,
and high intensity in medium energy accelerator
regime.
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revival
Magnet can be made with 3-D modeling code
With an accuracy of 1%, 3-D design
of magnet with complex shape becomes possible.
Spiral shaped magnet for Kyoto-U
FFAG (yoke with blue).
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revival
RF cavity with new material (MA)
mQF remains constant at
high RF magnetic RF (Brf)
more than 2 kG
• Ferrite has larger value at
low field, but drops rapidly.
– RF field gradient is
saturated.
•
Magnetic Alloy also has
• High curie temperature
~570 deg.
• Thin tape (large core can be made)
~18 mm
• Q is small (broadband)
~0.6
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revival
Magnet for large acceptance
• From 1980s’, high intensity machine is demanded,
not only high energy.
• Ordinary AG machine needs large aperture magnet
to accommodate large emittance beam.
Quad of J-PARC 3 GeV synchrotron
Magnet of 150 MeV FFAG
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revival
First proton FFAG at KEK
• With all those new technology, proton FFAG (proof of
principle) was constructed and a beam is accelerated
in June 2000.
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revival
What we achieved from PoP FFAG
• Design procedure.
– FFAG accelerator works as we expected.
– 3-D modeling of magnet is accurate enough.
• 1 ms acceleration (1 kHz operation) is possible.
– MA cavity gives enough voltage.
• Enough acceptance in both longitudinal and
transverse.
• Beam dynamics study
– Multi-bucket acceleration
– Acceleration with fixed frequency RF bucket
– Resonance crossing, preliminary result
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revival
1.
2.
3.
4.
5.
6.
Cyclotron, synchrotron, and FFAG (11)
Revival (6)
Recent activities (12)
Non-scaling FFAG for muon acceleration (13)
Non-scaling FFAG for other applications (1)
Summary (1)
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Three new programs started in Japan
• Hadron therapy prototype
– 150 MeV (initially aimed at 200 MeV)
– Status: Completed.
• Muon phase rotation
– PRISM
– Status: Under construction.
• ADSR (accelerator driven sub-critical reactor)
– Three cascade FFAGs to 150 MeV as a neutron source
– Status: 1st spiral FFAG just starts commissioning.
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Recent activities
Hadron therapy prototype
• 150 MeV, 100 Hz, ~10 nA
• Why FFAG for hadron therapy ?
– Easy operation.
– High average intensity (more dose, more patients per year).
– Spot scanning with high repetition pulses is possible.
– Variable energy and acceleration of many ion species.
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Recent activities
Broad beam method (Conventional) vs.
Spot scanning method
• Inevitable irradiation outside of the treatment field.
• Each patient needs his own shaped bolus.
• A small beam spot makes it possible to irradiate a well defined area.
• Non-uniform irradiation in the area is possible.
Ridge filter
vs.
Bolus
Final
collimator
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Recent activities
Acceleration and extraction
Beam signal during acceleration.
Extraction efficiency is ~60% at the moment. (1.5 nA.)
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Recent activities
PRISM
• Momentum acceptance of +- 30%.
• Central momentum is 68 MeV/c.
• Why FFAG for phase rotation ?
– Large acceptance in longitudinal
and transverse.
– Multiple use of RF cavity.
– Prototype of muon accelerator.
• Injection and extraction kicker are
necessary.
r
cm
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Recent activities
Accelerator Driven Sub-critical Reactor
• 150 MeV (1 GeV in future), 1 mA (100 mA in future).
• Why FFAG for ADSR ?
– Stable operation (a fewer trip) compared with linac.
– Almost DC beams. No difference between DC and 1 kHz for
target.
– 1 GeV machine is no problem
compared with cyclotron.
– High average current.
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Recent activities
Spiral injector FFAG
• Commissioning just started.
• Variable energy with different k value is demonstrated.
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Recent activities
More projects are coming
•
•
•
•
Hadron therapy machine in Ibaraki prefecture
Neutron source for BNCT
Industrial applications
Neutrino factory
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Recent activities
Hadron therapy machine in Ibaraki prefecture
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Recent activities
Neutron source of BNCT
(Boron Neutron Capture Therapy)
• Reactor was the only neutron source.
• With FFAG, similar neutron intensity is expected.
Kyoto-U reactor
Proposed neutron source (Mori)
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Recent activities
Neutrino factory
• In 2001, Japanese proposed neutrino factory based
on FFAG muon accelerator.
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Recent activities
Problems to be solved
(there are still many)
• Interference between main magnet and peripheral
devices such as injection, extraction, and RF
elements.
• Beam diagnostics.
• High intensity operation.
• H- injection.
• More efficient RF cavity.
• …
• Projects and R&Ds are going on in parallel.
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Recent activities
1.
2.
3.
4.
5.
6.
Cyclotron, synchrotron, and FFAG (11)
Revival (6)
Recent activities (12)
Non-scaling FFAG for muon acceleration (13)
Non-scaling FFAG for other applications (1)
Summary (1)
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All of those FFAGs are conventional
scaling FFAG
• If we can break scaling law, FFAG will be much
simpler and magnet will be smaller.
Bz(r)
No gentle slope at low momentum.
- Orbit excursion is shorter.
Constant gradient.
- Linear magnet.
Bz(r)
r
r
• Why do we keep scaling (constant tune) during
acceleration?
Because of resonance in accelerator.
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Non-scaling FFAG for muon acceleration
Resonances in accelerators
• There are many resonances near operating tune. Once a
particle hits one of them, (we think) it will be lost.
Tune diagram of 150 MeV FFAG
In reality, however,
operating tune moves
due to imperfection
of magnet (red zigzag line).
• Particles can survive after
crossing resonances
if resonance is weak and
crossing is fast.
ny
nx
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Non-scaling FFAG for muon acceleration
Non-scaling FFAG
• Muons circulate only a few (~15) turns in FFAG.
• Is resonance really harmful to a beam? Maybe not.
• Forget scaling law !
• Let us operate ordinary AG synchrotron without
ramping magnet.
• Orbit moves as momentum increases.
– Large ap makes the orbit shift small.
• Focusing force decreases as momentum increases.
dL 1 dp

L ap p
1
B
k1  
f p /e
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Non-scaling FFAG for muon acceleration
Orbit for different momentum
• Orbit shifts more at larger dispersion section.
• No similar shape unlike scaling FFAG.
high p
low p
non-scaling
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Non-scaling FFAG for muon acceleration
Tune variation in a cycle
• Tune decreases as a beam is accelerated.
• dn(tune)/dT(turn)~1 for muon rings.
low p
high p
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Non-scaling FFAG for muon acceleration
Acceleration (1)
time of flight
voltage
• Acceleration is so quick that RF frequency cannot be synchronized
with revolution frequency of muons.
• In a first half of a cycle, path length becomes shorter and revolution
frequency becomes higher. In a second half of a cycle, path length
becomes longer and revolution frequency becomes lower.
• Suppose we choose RF frequency that is synchronized with
revolution frequency at the center. In the first half of a cycle, a particle
lags behind the RF. At the center, a particle is synchronized with RF.
In the second half, a particle lags again.
low center high
time
momentum
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Non-scaling FFAG for muon acceleration
Acceleration (2)
• In the longitudinal phase space, a particle follows the path with
constant color.
• If there is enough RF voltage, a particle can be accelerated to
the top energy.
extraction
dp/p (normalized)
• This is called
“Gutter acceleration”.
injection
Phase (1/2 pi)
Non-scaling FFAG for muon acceleration
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Beam dynamics issues
• Acceleration out of RF bucket. “Gutter” acceleration.
– Mismatch in longitudinal and transverse .
– With finite initial transverse amplitude.
• Crossing of many resonances during acceleration.
– Structure resonance has some effects.
– With alignment errors, integer resonances have to be
considered.
• Huge acceptance (30,000 p mm-mrad) for muons.
– Dynamic aperture without acceleration at injection energy.
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Non-scaling FFAG for muon acceleration
“Gutter” acceleration
Finite transverse amplitude
Longitudinal phase space (phi, momentum)
5 to 10 GeV ring
without transverse amplitude
with finite transverse amplitude
Horizontal is 5,000 pi mm mrad
Vertical is zero
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Non-scaling FFAG for muon acceleration
Resonance crossing
without errors

Vertical is 5,000 p mm-mrad, normalized, zero horizontal
emittance.
vertical emittance
5 GeV
horizontal emittance
10 GeV


Shows the coupling due to nx-2ny=0 (structure) resonance.
If we start finite horizontal and zero vertical emittance, no
exchange of emittance.
Non-scaling FFAG for muon acceleration
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Resonance crossing
without errors, amplitude dependence
5,000 pi mm-mrad
500 pi mm-mrad
0.5 pi mm-mrad
46
Non-scaling FFAG for muon acceleration
Resonance crossing
with alignment errors
Beam has to face many integer tunes.
25
20
15
10
5
0
0
tune per cell
5
10
15
20
25
tune per ring
47
Non-scaling FFAG for muon acceleration
Resonance crossing
with alignment errors, envelope


Horizontal is 10,000 p mm-mrad, normalized, zero vertical emittance.
Errors of 0, 0.05, 0.10, 0.20 mm (rms).
Horizontal phase space
(x, xp)
0. mm
0.05 mm
0.10 mm
0.20 mm
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Non-scaling FFAG for muon acceleration
1.
2.
3.
4.
5.
6.
Cyclotron, synchrotron, and FFAG (11)
Revival (6)
Recent activities (12)
Non-scaling FFAG for muon acceleration (13)
Non-scaling FFAG for other applications (1)
Summary (1)
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Issues
• Emittance is much smaller than muons.
– 30,000 pi mm-mrad vs. 300 pi mm-mrad
– Half of the problems go away
• Acceleration is much slower.
– 15 turns vs. 15,000 turns
– RF frequency modulation is possible.
• Resonance crossing is much more serious problem.
– Alignment tolerance
– Errors of fields strength
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Non-scaling FFAG for other applications
Summary
•
•
•
•
FFAG has a potential as medium energy accelerator.
Several projects are currently running in Japan.
It still needs R&Ds (even for scaling FFAG).
Non-scaling FFAG was proposed for muon
acceleration.
• Simulation study for muon acceleration is going on.
• Need study to apply non-scaling FFAG to other
applications.
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