Transcript Document 7348546

Fixed Field Alternating Gradient (FFAG) Accelerator
Part I
Shinji Machida
ASTeC/RAL
3rd March, 2008
The Cockcroft Institute Lecture Course
1
Part I (Monday, 3rd March 2008)
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Accelerators in various fields
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Evolution of accelerators
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Three major uses of particle accelerators
Remark: particle and beam
Remark: stable and unstable particles
Why high energy frontier was synchrotron?
Why synchrotron light source was synchrotron?
Is a synchrotron for high beam power?
Beam power of accelerator
Future of high beam power accelerator.
FFAG and early developments
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FFAG basics (1) alternating gradient
FFAG basics (2) remark: alternating gradient and strong
focusing
FFAG basics (3) constant tune
FFAG basics (4) cardinal conditions of a FFAG
FFAG basics (5) field profile
FFAG basics (6) simple case
New era of FFAG
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Different kinds of accelerator (1) linear accelerator
Different kinds of accelerator (2) conventional cyclotron (1) (2)
Different kinds of accelerator (3) betatron
Different kinds of accelerator (4) Thomas Azimuthal Varying
Field cyclotron (1) (2)
Different kinds of accelerator (5) synchrocyclotron
Different kinds of accelerator (6) weak focusing synchrotron
Different kinds of accelerator (7) strong focusing (alternating
gradient) synchrotron
Different kinds of accelerator (8) Fixed Field Alternating Gradient
(FFAG) synchrotron
Different kinds of accelerator (9) AVF cyclotron
Different kinds of accelerator (1) summary
Accelerator for high beam power (1) beam power of accelerator
Accelerator for high beam power (2) future of high beam
Accelerator for high beam power (3) fixed or pulse B field
Accelerator for high beam power (4) weak or strong focusing
Accelerator for high beam power (5) possibility of high energy
Accelerator for high beam power (6) other considerations
FFAG basics (7) a way to realize AG
FFAG basics (8) another way (1) (2)
FFAG basics (9) comparison
MURA (1) birth
MURA (2) photo of MURA machines
MURA (3) remarkable outcome in accelerator physics
MURA (4) collider
MURA (5) closure
PoP machine at KEK (1) aim
PoP machine at KEK (2) components
Gradient magnet (1) FDF triplet
Gradient magnet (2) modeling with 3D code
rf cavity (1) requirements
rf cavity (2) ferrite loaded cavity
rf cavity (3) magnetic Alloy cavity
rf cavity (4) core make by Magnetic Alloy
rf cavity (5) shunt impedance
Optics design (1) simplified model
Optics design (2) lattice functions
Optics design (3) when F and D are separated
Optics design (4) lattice functions
Optics design (5) modeling of spiral sector
Optics design (6) lattice functions
Commissioning (1) beam signal
Commissioning (2) tune measurement
Commissioning (3) synchrotron tune and beam position
Commissioning (4) remark
Part II (Monday, 10th March 2008)
•
FFAG developments in UK
•
Applications
•
Research subjects
2
Accelerators in various fields
3
Three major uses of particle accelerators
High energy frontier
LHC, ILC
Energy of each particle
•Always a driving force of accelerator development.
•Small emittance is preferred.
Synchrotron light source
High power source
ESRF, DIAMOND
m, K, n factory, Neutron source
Brightness of light
Energy carried by a beam
•Ultimate goal is a beam as a point source.
(or zero emittance.)
•Beam optics development.
–Lattice
–Stabilities
•Large emittance to avoid multi particle effects
4
Accelerators in various fields (1)
Remark: Particle and beam
• A beam is a group of particles confined in the small volume
in 6-D phase space.
• Our machine is a “beam” accelerator, not a “particle”
accelerator.
– “particle” acceleration mechanism in the universe.
– Laser driven acceleration: from a particle accelerator to a beam
accelerator.
5
Accelerators in various fields (2)
Remark: Stable and unstable particles
• Accelerators used to accelerate stable (or long life)
particles such as proton and electron.
• New challenge is to accelerate unstable (or short life)
particles.
• For example, acceleration of muons.
– Muon collider: high energy frontier
– Neutrino factory: high power (intensity) source
6
Accelerators in various fields (3)
Why high energy frontier machine has been
always a synchrotron?
• Repetitive use of rf cavities to increase energy.
– Must be a circular type.
– Linac is not efficient.
• Relatively small magnets.
– Number of magnets tends to be large.
– Cyclotron is out of question.
• High energy proton machine should be still a synchrotron
(with superconducting magnet.)
• However
– Synchrotron radiation from electron becomes significant and the
next electron machine should be linear.
7
Accelerators in various fields (4)
Why synchrotron light source machine has
been always a synchrotron?
• Repetitive use of rf cavities to maintain energy level.
– Must be a circular type.
– Need bending magnet to produce light
• Electron is ultra relativistic.
– Cyclotron is out of question.
• However
– Emittance blows up in a synchrotron even if emittance at the source
is very small.
– Deterioration of emittance suggests use of linac.
– Instead of using rf cavities repetitively, use “rf energy” many time,
which is Energy Recovery Linac (ERL).
8
Accelerators in various fields (5)
Is a synchrotron the best for high power source
machine?
• First generation was cyclotron.
– PSI (Swiss) and TRIUMF (Canada) have ~500 MeV cyclotron for
meson production.
• Second generation was either synchrotron or linac plus
storage ring.
– ISIS (UK) uses 800 MeV proton synchrotron.
– PSR (US) uses 800 MeV linac and storage ring.
• Trend is still the same.
– J-PARC (Japan) is 3 GeV proton synchrotron under commissioning.
– SNS (US) is 1 GeV linac and storage ring under commissioning.
9
Accelerators in various fields (6)
Beam power of accelerator
Energy of each particle [GeV]
Higher energy is preferable, but size should be moderate
x
Number of particle per beam [ppp]
Enlarge aperture as much as possible
x
Repetition rate [Hz]
Continuous operation is the best, but very high repetition is acceptable
Low loss
Keep accessibility
Reliability
Hardware failures cut integrated beam power
10
Accelerators in various fields (7)
Future of high beam power machine
• Type of accelerators depends on the needs of users, physics
limitations, available technologies, and cost.
– Physics limitations
• Synchrotron radiation
• Repulsive force among particles
– Technical limitations
• Maximum strength of magnets
• Ramping rate of pulsed magnets
• rf field gradient
• Modulation rate of rf frequency
• Emittance from a source
(example)
(6-10 T)
(50 Hz)
(50 kV/m in a few MHz)
(1-10 kHz)
(1 p mm mrad)
• High energy frontier machine (of electron) is now linac.
• Next generation synchrotron light source will be linac (or
Energy Recovery Linac).
• What about high power beam accelerator?
11
Accelerators in various fields (8)
Evolution of accelerators
12
Different kinds of accelerator (1)
linear accelerator (linac)
• Sequence of rf accelerating structure
– Cell length is proportional to
L  
– Synchrotron oscillations

13
Evolution of accelerators (1)
Different kinds of accelerator (2)
conventional cyclotron (1)
• Repetitive use of rf acceleration.
• Energy is limited to about 12 MeV (Bethe and Rose)
– Non-relativistic case
m0v 2
 evB so that
r
r
m0v
and
eB

eB
m
– Relativistic2 case
m 0v

r
eB
m0v


 evB so
r

and
 that
m
eB
• When B is constant,  varies.



14
Evolution of accelerators (2)
Different kinds of accelerator (2)
conventional cyclotron (2)
• Focusing in both directions at the same time.
Fz  ev Br  ev
Br Bz

0
z
r
Br
z
z
When Bz decreases as radius.

d 2z
ev Bz
 2   z2 z  0  z2   
dt
m r

B
– With field index n  r z , stability for horizontal and vertical
Bz r
requires

1  n  0
– F. Cole said


If you went to graduate
school in the 1940’s, this
inequality was the end of
the discussion of
accelerator theory [1].
15
Evolution of accelerators (3)
Different kinds of accelerator (3)
betatron
• First use of pulsed magnet.
– Ampere’s law
pr 2
dBav
 2prE
dt
dBav 2E

dt
r
– Equation of motion


dp
 eE
dt
– Betatron principle

1
p  eBav r  eBorbitr
2
16
Evolution of accelerators (4)
Different kinds of accelerator (4)
Thomas (or AVF) cyclotron (1)
• One way to overcome relativity
n
– Increase B as orbit goes outward.
eB
m v
r  0 and  
m
eB
r Bz
Bz r
n<0
vertical focus

n>0
vertical defocus
– This makes vertical defocusing
index n>0.
because field

• Vertical focusing is obtained at
the edge.
– Sort of strong focusing.
17
Evolution of accelerators (5)
Different kinds of accelerator (4)
Thomas (or AVF) cyclotron (2)
• Edge focusing
Bz
y
x

x


1 
e 
pz 
 Fz dx  v  v x By  v y Bx dx
v x 
x 
Bx Bz

  x Bz 0
Bx   x Bz0 z
z
x
e 
pz 
 v y Bx dx  eBz0 tan   z
v x 

– F. Cole said
The problem with Thomas’ paper
was that it was couched in very
unfamiliar mathematics, … Nobody
understood it at the time and it
remained a mystery to most [1].
18
Evolution of accelerators (6)
Different kinds of accelerator (5)
synchrocyclotron
• Another way to overcome relativity
– Modulate  as  increases.
r
m0v
eB
eB
and   m
– Focusing in the both direction at the same time.
– Only one momentum
beam at a time.

p()
p

t
Only one beam exists at the
same time.
t
Many beam are accelerated
simultaneously.
19
Evolution of accelerators (7)
Different kinds of accelerator (6)
Weak focusing synchrotron
• The other way to overcome relativity.
– Use pulsed magnet and frequency modulation.
– Focusing in both directions at the same time.
Cosmotron at BNL
20
Evolution of accelerators (8)
Different kinds of accelerator (7)
strong focusing (alternating gradient) synchrotron
• Courant, Livingston, and Snyder invented alternating
gradient focusing.
– Beam size and therefore magnet size is considerably reduced.
PS at CERN
21
Evolution of accelerators (9)
Different kinds of accelerator (8)
fixed field alternating gradient (FFAG)
Alternating gradient synchrotron can be operated with fixed
field magnet !
–Synchrocyclotron with alternating gradient focusing or
–AVF cyclotron with frequency modulation.
• What is advantage?
– DC magnet is easier to
operate.
– Repetition rate can be high so
the current become higher.
– Beam current of synchrotron in
early days was not enough.
• Price we have to pay
– Larger magnets to
accommodate orbit shift in
horizontal direction.
– Orbit shift can be minimized by
using a high gradient magnet.
22
Evolution of accelerators (10)
Different kinds of accelerator (9)
AVF cyclotron
• Proliferation in the 1960’s.
– PSI cyclotron
– TRIUMF
– And many other small ones
PSI cyclotron
23
Evolution of accelerators (11)
Different kinds of accelerator (10)
time
summary
AVF cyclotron
FFAG
Fixed magnet with strong focusing
AG synchrotron
Synchrocyclotron
Overcome relativistic effects
by synchronized rf
Thomas cyclotron (only idea)
Reduce size of magnets
by strong focusing (alternating
gradient)
Synchrotron
Overcome relativistic effects
by pulsed magnet and
synchronized rf
Overcome relativistic effects
by strong focusing (edge)
Betatron
Cyclotron
Induction to push particles
with pulsed magnets
Repetitive use of linac
Linac
Push particles
24
Evolution of accelerators (12)
Accelerator for high beam power (1)
beam power of accelerator
Energy of each particle [GeV]
Higher energy is preferable, but size should be moderate
x
Number of particle per beam [ppp]
Enlarge aperture as much as possible
x
Repetition rate [Hz]
Continuous operation is the best, but very high repetition is acceptable
Low loss
Keep accessibility
Reliability
Hardware failures cut integrated beam power
25
Evolution of accelerators (13)
Accelerator for high beam power (2)
future of high beam power machine
• Type of accelerators depends on the needs of users, physics
limitations, available technologies, and cost.
– Physics limitations
• Synchrotron radiation
• Repulsive force among particles
– Technical limitations
• Maximum strength of magnets
• Ramping rate of pulsed magnets
• rf field gradient
• Modulation rate of rf frequency
• Emittance from a source
(example)
(6-10 T)
(50 Hz)
(20 kV/m in a few MHz)
(1-10 kHz)
(1 p mm mrad)
26
Evolution of accelerators (14)
Accelerator for high beam power (3)
fixed or pulsed B field
Energy of each particle [GeV]
x
Number of particle per beam [ppp]
x
Repetition rate [Hz]
•Modulation of B field cannot be
fast.
e.g. 50 Hz of ISIS is the fastest.
•Modulation of freq. can be 1 kHz
or more.
Variable B
(Fixed path)
Fixed B
(Variable path)
Fixed frequency
Betatron
e synchrotron
Cyclotron
Thomas cyclotron
Microtron
Variable frequency
p synchrotron
Synchrocyclotron
FFAG
27
Evolution of accelerators (15)
Accelerator for high beam power (4)
weak or strong focusing
Energy of each particle [GeV]
x
Number of particle per beam [ppp]
x
Repetition rate [Hz]
Strong focusing can
accommodate a higher number
of particles with limited aperture.
Variable B
(Fixed path)
Fixed B
(Variable path)
Weak focusing
WF synchrotron
Betatron
Cyclotron
Synchrocyclotron
Microtron
Strong focusing
SF synchrotron
FFAG
Thomas cyclotron
28
Evolution of accelerators (16)
Accelerator for high beam power (5)
possibility of high energy
Energy of each particle [GeV]
x
Number of particle per beam [ppp]
x
Repetition rate [Hz]
Because of larger orbit shift,
higher energy (>1GeV)
cyclotron is not realistic.
Variable B
(Fixed path)
Fixed B
(Variable path)
Weak focusing
WF synchrotron
Betatron
Cyclotron
Synchrocyclotron
Microtron
Strong focusing
SF synchrotron
FFAG
Thomas cyclotron
29
Evolution of accelerators (17)
Accelerator for high beam power (6)
other considerations
• FFAG seem to be the best choice for a high beam power
machine !
• However, there are other considerations.
– As a neutron source, large number of particles with less repetition
(~10 Hz) is preferable.
• Need a storage ring if cyclotron (or linac) is a main accelerator.
– Almost no development of FFAG until recently.
• No one wants to take a risk.
30
Evolution of accelerators (18)
FFAG and early developments
EMMA is a little different from what I describe as FFAG here.
31
FFAG basics (1)
alternating gradient
• Use “Fixed Field” magnet like cyclotron.
• Gradient is determined by focusing condition, not by
isochronism condition.
eB

m
 constant
• Alternating gradient is a focusing scheme with both sign of
gradient magnets, focusing and defocusing elements.

horizontal
vertical
32
FFAG and early developments (1)
FFAG basics (2)
remark: alternating gradient and strong focusing
• Strong focusing <-> weak focusing (-1<n<0)
• Thomas (AVF) cyclotron uses a combination of focusing
(from the body) and defocusing (from the edge) elements
to realize net focusing.
• Strong focusing synchrotron by Courant, Livingston and
Snyder uses large gradient magnets with alternating sign.
• Alternating gradient is one way to realize strong focusing.
– However, they are used in the same meaning.
– There is even a FFAG without alternating gradient magnets !
33
FFAG and early developments (2)
FFAG basics (3)
constant tune
Transverse tune has to be constant during acceleration.
Conventional strong
focusing synchrotron
Resonance in accelerator
Same orbit

Tune diagram of 150 MeV FFAG
Qy
Bt L
pt  /e
Same focal length
1 dBt  dx  L

f
pt /e

FFAG

Qx
“cardinal condition”
34
FFAG and early developments (3)
FFAG basics (4)
cardinal conditions of a FFAG
Constancy of k at
corresponding orbit points
Geometrical similarity
   
0
 
p 0   const.
k
0
p  
const.
0 : average curvature
 : local curvature

: generalized azimuth

Bz(r)
Orbit of
low p

r B 
k   
B r 
Orbit of
high p
Gradient of
high p
Gradient of
low p
r
35
FFAG and early developments (4)
FFAG basics (5)
field profile
If the field profile has the shape of
 r k
Br,   B0  F  
r0 
Bz(r)

Cardinal condition is satisfied.

r
36
FFAG and early developments (5)

FFAG basics (6)
simple case
Bz(r)
 r 
Br,   B0  F  
r0 
k
r
F    F  
Radial sector type
Alternating magnet has
opposite sign of bending.
r


Bz(r)
machine center
37
FFAG and early developments (6)
FFAG basics (7)
a way to realize AG
Conventional strong
focusing synchrotron
FFAG
Bending a beam in the
opposite direction to
change the sign.
Bending a beam in the same
direction.
Bz
focusing
defocusing
focusing
defocusing
z
z
z
z
r
r
Bz
r
r
38
FFAG and early developments (7)

FFAG basics (8)
another way (1)
Bz(r)
 r 
Br,   B0  F  
r0 
k
r
F    F  
Radial sector type
with edge focusing.
Bz(r)
In practice, edge
focusing is not strong
enough.

r
machine center
39
FFAG and early developments (8)
FFAG basics (8)
another way (1)
 r k
Br,   B0  F  
r0 

r 
F    F   tan  ln 
r0 

Spiral sector type
rd
 tan
dr
  0  tan  ln

Spiral angle gives 
stronger edge focusing.

e
pz 
vx

 v B dx  eB
y

x
z0
tan   z
r
r0
Bz(r)

machine center
r
40
FFAG and early developments (9)
FFAG basics (9)
comparison
Thomas (AVF) cyc FFAG
Strong focus sync
B field
Fixed
Fixed
Pulsed
Strong focus
Body and edge
AG or
Body and edge
Alternating
Gradient
Tune
Small
Large
Large
Isochronism
Yes
No
No
RF freq.
Fixed
Varied
Varied
Duty
100% (CW)
Large
Small
Longitudinal
focusing
No
Yes
Yes
Tune
Change
Constant
Constant
41
FFAG and early developments (10)
MURA (1)
birth
• Birth of FFAG at Midwestern Universities Research
Association (MURA) in 1950’s.
• Three inventors
– Symon and Kerst in US
– Ohkawa in Japan
– Kolomensky in USSR
• They discussed FFAG as the main accelerator in
Midwestern region of US.
42
FFAG and early developments (11)
MURA (2)
Chandrasekhar
400 keV radial sector
40 MeV two beam
accelerator
Bohr
180 keV spiral sector
All are electron
FFAGs.
43
FFAG and early developments (12)
MURA (3)
remarkable outcome in accelerator physics
• Three Electron models were constructed.
• Accelerator physics issues
• Beam stacking.
• Hamiltonian theory of longitudinal motion.
• Useful colliding beams
• Storage ring
• Spiral sector geometry
• Lattice with zero dispersion and low beta
section for colliding beams.
• Multiturn injection into a strong focusing
lattice.
• First calculations of the effects of
nonlinear forces in accelerators.
• First space charge calculations including
effects of the beam surroundings.
•First experimental measurement of space
charge effects.
• Theory of negative mass and other
collective instabilities and correction
systems.
• The use of digital computation in design
of orbits, magnets and rf structures.
• Proof of the existence of chaos in digital
computation
• Synchrotron radiation rings.
[1] F. T. Cole, “A Memoir of the MURA years.”
http://accelconf.web.cern.ch/AccelConf/c01/cy
c2001/extra/Cole.pdf
44
FFAG and early developments (13)
MURA (4)
collider
• Concept of a beam collider
• In one ring, a particle can rotate in both directions.
Colliding point
……
Head-On Accelerator. Another team of dealers
in magnetic fields. Dr. Lawrence W. Jones of the
University of Michigan and Tihiro Ohkawa of
Tokyo University, told their colleagues about a
new and cataclysmic kind of atom smasher. The
most powerful one in operation at present is the
Bevatron at Berkeley (6 billion electron volts),
and a 25-Bev monster is under construction at
Brookhaven National Laboratory on Long
Island. These are rather puny little gadgets,
think Jones and Ohkawa. The way to get real
power is to force head-on collisions between
high-speed particles. ……
TIME, February 11, 1957
http://www.time.com/time/magazine/article/
0,9171,809067-1,00.html
45
FFAG and early developments (14)
MURA (5)
closure
• Closure of MURA because
– Synchrotron turned out to be the best choice for high energy
frontier machine.
– Magnet fabrication was complicated. No tool to model 3D magnetic
fields.
– RF cavities was not matured enough for high repetition and high
gradient with wide aperture.
• Activities in 1980’s
– Design study at Argonne (US), Juelich (Germany), and KEK
(Japan).
46
FFAG and early developments (15)
New era of FFAG
47
PoP machine at KEK (1)
aim
Proof of principle (proton
acceleration with rf cavity)
machine was constructed in
2000.
Demonstrate acceleration
from 50 keV to 500 keV in
1 ms.
48
New era of FFAG (1)
PoP machine at KEK (2)
components
Everything except extraction channel.
49
New era of FFAG (2)
Gradient magnet (1)
FDF triplet
Instead of using F and D
magnets separately,
combine FDF together
(triplet).
Gradient is made by gap
shape.
high momentum
50
New era of FFAG (3)
Gradient magnet (2)
modeling with 3D code
OPERA3D(TOSCA) models a magnet with complex shape
accurately, less than 1% accuracy.
In this example, gradient is made
by distributed currents, instead
of shaping a gap.
51
New era of FFAG (4)
rf cavity (1)
requirements
• rf cavity must be
– Broad band
• Cover frequency modulation of, for example, 1.5 to 5 MHz.
– High gradient
• Make fast acceleration possible.
– Large aperture
• Especially in horizontal to accommodate orbit shift.
52
New era of FFAG (5)
rf cavity (2)
ferrite loaded cavity
f rf 
1
2p LC
L  mL0
L0 is the air-cored inductance.
B
mm0 
depends on DC bias.
H



B: magnetic flux density
H: magnetic field
53
New era of FFAG (6)
rf cavity (3)
Magnetic Alloy (instead of Ferrite) cavity
• Large permeability
~2000 at 5 MHz
High shunt impedance
(Efficient use of rf power)
• High curie temperature
~570 deg.
Can sustain large rf power
• Thin tape
~18 mm
Any shape can be possible
• Q is small
~1
Do not need tuning of resonant
frequency
54
New era of FFAG (7)
rf cavity (4)
core made by Magnetic Alloy tape
• Wide aperture to accommodate orbit shift.
• Difficult to make a large ferrite core.
55
New era of FFAG (8)
rf cavity (5)
shunt impedance (efficiency of a cavity)
In the range of operation, shunt impedance is not flat.
However, tuning is still not necessary.
Frequency (MHz)
56
New era of FFAG (9)
Optics design (1)
simplified model
From the center of F to the center of drift
F
r0

tan F
sin F  1 cos F tan F
F sinF
sin F
 D sin  F

 F sin  F
p

p
 p

sin    F  cos   F t an   F   D 
r1 




N

N
 N




p  
p  p
sin  F   1 cos F  tan   F   D 



N  
N  N
Edge focusing
F 
D,F


F   F
2F
  F
 F
D

p
D,O   N
 F  D
D
57
New era of FFAG (10)
Optics design (2)
lattice functions
With the approximation, synchrotron optics code such as MAD
can calculate lattice functions (for fixed momentum).
58
New era of FFAG (11)
Optics design (3)
when F and D are separated
From the center of F to the center of D
F
r0
D



r2

tan F
sin F  1 cos F tan F

sin D
sinD
r1 
F sinF
sin F

r2  F 
1
 1 1

r0 
 r0  sin p   F 


tanp   F 


p
 p

cos   D tan   D  tanp  F 
N
 N


Edge focusing
F   F
2 F
  D
D  D
2 D
F 

59
New era of FFAG (12)
Optics design (4)
lattice functions
• This example uses the identical magnet for F and D with
opposite currents.
• A beam can rotate in either direction.
60
New era of FFAG (13)
Optics design (5)
modeling of spiral sector
• Spiral optics is nothing special.
• Proper modeling of edge with only F magnet gives lattice functions.
Edge focusing
1 

2 

p
N

F
 
p
N
F
F
2

F
2
in MAD format

61
New era of FFAG (14)
Optics design (6)
lattice functions
• One edge gives focusing and another edge gives defocusing.
• Lattice function is asymmetric.
62
New era of FFAG (15)
Commissioning (1)
beam signal
Beam position monitor tells
•
total charge
•
position
•
time structure
Frequency analysis gives tune.
beam
less charge
more charge
kHz
kHz
63
New era of FFAG (16)
Commissioning (2)
tune measurement
Keeping the total bending
angle same, change the
strength of F and D.
F
D
Vertical focusing should be
sensitive to F/D because of
edge effects.
64
New era of FFAG (17)
Commissioning (3)
synchrotron tune and beam position
With acceleration, synchrotron oscillation frequency
and radial position move.
synchrotron oscillation frequency
radius position
65
New era of FFAG (18)
Commissioning (4)
remark
• It is nice to have such a small and “homemade” accelerator.
– Easy to operate but still have all aspects of accelerator.
• EMMA at Daresbury will be a gadget every one can play
with !
PoP FFAG at KEK
EMMA
66
New era of FFAG (19)