Betatron tuneMeasurement
Tom UESUGI, Y. Kuriyama, Y. Ishi
FFA school, Sep. 8-9, Osaka, 2018
KURNS
CONTENTS
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Betatron oscillation and tune
How to measure tunes
KURNS FFAG, Diagnostics
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
BETATRON OSCILLATIONAND TUNE
You know what is betatron oscillation
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
A particle in a circular accelerator affects focusing forces by gradient field,
and oscillates in transverse directions at closed orbit. = betatron oscillation
Horizontal ( ) and vertical ( ) frequencies are different, in general.fx
fy
Its frequency depends on field gradient.
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4Horizontal tune Qx
Vert
ical
tune
Qy
Betatron tunes
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
`Qx
+mQy
= n (`,m, n = small integers)
(Qx
, Qy
) =
✓fx
frev
,fy
frev
◆
are the frequencies of the betatron oscillations, divided by the revolution frequency.
It is very important parameters in a circular accelerator.
Beams tend to be lost if the tunes satisfy the resonance condition;
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
HOW TO MEASURETUNES
keywords
Beam position monitorCoherent betatron oscillations
Spectrum with betatron sidebands
Electro-static beam position monitor
longitudinal charge distribution can be detected. … Bunch monitor
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Beam
is composed of a electrode installed in the vacuum chamber.
When a charged particle beam pass through,
Positive charge of the beam
Negative image charge
Electro-static beam position monitor
is sensitive to the beam center position.
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Beam
Positive charge of the beam
Negative image charge
Coherent oscillations are necessaryto measure the frequency by BPM
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Beam center
0
0
Transverse position
Turn number
Particles
BPM can detect only the position of beam center.
It needs to excite coherent oscillations to observe the betatron oscillation.
How to excite coherent oscillations
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
(1) Strong pulse kick
(2) Rf shaker
Coherent oscillations can be observed, if the kick angle is large enough.
Amplitude of coherent oscillations areresonantly grow up,
= �q ·B`
p= �
B`
0.48 [T ·m]( 11 MeV proton )
In KURNS FFAG, extraction kicker is available,
only around the extraction orbit.
= �B`
1.48 [T ·m]
if the shaker frequency is close to the betatron frequency.
xamplitude ' ��x
0
( 100 MeV proton )
Applies transverse field for long duration time.
Strong pulse kick
Rf shaker
Detect coherent oscillations
tuning its frequencyDetect coherent oscillations
Measure the frequency
Measure the frequency
Beam loss
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Signal from Beam Position Monitor
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
T
Signal from Beam Position Monitor
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Short bunch approximation
AM factor
V (t) =1X
n=0
V0 �(t� nT0)
V (t) =1X
n=0
(V0 +�V cos!�t) �(t� nT0)
T0 Revolution timeProportional to beam intensityV0
!�
Betatron amplitudeBetatron (angular) frequency
�V
0
0
Out
put
TimeTime
0
0
Out
put
TimeTime
In presence of coherent betatron oscillations
Spectrum
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
V (t) =1X
n=0
V0 �(t� nT0)
T0 Revolution timeProportional to beam intensityV0
˜V (!) =
Z 1X
n=0
V0 �(t� nT0) exp(i!t) dt
= V0
1X
m=�1exp(im!T0)
= !0V0
1X
n=�1�(! � n!0)
0
0
Out
put
Time
0
0
Out
put
FrequencyFrequency
!0 2!0 3!0 4!0
Time
Spectrum ( with betatron oscillation )
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
V (t) =1X
n=0
(V0 +�V cos!�t) �(t� nT0)
˜V (!) =
Z 1X
n=0
(V0 +�V cos!�t) �(t� nT0) exp(i!t) dt
T0 Revolution timeProportional to beam intensityV0
!�
Betatron amplitudeBetatron (angular) frequency
�V
!0 =2⇡
T0
0
0
Out
put
Time
Time
0
0
Out
put
FrequencyFrequency
!0 2!0 3!0 4!0
= !0V0
1X
n=�1�(! � n!0) +
�V
2
1X
m=�1
⇣eim(!+!�)t + eim(!�!�)t
⌘
= !0V0
1X
n=�1�(! � n!0) +
!0�V
2
1X
m=�1
⇣�[! � (m!0 � !�)] + �[! � (m!0 + !�)]
⌘
AM
Ambiguity of measured tune
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
0 5
Q=0.32
0 5
Q=0.68
0 5
Q=1.32
0 5
Q=1.68
0 5
Q=2.32
0 5
Q=2.68
Signal are the same for these Q values
m!0
m!0 + !� = !0(m+Q)! =
= !0(m�Q)m!0 � !�
8>><
>>:
m = 0 , ±1 , ±2 , ±3 , · · ·
= !0V0
1X
n=�1�(! � n!0) +
!0�V
2
1X
m=�1
⇣�[! � (m!0 � !�)] + �[! � (m!0 + !�)]
⌘
You must choose one of them, knowing designed tune value.
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
KURNS FFAG, DIAGNOSTICS
keywords
Beam position monitorRf shaker
Frequency, Amplitude, Waveform
KURNS FFAG Main Ring
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
2nd stage operation (with H- beam from LINAC)
Main ring
to Reactor
from Linac
charge-strippinginjection
KURNS FFAG Main Ring
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Main Parameters
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Particle Proton ( H- beams are injected)
Cell Scaling FFAG, Radial DFD x 12, k=7.6
Revolution 1. 6 - 4.3 MHz
Orbit radius 4.6 - 5.3 m
Designed tune ~( 3.7, 1.4 )
BPM in KURNS FFAGfor vertical position pickup for horizontal position pickup
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
to control room
1 M⌦
46 dB
⇠ 100 pF
Beam
1 M⌦
46 dB
⇠ 10 pF
Beam
Wide electrode Triangular electrodes
Shaker in KURNS FFAG
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
charged-particle beam
VsinWt
charged-particle beam
VsinWt
for Vertical excitation
for Horizontal excitation
Remote controlled in horizontal direction
Same as the vertical BPM
Positions of the monitors and shakers
Beam position monitor
Rf shaker
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
Summary
Tom UESUGI, FFA SCHOOL, Osaka, Sep, 2018
AmplitudeFrequencyBurst lengthTrigger time
Amplifier
Oscilloscope
Spectrum analyzer
Coherent oscillationsBeam loss
Signal generator
Sideband frequency
Beam position monitor
Shaker
Amp
Control roomAccelerator room
Lets go to the control room !