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 !