Betatron tune Measurement

Transcription

1 Betatron tune Measurement Tom UESUGI, Y. Kuriyama, Y. Ishi FFA school, Sep. 8-9, Osaka, 218

2 CONTENTS Betatron oscillation and tune How to measure tunes KURNS FFAG, Diagnostics

3 BETATRON OSCILLATION AND TUNE

4 You know what is betatron oscillation A particle in a circular accelerator affects focusing forces by gradient field, and oscillates in transverse directions at closed orbit. = betatron oscillation Its frequency depends on field gradient. Horizontal ( f x ) and vertical ( f y ) frequencies are different, in general.

5 Betatron tunes are the frequencies of the betatron oscillations, divided by the revolution frequency. fx f y ( Q x,q y )=, f rev f rev It is very important parameters in a circular accelerator. Beams tend to be lost if the tunes satisfy the resonance condition; `Q x + mq y = n (`, m, n = small integers) Vertical tune Qy Horizontal tune Qx

6 HOW TO MEASURE TUNES keywords Beam position monitor Coherent betatron oscillations Spectrum with betatron sidebands

7 Electro-static beam position monitor is composed of a electrode installed in the vacuum chamber. When a charged particle beam pass through, longitudinal charge distribution can be detected. Bunch monitor Positive charge of the beam Negative image charge Beam

8 Electro-static beam position monitor is sensitive to the beam center position. Positive charge of the beam Negative image charge Beam

9 Coherent oscillations are necessary to measure the frequency by BPM Beam center BPM can detect only the position of beam center. It needs to excite coherent oscillations to observe the betatron oscillation.

10 How to excite coherent oscillations (1) Strong pulse kick Coherent oscillations can be observed, if the kick angle is large enough. x amplitude ' x = q B` p = B`.48 [T m] ( 11 MeV proton ) In KURNS FFAG, extraction kicker is available, only around the extraction orbit. = B` 1.48 [T m] ( 1 MeV proton ) (2) Rf shaker Applies transverse field for long duration time. Amplitude of coherent oscillations are resonantly grow up, if the shaker frequency is close to the betatron frequency.

11 Strong pulse kick Detect coherent oscillations Measure the frequency Rf shaker tuning its frequency Detect coherent oscillations Measure the frequency Beam loss

12 Signal from Beam Position Monitor T

13 Signal from Beam Position Monitor Short bunch approximation V (t) = 1X V (t nt ) Output Time n= T V Revolution time Proportional to beam intensity In presence of coherent betatron oscillations Output V (t) = 1X (V + V cos! t) (t nt ) n= AM factor Time V! Betatron amplitude Betatron (angular) frequency

14 Spectrum! 2! 3! 4! Output Output Time Frequency V (t) = T V 1X V (t nt ) n= Revolution time Proportional to beam intensity Z Ṽ (!) = 1 X n= V (t nt )exp(i!t)dt X 1 = V exp(im!t ) m= 1 X 1 =! V (! n! ) n= 1

15 Spectrum ( with betatron oscillation )! 2! 3! 4! Output Output V (t) = 1X (V + V cos! t) (t nt ) n= Ṽ (!) = Z 1 X n= =! V 1 X n= 1 =! V 1 X n= 1 Time Time AM (V + V cos! t) (t nt )exp(i!t)dt (! n! ) + V 2 (! n! ) +! V 2 1X m= 1 1X m= 1 V! T V! = 2 T Frequency e im(!+! )t im(!! + e )t Betatron amplitude Betatron (angular) frequency Revolution time Proportional to beam intensity [! (m!! )] + [! (m! +! )]

16 Ambiguity of measured tune =! V 1 X n= 1 Q=.32 5 Q=1.32 (! n! ) +! V 2 Q=.68 5 Q=1.68 1X m= 1 [! (m!! )] + [! (m! +! )]! = 8 >< >: m! m! +! =! (m + Q) m!! =! (m Q) m =, ±1, ±2, ±3, Signal are the same for these Q values 5 5 Q=2.32 Q=2.68 You must choose one of them, knowing designed tune value. 5 5

17 KURNS FFAG, DIAGNOSTICS keywords Beam position monitor Rf shaker

18 KURNS FFAG Main Ring

19 KURNS FFAG Main Ring

20 Main Parameters Particle Cell Orbit radius Revolution Proton ( H- beams are injected) Scaling FFAG, Radial DFD x 12, k= m MHz Designed tune ~( 3.7, 1.4 )

21 BPM in KURNS FFAG for vertical position pickup for horizontal position pickup Wide electrode Triangular electrodes Beam 1 pf Beam 1 pf 1 M 46 db to control room 1 M 46 db

22 Shaker in KURNS FFAG VsinWt charged-particle beam for Vertical excitation Same as the vertical BPM VsinWt for Horizontal excitation Remote controlled in horizontal direction charged-particle beam

23 Positions of the monitors and shakers Beam position monitor Rf shaker

24 Summary Accelerator room Control room Shaker Amplifier Signal generator Amplitude Frequency Burst length Trigger time Lets go to the control room! Oscilloscope Coherent oscillations Beam loss Beam position monitor Amp Spectrum analyzer Sideband frequency