FFTB RESULTS: ARE THEY SUFFICIENT?

Tim Slaton22-June-1998

A few comments on and examples of beam jitter.

Ground and Structural/Mechanical vibrations.

Summarization of measured verse real, *, and .

Conclusions.

A 12 hour period of quiet running were the main goal was to producea small spot.

B e a m j i t t e r L a s e r h o u r g l a s s e f f e c t L a s e r p o w e r i m b a l a n c e e f f e c t B e a m l i n e a b e r r a t i o n s

S t r u c t u r a l / M e c h a n i c a l v i b r a t i o n s B e a m l i n e a b e r r a t i o n s T u n i n g r e s o l u t i o n s

r e a lm e a s u r e d n o i s e

r e a l

22 2

21

( )

KEK BSMRF-BPMsWS3

The FFTB BPMs can be used to project the beam jitter to WS3 forcomparison with the beam sigma.As expected, the beam jitter to beam sigma ratio is 30%.

The 1 Hz peak isa signature of beamjitter in the SLC dueto beam motion feed-backs.

With their close spacing (5 cm)and high resolution (30 nm)the RF-BPMs can be usedto measure the beam’s jitteremittance at the entrance to theFinal Transformer. The jitter emittance at the RF-BPMs is about1/10th of the beam emittance measured in sector 28. This isconsistent with the 30% beam jitterto beam sigma ratio.

Inflection point

Each point is for 20 laser onpulses or 2 seconds of data. Theerror bars are a measurement of the beam’s rms motion during the2 second period.

Beam jitter at the IP can bemeasured by placing the beamat an inflection point on the KEKBSM fringe pattern.

The histogram of the above errorbars shows beam jitter relativeto the fringe pattern of 41 nm. Thisis about a factor of 2 larger then whatis expected for the 30% beam jitterto beam sigma ratio.

Transformation of beam displacement before

a quadrupole to after the quadrupole.

Beam transformation before a quadrupole with

a positive vertical displacement.

Y

Y

R R

R R

Y

Y

Y

Y

R R

R R

Y Y

Y

Y

Y

R Y Y R Y

R Y Y R Y

aB

aB

bB

bB

aB

aB

aB Q

aB

aB

aB

bB Q bB

bB Q bB

' '

' '

'

'

'

LNMOQPLNMOQPLNMOQP

LNMOQPLNMOQP

LNM

OQP

LNMOQP

LNMM

OQPP

33 34

43 44

33 34

43 44

33 34

43 44

c hc h

Remove the transformation after the quadrupole.

Seperate beam displacement from quadrupole displacement.

+1-R

-R

Looking only at quadrupole vertical displacement.

33

44

+

Y

Y

R Y Y R Y Y

R Y Y R Y

Y

Y

R R

R R

Y

YY

Y M M Y

Y C Y C

aB

aB

bB Q bB Q

bB Q bB

aB

aB

bB

bBQ

IP IP Q Q Q

IP

'

'

'

' '

LNMOQP

LNMM

OQPP

LNMOQPLNMOQPLNMOQPLNMOQP

33 34

43 44

33 34

43 44

1 1 2

c hc h

Y C Y

whereC R R R R R

Y C Y C Y C Y C Y C

Y C Y

Y C Y R Y

R C

Y CZ R Z

n n

nIP Q IP Q Q IP Q Q

n n IP IP IP

i ii

n

i ii

nIP B

B

IP Bi

i

n

i ii

nIP B

B

n n n n n

2

33 33 33 34 43

1 1 2 2

1

133

331

133

1

+...+

+ +...+ + =

; -

In adding beam motion that is correlated to

ground motion, two conditions need to be satisified.

c hmin

min

min

min

Z

CZ

CB

i ii

n

ii

n

1

1

beam

beam

IP Q1 Q2 … Qn

beam

YQ

Final Transformer Quadrupole Parameters

QC1 QX1 QC2 QC3 QC4 QC5BDES(kG) -1801.40 -399.57 737.58 -164.18 -40.70 -241.53

leff(m) 1.12000 0.31000 2.02600 0.46700 0.46092 0.46092Bore radius(mm) 11.5 11.5 17.5 26.0 10.0 6.5Z(m) upstream of IP 1.537 1.989 4.964 10.289 21.168 34.025 ZB 40.871Coefficient 0.8937 0.2648 -0.4062 0.2237 0.0621 0.2838 RB

33 -0.0381

Y C Y for the static case

Y Y Y looking over time

Y CC Y Y

Y CC Y Y in terms of frequency real part

Y Y the total rms

Y C C C

Y Y Y Y Y Y

Y Y Y

ii

n

rms

rms i jj

n

i

n

rms i jj

n

i

n

i j

rms rmsf

rms n

n

i

i j

f f f

f

f

f f f f f f

f f

min

min min

*

* * *

*

1

2

2

11

2

11

2

21 2

1 1 1 2 1

2 1

( )

Matrix format can be used in determining how correlations

contribute to total rms.

,

,

e j

2 2 2

1 2

1

2

2

21

f f f f

f f f f n f n f

f f f

Y Y Y

Y Y Y Y Y Y

C

C

C

Y R Y Y R convenient formula inMatlab

N MN Q N Q

R N Q

n

n n n

rms i jT

um easum uad um uad

edundancy um uad

* *

* * *

*cov( )

L

N

MMMMM

O

Q

PPPPP

L

N

MMMM

O

Q

PPPP

Using only two measurement devices.

( ) -

-

2

ground

concrete block

quadrupole table

beamdirection

KEK BSM tableIP flange

piezo electric supports

QC2QC1 QX1

The Final Transformer quadrupoles sit on piers or concrete blocks descending approximately 10 feet to a sandstone foundation.

A measurement showing * of126 um. What is not completelyunderstood is the 77 nm offset when goes to 0. Although in previousruns the offset has be around 50 nm.

At times the measured emittancein sector 28 can be almost a factorof 4 less then the original designemittance for the FFTB.

A summary of PT's spot size analysis from the last FFTB run:

= 0.2x10-11 m. * = 120 ± 24 um.

expected = 58 ± 8 nm with synchrotron radiation, aberrations, and 38 nm of beam jitter.

measured = 70 ± 7 nm after hourglass and power imbalance corrections.

C o n c l u s i o n : j i t t e r K E K b e a m v i b r a t i o n s n m 3 0 % 3 0 % 7 0 3 5 4 12 2 2 2* ( * )

W h a t i s s u f f i c i e n t : N e e d g e o m e t r i c s e x t u p o l e s t o p r o d u c e s p o t s i z e s b e l o w 1 0 0 n m . C a n u s e K E K B S M f r i n g e p a t t e r n t o m e a s u r e b e a m j i t t e r a t I P . P r o d u c e d s i m i l a r r e s u l t s t o t h e r u n s i n 1 9 9 4 .

W h a t i s s e m i - s u f f i c i e n t :

m e a s u r e d v e r s e r e a l .

* . O f f s e t o f 2 v e r s e m e a s u r e m e n t s .

W h a t i s n o t s u f f i c i e n t : B e a m j i t t e r v e r s e e m i t t a n c e , o f f s e t s h o u l d b e j i t t e r f r o m s t r u c t u r a l

v i b r a t i o n s . E l i m i n a t e s t r u c t u r a l v i b r a t i o n s a n d s e e i f t h e m e a s u r e d s p o t s i z e i s

r e d u c e d . D i r e c t c o r r e l a t i o n o f g r o u n d m o t i o n t o b e a m m o t i o n ( m i g h t b e t o

d i f f i c u l t w i t h t h e l a s e r f i r i n g a t o n l y 1 0 H z ) .

m e a s u r e d e q u a l s e x p e c t e d .