IPBSM response tonon-Gaussian beam

20130211 K. KUBO

Motivation of this study

• We sometimes observe apparent discrepancies between beam sizes measured with different IPBSM crossing angles (different modulation pitches)

• May come from systematic errors of IPBSM• But, may come from non-Gaussian beam shape, because

beam size is evaluated assuming Gaussian beam.– How IPBSM measurement depends on beam shape?

What IPBMS measures

)/2cos(12

),( hyaA

yp

Interference of two laser beams: photon density is

Scanning the phase , “modulation” is

For electron density (y), signal height is

dyhyyadyhyya

dyyG

)/2sin()(sin)/2cos()(cos

)()(

dyy

dyhyiya

GG

GGM

)(

)]/2(exp[)(

maxmax

maxmax

Modulation is, basically, amplitude of Fourier transformation of electron density.

1+a

1-a

2

2

2exp)(

yy

2

222exp

haM

M

ah ln

2

1

For Gaussian beam

For two Gaussians beam

2

2

2

2

2exp

2exp)(

TC

yT

yCy

TC

hT

hC

aM

TC

2

22

2

22 2exp

2exp

Cannot tell beam size and beam shape.Effect of tail is different for different fringe pitch (crossing angle).But, only important if T is comparable with C.

Modulation for beam of sum of two Gaussians

0

0.2

0.4

0.6

0.8

1

0 1 10-7 2 10-7 3 10-7 4 10-7 5 10-7

30 deg174 degCalc for 174 deg from 30 deg modulation

Mod

ulat

ion

sigma of 2nd part of beam (m)

Calculated modulations as functions of sigma of 2nd part (tail) of the beam. Population of 1st and 2nd part =1:1Dashed line: Modulation with 174 deg, calculated from the modulation with 30 deg, assuming a single Gaussian beam.

Sigma of 1st part =37 nm

Rectangular beam

)(0

)(1)(

by

byy

)/2(

)/2sin(

hb

hbaM

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500 600

Gauussian bunch, 7 deg modeGauussian bunch, 30 deg modeGauussian bunch, 174 deg modeRectangular bunch, 7 deg modeRectangular bunch, 30 deg modeRectangular bunch, 174 deg modeM

odu

lati

on

RMS (nm)

Tracking simulation of ATF2 beam line IPBSM modulation

0

0.2

0.4

0.6

0.8

1

0 0.001 0.002 0.003 0.004 0.005 0.006

174 deg.

30 deg

Mod

ula

tion

sigma_E/E

Set very large energy spread might simulate large non-linear effects (?) large tail

0

1000

2000

3000

4000

-2 10-6 -1 10-6 0 1 10-6 2 10-6

sigmaE/E=0.5%

Cou

nts

y (m)

Tracking simulation of ATF2 beam line IPBSM modulation

Set strong transverse wakefield

0

200

400

600

800

1000

-5 10-7 -4 10-7 -3 10-7 -2 10-7 -1 10-7 0 1 10-7

MREF3FF 1.6 mm offsetemity 12 pm

Cou

nt

y (m)40

60

80

100

120

140

160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.002 -0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002

sigmay (nm) modulation

sigm

ay

(nm

) modu

lation

MREF3 offset

Conclusion

We should keep in mind that

•IPBSM is not necessarily measuring sigma or RMS beam size.

•Modulation is not necessarily monotonic function of RMS, or sigma of core part of the beam.

•Evaluated beam size from modulation assuming Gaussian beam can be different for different crossing angle on leaser beams.

If electron beam shape is far from Gaussian.

No conclusion about the actual beam size and beam shape.

Here, only possibilities are shown.