1

IP Characterization Measuring the Boost Vector

Matt Weaver

PEP Meeting

May 15, 2006

2

Motivation

• Measure parameters contributing to luminosity to quantitatively verify that we’re generating all we can.

• Machine behavior in collision may have surprises that we can benefit from understanding.

3

Boost Trajectory Measurement

e+e-

LH

LLHHxB EE

xExEp

px

''

'Measure collision point {x,y,z}

and trajectories of pair {x’,y’}

z mean, spread, distribution x,y mean, spread, correlation with zx’,y’ mean, spread, correlation with z

correlation with x,y

B

z resolution ~ 60 mx,y resolution ~ 30 mx’,y’ resolution ~ 0.6 mrad

4

Boost Vector Properties

Near the waist (z << *), x and x’ are uncorrelatedx

z *2

*22

'L

LL

H

HHX ff

B

LLHHB xfxfx '''

LH

LHLH EE

Ef

)()( this 9 times

greater than

Expect that X measurements behave like this (z << *X)Boost X’ spread largely reflects HER X’ angular spread

5

Lu

min

ou

s X

-siz

e (

m)

HE

R X

’-sp

read

(m

rad

)

Move to half-integer x-tune

dynamic

dynamic

6

Far from the waist (z >> *), x and x’ are highly correlated

x

z

**

**2'

L

L

H

H

L

L

H

H

X B

zx

x B '

Boost Vector Properties

Bunch lengths are small compared to *X and comparable to *Y,

so we never see these relations fully.

However, the transition must develop on a z-scale of *, so the z-dependence of these msmts must be a measure of *

7

Boost Vector Z-Dependence

LH

LHBB

xx

'

' (luminosity-weighted)

22*22*'

z

zf

z

zfxx

L

L

H

HB

LH

LHBx

xB

2

2'

'

22

222

2

2'

2

2'

2

22

2

222'

LH

LH

L

L

H

H

LH

Bxx

xx

x

xxL

x

xxH

x

LL

x

HHx

ffff

*2*2

H

HHHH

x

xxxx z

*2'

H

HH

x

xxx z

8

Monte Carlo Validation 14mm * 14mm *

10mm * 10mm *

6mm * 6mm *

y’dy’/dy

z (cm)z (cm)

mra

d-c

m

mra

d

~ 1 week data

5 fit parametersY*

y-waist z offsetH

L

2YY’ detector error

Fit 2 is a simple sumof the two 2s

No y’ dy’/dy} covariance terms included

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Example measurement of angular spread

Non-zero slope is reminiscentof lumi X-size measurements.

Implies X-waist offset.

“Width” is measure of *.“Height” is measure of *.

Value at z-centroid is well-determined.Limit for z>>* not reached.

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Example measurement of collision position-boost angle correlation

“Z >0”“Z <0”

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Run5 Fit Results*

(m

m)

z (

mm

)

H

(nm

)

L

(nm

)

waistlumi centroid

12

Y

(m

)S

pec

ific

Lu

min

osi

ty

Y derived from combined-fit results shows good anti-correlation with specific luminosity

13

X s

izes

(m

) X

/

XL

“X”

XL

1

2

2.5

Ratio

of b

eam x-s

izes

X derived from Y measurements

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Fit Results*

(m

m)

wai

st z

(m

m)

H

(nm

)

L

(nm

)

waistlumi centroid

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Plans

Separately determine HER, LER *Y and y-waist locations

Estimate impact of coupling, dispersion {Y, Y’}

Make a measure of coupling y’B(x), x’B(y)

What to do with x? 3 measurements { X,X’,x’B(x)}, at least 4 parms

Make quantitative comparisons to beam-beam simulationversus bunch current, tune?

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Extra Slides

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Boost Trajectory Measurement

e+e-

n

momenta poorly measured trajectories well measured

reconstruct decay plane normal n

z

x

y

n

n

tan = - x’Bcos – y’Bsin≈

x’(or y’)B = EH x’H – EL x’L EH - EL

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Y-Y’ Correlation in Run5 Data

y (cm)

y’ (

mra

d)

y (cm)

Y distribution

y’ vs y invarious z-bins

y’ vs y invarious z-bins

dy’

/dy

z (cm)

dy’/dyversus z

Shift in mean

Y-mean dependsupon

More work to do here

Less S-shape

19

d

x’H

/ d

z (m

rad

/cm

)Slope of x’ angular spread

Need to know emittances and beta*s to convert into a waist shift

Move to half-integer x-tune

20

X-w

aist

off

set

(cm

)From x-x’ correlation measurement assuming common waist

Move to half-integer x-tune

21

*

(mm

)

wai

st z

(m

m)

H

(nm

)

L

(nm

)

generated value

Monte Carlo Fit Results

combined fity’(z) fit only

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Toy Monte Carlo Tests *= L*=10mmzH=zL=0

y’dy’/dy

z (cm)z (cm)

mra

d-c

m

mra

d

≤ 1 week data

7 fit parameters*H, *L

y-waist z offsets (H,L)H, L

2YY’ detector error

Correlated detector errorsare not modeled

*= L*=10mmzH=zL=0

*= L*=10mmzH=+4mmzL=-4mm

*= 8.23mmL*=13.72mmzH=zL=0

*= L*=10mmzH=+4mmzL=-4mm

*= 8.23mmL*=13.72mmzH=zL=0

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*H

(mm

)

*L

(mm

)

z H

(mm

)

z L

(mm

)

generated value

Toy Fit Results

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Fit Results*

(m

m)

wai

st z

(m

m)

H

(nm

)

L

(nm

)

25

Y

(m

)S

pec

ific

Lu

min

osi

ty

Y derived from combined-fit results shows good anti-correlation with specific luminosity

26

Y

(m

)