beam-beam & the lum in ous region - update

W. Kozanecki 4 Mar 05 Slide 1

Beam-beam & the lumBeam-beam & the lumininous region - updateous region - update

““To do” list left over from BaBar week To do” list left over from BaBar week

Understand whether the y-truncation of the luminous region (|y| < 25 in the present luminous-region analysis) significantly biases the vertical luminous size at high |z|

Check z-y correlations

Clarify whether the overestimate of *y in the luminous-region fits occurs both in “*” fits [ 2

y(z) ] & in “bunch-length” fits [ L(z) ]

Understand the discrepancies between the z-dependence of the vertical luminous size directly obtained from the simulation, and that inferred from the individual, single-beam charge y-z distributions

W. Kozanecki

4 March 05


RMS Luminous y-size (low current)

2

3

4

5

6

7

8

9

10

-40 -20 0 20 40z (mm)

sigmayy_L (microns)

Low I (full sim, RMS)

Low I (from single beams)

Low I (gen)

Any truncation bias at high |y|, high |z| ?Any truncation bias at high |y|, high |z| ?

Y (m)L

/bu

nch

(10

24 c

m-2 s

-1)

z ~ 0

z ~ 16 mm

z ~ 26 mm

Could the systematic discrepancy in yL at high z, be due to y-truncation imposed

in the luminosity computation by the simulation?


2

3

4

5

6

7

8

9

10

-40 -20 0 20 40z (mm)

sigmayy_L (microns)

Low I (full sim, RMS)Low I (from single beams)Low I (gen)Low I I (full sim, 1G fit))


y-z correlations in single-beam charge distributionsy-z correlations in single-beam charge distributions

So farSo far ignored z-slice info in b-b sim output, i.e. assumed x, y, z uncorrelated

NowNow

‘sample’ each z slice as it crosses the IP, i.e. plot y*, yp = f( zslice)

bunch<-- tail head -->

e+

e-

(y*) low I

dN

/dy*

z (mm)


Single-beam y-z correlations : low vs. high currentSingle-beam y-z correlations : low vs. high current

bunch<-- tail head -->

e+

e-

(y*) low I

(yp) low I

(y*) high I

Y. Cai: “pinch effect” !

• akin to what is happening in LC

• distinct from dyn.

(yp) High I


z-dependence of z-dependence of effectiveeffective yy, , **y y : high current: high current

y eff , high current *y eff , high current

e- e-e+ e+


z-dependence of z-dependence of effectiveeffective yy, , **y y : low current: low current

Could the “low current” still be too high?

Ilya will generate a very low current data set

y eff , low current *y eff , low current

e+e+e-

e-


**yy ‘measurements’ (on b-b simulations, no detector effects!) ‘measurements’ (on b-b simulations, no detector effects!)

, , * = simulation input parameters* = simulation input parameters

Compute Compute effectiveeffective values of values of , , ** (LER or HER) from (LER or HER) from ee++/e/e-- charge charge distributionsdistributions::

yy = = **yy ’’yy = = **yy

Fit z-dependence of vertical beam size (LER or HER):Fit z-dependence of vertical beam size (LER or HER):

yy (z) = (z) = yy

22 + + ’’yy2 2 zz22 = ( = (**yy)) + (+ (**yy)) zz22

Fit z-dependence of luminous regionFit z-dependence of luminous region

z-dependence of vertical luminous size z-dependence of vertical luminous size yyL L (z, (z, yy**LERLER, , yy**HERHER) )

(bunch-length independent) (bunch-length independent)

longitudinal luminosity distribution Llongitudinal luminosity distribution L (z, (z, yy**LERLER, , yy**HERHER, , z, LERz, LER, , z, HERz, HER))


Single-beam Single-beam yy, , **yy fits (updated for actual z-dependence) fits (updated for actual z-dependence)

Low I High I

LER

HER

LER y 2 (z)

(Low current)

HER y 2 (z)

(Low current)

LER y 2 (z)

(High current)

HER y 2 (z)

(High current)


Single-beam Single-beam **yy fits fits ((highighh//lowlow ))

VariableVariable Simulation Simulation inputinput

Computed Computed from from , , ''

Fit Fit , , **yy to to

(y(yRMSRMS))22 vs. z vs. z

(single (single beam)beam)

yy*+ *+ (mm)(mm)

12.112.1

10.710.7

11.911.9

13.613.6

13.213.2

yy+ + (nm)(nm)

1.401.40

4.324.32

1.441.44

3.263.26

1.341.34

yy*- *- (mm)(mm)

12.512.5

11.811.8

12.512.5

12.212.2

13.313.3

yy- - (nm)(nm)

2.332.33

3.483.48

2.352.35

3.133.13

2.272.27

These results updated for y-z

correlations


z-dependence of vertical spot sizez-dependence of vertical spot size

LER vertical beam size squared

0

50

100

150

200

250

300

350

400

450

500

-40 -20 0 20 40z (mm)

sigy**2 (mu**2)

LER, high I (sim, RMS)

LER, high I (fitted)

LER, low I (sim, RMS)

LER, low I (fitted)

HER vertical beam size squared

0

50

100

150

200

250

300

350

400

450

500

-40 -20 0 20 40z (mm)

sigy**2 (mu**2)

HER, high I (sim, RMS)

HER, high I (fitted)

HER, low I (sim, RMS)

HER, low I (fitted)


2

3

4

5

6

7

8

9

10

-40 -20 0 20 40z (mm)

sigmayy_L (microns)

Low I (full sim, RMS)

Low I (from single-beam fits)

Low I (gen)Low I I (full sim, 1G fit))


Fitting the z-dependence of the vertical luminous sizeFitting the z-dependence of the vertical luminous size

LyLy22 ~ z ~ z22 (2 parameters), but we need 4: (2 parameters), but we need 4: yy

LERLER, , yyHER HER , , yy

LER LER , , yyHERHER

Several possibilities, e.g.:Several possibilities, e.g.:

Fix yLER, y

HER , yHER Fit y

LER

Fix yHER / y

LER , yHER Fit y

LER, yLER

y L

(z)

(m)

Low current Low current

y L

(z)

(m)

z (mm) z (mm)


**yy fits fits ((highighh//lowlow ) using the vertical -beam or -luminous size) using the vertical -beam or -luminous size





Fit Fit **yy++

yy

LumLum (z) (z)

Fit Fit **yy++, , yy

+ +

yy

LumLum (z) (z)

yy*+ *+ (mm)(mm)

12.112.1

13.613.6

13.213.2

17.417.4

12.812.8

16.316.3

16.516.5

yy+ + (nm)(nm)

1.401.40

3.263.26

1.341.34= sim input= sim input

1.441.44

1.191.19

yy*- *- (mm)(mm)

12.512.5

12.212.2

13.313.3= sim input= sim input = sim input= sim input

yy- - (nm)(nm)

2.332.33

3.133.13

2.272.27= sim input= sim input

yy-- / / yy

++ = sim = sim

inputinput


Bunch length fits to L(z) distribution (Bunch length fits to L(z) distribution (high/high/lowlow ))


FitFit zz++ only only

Fit Fit zz++

and and yy

*+*+

Fit Fit zz++

and and yy

*+*+ = = yy*-*-

yy*+ *+ (mm)(mm) 12.112.1 = Simulation = Simulation

inputinput

15.215.2

16.916.9

13.413.4

14.014.0

yy*- *- (mm)(mm) 12.512.5 = Simulation = Simulation

inputinput= Simulation = Simulation

inputinput

13.413.4

14.014.0

zz+ + (mm)(mm)

High High

Low Low

10.510.5 10.810.8

11.011.0

10.510.5

10.510.5

10.410.4

10.510.5

zz- - (mm)(mm) 12.512.5 = Simulation = Simulation



inputinput

Fitting code from B. Viaud

Fixed -normalization

method


Why is the fitted bunch length so stable?Why is the fitted bunch length so stable?

Fit z+ only

Fit z+, y

+

Fit z+ only

Fit z+, y

+

Fit z+ only

Fit z+, y

+

z (mm)

z (mm)

Fit

ted

/ ‘

mrs

d’

Ra

tio

of

fitt

ed

fu

nc

tio

ns

L (arb. units)

L(z) appears insensitive to * for |z| < 20 mm


Summary of Summary of **yy fits fits ((highighh//lowlow ))





Fit Fit **yy++, , yy

+ +

yy

LumLum (z) (z)

Fit Fit zz++, , **yy

++ to to

L L (z)(z)

yy*+ *+ (mm)(mm)

12.112.1

13.613.6

13.213.2

16.316.3

16.516.5

15.215.2

16.916.9

yy+ + (nm)(nm)

1.401.40

3.263.26

1.341.34

1.441.44

1.191.19

zz++ = 10.5 = 10.5

zz++ = 10.5 = 10.5

yy*- *- (mm)(mm)

12.512.5

12.212.2

13.313.3

= simulation = simulation inputinput

= simulation = simulation inputinput

yy- - (nm)(nm)

2.332.33

3.133.13

2.272.27

yy-- / / yy

++ = sim = sim

inputinput

zz-- = =

simulation simulation inputinput


Summary (I)Summary (I)

A beam-beam ‘pinch effect’ is apparent in the z-slice dependence of A beam-beam ‘pinch effect’ is apparent in the z-slice dependence of the vertical beam sizes, resulting in large variations in effective the vertical beam sizes, resulting in large variations in effective vertical emittance & vertical emittance & -function along the bunch.-function along the bunch.

the effect is spectacular at nominal bunch current

it may still be significant at low (10%) bunch current, and may be responsible for the small bias observed in the single-beam *y fits.

The bunch length fit [ L(z) ] and the fit to the vertical luminous size The bunch length fit [ L(z) ] and the fit to the vertical luminous size [ [ yy

LL(z) ] return (z) ] return **yy values consistent with each other, but values consistent with each other, but

overestimated by ~ 4-5 mm (as suggested by real data). This bias overestimated by ~ 4-5 mm (as suggested by real data). This bias may be due to the above-mentioned pinch effect. may be due to the above-mentioned pinch effect.

Additional beam-beam simulations at very low current (1% nominal) are in progress to verify this interpretation.

Bunch-length fits of the longitudinal luminosity distributionBunch-length fits of the longitudinal luminosity distribution return the correct (MC truth) bunch length within < 5%, at both low & high

, under all considered *y scenarios:

both *y’s fixed to true (input) values

one or both *y’s floated in the fit

The robustness of the bunch length fit is attributed to the fact that *y does not significantly affects the L(z) distribution until |z| > 20 mm.


However...However...

Still open / to be understood in the simulationStill open / to be understood in the simulation is the pinch effect really the culprit, i.e. will we get the correct * from the

luminous-region analyses at very low current (1% nominal) ?

what is the physics of the pinch effect? how is it different from the dynamic- effect?

Is it effectively a steady-state phenomenon?

on what time scale (# turns) does it stabilize?

what diagnostics can we run on the simulation to understand it better?

why does the ‘pinch effect’ (if it really is the culprit) induce similar * distortions at nominal and at low (10%) bunch current?

the error treatement is not correct in the (simulated) luminous-region analyses, in that it ignores the peculiar statistical-fluctuation mechanism: in the simulation, fluctuations are driven by the # of macroparticles in each bin, not by the luminosity as in the real world). Could the bias be worse than the present studies suggests? (The statistical treatement of the single-beam simulations IS correct, though.)

...and in the data...and in the data why does floating y change the fitted z

+ value?

why does the data fit @ fixed y look bad, while the same fit on the simulation looks decent (up to clarifying the stat. error issues above) ?

beam-beam & the lum in ous region - update

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