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Beam-beam & the lum in ous region - update. W. Kozanecki 4 March 05. “To do” list left over from BaBar week Understand whether the y-truncation of the luminous region (|y| < 25 m in the present luminous-region analysis) significantly biases the vertical luminous size at high |z| - PowerPoint PPT Presentation
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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
W. Kozanecki 4 Mar 05 Slide 2
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?
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)Low I I (full sim, 1G fit))
W. Kozanecki 4 Mar 05 Slide 3
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)
W. Kozanecki 4 Mar 05 Slide 4
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
W. Kozanecki 4 Mar 05 Slide 5
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+
W. Kozanecki 4 Mar 05 Slide 6
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-
W. Kozanecki 4 Mar 05 Slide 7
**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))
W. Kozanecki 4 Mar 05 Slide 8
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)
W. Kozanecki 4 Mar 05 Slide 9
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
W. Kozanecki 4 Mar 05 Slide 10
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)
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-beam fits)
Low I (gen)Low I I (full sim, 1G fit))
W. Kozanecki 4 Mar 05 Slide 11
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)
W. Kozanecki 4 Mar 05 Slide 12
**yy fits fits ((highighh//lowlow ) using the vertical -beam or -luminous size) using the vertical -beam or -luminous size
VariableVariable Simulation Simulation inputinput
Fit Fit , , **yy to to
(y(yRMSRMS))22 vs. z vs. z
(single (single beam)beam)
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
W. Kozanecki 4 Mar 05 Slide 13
Bunch length fits to L(z) distribution (Bunch length fits to L(z) distribution (high/high/lowlow ))
VariableVariable Simulation Simulation inputinput
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= Simulation = Simulation
inputinput= Simulation = Simulation
inputinput
Fitting code from B. Viaud
Fixed -normalization
method
W. Kozanecki 4 Mar 05 Slide 14
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
W. Kozanecki 4 Mar 05 Slide 15
Summary of Summary of **yy fits fits ((highighh//lowlow ))
VariableVariable Simulation Simulation inputinput
Fit Fit , , **yy to to
(y(yRMSRMS))22 vs. z vs. z
(single (single beam)beam)
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
W. Kozanecki 4 Mar 05 Slide 16
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.
W. Kozanecki 4 Mar 05 Slide 17
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) ?