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Beta Beams,EUROnu WP4
Intensities & Collective Effects
Christian Hansen20/10/2011, Beta Beam Meeting, Naples
Many thanks to: E. Benedetto, A. Chancé, E. Fernandez-Martinez, K. Li, E. Metral, N. Mounet, G. Rumolo, B. Salvant, R. Thomas & E. Wildner
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Outline
• Large θ13 Implication
➡ Required Intensities
➡ BB Intensities
➡ Accumulation
➡ Fluxes
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Implications from T2K’s Indications• T2K indicates
with 2 .5σ thats in22θ 13 > 0 .03(Δm232 > 0)
• → SF not as cruc ia l for Beta Beams; SF = 2% a l lowed!Even 2 .3% … ?(before SF = 0 .58%)
• DR’s Duty Cycle 4 t imeslarger → 80 bunches ( instead of 20)
Comparison with sbeam is incomplete
due to unknown systemat ic errors
(here put to 5% for s igna l and 10%
for bkg for both βbeams and sbeams)
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Implications from T2K’s Indications• T2K indicates
with 2 .5σ thats in22θ 13 > 0 .03(Δm232 > 0)
• → SF not as cruc ia l for Beta Beams; SF = 2% a l lowed!Even 2 .3% … ?(before SF = 0 .58%)
• DR’s Duty Cycle 4 t imeslarger → 80 bunches ( instead of 20)
E. Fernandez-Martinez
Comparison with sbeam is incomplete
due to unknown systemat ic errors
(here put to 5% for s igna l and 10%
for bkg for both βbeams and sbeams)
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Required DR Intensitiesϕ 0=1.1e18 ν /yearϕ 0=2.9e18 ν /year
8.8e11 18Ne/bunch11.6e11 6He/bunch
80 bunches→
14 .4s (18 Ne)
& 16.8s (6 He)
→
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
6He Intensities for SF=2.3%
http
s://
espa
ce.cer
n.ch
/betan
u/Co
des/
Gen
eral/b
bInt
ensities
.nb
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
6He Intensities for SF=2.3%
• Product ion
➡ 5.0e13 6He/s
• ECR Source (pulse)
➡ 1.44e12 6He/ECR Accumulat ion
• RCS (1 bunch)
➡ 7.00e11 6He/bunch
• PS (20 bunches)
➡ 4.02e11 6He/bunch
http
s://
espa
ce.cer
n.ch
/betan
u/Co
des/
Gen
eral/b
bInt
ensities
.nb
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
6He Intensities for SF=2.3%
γ = 100
• Product ion
➡ 5.0e13 6He/s
• ECR Source (pulse)
➡ 1.44e12 6He/ECR Accumulat ion
• RCS (1 bunch)
➡ 7.00e11 6He/bunch
• PS (20 bunches)
➡ 4.02e11 6He/bunch
• SPS (80 bunches)
➡ 2.48e11 6He/bunch http
s://
espa
ce.cer
n.ch
/betan
u/Co
des/
Gen
eral/b
bInt
ensities
.nb
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
18Ne Intensities for SF=2.3%
http
s://
espa
ce.cer
n.ch
/betan
u/Co
des/
Gen
eral/b
bInt
ensities
.nb
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
18Ne Intensities for SF=2.3%
• Product ion
➡ 1.2e13 18Ne/s
• ECR Source (pulse)
➡ 2.43e12 18Ne/ECR Accumulat ion
• RCS (1 bunch)
➡ 1.2e11 18Ne/bunch
• PS (20 bunches)
➡ 1.00e11 18Ne/bunch
http
s://
espa
ce.cer
n.ch
/betan
u/Co
des/
Gen
eral/b
bInt
ensities
.nb
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
18Ne Intensities for SF=2.3%
γ = 100
• Product ion
➡ 1.2e13 18Ne/s
• ECR Source (pulse)
➡ 2.43e12 18Ne/ECR Accumulat ion
• RCS (1 bunch)
➡ 1.2e11 18Ne/bunch
• PS (20 bunches)
➡ 1.00e11 18Ne/bunch
• SPS (80 bunches)
➡ 0.86e11 18Ne/bunch http
s://
espa
ce.cer
n.ch
/betan
u/Co
des/
Gen
eral/b
bInt
ensities
.nb
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Accumulation by Merging
http://svnweb.cern.ch/world/wsvn/bbphase
Required 18Ne Bunch Intensity
Required 6He Bunch Intensity
0.86e11 18Ne/bunch2.48e11 6He/bunch
Nbsat=12.0e11 6He/bunch Nbsat=8.2e11 18Ne/bunch
30% collimated70% decayed
44% collimated56% decayed
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Flat vs. Parabolic
Distribution:Distribution:
Flat Parabolic
6HeCollimated 30% 11%
6HeDecayed 70% 89%
18NeCollimated 44% 28%
18NeDecayed 56% 62%
80 bunches
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Flat vs. Parabolic
Distribution:Distribution:
Flat Parabolic
6HeCollimated 30% 11%
6HeDecayed 70% 89%
18NeCollimated 44% 28%
18NeDecayed 56% 62%
80 bunches
See Antoine’sTalk
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Flat vs. Parabolic
Distribution:Distribution:
Flat Parabolic
6HeCollimated 30% 11%
6HeDecayed 70% 89%
18NeCollimated 44% 28%
18NeDecayed 56% 62%
80 bunches
See Antoine’sTalk
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Achieved ν Fluxes8.2e11 18Ne/bunch12.0e11 6He/bunchNbsat=
ϕ=1.0e18 ν /yearϕ=3.0e18 ν /year
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
SF Increase
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Latest Results
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
⋯ and TMCIs ?
http://svnweb.cern.ch/world/wsvn/bbcollective
Friday, October 21, 2011
A new Space ChargeImplementation into HEADTAIL
Christian Hansen
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Two Cases• Round beam with quasi
parabolic distribution function
• Round beam with Gaussiandistribution function
jx =�x2 + x�2β2
x
�/10σx
∆Qxincoh = − Nbrp
5πBβγ2εnormrms
�1− 9
8jx − 3
4jy +
5
8j2x +
3
4jxjy +
3
8j2y − 35
256j3x − 15
64j2xjy −
27
128jxj
2y − 5
64j3y
�
B = σz/�√
2πR�
Stability Diagrams for Landau Damping with Two-Dimensional Betatron Tune Spread from Both Octupoles and Non-Linear Space Charge, E. Metral et ali.
Head-tail modes for strong space charge, A. Burov
∆Q = Qmax
� 1
0
�I0
�Jx
z2
�− I1
�Jx
z2
��I0
�Jy
z2
�
exp�(Jx + Jy)
z2
� dz
Qmax =λrpR
2εxγ3β2 λ =Nslice
∆zsliceJx =
x2
2βxεx+
βxpx2εx
See backup slide
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Round Quasi Parabolic• SPS
γ = 27.7Nb = 1e11σz = 0.12 mδ = 2e-3
Qs = 5.9e-3ɛN = 3 μm
βx,y = 41 m
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Round Gaussian• SPS
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Canonical Variable J
Transform:
then
H = Jx/βx
x =�
2Jxβx cosψ
px = −�
2Jx/βx sinψH =
�x2
2+
p2x
2
�1
βx
∂H
∂Jx= 1
∂H
∂ψ= 0
“Smooth Approximation”:
β�x = 0
Get Jx as function of x and px by using cos2Ψ+sin2Ψ=1
Jx =x2
2βxεx+
βxpx2εx
εx is rms not normalized emittance
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
Backup Slides
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
18Ne## TIME = 399.787 sBunch 0: # running = 0, # decayed = 56, # collim. = 44, decayed/collim. = 1.27272727Bunch 1: # running = 1, # decayed = 55, # collim. = 44, decayed/collim. = 1.25Bunch 2: # running = 3, # decayed = 53, # collim. = 44, decayed/collim. = 1.20454545Bunch 3: # running = 4, # decayed = 51, # collim. = 45, decayed/collim. = 1.13333333Bunch 4: # running = 1, # decayed = 58, # collim. = 41, decayed/collim. = 1.41463415Bunch 5: # running = 4, # decayed = 55, # collim. = 41, decayed/collim. = 1.34146341Bunch 6: # running = 7, # decayed = 52, # collim. = 41, decayed/collim. = 1.26829268Bunch 7: # running = 10, # decayed = 56, # collim. = 34, decayed/collim. = 1.64705882Bunch 8: # running = 17, # decayed = 55, # collim. = 28, decayed/collim. = 1.96428571Bunch 9: # running = 16, # decayed = 53, # collim. = 31, decayed/collim. = 1.70967742Bunch 10: # running = 15, # decayed = 51, # collim. = 34, decayed/collim. = 1.5Bunch 11: # running = 23, # decayed = 53, # collim. = 24, decayed/collim. = 2.20833333Bunch 12: # running = 23, # decayed = 52, # collim. = 25, decayed/collim. = 2.08Bunch 13: # running = 26, # decayed = 51, # collim. = 23, decayed/collim. = 2.2173913Bunch 14: # running = 28, # decayed = 51, # collim. = 21, decayed/collim. = 2.42857143Bunch 15: # running = 44, # decayed = 47, # collim. = 9, decayed/collim. = 5.22222222Bunch 16: # running = 42, # decayed = 44, # collim. = 14, decayed/collim. = 3.14285714Bunch 17: # running = 44, # decayed = 40, # collim. = 16, decayed/collim. = 2.5Bunch 18: # running = 52, # decayed = 39, # collim. = 9, decayed/collim. = 4.33333333Bunch 19: # running = 58, # decayed = 35, # collim. = 7, decayed/collim. = 5Bunch 20: # running = 58, # decayed = 31, # collim. = 11, decayed/collim. = 2.81818182Bunch 21: # running = 63, # decayed = 30, # collim. = 7, decayed/collim. = 4.28571429Bunch 22: # running = 64, # decayed = 29, # collim. = 7, decayed/collim. = 4.14285714Bunch 23: # running = 67, # decayed = 22, # collim. = 11, decayed/collim. = 2Bunch 24: # running = 73, # decayed = 20, # collim. = 7, decayed/collim. = 2.85714286Bunch 25: # running = 76, # decayed = 17, # collim. = 7, decayed/collim. = 2.42857143Bunch 26: # running = 76, # decayed = 13, # collim. = 11, decayed/collim. = 1.18181818Bunch 27: # running = 83, # decayed = 6, # collim. = 11, decayed/collim. = 0.545454545
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
6He## TIME = 399.781 sBunch 0: # running = 0, # decayed = 70, # collim. = 30, decayed/collim. = 2.33333333Bunch 1: # running = 0, # decayed = 67, # collim. = 33, decayed/collim. = 2.03030303Bunch 2: # running = 0, # decayed = 67, # collim. = 33, decayed/collim. = 2.03030303Bunch 3: # running = 0, # decayed = 71, # collim. = 29, decayed/collim. = 2.44827586Bunch 4: # running = 2, # decayed = 64, # collim. = 34, decayed/collim. = 1.88235294Bunch 5: # running = 3, # decayed = 70, # collim. = 27, decayed/collim. = 2.59259259Bunch 6: # running = 0, # decayed = 64, # collim. = 36, decayed/collim. = 1.77777778Bunch 7: # running = 3, # decayed = 72, # collim. = 25, decayed/collim. = 2.88Bunch 8: # running = 5, # decayed = 67, # collim. = 28, decayed/collim. = 2.39285714Bunch 9: # running = 4, # decayed = 69, # collim. = 27, decayed/collim. = 2.55555556Bunch 10: # running = 9, # decayed = 69, # collim. = 22, decayed/collim. = 3.13636364Bunch 11: # running = 7, # decayed = 66, # collim. = 27, decayed/collim. = 2.44444444Bunch 12: # running = 12, # decayed = 65, # collim. = 23, decayed/collim. = 2.82608696Bunch 13: # running = 20, # decayed = 60, # collim. = 20, decayed/collim. = 3Bunch 14: # running = 20, # decayed = 59, # collim. = 21, decayed/collim. = 2.80952381Bunch 15: # running = 27, # decayed = 56, # collim. = 17, decayed/collim. = 3.29411765Bunch 16: # running = 31, # decayed = 53, # collim. = 16, decayed/collim. = 3.3125Bunch 17: # running = 35, # decayed = 52, # collim. = 13, decayed/collim. = 4Bunch 18: # running = 37, # decayed = 50, # collim. = 13, decayed/collim. = 3.84615385Bunch 19: # running = 43, # decayed = 44, # collim. = 13, decayed/collim. = 3.38461538Bunch 20: # running = 53, # decayed = 34, # collim. = 13, decayed/collim. = 2.61538462Bunch 21: # running = 57, # decayed = 27, # collim. = 16, decayed/collim. = 1.6875Bunch 22: # running = 64, # decayed = 20, # collim. = 16, decayed/collim. = 1.25Bunch 23: # running = 71, # decayed = 13, # collim. = 16, decayed/collim. = 0.8125
Friday, October 21, 2011
Christian Hansen, BE-ABP, CERN Oct 20, 2011
6He
49% collimated51% decayed
Nbsat=11.0e11 6He/bunch
Required 6He Bunch Intensity
Friday, October 21, 2011