Intensities Collective Effects - CERN · 2011. 10. 21. · Christian Hansen, BE-ABP, CERN Oct 20,...

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



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)



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)



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)

→



6He Intensities for SF=2.3%

http

s://

espa

ce.cer

n.ch

/betan

u/Co

des/

Gen

eral/b

bInt

ensities

.nb


http://svnweb.cern.ch/world/wsvn/bbphase
























































































































• 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)


http

s://

espa

ce.cer

n.ch

/betan

u/Co

des/

Gen

eral/b

bInt

ensities

.nb


























































































































γ = 100

• Product ion

➡ 5.0e13 6He/s


➡ 1.44e12 6He/ECR Accumulat ion

• RCS (1 bunch)


• PS (20 bunches)


• SPS (80 bunches)

➡ 2.48e11 6He/bunch http

s://

espa

ce.cer

n.ch

/betan

u/Co

des/

Gen

eral/b

bInt

ensities

.nb

























































































































18Ne Intensities for SF=2.3%

http

s://

espa

ce.cer

n.ch

/betan

u/Co

des/

Gen

eral/b

bInt

ensities

.nb


























































































































• Product ion

➡ 1.2e13 18Ne/s


➡ 2.43e12 18Ne/ECR Accumulat ion

• RCS (1 bunch)

➡ 1.2e11 18Ne/bunch

• PS (20 bunches)


http

s://

espa

ce.cer

n.ch

/betan

u/Co

des/

Gen

eral/b

bInt

ensities

.nb


























































































































γ = 100

• Product ion

➡ 1.2e13 18Ne/s


➡ 2.43e12 18Ne/ECR Accumulat ion

• RCS (1 bunch)


• PS (20 bunches)


• SPS (80 bunches)

➡ 0.86e11 18Ne/bunch http

s://

espa

ce.cer

n.ch

/betan

u/Co

des/

Gen

eral/b

bInt

ensities

.nb

























































































































Accumulation by Merging


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






Flat vs. Parabolic

Distribution:Distribution:

Flat Parabolic

6HeCollimated 30% 11%

6HeDecayed 70% 89%

18NeCollimated 44% 28%

18NeDecayed 56% 62%

80 bunches



Flat vs. Parabolic

Distribution:Distribution:

Flat Parabolic

6HeCollimated 30% 11%

6HeDecayed 70% 89%

18NeCollimated 44% 28%

18NeDecayed 56% 62%

80 bunches

See Antoine’sTalk



Achieved ν Fluxes8.2e11 18Ne/bunch12.0e11 6He/bunchNbsat=

ϕ=1.0e18 ν /yearϕ=3.0e18 ν /year



SF Increase



Latest Results



⋯ and TMCIs ?

http://svnweb.cern.ch/world/wsvn/bbcollective




A new Space ChargeImplementation into HEADTAIL

Christian Hansen



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



Round Quasi Parabolic• SPS

γ = 27.7Nb = 1e11σz = 0.12 mδ = 2e-3

Qs = 5.9e-3ɛN = 3 μm

βx,y = 41 m



Round Gaussian• SPS



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



Backup Slides



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



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



6He


Nbsat=11.0e11 6He/bunch

Required 6He Bunch Intensity


Intensities Collective Effects - CERN · 2011. 10. 21. · Christian Hansen, BE-ABP, CERN Oct 20,...

Documents

Transcript of Intensities Collective Effects - CERN · 2011. 10. 21. · Christian Hansen, BE-ABP, CERN Oct 20,...