Post on 18-Feb-2016
description
Luminosity energy scaling.
V. Ptitsyn, A. Fedotov, V.N. Litvinenko
December 02, 2010
eRHICp e
Energy, GeV 325 20Number of bunches/ Bunch frequency, MHz 166 14.08Bunch intensity, 1011 2.0 0.22Beam current, mA 415 50Rms normalized emittance, 1e-6 m 0.18 20
Rms emittance, 1e-9 m 0.52 0.52β*, cm 5 5Beam-beam parameter for p; Disruption for e 0.015 27.1rms bunch length, cm 4.9 0.2Space charge parameter 0.035Angular spread in the IP, mrad 0.1 0.1Luminosity, x 1033, cm-2s-1
(with hourglass reduction) 15
What is a dependence of a maximum luminosity on g ?
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L =AZ 2rp
Necβ*
2πσ sC2 γ 3β2 f
σ sβ*
⎛ ⎝ ⎜
⎞ ⎠ ⎟ΔQsc
iscssi
p
QfC
crZAL
g
*
242*24
2 24
g
*2
2
*2 12 si
p
fCcN
rZAL
Luminosity optimization
Max p
(for given Ne)Max Qsp
Np
p
€
L ~NeN p
ε pMax angular spread(IR magnet aperture)
Max luminosity
p0, Np0
€
p0 = k1Neγ pξp
€
N p0 = k2γ p2 ΔQspξp
Ne
€
Lmax (Ne,ΔQsp ,ξp ) = k0γ3NeΔQsp
Luminosity behavior in combined space charge, beam-beam and electron current limit
• Maximum luminosity scales with the proton energy as g3.• Parameter scaling for maximum luminosity (at fixed p): np =const, Np ~ g2
• One can go away from the beam-beam limit without losing the luminosity by keeping the ration Np/p constant
• If we can go beyond 50mA electron current the luminosity can be increased. The following rule: L -> nL => Ne -> nNe, Np->nNp, p -> np
€
L =AZ 2rp
Necβ*
2πσ sC2 γ 3β2 f
σ sβ*
⎛ ⎝ ⎜
⎞ ⎠ ⎟ΔQsc
eRHICp e
Energy, GeV 50 5Number of bunches/ Bunch frequency, MHz 166 14.07
Bunch intensity, 1011 0.047 (0.2) 0.22
Beam current, mA 10 (42) 50
Rms normalized emittance, 1e-6 m 0.18 (0.77) 33
Rms emittance, 1e-9 m 3.4 (14.5) 3.4
β*, cm 5 5 (21)
Beam-beam parameter for p; Disruption for e 0.015 (0.0035) 0.4
rms bunch length, cm 4.9 0.2Space charge parameter 0.035
Angular spread in the IP, mrad 0.26 (0.54)
0.26 (0.13)
Luminosity, x 1033, cm-2s-1
(with hourglass reduction) 0.054
CME dependence of luminosityAssumed limits: Ie = 50 mA, p =0.015, Qsp = 0.035
Qsp = 0.035: L > 1033 s-1 cm-2
CME > 51 GeVEp > 130 GeV
Qsp = 0.07:L > 1033 s-1 cm-2
CME > 46 GeVEp > 106 GeV
What should be a design value for Qsp ?
The value used in ELIC
Study plans for the luminosity at lower CME
• Simulations are planned to explore the interplay of beam-beam and space charge effects for proton beam. That will help to better determine maximum Qsp .
• Larger proton bunch length (combined with increased proton bunch intensity) can lead to the luminosity increase. We plan to explore this, together with the requirements on crab cavities.
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