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

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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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