# Luminosity

High-precisision measurements at an EIC will require a sufficiently large beam luminosity.
This page contains information concerning the achievable luminosity of eRHIC based on the collider design as described in the eRHIC Design study.

### eRHIC as in the EIC White Paper

The eRHIC design has an electron beam with energies ranging from 15.9 to 21.2 GeV with longitudinal polarisation of ~80%.
The hadron beam energy can be varied and has it maximum at 250 GeV for protons, giving a maximum centre of mass energy of 145 GeV.
It is planned to also have polarized He-3 beams (Emax=166 GeV).
The proton and He-3 beams can have at all energies either longitudinal and transverse polarization.
Maximum beam energy for gold nuclei is 100 GeV/A. RHIC can run a huge variety of nuclei from D, over Si, Cu to Au,U,Pb
Protons as well as nuclei beams can be run at lower energies as 250 / 100 GeV/c/A, the luminosity scales for the lower energies as described in the figure/table below.
The eRHIC design assumes CeC (Litvinenko and Derbenev, 2009) and crab cavities to be implemented.

For all stages of eRHIC the first machine elements are at 4.5m from the IP.

The luminosities are given for one IR. With each additional IR this luminosity must be shared. The sharing can happen at any ratio, but for a 50:50 sharing the luminosity per IR with a 2 IR setup gets reduced by a factor of 2.

The luminosity and beam parameters for the eRHIC Design study are given in the table below.

Note: all eA luminosities are given per nucleon, this is different to the normal standard at RHIC, which gives pA and AA luminosities per nucleus

Luminosity and beam parameters of the eRHIC Design study.

Luminosity as function of lepton and hadron beam energy.

Some remarks on the luminosity:

• The luminosity does not depend on the electron beam energy below 21.2 GeV
• The luminosity is proportional to the hadron beam energy: L ~ Eh/Etop (Etop=250 GeV)
• As the luminosity is shared between IRs
• 2 IRs lead to a factor 2 reduction compared to the luminosity shown in the figure above assuming a 50:50 sharing of luminosity between the 2 IRs
• The luminosity scales linear with the L*
• L* being the distance between the IP and the first focusing magnet
• eRHIC default design L*=4.5m
• No difference in ep or eA luminosity as function of √s

### Fast Track eRHIC Design

To realize an EIC on a faster time scale implications of a machine with reduced risk/cost have been studied. The changes to the above design are operating the hadron beam with a bunch 15% of the current RHIC. This would reduce the requirements on the coherent electron cooling. In addition it allows to operate with present RHIC vacuum chamber (e.g. no coating is needed) and without space-charge compensation at lower hadron energies. The luminosity of such an eRHIC machine would be a factor of 10 lower, but all other features of the machine as described above would be conserved.

The resulting luminosities are described in the table below.

fast track eRHIC luminosity for one IR:

sqrt(s) 55 67 77 122
Beam Energies 15x50 15x75 15x100 15x250
ep/eA 1.0e+33 1.5e+33 1.5e+33 1.5e+33
Integrated luminosity / month1 0.3 fb-1 0.6 fb-1 1.2 fb-1 3.0 fb-1

1 an conservative 50% overall running efficiency is assumed to calculate the Integrated luminosity / month

eRHIC luminosity for one IR after vacuum chamber coating: a 10-fold higher luminosity can be reached'

sqrt(s) 45 55 64 100
Beam Energies 10x50 10x75 10x100 10x250
ep/eA 0.25e+34 0.5e+34 1.0e+34 2.5e+34
Integrated luminosity / month1 3 fb-1 6 fb-1 12 fb-1 30 fb-1

1 an conservative 50% overall running efficiency is assumed to calculate the Integrated luminosity / month