IR Design Requirements

This page discusses the requirements imposed by the EIC physics on the IR design.
The following requirements will be discussed in more detail below

1. the detection of neutrons of nuclear break up in the outgoing hadron beam direction
2. the detection of the scattered protons from exclusive and diffractive reaction in the outgoing proton beam direction
3. the detection of the spectator protons from ³He in polarized e+³He collisions (and in e+d)
4. the beam element free region around the IR and the requirements on the magnetic field of the detector
5. space for low Q² scattered lepton detection
6. space for the luminosity monitor in the outgoing lepton beam direction
7. space for lepton polarimetry

Breakup Neutrons

For exclusive and diffractive reactions in e-A scattering it is essential to detect the neutron of the nuclear break up in the direction of the outgoing beam. The figures below shows the scattering angle distribution for breakup neutrons for different Au beam energies and from a gold nucleus for different excitation energies of the nucleus.

These distributions lead to the requirement of a angular acceptance of +/- 4mrad to allow to detect these neutrons in the ZDC

Scattered protons

To reconstruct the Mandelstam variable t, which represents the momentum transfer to the proton in exclusive reactions, it is critical to detect the forward going scattered proton. t is essential in exclusive reactions as it can be fourier transformed to the impact parameter b, which gives the transverse spatial distribution of partons in the proton. t is for exclusive reaction pt² of the proton. The figure below shows the scattering angle θ for three different center-of-mass energies as a function of the scattered proton momentum. Also shown are projections for the longitudinal momentum for 2 different proton beam energies.

This poses the following requirement that for different hadron beam energies 100 GeV and 250 GeV protons with a momentum at a maximum of 10% lower then the proton beam energy and a scattering angles up to 10 mrad need to be transported through the different magnets.
There is basically no correlation between the momentum and the scattering angle. For diffractive events an acceptance of 5% of the beam momentum would be totally acceptable as well. These protons cannot be detected in the main detector. The standard detectors used to detect the scattered proton are roman pots placed at different distances from the IR. Using this detector technology poses an other requirement on the machine performance. To reach as small scattering angles as possible a small emittance of the beam is crucial as there is also an additional requirement of 10 σ clearance from the core of the beam.
This translate in the requirement thet we need an acceptance in pt² of 0.17 GeV to 1.3 GeV, which translates into a t acceptance of 0.03 GeV² to 1.6 GeV² at 100 GeV and 250 GeV proton beam energy. To have good acceptance at low scattering angle the beam needs to be cooled in transverse direction to achieve a beam angular divergence of ~100μrad

Spectator protons

-Crucial for identifying processes with a neutron “target” (e+n) in e+³He (and e+d).
-Spectator neutron (<~3 mrad) can be measured by ZDC.
-Tagging spectator protons from ³He (and d):

• Relying on separation from magnetic rigidity (B_r) changes ³He: p = 3/2:1 (d:p = 2:1)
• No need to reconstruct momentum but need clean identification: position+directional measurement
• Common detectors (Roman Pots) can be utilized for tagging forward proton from DVCS and the spectator protons from ³He

Scattering angle vs. momentum of spectator protons in e+³He at 10(e)x100(N) GeV [left]. The projections in angle (rad) and momentum (GeV/c) are shown in the center and right panels. The acceptance of the protons at the detector depends on the IR optics of the beam. The calculation was done using DPMJETIII with Fluka implementation. The requirements of the detectors for the spectator tagging with an IR design can be found here. The distributions are similar for spectator protons in e+d as the dominant contribution to the angular and momentum distributions are from fermi momenta in the "target" nucleus.

Detector Space and Magnetic Field

the detector needs a +/- 4.5m beam element free region.
Any magnetic field which is introduced in addition to the solenoidal field of the detector, needs to obey the following requirements.

• the region of the RICH in the forward and backward direction should be free of any magnetic field
• the magnetic field homogeneity needs to obey the requirements posed by the TPC
• the bore of the solenoid must have at least a radius of 1m
• the forward tracking resolution must be retained

low Q2-tagger

for many physics topics it is important to tag the scattered lepton at very small scattering angles and such as very low Q².
The main detector covers -4 to 4 in rapidity for the scattered lepton. So scattered leptons with a scattering angle > 178 degree will not be detected in the main detector. The plots below correlate the momentum of the scattered lepton with its scattering angle and its Q². To see some of these low Q² leptons it is important to separate the scattered lepton from the outgoing lepton beam. To have a reasonable low Q² acceptance the requirement for the IR is to transport
leptons with 10% momentum of the full beam energy (E_e' >= 0.9 E) and with a scattering angle from 179.5 to 178 degree (180 degree being the outgoing beam) through the magnets.
The resulting Q² distribution after applying all the requirements listed above is shown in the 4th row below.

20 GeV x 100 GeV	10 GeV x 100 GeV	5 GeV x 100 GeV
20 GeV x 100 GeV	10 GeV x 100 GeV	5 GeV x 100 GeV
20 GeV x 100 GeV	10 GeV x 100 GeV	5 GeV x 100 GeV
20 GeV x 100 GeV	10 GeV x 100 GeV	5 GeV x 100 GeV

Luminosity Monitor

to achieve the precision needed for the luminosity measurement to match the statistical uncertainties anticipated for eRHIC, it is important to follow and improve the concept of luminosity measurements at HERA as described in here. The technique involves a electromagnetic calorimeter for photon detector and a pair spectrometer. The picture below shows a schematic view of the ZEUS layout a similar layout needs to be realized for eRHIC.

It is planned to use the Bethe-Heitler process (e+p → e+p+γ) to measure the luminosity. It is proposed to use this process because the cross section is large and it is a calculable process in QED (see reference paper and references within). The analytical expression for the photon energy distribution and the approximate angular distribution from paper are implemented in a Monte Carlo event generator. The event generator DJANGOH was used was also used to simulate this process. The results for the expected scattering angle distribution of the photons is shown below.

Lepton polarimetry

requirements need still to be worked out