An e+e−/γγ/ep Accelerator Complex at a Future Circular Collider

This is the second paper by the author describing versatile accelerator complexes that could be built at a Future Circular Collider (FCC) in order to produce e e + − , γγ and ep collisions. The facility described here features an ILC-based e e + − collider placed tangentially to the FCC tunnel. If the collider is positioned asymmetrically with respect to the FCC tunnel, electron (or positron) bunches could be accelerated by both linacs before they are brought into collision with the 50-TeV beams from the FCC proton storage ring (FCC-pp). The two linacs may also form a part of the injector chain for FCC-pp. The facility could be converted into a γγ collider or a source of multi-MW beams for fixed-target experiments.

(c.m.) energies ee s considerably exceeding those attainable at circular e e + − colliders. For instance, one has to measure separately the HWW, HHH and Htt couplings at 500 GeV ee s  in order to determine the corresponding SM loop contributions to the effective HZZ coupling [7]. This would not be possible to accomplish using the proposed FCC-ee facility.
The Htt coupling cannot be directly measured in e e + − interactions below 500 GeV ee s ≈ , since the cross-section for the relevant process is negligible (see Figure 1). The HHH coupling can be directly measured at energies above the kinematic threshold for ZHH e e + − → , or by using the WW-fusion channel at 1 TeV ee s  . Indirect and model dependent measurements of the HHH coupling are possible at lower energies by exploiting the loop corrections to single Higgs channels. However, the sensitivity of such measurements is very low, as can be inferred from Figure 4 in [8].  [12].
Since the Higgs-boson mass affects the values of electroweak observables through radiative corrections, high-precision electroweak measurements provide a natural complement to direct studies of the Higgs sector. All the measurements made at LEP and SLC could be repeated at the facility described in this note, but at much higher luminosities and using 80% polarized electron beams [9]. The importance of beam polarization for some high-precision measurements was already stressed.
If electron or positron bunches are brought into collision with the 50-TeV proton beams from the FCC-pp storage ring, one would obtain an important source of deep-inelastic ep interactions. 1 Such interactions would yield valuable 1 The proposed FCC-eh electron-proton collider [10] would provide a higher luminosity than the facilities described in this paper and [3], but would have a considerably lower electron beam energy (around 60 GeV). Journal of High Energy Physics, Gravitation and Cosmology information on the quark-gluon content of the proton, which is crucial for precision measurements at the FCC-pp. The physics potential of a TeV-scale ep collider is comprehensively discussed in [11].
A two-linac collider or an SLC-type facility [3] could be constructed in several stages, each with distinct physics objectives that require particular centre-of-mass energies (see Figure 1):

An ILC-Based e + e − /γγ/ep Facility at FCC
The ILC-based facility at a Future Circular Collider (FCC) shown in Figure 2 features a superconducting two-linac e e + − collider placed tangentially to the FCC tunnel. Using an optical free-electron laser, the linacs could be converted into a high-luminosity γγ collider. As mentioned in the Introduction, the maximum luminosity at a circular e e + − collider is severely constrained by beamstrahlung effects at high energies; Figure 2. An ILC-based facility at FCC (BC stands for bunch compression). Electron (or positron) bunches are accelerated by both linacs before their collision with the 50-TeV proton beam from the FCC-pp storage ring. The two superconducting L-band linacs may form the low-energy part of the FCC-pp injector chain. A much cheaper alternative to this facility is described in [3]. Journal of High Energy Physics, Gravitation and Cosmology also, it is very difficult to achieve a high degree of beam polarization. At the e e + − facilities described in this paper and [3], luminosity grows almost linearly with the beam energy and the electron beam polarization can reach 80%.
The baseline parameters for the proposed ILC collider, shown in Table 1, reflect the need to balance the constraints imposed by the various accelerator sub-systems, as explained in [13]. The rf power is provided by 10 MW mul- In order to maximize luminosity at low centre-of-mass energies, the beam power could be increased by increasing the pulse repetition rate rep f while reducing the accelerating gradient of the main linacs. At 25 G V 0 e ee s = , the power consumption of the main 250-GeV linacs is reduced by over a factor of two when they are running at half their nominal gradient. Under these conditions, one can run the accelerator at the maximum repetition rate of 10 Hz (determined by the cryogenic system and the beam damping time damp 80 t ≈ ms), thus doubling its luminosity.
The two superconducting L-band linacs in Figure 2 may also form a part of the FCC-pp injector chain. Since the collider is positioned asymmetrically with respect to the FCC tunnel, electron (or positron) bunches could be accelerated by both linacs before they are brought into collision with the 50-TeV beams from the FCC-pp proton storage ring. The entire accelerator complex would serve as a source of e e + − , γγ , pp and ep interactions. Journal of High Energy Physics, Gravitation and Cosmology

Main Parameters of a Linac-Ring ep Collider at FCC
The idea to combine a 140-GeV electron linac and a 20-TeV proton storage ring in order to produce ep interactions at very high c.m. energies was put forward in 1979 as a possible option at the SSC proton collider [14]. In 1987 it was proposed to place a 2-TeV linear e e + − collider (VLEPP) tangentially to a 6-TeV proton-proton collider (UNK) at IHEP in Protvino [15], with the aim of obtaining both ep and p γ collisions. Similar proposals for lepton-hadron and photon-hadron colliders at HERA, LHC and FCC have since been made (see [16] and references therein).
The facility shown in Figure 2 is an ILC-based version of the original VLEPP⊗UNK design. Since the collider is positioned asymmetrically with respect to the FCC tunnel, electron (or positron) bunches could be accelerated by both linacs (which contain standing wave cavities) before they are brought into collision with the 50-TeV beams from the FCC-pp proton storage ring.
An ILC-type linac is a suitable source of electron beams for an electron-proton collider, because: 1) the spacing between electron bunches can be made to match that between the proton bunches in the FCC-pp storage ring, and 2) the length of an electron "bunch train" corresponds roughly to the FCC ring circumference.
This is not the case, for instance, with an X-band linac, where the electron bunch spacing (~1 ns) is much shorter than that between proton bunches at the FCC-pp (see Table 2).  In Equation (1),  is a product of three correction factors with values typically close to unity: The factor  Table 2), the "length" of the proton beam is where e ε and p ε denote geometric emittances [11] [21] (the normalized emittance n ε γ ε = is invariant under acceleration); erfc(z) is the "complementary error function" (defined as the area under the "tails" of a Gaussian distribution).
The enhancement factor pinch H in Equation (2) is due to the attractive beam-beam force. Since the electron bunch charge is relatively small and the proton energy is high, the beam-beam force acting on electrons has a much greater strength than that acting on protons. Consequently, the electron bunch is R. Belusevic Journal of High Energy Physics, Gravitation and Cosmology focused by the protons during a collision. This leads to a reduction in the transverse electron beam size ("pinch effect") and hence to an increase in the luminosity. The effect can be simulated using the program Guinea-Pig (see [10] and references therein, as well as Table 3).    Table 1 in [18]).
As already mentioned, the luminosity of an ep collider is proportional to the proton beam brightenss N p p N ε (see Equation (1)). Together with a given bunch length and energy spread, the beam brightness is a measure of the phase-space density. In the low-energy part of a proton injector, the quantity n p p N ε is limited by space-charge forces that induce a transverse tune shift 3 Here p v is the proton velocity and c is the speed of light in vacuo [24] [25].
In order to reduce the effect of space-charge forces at low energies and deliver proton bunches a few mm long, the facility in Figure 2 features a single 3-GeV proton injector linac similar to that currently being built at the European Spallation Source (ESS) [26].
At high energies, the beam brightness in a storage ring slowly diminishes due to Coulomb scattering of protons within a bunch (intra-beam scattering) [27].
In the presence of dispersion (see footnote 4), the intra-beam scattering also leads to an increase in emittance. This sets the ultimate limit on the phase-space density in a proton storage ring. The growth of a beam of charged particles due to intra-beam scattering is characterized by the horizontal growth rate [28]. 3 The "tune" or Q value is defined as the number of betatron oscillations per revolution in a circular accelerator. The charge and current of a high-inensity beam in an accelerator create self-fields and image fields that alter the beam dynamics and influence the single-particle motion as well as coherent oscillations of the beam as a whole. The effect of space-charge forces is to change Q by an amount sc Q ∆ ("tune shift") [24].
The parameter p Q ∆ must be limited to about 3 4 10 − × in order to stem the emittance growth due to random fluctuations of the electron bunch parameters [30]. This imposes an upper limit of  Since ξ grows linearly with the distance between the final-focus quadrupole and the interaction point, it is desirable to make this distance as small as possible.
For the interaction region at an electron-proton collider, a novel design technique called the achromatic telescopic squeezing (ATS) has been proposed "in order to find the optimal solution that would produce the highest luminosity while controlling the chromaticity, minimizing the synchrotron radiation power and maintaining the dynamic aperture required for [beam] stability" [34] [35] (dynamic aperture is the stability region of phase space in a circular accelerator).
The issue of beam stability was addressed earlier concerning the optimization of the proton bunch length. The proton bunches inside an ILC-type linac are much shorter than those inside the FCC storage ring (the 3-GeV injector linac mentioned earlier would deliver bunches a few millimetres long). Thus, , z p σ has to be increased in order to attain the baseline FCC-pp value (see Table 2). In principle, the easiest way to increase the bunch length in a circular accelerator is to switch all RF systems off and let the bunches "decay" due to dispersion. 4 A faster and more subtle method-which could be implemented using a 3-TeV proton booster placed inside the FCC tunnel-is described in [36].
The expressions for beam-beam tune shift, electron beam disruption and beam growth rate given above do not accurately describe the time-dependent beam dynamics during collisions. To study the time-dependent effects caused by varying beam sizes, collision point simulations for linac-ring ep colliders have been performed using the ALOHEP software [37]. This numerical program optimizes a set of electron and proton beam parameters in order to maximize luminosity [38].
The luminosity ep  is independent of the electron bunch charge and the collision frequency as long as their product, expressed in terms of the beam power e  , is constant. One can therefore rewrite Equation (1) as follows [17] [39] is the inverse of the bunch interval (see Table 3).