The Future Circular Collider – electron-positron (FCC-ee) – is a proposed successor to the High Luminosity Large Hadron Collider (HL-LHC) at CERN. Designed to cover a broad physics programme across four energy points, from 45.6 to 182.5 GeV, the FCC-ee operates under a crucial constraint: a fixed synchrotron radiation power budget of 100 MW.

In circular electron-positron colliders, synchrotron radiation is the dominant energy loss mechanism, and the power budget directly impacts the beam dynamics. The total synchrotron radiation power is distributed among all the circulating particles, meaning that at lower energies, where the synchrotron radiation losses per particle are smaller, the collider must operate with a higher beam current to maintain the 100 MW budget. Conversely, at higher energies, synchrotron radiation losses grow rapidly, and the same power budget limits the beam current, requiring a significantly higher radiofrequency (RF) voltage to compensate for these losses.

As a result, the FCC-ee must accommodate very different RF system requirements at different energy points: at the lowest energy (45.6 GeV), it requires relatively low RF voltage (~90 MV) and needs to withstand a high beam current (~1.3 A). At the highest energy (182.5 GeV), the collider operates with a low beam current (~5 mA) but an extremely high RF voltage (~11 GV) must be achieved in a compact and cost-efficient way. This presents significant challenges in the design and implementation of the RF system, as it must efficiently handle both extreme cases without excessive reconfiguration or downtime.

Addressing RF system challenges

A staged installation approach was initially proposed in the FCC-ee conceptual design report to accommodate these differing RF needs. This approach suggested deploying 400 MHz low-impedance single-cell cavities at lower energies (Z pole), and transitioning to 400 MHz and 800 MHz multi-cell cavities at higher energy points (WW, ZH, and ttbar). While effective in principle, this solution required a predefined operational sequence and time-consuming reconfigurations of the RF system, posing logistical constraints.

A significant step towards simplifying this setup was made in 2022 with the adoption of a two-cell cavity design for the WW operating point, capable of supporting a high beam current (135 mA) while maintaining a moderate gradient, providing up to 1 GV of RF voltage. This design allows for a smoother transition between the WW and ZH operating points by enabling ZH beams to pass through both RF systems simultaneously. However, the challenge remained for the Z pole, where a traditional staged approach would still be necessary, requiring fundamental power coupler (FPC) modifications to accommodate the vastly different RF voltage demands of the Z and WW energy points.

Introducing reverse phase RF operation (RPO)

During the FCC Week in June 2024, discussions with colleagues from the Electron-Ion Collider (EIC) project led to an evaluation of an alternative solution: Reverse phase RF operation (RPO). Originally developed at Japan’s High Energy Accelerator Research Organization (KEK) for the SuperKEKB upgrade, this scheme was successfully tested in 2009-2010 but was not implemented due to changes in the SuperKEKB machine parameters.

RPO operates by adjusting the phase relationship between different groups of RF cavities. Rather than requiring an entirely separate RF system for the Z pole, two groups of cavities operate in opposing phases, generating the required total RF voltage while preserving optimal cavity coupling (Fig. 1). This allows the higher cavity voltage required for WW operation (8 MV) to be leveraged for the Z pole without hardware modifications, thereby enabling seamless switching between Z, WW, and ZH operating points.

Further analysis was performed to confirm feasibility of RPO for the FCC-ee. It was found that the beam current modulation for the baseline filling scheme leads to enormous bunch-by-bunch RF voltage modulations (blue points in Fig. 2), which can compromise beam stability and degrade luminosity.

Two mitigation schemes were proposed to reduce the RF voltage modulations: a higher RF voltage or an adjustment of the filling scheme by introducing shorter gaps between bunch trains. Higher total RF voltage options were discarded due to the negative impact on beam stability and lifetime demonstrated with macroparticle simulations. Instead, a new filling scheme with twice shorter gaps was implemented (orange points in Fig. 2) thanks to modifications of the injection and extraction system layouts. This solution was found in close collaboration with colleagues from various groups at CERN as well as other FCC Feasibility Study members and the support of the EU-funded FCCIS project.

Final Design and Future Considerations

With the adoption of a 400 MHz RF system with two-cell cavities (Fig. 3), the FCC-ee gains greater operational flexibility, allowing the collider to transition smoothly between Z, WW, and ZH energy points. The plan would be that after nine years of operation, 800 MHz six-cell cavities would be introduced to support the high-voltage requirements of the ttbar energy point.

A remaining challenge is ensuring RF system recovery in case of failures. High efficiency and reliability RF subsystem designs will be crucial to minimising downtime and guaranteeing operational continuity. Addressing these aspects will be a key focus moving forward. By leveraging RPO, the FCC-ee can achieve a more efficient and adaptable RF system, reducing hardware modifications while maintaining high-performance operation across its energy range. The continued refinement of this approach, in collaboration with experts from other accelerator projects, will help shape the next-generation collider infrastructure.