Cooling time reachable for 275 GeV protons by microbunched electron cooling

In plain words

An electron-ion collider needs to cool its high-energy proton beam faster than collisions inside the bunch heat it; whether coherent cooling can do this is unsettled.

Precise statement

For protons at 275 GeV with electron-ion-collider-like emittances and bunch intensities, compute the minimal cooling time of longitudinal and transverse emittance by microbunched electron cooling, including amplifier saturation, electron-beam noise, heating from electron shot noise, and finite overlap. State whether $\tau_{\mathrm{cool}}$ shorter than the intrabeam-scattering growth time (of order hours) is reachable.

What would settle it

A 3D simulation with real particle numbers and validated amplifier models that gives $\tau_{\mathrm{cool}}$ and its heating budget.

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