Fundamental trade-off between efficiency and beam-breakup instability
In plain words
To be efficient, the accelerated bunch must extract much of the wake's energy, but that also makes the bunch wobble sideways and break up. How efficient a stable plasma accelerator can be is not known.
Precise statement
Strong beam loading raises wake-to-witness energy-transfer efficiency but also strengthens the transverse wakefield that drives the hosing (beam-breakup) instability. Determine the maximum efficiency compatible with a given tolerable emittance growth and driver-witness misalignment, including damping by energy spread, ion motion and plasma-density tailoring. An answer is an upper bound on efficiency versus tolerance, validated by simulation.
What would settle it
A derived bound confirmed by 3D particle-in-cell simulations and by measured instability growth in a high-efficiency stage.
Status in the literature
Unverified note
Lebedev, Burov and Nagaitsev (2017, https://doi.org/10.1103/PhysRevAccelBeams.20.121301) derived an efficiency-instability relation; 2025 simulations (arXiv:2501.10602) show it is only a lower limit on instability strength, and a bound including all damping mechanisms is lacking.