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Beam-beam interaction constraints modify the basic plasma density scalings for a linear collider based on laser-plasma accelerators. In the quantum beamstrahlung regime, it is shown that operating at low plasma density increases beamstrahlung effects, owing to the higher bunch charge and longer bunch length. At high plasma density, the bunch charge is limited by beam loading, and the required power is proportional to the square root of the plasma density. At low plasma density, the bunch charge is limited by beamstrahlung, which, for fixed luminosity, requires operation at higher laser repetition rate and, hence, higher power requirements, or the use of multibunch trains. If round beams are used in a multibunch train format with fixed beam loading, and the collider is constrained by beamstrahlung, then the required collider power is independent of plasma density

Beamstrahlung considerations in laser-plasma-accelerator-based linear colliders