  Accelerating particles to high energies in plasma wakefields is considered to
be a promising technique with good energy efficiency and high gradient. While
important progress has been made in plasma-based electron acceleration,
positron acceleration in plasma has been scarcely studied and a fully
self-consistent and optimal scenario has not yet been identified. For high
energy physics applications where an electron-positron collider would be
desired, the ability to accelerate positrons in plasma wakefields is however
paramount. Here we show that the preservation of beam quality can be
compromised in a plasma wakefield loaded with a positron beam, and a trade-off
between energy efficiency and beam quality needs to be found. For electron
beams driving linear plasma wakefields, we have found that despite the
transversely nonlinear focusing force induced by positron beam loading, the
bunch quickly evolves toward an equilibrium distribution with limited emittance
growth. Particle-in-cell simulations show that for {\mu}m-scale normalized
emittance, the growth of uncorrelated energy spread sets an important limit.
Our results demonstrate that the linear or moderately nonlinear regimes with
Gaussian drivers provide a good trade-off, achieving simultaneously
energy-transfer efficiencies exceeding 30% and uncorrelated energy spread below
1%, while donut-shaped drivers in the nonlinear regime are more appropriate to
accelerate high-charge bunches at higher gradients, at the cost of a degraded
trade-off between efficiency and beam quality.
