  Plasma wake-field acceleration is one of the main technologies being
developed for future high-energy colliders. Potentially, it can create a
cost-effective path to the highest possible energies for e+e- or
{\gamma}-{\gamma} colliders and produce a profound effect on the developments
for high-energy physics. Acceleration in a blowout regime, where all plasma
electrons are swept away from the axis, is presently considered to be the
primary choice for beam acceleration. In this paper, we derive a universal
efficiency-instability relation, between the power efficiency and the key
instability parameter of the trailing bunch for beam acceleration in the
blowout regime. We also show that the suppression of instability in the
trailing bunch can be achieved through BNS damping by the introduction of a
beam energy variation along the bunch. Unfortunately, in the high efficiency
regime, the required energy variation is quite high, and is not presently
compatible with collider-quality beams. We would like to stress that the
development of the instability imposes a fundamental limitation on the
acceleration efficiency, and it is unclear how it could be overcome for
high-luminosity linear colliders. With minor modifications, the considered
limitation on the power efficiency is applicable to other types of
acceleration.
