  The acceleration of polarized electron beams in the blowout regime of
plasma-based acceleration is explored. An analytical model for the spin
precession of single beam electrons, and depolarization rates of zero emittance
electron beams, is derived. The role of finite emittance is examined
numerically by solving the equations for the spin precession with a spin
tracking algorithm. The analytical model is in very good agreement with the
results from 3D particle-in-cell simulations in the limits of validity of our
theory. Our work shows that the beam depolarization is lower for high-energy
accelerator stages, and that under the appropriate conditions, the
depolarization associated with the acceleration of 100-500 GeV electrons can be
kept below 0.1-0.2%.
