  (Abridged) We examine the effects of charge transfer inefficiency (CTI)
during CCD readout on galaxy shape measurements required by studies of weak
gravitational lensing. We simulate a CCD readout with CTI such as that caused
by charged particle radiation damage. We verify our simulations on data from
laboratory-irradiated CCDs. Only charge traps with time constants of the same
order as the time between row transfers during readout affect galaxy shape
measurements. We characterize the effects of CTI on various galaxy populations.
We baseline our study around p-channel CCDs that have been shown to have charge
transfer efficiency up to an order of magnitude better than several models of
n-channel CCDs designed for space applications. We predict that for galaxies
furthest from the readout registers, bias in the measurement of galaxy shapes,
Delta(e), will increase at a rate of 2.65 +/- 0.02 x 10^(-4) per year at L2 for
accumulated radiation exposure averaged over the solar cycle. If uncorrected,
this will consume the entire shape measurement error budget of a dark energy
mission within about 4 years. Software mitigation techniques demonstrated
elsewhere can reduce this by a factor of ~10, bringing the effect well below
mission requirements. CCDs with higher CTI than the ones we studeied may not
meet the requirements of future dark energy missions. We discuss ways in which
hardware could be designed to further minimize the impact of CTI.
