  Energy Recovery Linacs provide high-energy beams, but decelerate those beams
before dumping them, so that their energy is available for the acceleration of
new particles. During this deceleration, any relative energy spread that is
created at high energy is amplified by the ratio between high energy and dump
energy. Therefore, Energy Recovery Linacs are sensitive to energy spread
acquired at high energy, e.g. from wake fields. One can compensate the
time-correlated energy spread due to wakes via energy-dependent time-of-flight
terms in appropriate sections of an Energy Recovery Linac, and via
high-frequency cavities. We show that nonlinear time-of-flight terms can only
eliminate odd orders in the correlation between time and energy, if these terms
are created by a beam transport within the linac that is common for
accelerating and decelerating beams. If these two beams are separated, so that
different beam transport sections can be used to produce time-of-flight terms
suitable for each, also even-order terms in the energy spread can be
eliminated. As an example, we investigate the potential of using this method
for the Cornell x-ray Energy Recovery Linac. Via quadratic time-of-flight
terms, the energy spread can be reduced by 66%. Alternatively, since the energy
spread from the dominantly resistive wake fields of the analysed accelerator is
approximately harmonic in time, a high-frequency cavity could diminish the
energy spread by 81%. This approach would require bunch-lengthening and
recompression in separate sections for accelerating and decelerating beams.
Such sections have therefore been included in Cornell's x-ray Energy Recovery
Linac design.
