  In a multipass energy recovery linac (ERL), each cavity must regain all
energy expended from beam acceleration during beam deceleration, and the beam
should achieve specific energy targets during each loop that returns it to the
linac. For full energy recovery, and for every returning beam to meet loop
energy requirements, we must specify and maintain the phase and voltage of
cavity fields in addition to selecting adequate flight times. These parameters
are found with a full scale numerical optimization program. If we impose
symmetry in time and energy during acceleration and deceleration, fewer
parameters are needed, simplifying the optimization. As an example, we present
symmetric models of the Cornell BNL ERL Test Accelerator (CBETA) with solutions
that satisfy the optimization targets of loop energy and zero cavity loading.
An identical cavity design and nearly uniform linac layout make CBETA a
potential candidate for symmetric operation.
