  In the dynamically assisted Schwinger mechanism, the pair production
probability is significantly enhanced by including a weak, rapidly varying
field in addition to a strong, slowly varying field. In a previous paper we
showed that several features of dynamical assistance can be understood by a
perturbative treatment of the weak field. Here we show how to calculate the
prefactors of the higher-orders terms, which is important because the dominant
contribution can come from higher orders. We give a new and independent
derivation of the momentum spectrum using the worldline formalism, and extend
our WKB approach to calculate the amplitude to higher orders. We show that
these methods are also applicable to doubly assisted pair production.
