The amplification of magnetic field frozen to a two-dimensional spatially periodic flow consisting of two distinct pulsed Beltrami waves is investigated. The period α of each pulse is long (α » 1) so that fluid particles make excursions large compared with the periodicity length. The action of the flow is reduced to a mapTof a complex vector field Z measuring the magnetic field at the end of each pulse. Attention is focused on the mean field <Z> produced. Under the assumption, <Tk+2Z>−|λ7infin;|2<TKZ>→0asK→∞ an asymptotic representation of the complex constant λ∞ is obtained, which determines the growth rate α−1In (α|λ|). The main result is the construction of a family of smooth vector fields ZNand complex constants λNwhich, for evenN, have the properties <TK+2ZN> =O(α−3(N+2)/4and λN-∞= O(for all integersK(> 0). In the case of the dissipative problem at large but finite magnetic Reynolds numberR(> α), it is argued that the fastest growing mode Z with amplification factor λ is approximated best by ZNc, whereNc ∼ frac12(InR)/(In α) and λ−λNc= O[(α/R⅜].