AN ASYMPTOTIC SOLUTION OF A FAST DYNAMO IN A 2-DIMENSIONAL PULSED FLOW

The amplification of magnetic field frozen to a two-dimensional spatia lly periodic flow consisting of two distinct pulsed Beltrami waves is investigated. The period alpha of each pulse is long (alpha >> 1) so t hat fluid particles make excursions large compared with the periodicit y length. The action of the flow is reduced to a map T of a complex ve ctor field Z measuring the magnetic field at the end of each pulse. At tention is focused on the mean field <Z> produced. Under the assumptio n, [T(K+2)Z] - \lambda(infinity\2[T(K)Z] --> 0 as K --> infinity, an a symptotic representation of the complex constant lambda(infinity) is o btained, which determines the growth rate alpha-1 ln(alpha\lambda(infi nity)\). The main result is the construction of a family of smooth vec tor fields Z(N) and complex constants lambda(N) which, for even N, hav e the properties [T(K+2)Z(N)] - \lambda(N)\2[T(K)Z(N)] = O(alpha-3(N+2 )/4) and lambda(N) - lambda(infinity) = O(alpha-3(N+2)/4) for all inte gers K(>0). In the case of the dissipative problem at large but finite magnetic Reynolds number R(>> alpha), it is argued that the fastest g rowing mode Z with amplification factor lambda is approximated best by Z(Nc), where N(c) is equal to 1/2(ln R)/(ln alpha) and lambda = O[(al pha/R)3/8].