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The dynamo mechanism is a process of magnetic field self-excitation in amoving electrically conducting fluid. One of the most interesting applicationsof this mechanism related to the astrophysical systems is the case of a randommotion of plasma. For the very first stage of the process, the governing dynamoequation can be reduced to a system of first order ordinary differentialequations. For this case we suggest a regular method to calculate the growthrate of magnetic energy. Based on this method we calculate the growth rate forrandom flow with finite memory time and anisotropic statistical distribution ofthe stretching matrix and compare the results with corresponding ones forisotropic case and for short-correlated approximation. We find that formoderate Strouhal numbers and moderate anisotropy the analytical resultsreproduce the numerically estimated growth rates reasonably well, while forlarger governing parameters the quantitative difference becomes substantial. Inparticular, analytical approximation is applicable for the Strouhal numberss<0.6 and we find some numerical models and observational examples for whichthis region might be relevant. Rather unexpectedly, we find that the mirrorasymmetry does not contribute to the growth rates obtained, although the mirrorasymmetry effects are known to be crucial for later stages of dynamo action.

Finite memory time and anisotropy effects for initial magnetic energy growth in random flow of conducting media