FLUCTUATION DYNAMO AT FINITE CORRELATION TIMES AND THE KAZANTSEV SPECTRUM

Fluctuation dynamos are generic to astrophysical systems. The only analytical model of the fluctuation dynamo is the Kazantsev model which assumes a velocity field that is delta-correlated in time. We derive a generalized model of fluctuation dynamos with finite correlation time, tau, using renovating flows. For tau -> 0, we recover the standard Kazantsev equation for the evolution of longitudinal magnetic correlation, M-L. To the next order in tau, the generalized equation involves third and fourth spatial derivatives of ML. It can be recast to one with at most second derivatives of M-L using the Landau-Lifschitz approach. Remarkably, we then find that the magnetic power spectrum remains the Kazantsev spectrum of M(k) alpha k(3/2), in the large k limit, independent of tau.