MS. PALLAVI BHAT

Turbulent astrophysical systems like galaxies and galaxy clusters generically host fluctuation dynamos, which even for modest magnetic Reynolds numbers, can act to convert kinetic energy into magnetic energy on the short eddy turn over time-scales. The only analytical model for fluctuation dynamos was given by Kazantsev (in 1968) which assumed a delta-correlated in time velocity field. We derive a generalized model of fluctuation dynamo with finite correlation time, $\tau$, using renovating flows. For $\tau \to 0$, 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 $M_L$. It can be recast using the Landau-Lifschitz approach, to one with at most second derivatives of $M_L$. We show an intriguing result that the magnetic power spectrum, remains the Kazantsev spectrum of $M(k) \propto k^{3/2}$, in the large $k$ limit, independent of $\tau$.