Small-scale dynamo with finite correlation times.

Abstract

Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behavior, but they are based on simplifying assumptions. For instance, the well-known Kazantsev model assumes an incompressible flow that is δ-correlated in time. However, these assumptions can break down in the interstellar medium as it is highly compressible and the velocity field has a finite correlation time. Using the renewing flow method developed by Bhat and Subramanian (2014), we aim to extend Kazantsev's results to a more general class of turbulent flows. The cumulative effect of both compressibility and finite correlation time over the Kazantsev spectrum is studied analytically. We derive an equationfor the longitudinal two-point magnetic correlation function in real space to first order in the correlation time τ and for an arbitrary degree of compressibility (DOC). This generalized Kazantsev equationencapsulates the original Kazantsev equation. In the limit of small Strouhal numbers St∝τ we use the Wentzel-Kramers-Brillouin approximation to derive the growth rate and scaling of the magnetic power spectrum. We find the result that the Kazantsev spectrum is preserved, i.e., M_{k}(k)∼k^{3/2}. The growth rate is also negligibly affected by the finite correlation time; however, it is reduced by the finite magnetic diffusivity and the DOC together.