Smallscale 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 behaviour but they are based on simplifying assumptions. For instance the wellknown Kazantsev model assumes an incompressible flow that is deltacorrelated 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 equation for the longitudinal twopoint magnetic correlation function in real space to first order in the correlation time $\tau$ and for an arbitrary degree of compressibility (DOC). This generalised Kazantsev equation encapsulates the original Kazantsev equation. In the limit of small Strouhal numbers $St \propto \tau$ we use the WKB 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. $M_k(k)\sim k^{3/2}$. 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.01097
 arXiv:
 arXiv:2303.01097
 Bibcode:
 2023arXiv230301097C
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Physics  Plasma Physics