Critical magnetic Reynolds number of the turbulent dynamo in collisionless plasmas

Abstract

The intracluster medium of galaxy clusters is an extremely hot and diffuse, nearly collisionless plasma, which hosts dynamically important magnetic fields of $\sim \mu \mathrm{G}$ strength. Seed magnetic fields of much weaker strength of astrophysical or primordial origin can be present in the intracluster medium. In collisional plasmas, which can be approximated in the magneto-hydrodynamical (MHD) limit, the turbulent dynamo mechanism can amplify weak seed fields to strong dynamical levels efficiently by converting turbulent kinetic energy into magnetic energy. However, the viability of this mechanism in weakly collisional or completely collisionless plasma is much less understood. In this study, we explore the properties of the collisionless turbulent dynamo by using three-dimensional hybrid-kinetic particle-in-cell simulations. We explore the properties of the collisionless turbulent dynamo in the kinematic regime for different values of the magnetic Reynolds number, $\mathrm{Rm}$, initial magnetic-to-kinetic energy ratio, $(E_{\mathrm{mag}}/E_{\mathrm{kin}}{)}_{\mathrm{i}}$, and initial Larmor ratio, $(r_{\mathrm{Larmor}}/L_{\mathrm{box}}{)}_{\mathrm{i}}$, i.e., the ratio of the Larmor radius to the size of the turbulent system. We find that in the `un-magnetised' regime, $(r_{\mathrm{Larmor}}/L_{\mathrm{box}}{)}_{\mathrm{i}}>1$, the critical magnetic Reynolds number for the dynamo action ${\mathrm{Rm}}_{\mathrm{crit}}\approx 107\pm 3$. In the `magnetised' regime, $(r_{\mathrm{Larmor}}/L_{\mathrm{box}}{)}_{\mathrm{i}}\lesssim 1$, we find a marginally higher ${\mathrm{Rm}}_{\mathrm{crit}}=124\pm 8$. We find that the growth rate of the magnetic energy does not depend on the strength of the seed magnetic field when the initial magnetisation is fixed. We also study the distribution and evolution of the pressure anisotropy in the collisionless plasma and compare our results with the MHD turbulent dynamo.

17 pages, 16 figures

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