Fluctuation Dynamo in a Collisionless, Weakly Magnetized Plasma

Abstract

Results from a numerical study of fluctuation dynamo in a collisionless, weakly magnetized plasma are presented. The key difference between this dynamo and its magnetohydrodynamic (MHD) counterpart is the adiabatic production of magnetic-field-aligned pressure anisotropy by the amplification of a weak seed field. This in turn drives kinetic instabilities on the ion-Larmor scale---namely, firehose and mirror---which sever the adiabatic link between the thermal and magnetic pressures, thereby allowing the dynamo to proceed. After an initial phase of rapid growth driven by these instabilities, the magnetic energy grows exponentially and exhibits a $k^{3/2}$ spectrum that peaks near the resistive scale, similar to the large-magnetic-Prandtl-number ($\mathrm{Pm}\gg{1}$) MHD dynamo. The magnetic field self-organizes into a folded-sheet topology, with direction reversals at the resistive scale and field lines curved at the parallel scale of the flow. The effective $\mathrm{Pm}$ is determined by whether the ion-Larmor scale is above or below the field-reversing scale: in the former case, particles undergo Bohm-like diffusion; in the latter case, particles scatter primarily off firehose fluctuations residing at the ends of the magnetic folds, and the viscosity becomes anisotropic. The magnetic field ultimately saturates at dynamical strengths, with its spectral peak migrating towards larger scales. This feature, along with an anti-correlation of magnetic-field strength and field-line curvature and a gradual thinning of magnetic sheets into ribbons, resemble the saturated state of the large-$\mathrm{Pm}$ dynamo, the primary differences manifesting in firehose/mirror-unstable regions. These results have implications for magnetic-field growth in the weakly collisional intracluster medium of galaxy clusters.