Magnetorotational Turbulence and Dynamo in a Collisionless Plasma

We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disk. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is biased with respect to the magnetic-field direction and spatiotemporally variable. Energy spectra suggest an Alfvén-wave cascade at large scales and a kinetic-Alfvén-wave cascade at small scales, with strong small-scale density fluctuations and weak nonaxisymmetric density waves. Ions undergo nonthermal particle acceleration, their distribution accurately described by a $\kappa$ distribution. These results have implications for the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.

Figure 1

Evolution of box-averaged (a) magnetic energy and thermal pressure, (b) kinetic energy, (c) pressure anisotropy (compared to magnetic energy), and (d) $xy$ components of the total, Maxwell, viscous, and Reynolds stresses, all normalized to the initial thermal pressure $p_0$. The inset in (c) shows a slice of the magnetic-field strength in the $x\text{−}z$ plane at the time marked by the dot; mirror-mode parasites, which feed off the pressure anisotropy generated by the MRI, are evident. The plus sign in panel (d) denotes the value of $⟪T_{xy}/p_0⟫$ obtained in a MHD simulation of the zero-net-flux MRI with $\mathrm{Pm}=16$ [26].

Figure 2

Distribution of the ion temperature anisotropy $T_{\perp i}/T_{\parallel i}$ vs the parallel ion ${\beta }_{\parallel i}$ (top left) initially, (top right) during the channel phase, (bottom left) at peak channel amplitude, and (bottom right) in the saturated state. The solid, dot-dashed, and dashed lines denote approximate mirror, ion-cyclotron, and firehose instability thresholds, respectively.

Figure 3

$x$ and $y$ components of the magnetic field (normalized to $B_0$) and the momentum (normalized to $n_{i0}{v}_{A0}$) at ${\mathrm{\Omega }}_{\text{rot}}t=47.4$.

Figure 4

Slices of (left) Maxwell stress (normalized to $p_0$), (left center) magnetic-field strength (normalized to $B_0$), and (right center) density fluctuation (normalized to $n_{0i}$) at $z=0$. Right: vertically averaged density fluctuation (normalized to $n_{0i}$). All frames are taken at ${\mathrm{\Omega }}_{\text{rot}}t=47.4$.

Figure 5

Energy spectra of (top) magnetic fluctuations and (bottom) velocity and density fluctuations in the saturated state, defined by ${\mathcal{E}}_A(k)\equiv \int d{\mathrm{\Omega }}_k(kH/2\pi {)}^2|A_k{|}^2$ with $\int d(kH/2\pi ){\mathcal{E}}_A(k)=⟨A^2⟩$. Characteristic slopes are shown as labeled dashed lines; the vertical dotted line marks $k{\rho }_i=1$.

Figure 6

Box-averaged ion distribution function at ${\mathrm{\Omega }}_{\text{rot}}t=51$ (solid line), binned logarithmically in $ϵ\equiv (m_i/2)|\mathit{v}-{\mathit{u}}_i(\mathit{r}){|}^2$. A $\kappa =5$ distribution and a Maxwell distribution, both with temperature $⟨T_i⟩\simeq 5.4T_{0i}$, are overlaid; the former is a good fit, indicating nonthermal particle acceleration.