Fully kinetic large scale simulations of the collisionless Magnetorotational instability

Abstract: We present two-dimensional particle-in-cell (PIC) simulations of the fully kinetic collisionless magnetorotational instability (MRI) in weakly magnetized (high $\beta$) pair plasma. The central result of this numerical analysis is the emergence of a self-induced turbulent regime in the saturation state of the collisionless MRI, which can only be captured for large enough simulation domains. One of the underlying mechanisms for the development of this turbulent state is the drift-kink instability (DKI) of the current sheets resulting from the nonlinear evolution of the channel modes. The onset of the DKI can only be observed for simulation domain sizes exceeding several linear MRI wavelengths. The DKI, together with ensuing magnetic reconnection, activate the turbulent motion of the plasma in the late stage of the nonlinear evolution of the MRI. At steady state, the magnetic energy has an MHD-like spectrum with a slope of $k^{-5/3}$ for $k\rho<1$ and $k^{-3}$ for sub-Larmor scale ($k\rho>1$). We also examine the role of the collisionless MRI and associated magnetic reconnection in the development of pressure anisotropy. We study the stability of the system due to this pressure anisotropy, observing the development of mirror instability during the early-stage of the MRI. We further discuss the importance of magnetic reconnection for particle acceleration during the turbulence regime. In particular, consistent with reconnection studies, we show that at late times the kinetic energy presents a characteristic slope of $\epsilon^{-2}$ in the high-energy region.

• The paper demonstrates that simulation domains over eight times the most unstable MRI wavelength are essential to capture sustained turbulence driven by drift-kink instabilities and magnetic reconnection.
• The paper shows that kinetic effects induce pressure anisotropies that trigger mirror instabilities and reconnection, leading to significant particle acceleration.
• The paper reveals distinct energy spectra with a k^(-5/3) slope at scales above the Larmor radius and a k^(-3) decline at sub-Larmor scales, highlighting kinetic turbulence in MRI dynamics.

Fully Kinetic Large Scale Simulations of the Collisionless Magnetorotational Instability

The paper by Inchingolo et al. investigates the nonlinear evolution of the magnetorotational instability (MRI) in a collisionless, high-beta pair plasma using fully kinetic simulations. The study explores the dynamics of MRI in accretion disks, a topic fundamental for understanding the angular momentum transport and energy dissipation around compact objects such as black holes and neutron stars. The authors employ a two-dimensional Particle-in-Cell (PIC) simulation framework to capture kinetic effects, hypothesized to be crucial for understanding MRI saturation more accurately than traditional magnetohydrodynamics (MHD) approaches.

Key Insights

1. Simulation Domain and Turbulent Regimes: The research underscores the significance of selecting appropriately large simulation domains (greater than eight times the wavelength of the most unstable MRI mode) to capture the fully developed turbulent regime. Domains smaller than this threshold fail to achieve saturation, highlighting the role of drift-kink instabilities (DKI) and magnetic reconnection in transitioning to turbulence.
2. Pressure Anisotropy and Instabilities: Kinetic effects induce pressure anisotropies that activate mirror instabilities during the early MRI stages. As reconnection progresses, a pressure anisotropy favoring perpendicular velocities (i.e., $v_y > v_x$) emerges due to particle acceleration out of the plane of reconnection, violating mirror stability thresholds.
3. Turbulence and Energy Spectra: The turbulent state of MRI in the late-stage evolution is characterized by distinctive spectral slopes for magnetic energy. At scales larger than the Larmor radius, the energy spectrum exhibits an $k^{-5/3}$ slope typical of MHD turbulence, whereas at sub-Larmor scales, the spectrum shows a steeper $k^{-3}$ decline, consistent with predictions for kinetic Alfvénwave turbulence or reconnection-mediated turbulence.
4. Particle Acceleration: The simulations reveal significant particle acceleration during the turbulence regime, with the high-energy tail of the particle distribution following an $\epsilon^{-2}$ power law. This observation aligns with prior studies on magnetic reconnection, asserting that reconnection is a major mechanism for producing nonthermal particles in collisionless astrophysical plasmas.

Implications and Future Directions

These findings provide a deeper kinetic perspective on MRI, suggesting complex dynamics that include both reconnection and pressure-anisotropy-driven instabilities are critical for understanding MRI saturation and subsequent turbulence. These insights could lead to better models for accretion disk behavior, especially in regions where collisionless dynamics predominate.

The results prompt further investigations, particularly in extending this work to three-dimensional simulations and considering realistic ion-electron mass ratios. Such expansions could refine our understanding of MRI-related instabilities and their influences on energy transport in accretion disks. Future research could also integrate these kinetic insights into global disk simulations, enhancing the realism of accretion disk models. Moreover, exploring the interplay between kinetic instabilities at different scales (electron vs. ion) could unveil additional layers to MRI-induced dynamics.

Inchingolo et al.'s study addresses crucial aspects of collisionless MRI, expanding the knowledge of plasma dynamics in astrophysical contexts and establishing grounds for future explorations in kinetic plasma turbulence and reconnection phenomena in space plasmas.