The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle--particle collisions allows departures from local thermodynamic equilibrium. These departures exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present a numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart. If instead the parallel viscous stress is left unabated -- a situation relevant to recent kinetic simulations of the fluctuation dynamo and to the early stages of the dynamo in a magnetized ICM -- the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics of the saturated state of the large-Prandtl-number (${\rm Pm}\gtrsim{1}$) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches magnetic-energy spectra. A prediction of this model, confirmed by our simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.
In weakly collisional astrophysical plasmas, such as the intracluster medium of galaxy clusters, the amplification of cosmic magnetic fields by chaotic fluid motions is hampered by the adiabatic production of magnetic-field-aligned pressure anisotropy. This anisotropy drives a viscous stress parallel to the field that inhibits the plasma's ability to stretch magnetic-field lines. I demonstrate through the use of kinetic simulations that in high-$β$ plasmas, kinetic ion-Larmor scale instabilities sever the adiabatic link between the thermal and magnetic pressures, reducing this viscous stress a…
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, th…
We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect "magneto-immutability" by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-$β$) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-im…
This white paper, submitted for the Plasma 2020 Decadal Survey, concerns the physics of weakly collisional, high-beta plasmas -- plasmas in which the thermal pressure dominates over the magnetic pressure and in which the inter-particle collision time is comparable to the characteristic timescales of bulk motions. This state of matter, although widespread in the Universe, remains poorly understood: we lack a predictive theory for how it responds to perturbations, how it transports momentum and energy, and how it generates and amplifies magnetic fields. Such topics are foundational to the scient…
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 disc. 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 instabili…
The amplification and maintenance of the observed magnetic fields in the ICM are usually attributed to the turbulent dynamo action. This is generally derived employing a collisional MHD model. However, in the ICM the ion mean free path between collisions is of the order of the dynamical scales, thus requiring a collisionless MHD description. Unlike collisional MHD simulations, our study uses an anisotropic plasma pressure with respect to the direction of the local magnetic field, which brings the plasma within a parameter space where collisionless instabilities should take place. Within the ad…
Over the last decade, substantial efforts have been devoted to understanding the stability properties, transport phenomena, and long-term evolution of weakly-collisional, magnetized plasmas which are stratified in temperature. These studies have improved our understanding of the physics governing the intra-cluster medium (ICM), but assumed that ICM is a homogeneous. This, however, might not be a good approximation if heavy elements sediment in the inner region of the galaxy cluster. In this paper, we analyze the stability of a weakly-collisional, magnetized plane-parallel atmosphere which is s…
Black holes that accrete far below the Eddington limit are believed to accrete through a geometrically thick, optically thin, rotationally supported plasma that we will refer to as a radiatively inefficient accretion flow (RIAF). RIAFs are typically collisionless in the sense that the Coulomb mean free path is large compared to $GM/c^2$, and relativistically hot near the event horizon. In this paper we develop a phenomenological model for the plasma in RIAFs, motivated by the application to sources such as Sgr A* and M87. The model is derived using Israel-Stewart theory, which considers deviat…
Wave interference as the origin of the cyclic magnetorotational dynamo in accretion disks: insights from weakly nonlinear theory and local shearing box simulations
Institute for Advanced Study（高等研究院）；Princeton University（普林斯顿大学）；Perimeter Institute for Theoretical Physics（基础物理研究所）
These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in turbulent fluids and plasmas, blended with a review of current research in the field. The primary focus is on the physical and mathematical concepts underlying different (turbulent) branches of dynamo theory, with some astrophysical, geophysical and experimental context disseminated throughout the document. The text begins with an introduction to the rationale,…
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI satura…
Based on the new findings on the turbulent dynamo in \citet{XL16}, we examine the magnetic field amplification in the context of supernova remnants. Due to the strong ion-neutral collisional damping in the weakly-ionized interstellar medium, the dynamo in the preshock turbulence remains in the damping kinematic regime, which leads to {\it a linear-in-time growth of the magnetic field strength}. The resultant magnetic field structure enables effective diffusion upstream and shock acceleration of cosmic rays to energies above the "knee". Differently, the nonlinear dynamo in the postshock turbule…
In weakly collisional extragalactic plasmas such as the intracluster medium, viscous stress and the rate of change of the magnetic-field strength are proportional to the local pressure anisotropy, so subject to constraints imposed by the pressure-anisotropy-driven mirror and firehose instabilities and controlled by the local instantaneous plasma beta. The dynamics of such plasmas is dramatically different from a conventional MHD fluid. The plasma is expected to stay locally in a marginal state with respect to the instabilities, but how it does this is an open question. Two models of magnetic-f…
We present a systematic shearing-box investigation of MRI-driven turbulence in a weakly collisional plasma by including the effects of an anisotropic pressure stress, i.e. anisotropic (Braginskii) viscosity. We constrain the pressure anisotropy ($Δp$) to lie within the stability bounds that would be otherwise imposed by kinetic microinstabilities. We explore a broad region of parameter space by considering different Reynolds numbers and magnetic-field configurations, including net vertical flux, net toroidal-vertical flux and zero net flux. Remarkably, we find that the level of turbulence and …
Magnetic fields pervade the entire Universe and affect the formation and evolution of astrophysical systems from cosmological to planetary scales. The generation and dynamical amplification of extragalactic magnetic fields through cosmic times, up to $μ$Gauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions and on scales of at least tens of kiloparsecs, is a major puzzle largely unconstrained by observations. A dynamo effect converting kinetic flow energy into magnetic energy is often invoked in that context, however extragalactic plasmas are …
Weakly collisional plasmas dynamically develop pressure anisotropies with respect to the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρ_i and much below the mean free path λ_{mfp}. They have growth rates of a fraction of the ion cyclotron frequency - much faster than either the global dynamics or local turbulence. The instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. Their nonlinear evolution drives pressure anisotropies towards marginal stability, controlled by the pl…
This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-beta plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" reg…
In their early stages, protoplanetary discs are sufficiently massive to undergo gravitational instability (GI). This instability is thought to be involved in mass accretion, planet formation via gas fragmentation, the generation of spiral density waves, and outbursts. A key and very recent area of research is the interaction between the GI and magnetic fields in young protoplanetary discs, in particular whether this instability is able to sustain a magnetic field via a dynamo. We conduct three-dimensional, stratified shearing-box simulations using two independent codes, PLUTO and Athena++, to …
Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early nonlinear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasilinearly at a steady, low-amplitude lev…
In low-collisionality plasmas, anisotropic heat conduction due to a magnetic field leads to buoyancy instabilities for any nonzero temperature gradient. We study analogous instabilities in degenerate {\it collisional} plasmas, i.e., when the electron collision frequency is large compared to the electron cyclotron frequency. Although heat conduction is nearly isotropic in this limit, the small residual anisotropy ensures that collisional degenerate plasmas are also convectively unstable independent of the sign of the temperature gradient. We show that the range of wavelengths that are unstable …
A post-hypercritical accretion small-scale dynamo in newborn neutron stars
Universidad Nacional de Colombia（哥伦比亚国立大学）；Università degli Studi di Ferrara（费拉拉大学）；Sapienza Università di Roma（罗马大学）；INAF, Istituto di Astrofisica e Planetologia Spaziali（意大利国家天体物理研究所空间天体物理学和行星科学研究所）
We show that an alpha effect is driven by the cosmic ray Bell instability exciting left-right asymmetric turbulence. Alfven waves of a preferred polarization have maximally helical motion, because the transverse motion of each mode is parallel to its curl. We show how large-scale Alfven modes, when rendered unstable by cosmic ray streaming, can create new net flux over any finite region, in the direction of the original large-scale field. We perform direct numerical simulations (DNS) of an MHD fluid with a forced cosmic ray current and use the test-field method to determine the alpha effect an…
Large ${\rm Pm}$ small-scale kinematic dynamo in protoneutron stars
Indian Institute of Technology Kharagpur（印度理工学院哈格普尔分校）；Indian Institute of Technology Madras（印度理工学院马德拉斯分校）；Université Paris Cité, Université Paris-Saclay, CEA, CNRS, AIM（巴黎西岱大学、巴黎萨克雷大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理学信息与方法研究所）
Weakly collisional, magnetised plasmas characterised by anisotropic viscosity and conduction are ubiquitous in galaxies, halos and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with cosmic rays using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy ($Δp$) of the thermal plasma. We find that th…
