 Award ID(s):
 1804048
 NSFPAR ID:
 10204598
 Date Published:
 Journal Name:
 Journal of Plasma Physics
 Volume:
 85
 Issue:
 1
 ISSN:
 00223778
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Turbulence and mixing in a nearbottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zeroslope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zerovelocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the nonsloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slopeparallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.more » « less

null (Ed.)In a magnetized, collisionless plasma, the magnetic moment of the constituent particles is an adiabatic invariant. An increase in the magneticfield strength in such a plasma thus leads to an increase in the thermal pressure perpendicular to the field lines. Above a $\unicode[STIX]{x1D6FD}$ dependent threshold (where $\unicode[STIX]{x1D6FD}$ is the ratio of thermal to magnetic pressure), this pressure anisotropy drives the mirror instability, producing strong distortions in the field lines on ionLarmor scales. The impact of this instability on magnetic reconnection is investigated using a simple analytical model for the formation of a current sheet (CS) and the associated production of pressure anisotropy. The difficulty in maintaining an isotropic, Maxwellian particle distribution during the formation and subsequent thinning of a CS in a collisionless plasma, coupled with the low threshold for the mirror instability in a high $\unicode[STIX]{x1D6FD}$ plasma, imply that the geometry of reconnecting magnetic fields can differ radically from the standard Harrissheet profile often used in simulations of collisionless reconnection. As a result, depending on the rate of CS formation and the initial CS thickness, tearing modes whose growth rates and wavenumbers are boosted by this difference may disrupt the mirrorinfested CS before standard tearing modes can develop. A quantitative theory is developed to illustrate this process, which may find application in the tearingmediated disruption of kinetic magnetorotational ‘channel’ modes.more » « less

A heat flux in a high $\unicode[STIX]{x1D6FD}$ plasma with low collisionality triggers the whistler instability. Quasilinear theory predicts saturation of the instability in a marginal state characterized by a heat flux that is fully controlled by electron scattering off magnetic perturbations. This marginal heat flux does not depend on the temperature gradient and scales as $1/\unicode[STIX]{x1D6FD}$ . We confirm this theoretical prediction by performing numerical particleincell simulations of the instability. We further calculate the saturation level of magnetic perturbations and the electron scattering rate as functions of $\unicode[STIX]{x1D6FD}$ and the temperature gradient to identify the saturation mechanism as quasilinear. Suppression of the heat flux is caused by oblique whistlers with magneticenergy density distributed over a wide range of propagation angles. This result can be applied to high $\unicode[STIX]{x1D6FD}$ astrophysical plasmas, such as the intracluster medium, where thermal conduction at sharp temperature gradients along magneticfield lines can be significantly suppressed. We provide a convenient expression for the amount of suppression of the heat flux relative to the classical Spitzer value as a function of the temperature gradient and $\unicode[STIX]{x1D6FD}$ . For a turbulent plasma, the additional independent suppression by the mirror instability is capable of producing large total suppression factors (several tens in galaxy clusters) in regions with strong temperature gradients.more » « less

ABSTRACT The intracluster medium of galaxy clusters is an extremely hot and diffuse, nearly collisionless plasma, which hosts dynamically important magnetic fields of ∼μG 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 magnetohydrodynamical (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 using threedimensional hybridkinetic particleincell simulations. We explore the properties of the collisionless turbulent dynamo in the kinematic regime for different values of the magnetic Reynolds number, Rm, initial magnetictokinetic energy ratio, (Emag/Ekin)i, and initial Larmor ratio, (rLarmor/Lbox)i, i.e. the ratio of the Larmor radius to the size of the turbulent system. We find that in the ‘unmagnetized’ regime, (rLarmor/Lbox)i > 1, the critical magnetic Reynolds number for the dynamo action Rmcrit ≈ 107 ± 3. In the ‘magnetized’ regime, (rLarmor/Lbox)i ≲ 1, we find a marginally higher Rmcrit = 124 ± 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 magnetization 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.

Abstract We report on a firstprinciples numerical and theoretical study of plasma dynamo in a fully kinetic framework. By applying an external mechanical force to an initially unmagnetized plasma, we develop a selfconsistent treatment of the generation of “seed” magnetic fields, the formation of turbulence, and the inductive amplification of fields by the fluctuation dynamo. Driven largescale motions in an unmagnetized, weakly collisional plasma are subject to strong phase mixing, which leads to the development of thermal pressure anisotropy. This anisotropy triggers the Weibel instability, which produces filamentary “seed” magnetic fields on plasmakinetic scales. The plasma is thereby magnetized, enabling efficient stretching and folding of the fields by the plasma motions and the development of Larmorscale kinetic instabilities such as the firehose and mirror. The scattering of particles off the associated microscale magnetic fluctuations provides an effective viscosity, regulating the field morphology and turbulence. During this process, the seed field is further amplified by the fluctuation dynamo until energy equipartition with the turbulent flow is reached. By demonstrating that equipartition magnetic fields can be generated from an initially unmagnetized plasma through largescale turbulent flows, this work has important implications for the origin and amplification of magnetic fields in the intracluster and intergalactic mediums.