Theoretical astrophysics and plasma physics at RPC

Abstract:

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetised, turbulent plasma---and, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion discs around black holes. In the context of discs, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfv\'enic turbulence: collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, $\beta_\mathrm{i}$: it ranges from $\sim0.05$ at $\beta_\mathrm{i}=0.1$ to at least $30$ for $\beta_\mathrm{i} \gtrsim 10$. This energy partition is approximately insensitive to the ion-to-electron temperature ratio $T_\mathrm{i}/T_\mathrm{e}$. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfv\'enic turbulence will tend towards a nonequilibrium state in which one of the species is significantly hotter than the other, viz., hotter ions at high $\beta_\mathrm{i}$, hotter electrons at low $\beta_\mathrm{i}$. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high $\beta_i$ and a tendency for the ion heating to be mediated by nonlinear phase mixing (``entropy cascade'') when $\beta_\mathrm{i}\lesssim1$ and by linear phase mixing (Landau damping) when $\beta_\mathrm{i}\gg1$

Abstract:

We present three-dimensional eccentric disc models of the nucleus of M31, modelling the disc as a linear combination of thick rings of massless stars orbiting in the potential of a central black hole. Our models are non-parametric generalizations of the parametric models of Peiris and Tremaine. The models reproduce well the observed Wide Field Planetary Camera 2 photometry, the detailed line-of-sight velocity distributions from Space Telescope Spectroscopy Imaging Spectrograph observations along P1 and P2, together with the qualitative features of the OASIS kinematic maps. We confirm Peiris and Tremaine's finding that nuclear discs aligned with the larger disc of M31 are strongly ruled out. Our optimal model is inclined at 57° with respect to the line of sight of M31 and has position angle PA = θl + 90° = 55°. It has a central black hole of mass M• ≃ 1.0 × 108 Msun, and, when viewed in three dimensions, shows a clear enhancement in the density of stars around the black hole. The distribution of orbit eccentricities in our models is similar to Peiris and Tremaine's model, but we find significantly different inclination distributions, which might provide valuable clues to the origin of the disc.

Abstract:

Understanding magnetic-field generation and amplification in turbulent plasma is essential to account for observations of magnetic fields in the universe. A theoretical framework attributing the origin and sustainment of these fields to the so-called fluctuation dynamo was recently validated by experiments on laser facilities in low-magnetic-Prandtl-number plasmas ($\mathrm{Pm} < 1$). However, the same framework proposes that the fluctuation dynamo should operate differently when $\mathrm{Pm} \gtrsim 1$, the regime relevant to many astrophysical environments such as the intracluster medium of galaxy clusters. This paper reports a new experiment that creates a laboratory $\mathrm{Pm} \gtrsim 1$ plasma dynamo for the first time. We provide a time-resolved characterization of the plasma's evolution, measuring temperatures, densities, flow velocities and magnetic fields, which allows us to explore various stages of the fluctuation dynamo's operation. The magnetic energy in structures with characteristic scales close to the driving scale of the stochastic motions is found to increase by almost three orders of magnitude from its initial value and saturate dynamically. It is shown that the growth of these fields occurs exponentially at a rate that is much greater than the turnover rate of the driving-scale stochastic motions. Our results point to the possibility that plasma turbulence produced by strong shear can generate fields more efficiently at the driving scale than anticipated by idealized MHD simulations of the nonhelical fluctuation dynamo; this finding could help explain the large-scale fields inferred from observations of astrophysical systems.

Abstract:

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal-temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations. A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear. The break up of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system -- the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol{E}\times\boldsymbol{B}$ flow. By analysing the linear ITG modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

Abstract:

We present a study of the low-transport Dimits state (Dimits et al., 2000) and the transition to a high-transport saturated state in plasma turbulence driven by the ion-temperature-gradient instability. This thesis focuses on a fluid model derived in the cold-ion, long-wavelength asymptotic limit of the ion gyrokinetic equation in a magnetic field with constant curvature (a Z-pinch) and in the presence of an equilibrium temperature gradient. Numerical simulations reveal that the Dimits state is dominated by a quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows which have patch-wise constant shear. Such a structure is reminiscent of the so-called "ExB staircase" observed in global gyrokinetic numerical simulations (Dif-Pradalier et al., 2010). It suppresses turbulence in two complementary ways: first, by shearing turbulent eddies in the regions of strong zonal shear, and, secondly, by flattening the background temperature gradient at the turning points of the zonal flow, where the shear vanishes. The turbulent heat flux in the low-collisionality, near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al., 2016). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system --- the Reynolds stress and the advection of the diamagnetic flow by the ExB flow. The former acts to support the staircase by providing a net negative turbulent viscosity for the zonal flows and is opposed by the latter. The winner of this competition decides the type of saturated state. When the Reynolds stress dominates, the system enters the Dimits regime which is characterised by the aforementioned zonal staircase. Otherwise, if the diamagnetic stress prevails, strong turbulence-suppressing zonal flows cannot be maintained and turbulence reigns supreme. We show that the transition from low to high transport can be understood by analysing the linearly unstable ion-temperature-gradient modes. This is demonstrated by a semi-analytic model for the Dimits threshold in 2D and at large collisionality. In 3D, unless the system is restricted in the magnetic-field direction, a Dimits state arises for all values of the equilibrium parameters. This is explained by the existence of a "parasitic" small-scale slab-ITG instability which is driven by the gradients of large-scale 2D perturbation. The modes of this parasitic instability provide an effective thermal diffusion at large scales and act to move energy from large scales to small viscous scales where dissipation takes place, thus providing a mechanism for saturation. Although such a saturation mechanism was investigated as early as (Cowley et al., 1991), it is not part of the conventional discourse on strong ITG turbulence, which often follows simpler scenarios (e.g., critical balance, see Barnes et al., 2011).