Collisional Viscosity Research Articles

Growing neoclassical tearing modes seeded via transient-induced-multimode interactions

Nonlinear extended magnetohydrodynamics simulations demonstrating seeding of neoclassical tearing modes (NTMs) via magnetohydrodynamics-transient-induced multimode interactions are presented. Simulations of NTMs are enabled by two recent NIMROD code developments: the implementation of heuristic neoclassical stresses and the application of transient magnetic perturbations (MPs) at the boundary. NTMs are driven unstable by the inherently pressure driven kinetic bootstrap current, which arises due to collisional viscosity between passing and trapped electrons. These simulations use heuristic closures that model the neoclassical electron and ion stresses. NTM growth requires a seed island, which is generated by a transiently applied MP in simulations. The capability is demonstrated using kinetic-based reconstructions with flow of a DIII-D ITER Baseline Scenario discharge (La Haye et al., in Proceedings IAEA FEC, 2020). The applied MP seeds a 2/1 NTM that grows in two phases: a slow growth phase followed by a faster robust growth phase. Additionally, an evolving sequence of higher order core modes are excited at first. Power transfer analysis shows that nonlinear interactions between the core modes and the 2/1 helps drive the initial slow growth. Once the induced 2/1 magnetic island reaches a critical width, the NTM transitions to faster robust growth, which is well described by the nonlinear modified Rutherford equation. This work highlights the role of nonlinear mode coupling in seeding NTMs.

A recent origin for Saturn’s rings from the collisional disruption of an icy moon

The disruption of an icy moon in a collision with an interloping comet a few hundred million years ago is a simple way to create Saturn’s rings. A ring parent moon with a mass comparable to Mimas could be trapped in mean motion resonance with Enceladus and Dione in an orbit near the current outer edge of the rings just beyond the Roche zone. I present collisional N-body simulations of cometary impacts that lead to the partial disruption of a differentiated moon with a rocky core and icy mantle. The core can survive largely intact while the debris from the mantle settles into a ring of predominantly ice particles straddling the orbital radius of the parent moon. The nascent ring spreads radially due to collisional viscosity while mass re-accretes onto the remnant rocky core to form a new moon that can be identified as Mimas. The icy debris that migrates into the Roche zone evolves into Saturn’s ring system. Torques from tidal interaction with Saturn and resonant interactions with the rings push the recently formed Mimas outward to its current position on the same timescale of a few hundred million years. This scenario accounts for the high ice fraction observed in Saturn’s rings and explains why the ring mass is comparable to the mass of Mimas. The prior existence of a ring parent moon in mean motion resonance results in a tidal heating rate for Enceladus in the recent past that is significantly larger than the current rate.

Behavior of thin disk crystalline morphology in the presence of corrections to ideal magnetohydrodynamics.

We analyze an axisymmetric magnetohydrodynamics configuration, describing the morphology of a purely differentially rotating thin plasma disk, in which linear and nonlinear perturbations are triggered associated with microscopic magnetic structures. We study the evolution of the nonstationary correction in the limit in which the corotation condition (i.e., the dependence of the disk angular velocity on the magnetic flux function) is preserved and the poloidal velocity components are neglected. The main feature we address here is the influence of ideal (finite electron inertia) and collisional (resistivity, viscosity, and thermal conductivity) effects on the behavior of the flux function perturbation and of the associated small-scale modifications in the disk. We analyze two different regimes in which resistivity or viscosity dominates and study the corresponding linear and nonlinear behaviors of the perturbation evolution, i.e., when the backreaction magnetic field is negligible or comparable to the background one, respectively. We demonstrate that when resistivity dominates, a radial oscillating morphology (crystalline structure) emerges and it turns out to be damped in time, in both the linear and nonlinear regimes, but in such a way that the resulting transient can be implemented in the description of relevant astrophysical processes, for instance, associated with jet formation or cataclysmic variables. When the viscosity effect dominates the dynamics, only the nonlinear regime is available and a very fast instability is triggered.

Short-Lived Lattice Quasiparticles for Strongly Interacting Fluids

It is shown that lattice kinetic theory based on short-lived quasiparticles proves very effective in simulating the complex dynamics of strongly interacting fluids (SIF). In particular, it is pointed out that the shear viscosity of lattice fluids is the sum of two contributions, one due to the usual interactions between particles (collision viscosity) and the other due to the interaction with the discrete lattice (propagation viscosity). Since the latter is negative, the sum may turn out to be orders of magnitude smaller than each of the two contributions separately, thus providing a mechanism to access SIF regimes at ordinary values of the collisional viscosity. This concept, as applied to quantum superfluids in one-dimensional optical lattices, is shown to reproduce shear viscosities consistent with the AdS-CFT holographic bound on the viscosity/entropy ratio. This shows that lattice kinetic theory continues to hold for strongly coupled hydrodynamic regimes where continuum kinetic theory may no longer be applicable.

An accretion disc instability induced by a temperature sensitive α parameter

In the standard thin disc formalism the dimensionless $\alpha$ parameter is usually assumed to be constant. However, there are good theoretical reasons for believing, as well as evidence from simulations, that $\alpha$ is dependent on intrinsic disc properties. In this paper we analyse the conditions for the stability of a thin accretion disc in which $\alpha$ is a function of the magnetic Prandtl number, the ratio of collisional viscosity to resistivity. In the inner disc, where the free electron opacity and radiation viscosity dominate, the disc is unstable if $\alpha$ is proportional to the magnetic Prandtl number with an exponent, $n$, and $6/13<n<10/3$. This is within the range of values for the power-law index found in MHD simulations with simple energetics. We calculate the evolution of the unstable disc within the $\alpha$ formalism and show that the physically accessible solutions form a limit cycle, analogous to the behaviour seen in recurrent dwarf novae. It is noteworthy that the time-dependent global behaviour of the instability results in cyclic heating of the inner section of the disc, when parameters appropriate for an X-ray binary system are used. We calculate a model spectrum of the disc in the flaring and quiescent states and show that the behaviour is compatible with X-ray observations of the thermal accretion disc in flaring X-ray binary systems.

Anomalous viscosity of the quark-gluon plasma

The shear viscosity of the quark-gluon plasma is predicted to be lower than the collisional viscosity for weak coupling. The estimated ratio of the shear viscosity to entropy density is rather close to the ratio calculated by $\mathcal{N}=4$ super Yang--Mills theory for strong coupling, which indicates that the quark-gluon plasma might be strongly coupled. However, in the presence of momentum anisotropy, the Weibel instability can arise and drive the turbulent transport. Shear viscosity can be lowered by enhanced collisionality due to turbulence, but the decorrelation time and its relation to underlying dynamics and color-magnetic fields have not been calculated self-consistently. In this paper, we use resonance broadening theory for strong turbulence to calculate the anomalous viscosity of the quark-gluon plasma for nonequilibrium. For saturated Weibel instability, we estimate the scalings of the decorrelation rate and viscosity and compare these with collisional transport. This calculation yields an explicit connection between the underlying momentum-space anisotropy and the viscosity anomaly.

Stirring Unmagnetized Plasma

A new concept for spinning unmagnetized plasma is demonstrated experimentally. Plasma is confined by an axisymmetric multicusp magnetic field and biased cathodes are used to drive currents and impart a torque in the magnetized edge. Measurements show that flow viscously couples momentum from the magnetized edge (where the plasma viscosity is small) into the unmagnetized core (where the viscosity is large) and that the core rotates as a solid body. To be effective, collisional viscosity must overcome the ion-neutral drag due to charge-exchange collisions.

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.

Damping effects of finite parallel thermal conductivity on zonal flows

Effects of the finite parallel thermal conductivity on the zonal flows in a tokamak have been investigated. It has been found that the finite parallel thermal conductivity damps the geodesic acoustic modes, the high frequency branch of the zonal flows, with a damping rate similar to that induced by the collisional viscosity, while the finite parallel thermal conductivity has no damping effect on the low frequency branch of the zonal flows.

Cross-Scale Effects in Solar-Wind Turbulence

The understanding of the small-scale termination of the turbulent energy cascade in collisionless plasmas is nowadays one of the outstanding problems in space physics. In the absence of collisional viscosity, the dynamics at small scales is presumably kinetic in nature; the identification of the physical mechanism which replaces energy dissipation and establishes the link between macroscopic and microscopic scales would open a new scenario in the study of turbulent heating in space plasmas. We present a numerical analysis of kinetic effects along the turbulent energy cascade in solar-wind plasmas which provides an effective unified interpretation of a wide set of spacecraft observations and shows that, simultaneously with an increase in the ion perpendicular temperature, strong bursts of electrostatic activity in the form of ion-acoustic turbulence are produced together with accelerated beams in the ion distribution function.

Low-q resonances, transport barriers, and secondary electrostatic convective cells

Recent experimental observations have suggested key characteristics of internal transport barrier (ITB) formation near low-q surfaces in off-axis minimum-q (OAMq) discharges. These observations identify mean profile flattening localized to the low-q surface as a transition precursor in the absence of observable magnetic field perturbations. This observation suggests an electrostatic model of ITB formation which accounts for strong transport in the immediate vicinity of the low-q surface, as well as the formation of an ITB nearby the surface. Here, a low-m electrostatic convective cell driven by modulational instability of the background drift wave turbulence is discussed in the context of ITB formation near low-q resonances in OAMq discharges. Unlike pure m=n=0 zonal flows, convective cells are capable of intense mixing localized around low-q resonant surfaces, thus relaxing ∇T and ∇n profiles at the k∙B=0 resonance. However, nearby, but off the low-q resonant surface the magnitude of convective cell shear is maximal, providing an effective means of triggering a transport barrier there. Field line bending coupled with collisional viscosity are found to strongly damp the intensity of the vortical flows except in the case of weak magnetic shear. Furthermore, collisionless nonlinear saturation mechanisms such as nonlinear wave trapping are largely circumvented due to the strong mixing of the convective cell. This suggests that low-m convective cells may play a key role in the regulation of turbulent transport near low-q resonances for OAMq discharges.

Anomalous viscosity of an expanding quark–gluon plasma

We argue that an expanding quark–gluon plasma has an anomalous viscosity, which arises from interactions with dynamically generated colour fields. The anomalous viscosity dominates over the collisional viscosity for large velocity gradients or weak coupling. This effect may provide an explanation for the apparent near-perfect liquidity of the matter produced in nuclear collisions at RHIC without the assumption that it is a strongly coupled state.

The flavours of the quark–gluon plasma

Flavour probes depend on the transport properties of the quark–gluon plasma. An expanding quark–gluon plasma has an anomalous viscosity, which arises from interactions with dynamically generated colour fields. The anomalous viscosity dominates over the collisional viscosity for weak coupling and at not too late times. In addition to possibly providing an explanation for the apparent nearly ‘perfect’ liquidity of the matter produced in nuclear collisions at RHIC, similar anomalous effects can affect the rate of flavour equilibration and the diffusion constant of heavy quarks.

Anomalous Transport Processes in Anisotropically Expanding Quark-Gluon Plasmas

We derive an expression for the anomalous viscosity in an anisotropically expanding quark-gluon-plasma, which arises from interactions of thermal partons with dynamically generated color fields. The anomalous viscosity dominates over the collisional viscosity for large velocity gradients or weak coupling. This effect may provide an explanation for the apparent “nearly perfect” liquidity of the matter produced in nuclear collisions at RHIC without the assumption that it is a strongly coupled state.

Radial interchange motions of plasma filaments

Radial convection of isolated filamentary structures due to interchange motions in magnetized plasmas is investigated. Following a basic discussion of vorticity generation, ballooning, and the role of sheaths, a two-field interchange model is studied by means of numerical simulations on a biperiodic domain perpendicular to the magnetic field. It is demonstrated that a blob-like plasma structure develops dipolar vorticity and electrostatic potential fields, resulting in rapid radial acceleration and formation of a steep front and a trailing wake. While the dynamical evolution strongly depends on the amount of collisional diffusion and viscosity, the structure travels a radial distance many times its initial size in all parameter regimes in the absence of sheath dissipation. In the ideal limit, there is an inertial scaling for the maximum radial velocity of isolated filaments. This velocity scales as the acoustic speed times the square root of the structure size relative to the length scale of the magnetic field. The plasma filament eventually decelerates due to mixing and collisional dissipation. Finally, the role of sheath dissipation is investigated. When included in the simulations, it significantly reduces the radial velocity of isolated filaments. The results are discussed in the context of convective transport in scrape-off layer plasmas, comprising both blob-like structures in low confinement modes and edge localized mode filaments in unstable high confinement regimes.

Anomalous Viscosity of an Expanding Quark-Gluon Plasma

We argue that an expanding quark-gluon plasma has an anomalous viscosity, which arises from interactions with dynamically generated color fields. We derive an expression for the anomalous viscosity in the turbulent plasma domain and apply it to the hydrodynamic expansion phase, when the quark-gluon plasma is near equilibrium. The anomalous viscosity dominates over the collisional viscosity for weak coupling and not too late times. This effect may provide an explanation for the apparent "nearly perfect" liquidity of the matter produced in nuclear collisions at the Relativistic Heavy Ion Collider without the assumption that it is a strongly coupled state.

Nonlinear viscosity and its role in drift-Alfvén modes

The moment approach is used to analyze the part of the magnetized plasma viscosity related to the nonlinear character of the Landau collision integral in the Boltzmann kinetic equation (nonlinear viscosity), pointed out by Catto and Simakov [Phys. Plasmas 11, 90 (2004)]. It is shown that the results of these authors, who have used an alternative procedure based on a more detailed analysis of the kinetic equation, correspond to a 15-moment approach. In comparison with the 13-moment approach (density, temperature, velocity, heat flux, and the viscosity tensor) of Grad, the 15-moment approach takes into account two higher-order moments, one of which is the vector-type moment similar to the parallel heat flux and the second is the tensor-type moment similar to the parallel projection of the viscosity tensor. Both these higher-order moments enter into the Braginskii approximation. The nonlinear viscosity calculated in the scope of the 13-moment Grad approach is qualitatively the same as that found by Catto and Simakov. Its role is investigated for drift-Alfvén modes, driven by the combined effect of the dissipative part of perpendicular heat conductivity and the standard collisional viscosity, and it is shown to be essential for the radial transport of these modes. It is shown that the wave packet of drift-Alfvén modes, propagating in the diamagnetic drift direction and driven for reversed temperature gradient, is transported down the pressure gradient. In contrast to this, the wave packet propagating in the electron diamagnetic drift direction and driven for positive temperature gradient is transported up the pressure gradient.

A new, explicitly collisional contribution to the gyroviscosity and the radial electric field in a collisional tokamak

An additional contribution to the ion viscosity for a collisional plasma is evaluated and found to be the same order as other temperature gradient terms in the collisional perpendicular viscosity. The new contribution arises because of an explicitly collisional portion of the ion distribution function. The evaluation of the Pfirsch-Schlüter radial electric field in a collisional tokamak of arbitrary cross section is extended to retain the new contribution. In a spherical tokamak this new contribution must be retained in determining the radial electric field, while in a conventional tokamak it is small by 1∕q2, where q is the safety factor.

Evaluation of the neoclassical radial electric field in a collisional tokamak

The neoclassical electric field in a tokamak is determined by the conservation of toroidal angular momentum. In the steady state in the absence of momentum sources and sinks it is explicitly evaluated by the condition that radial flux of toroidal angular momentum vanishes. For a collisional or Pfirsch-Schlüter short mean-free path ordering with subsonic plasma flows we find that there are two limiting cases of interest. The first is the simpler case of a strongly up-down asymmetric tokamak for which the lowest order gyroviscosity does not vanish and must be balanced by the leading order collisional viscosity in order to determine the radial electric field. The second case is the more complicated case of an up-down symmetric tokamak for which the gyroviscosity must be evaluated to higher order and again balanced by the lowest order collisional viscosity to determine the radial electric field. In general, both the lowest and the next order contributions from the gyroviscosity must be retained.

Collisional and viscous damping of MHD waves in partially ionized plasmas of the solar atmosphere

Magnetohydrodynamic (MHD) waves are widely considered as a possible source of heating for various parts of the outer solar atmosphere. Among the main energy dissipation mechanisms which convert the energy of damped MHD waves into thermal energy are collisional dissipation (resistivity) and viscosity. The presence of neutral atoms in the partially ionized plasmas of the solar photosphere, chromosphere and prominences enhances the efficiency of both these energy dissipation mechanisms. A comparative study of the efficiency of MHD wave damping in solar plasmas due to collisional and viscous energy dissipation mechanisms is presented here. The damping rates are taken from Braginskii 1965 and applied to the VAL C model of the quiet Sun (Vernazza et al. 1981). These estimations show which of the mechanisms are dominant in which regions. In general the correct description of MHD wave damping requires the consideration of all energy dissipation mechanisms via the inclusion of the appropriate terms in the generalized Ohm's law, the momentum, energy and induction equations. Specific forms of the generalized Ohm's Law and induction equation are presented that are suitable for regions of the solar atmosphere which are partially ionised.