Edouard Siregar

Simulation of high-frequency solar wind power spectra using Hall magnetohydrodynamics

Solar wind frequency spectra show a distinct steepening of the ƒ−5/3 power law inertial range spectrum at frequencies above the Doppler-shifted ion cyclotron frequency. This is commonly attributed to dissipation due to wave-particle interactions. We consider the extent to which this steepening can be described, using a magnetohydrodynamic formulation that includes the Hall term. An important characteristic of Hall MHD is that although the ion cyclotron resonance is included, there is no wave-particle dissipation of energy. In this study we use a compressible Hall MHD code with a constant magnetic field and a polytropic equation of state. Artificial dissipation in the form of a bi-Laplacian operator is used to suppress numerical instabilities, allowing for a clear separation of the dissipative scales from the ion cyclotron scales. A distinct steepening appears in the simulation power spectra near the cyclotron resonance for certain types of initial conditions. This steepening is associated with the appearance of right circularly polarized fluctuations at frequencies above the ion cyclotron resonance. Similar steepenings and polarization enhancements are observed in solar wind magnetic field data.

An evolving MHD vortex street model for quasi‐periodic solar wind fluctuations

We use magnetohydrodynamic (MHD) simulation to provide a dynamical basis for the “vortex street” model of the quasi-periodic meridional flow observed by Voyager 2 in the outer heliosphere. Various observations suggest that near the current sheet at solar minimum one can expect to find a vorticity distribution of two opposite shear layers with an antisymmetric staggered vorticity pattern due to structured high-speed wind surrounding low-speed equatorial flow. We show that this flow pattern leads to the formation of a highly stable vortex street through the nonlinear interaction of the two shear layers. Spatial profiles of various simulated parameters (velocity, density, meridional flow angle and the location of magnetic sector boundaries) and their relative locations in the quasi-steady vortex street are generally in good agreement with the observations. A strong, flow-aligned magnetic field, such as would occur in the inner heliosphere, inhibits the development of the street which would then be masked by the background interplanetary turbulence. The flow produced by the street induces a (relatively small) transport of plasma and magnetic flux as a result of the meridional flow away from the ecliptic region.

Quasi-periodic transverse plasma flow associated with an evolving MHD vortex street in the outer heliosphere

We study a transverse (“meridional” in heliocentric coordinates) plasma flow induced by the evolution of a Karman vortex street using a Chebyshev-Fourier spectral algorithm to solve both the compressible Navier-Stokes and magnetohydrodynamic (MHD) equations. The evolving vortex street is formed by the nonlinear interaction of two vortex sheets initially in equilibrium, such as are naturally found either side of the heliospheric current sheet at solar minimum. We study spatial profiles of the total plasma velocity, the density, the meridional flow angle and the location of sector boundaries and find generally good agreement with Voyager 2 measurements of quasi-periodic transverse flow in the outer heliosphere. The pressure pulses associated with the meridional flows in the simulation are too small, although they are correctly located, and this may be due to the lack of any “warp” in the current sheet in this model. A strong flow-aligned magnetic field, such as would occur in the inner heliosphere, is shown to lead to weak effects that would be masked by the background interplanetary turbulence. We also study the plasma and magnetic transport resulting from the meridional flow, and find that deficits of magnetic quantities do occur near the ecliptic and that while the effect is relatively small, it is in general agreement with the most recent analysis of ‘flux deficit’ in the outer heliosphere.

North-south flows observed in the outer heliosphere at solar minimum: Vortex streets or corotating interaction regions?

During the last two solar minima in the distant heliosphere the equatorial heliospheric plasma velocity oscillated perpendicular to the ecliptic plane with an approximately 26-day period in the distant heliosphere. Two explanations have been proposed: compressive interactions between streams and velocity shear interactions that produce a Karman vortex street. The latter interpretation has been challenged on the basis that the velocity jumps are supersonic, thereby suppressing the Kelvin-Helmholtz (K-H) instability. Here we examine this issue using a time-dependent compressible magnetohydrodynamics code solved in spherical coordinates in the two-dimensional r – θ plane. We conclude that supersonic flow does suppress small-scale instabilities and that the classic Karman vortex street cannot be excited. Both velocity shear layers and stream interactions can, however, produce signatures in density, velocity, and magnetic field that resemble the observations. In particular, we find north-south variations of the flow velocity with a period that is approximately half that of the period of the variation in flow speed: a result insensitive to the thickness of the velocity shear layers. A depletion in density (and magnetic field magnitude) relative to the expected Parker value is predicted by the simulations that generate the north-south flow via velocity shear. The Voyager spacecraft observed a similar depletion in the outer heliosphere during the last two solar minima. When the effective tilt of the plasma sheet is increased, corotating interaction regions produce shock waves and other complex time-dependent evolution. We conclude that at solar minimum the observed north-south oscillations are a robust phenomenon that can form from either the interaction of fast and slow solar wind streams or from velocity shear. Which mechanism dominates is a consequence of the degree of tilt of the heliospheric current sheet, the magnitude of the velocity shear, and other physical parameters. However, the depletions seen in density and magnetic flux in the Voyager data suggest that velocity shear in the outer heliosphere at solar minimum may be the dominant cause of the observed north-south flow patterns.

Nonlinear entropy production operators for magnetohydrodynamic plasmas

A method for constructing closure relations based on the invariants of the tensors representing nonequilibrium thermodynamic forcing within the plasma is presented. This approach leads to closure relations that describe all higher‐order forcing effects contained within the continuum description. Nonlinear convective‐momentum transport and nonlinear momentum‐exchange operators are constructed as applications of the method. Closure is achieved by relating the pressure tensor to invariants of the rate of strain tensor, and the momentum‐exchange operator to invariants of the gradient of magnetic field tensor. These operators lead to positive definite viscous and Joule entropy production and enhance high wave number dissipative couplings over all other dissipative couplings. The nonlinear dissipative action is localized in physical space, where velocity and magnetic gradients are large, while allowing nearly ideal behavior elsewhere. The operators are computationally tested against the standard magnetohydrodyn...

A Vlasov moment description of cyclotron wave–particle interactions

A quasifluid formalism designed to capture some effects of cyclotron interactions is presented. Starting from the contractions of exact moments of the Vlasov equation, a closure for cyclotron interactions is achieved by using kinetic information directly. This nonperturbative approach does not require a priori assumptions about zeroth‐order particle velocity distributions. The nonlinear coupling between field‐aligned particle thermal velocities and transverse cyclotron wave and thermal motions are described by off‐diagonal elements of the pressure tensor. These elements are related to the growth and damping of cyclotron wave energy. A functional form for an effective wave–particle momentum transport coefficient is derived from the requirement of consistency between the energy and momentum moment equations, but its specific magnitude and sign, determined by threshold temperature anisotropy levels, must be input from kinetic theory. This effective transport coefficient has a nondefinite sign, reminiscent of...

On the dynamics of a plasma vortex street and its topological signatures

A plasma vortex street configuration can evolve when two velocity and one magnetic shear layer interact strongly. A study of the interaction between two‐ and three‐dimensional plasma modes and a mean sheared magnetic field is undertaken using a three‐dimensional magnetohydrodynamic spectral Galerkin computation. The initial state is a simple magnetic shear in a plane perpendicular to the plasma velocity shear plane. In a very weak magnetic field, secondary instabilities (three‐dimensional modes), expressed by the kinking of vortex tubes, lead to plasma flow along and around the axes of the vortex cores, creating characteristic patterns of kinetic helicity and linkages between vortex filaments. Three‐dimensionality leads to the vortex breakdown process. A strong sheared magnetic field inhibits the kinking of vortex tubes, maintaining two‐dimensionality. This inhibits vortex breakdown over long dynamical times. There is an anticorrelation in time between linkage indices of the vortex filament (related to ki...

Coarse-graining and nonlocal processes in proton cyclotron resonant interactions

Coarse-grained information from a hybrid simulation show that previously developed quasifluid equations of state capture some aspects of proton cyclotron resonant interactions for parallel propagation in a low β plasma. Direct kinetic information is used as a closure for the information exchanged with the higher-order moment quantities. The coarse-graining procedure involves averaging over many proton-inertial lengths and looking at long time scales associated with the wave envelopes. By use of the coarse-graining prior to statistical analysis, the anticorrelations predicted by the equations of state are very high for both the single resonant wave case and for a broadband spectrum centered on a resonant wave. These anticorrelations are also consistent with what one expects from a single particle orbit analysis. A similar analysis, but done without the prior averaging procedures, shows no relevant correlations, and no simple dynamics emerges from the kinetic data in this case. A comparison is made with a m...

Modeling the Dissipation Range of Magnetofluid Turbulence

Fluid descriptions of plasma phenomena are valuable tools for simulating large-scale phenomena. Fluid simulations, however, generally use idealized models to describe the dissipation of energy at small scales. The physical dissipation scale is usually considerably smaller than what can be evaluated numerically when using fluid descriptions of macroscopic phenomena. Here we review several approaches for describing dissipation in magnetofluid turbulence. These simulations divide into two general classes: those that employ mathematical models of the dissipation to concentrate dissipation to regions of large gradients in the fluid parameters, and those that use generalizations of Ohm’s law to model kinetic effects more completely described by the Vlasov-Maxwell equations. The former class includes using either hyperresistivity and hyperviscosity or nonlinear dissipation operators to locate dissipation in regions of strong gradients. These terms replace the standard Navier-Stokes dissipation term in the magnetohydrodynamic (MHD) equations. The second class of models includes one that modifies the magnetofluid equations by including the Hall and Finite Larmor radius corrections to Ohm’s Law and another approach that uses a coarse-grained fluid description to describe the effect of the ion cyclotron instability on the elements of the pressure tensor.

A model for cyclotron interaction effects on large scales

Starting from the contractions of exact moments of the Vlasov equation, we present a formalism for constructing a system of equations that describes aspects of cyclotron interactions using kinetic information. This non-perturbative approach does not require a priori assumptions about zero-order particle velocity distributions. The nonlinear coupling between field-aligned particle thermal velocities and transverse cyclotron wave and thermal motions is described by off-diagonal elements of the pressure tensor, and involves the growth rates of cyclotron waves. We derive the functional form of an effective wave-particle momentum transport coefficient whose magnitude and sign depend on the dynamically evolving temperature anisotropy. Finally, we present a coupled set of cyclotron equations of state for the evolution of the parallel and perpendicular pressures which provide a connection between kinetic and fluid phenomena.