P. Hunana

INHOMOGENEOUS NEARLY INCOMPRESSIBLE DESCRIPTION OF MAGNETOHYDRODYNAMIC TURBULENCE

The nearly incompressible theory of magnetohydrodynamics (MHD) is formulated in the presence of a static large-scale inhomogeneous background. The theory is an inhomogeneous generalization of the homogeneous nearly incompressible MHD description of Zank & Matthaeus and a polytropic equation of state is assumed. The theory is primarily developed to describe solar wind turbulence where the assumption of a composition of two-dimensional (2D) and slab turbulence with the dominance of the 2D component has been used for some time. It was however unclear, if in the presence of a large-scale inhomogeneous background, the dominant component will also be mainly 2D and we consider three distinct MHD regimes for the plasma beta ? 1, ? ~ 1, and? 1. For regimes appropriate to the solar wind (? 1, ? ~ 1), compared to the homogeneous description of Zank & Matthaeus, the reduction of dimensionality for the leading-order description from three dimensional (3D) to 2D is only weak, with the parallel component of the velocity field proportional to the large-scale gradients in density and the magnetic field. Close to the Sun, however, where the large-scale magnetic field can be considered as purely radial, the collapse of dimensionality to 2D is complete. Leading-order density fluctuations are shown to be of the order of the sonic Mach number and evolve as a passive scalar mixed by the turbulent velocity field. It is emphasized that the usual pseudosound relation used to relate density and pressure fluctuations through the sound speed as ?? = c 2 s ?p is not valid for the leading-order density fluctuations, and therefore in observational studies, the density fluctuations should not be analyzed through the pressure fluctuations. The pseudosound relation is valid only for higher order density fluctuations, and then only for short-length scales and fast timescales. The spectrum of the leading-order density fluctuations should be modeled as k ?5/3 in the inertial range, followed by a Bessel function solution K ?(k), where for stationary turbulence ? = 1, in the viscous-convective and diffusion range. Other implications for solar wind turbulence with an emphasis on the evolution of density fluctuations are also discussed.

PICKUP ION MEDIATED PLASMAS. I. BASIC MODEL AND LINEAR WAVES IN THE SOLAR WIND AND LOCAL INTERSTELLAR MEDIUM

Pickup ions (PUIs) in the outer heliosphere and the local interstellar medium are created by charge exchange between protons and hydrogen (H) atoms, forming a thermodynamically dominant component. In the supersonic solar wind beyond >10 AU, in the inner heliosheath (IHS), and in the very local interstellar medium (VLISM), PUIs do not equilibrate collisionally with the background plasma. Using a collisionless form of Chapman-Enskog expansion, we derive a closed system of multi-fluid equations for a plasma comprised of thermal protons and electrons, and suprathermal PUIs. The PUIs contribute an isotropic scalar pressure to leading order, a collisionless heat flux at the next order, and a collisionless stress tensor at the second-order. The collisionless heat conduction and viscosity in the multi-fluid description results from a non-isotropic PUI distribution. A simpler one-fluid MHD-like system of equations with distinct equations of state for both the background plasma and the PUIs is derived. We investigate linear wave properties in a PUI-mediated three-fluid plasma model for parameters appropriate to the VLISM, the IHS, and the solar wind in the outer heliosphere. Five distinct wave modes are possible: Alfven waves, thermal fast and slow magnetoacoustic waves, PUI fast and slow magnetoacoustic waves, and an entropy mode. The thermal and PUI acoustic modes propagate at approximately the combined thermal magnetoacoustic speed and the PUI sound speed respectively. All wave modes experience damping by the PUIs through the collisionless PUI heat flux. The PUI-mediated plasma model yields wave properties, including Alfven waves, distinctly different from those of the standard two-fluid model.

The transport of low-frequency turbulence in the super-Alfvénic solar wind

Understanding the transport of low-frequency turbulence in an expanding magnetized flow is very important in analyzing numerous problems in space physics and astrophysics. Zank et al 2012 developed six general coupled turbulence transport equations, including the Alfven velocity to describe the transport of low-frequency turbulence for any inhomogeneous flows, including sub-Alfvenic coronal flows, and super-Alfvenic solar wind flows. Here, we solve the 1D steady state six coupled turbulence transport equations of Zank et al 2012, and the transport equation corresponding to the solar wind temperature in the super-Alfvenic solar wind flows from 0.29 to 100 AU without the Alfven velocity. We calculate turbulent quantities corresponding to Voyager 2 data sets for three cases; i) a positive and negative sign of Br; ii) the azimuthal angle = tan-1(Bt/Br), and iii) a positive and negative sign of Bt, where Br and Bt are the radial and transverse components of the interplanetary magnetic field, respectively. We compare our theoretical results to the observational results, and find good agreement between them.

On the Parallel and Oblique Firehose Instability in Fluid Models

A brief analysis of the proton parallel and oblique firehose instability is presented from a fluid perspective, and the results are compared with kinetic theory solutions obtained by the WHAMP code. It is shown that the classical CGL model very accurately describes the growth rate of these instabilities at sufficiently long spatial scales (small wavenumbers). The required stabilization of these instabilities at small spatial scales (high wavenumbers) naturally requires dispersive effects, and the stabilization is due to the Hall term and finite Larmor radius corrections to the pressure tensor. Even though the stabilization is not completely accurate, since at small spatial scales a relatively strong collisionless damping comes into effect, we find that the main concepts of the maximum growth rate and the stabilization of these instabilities is indeed present in the fluid description. However, there are differences that are quite pronounced when close to the firehose threshold, and that clarify the different profiles for marginally stable states with a prescribed maximum growth rate in the simple fluid models considered here and the kinetic description.

The interaction of turbulence with parallel and perpendicular shocks

Interplanetary shocks exist in most astrophysical flows, and modify the properties of the background flow. We apply the Zank et al 2012 six coupled turbulence transport model equations to study the interaction of turbulence with parallel and perpendicular shock waves in the solar wind. We model the 1D structure of a stationary perpendicular or parallel shock wave using a hyperbolic tangent function and the Rankine-Hugoniot conditions. A reduced turbulence transport model (the 4-equation model) is applied to parallel and perpendicular shock waves, and solved using a 4th- order Runge Kutta method. We compare the model results with ACE spacecraft observations. We identify one quasi-parallel and one quasi-perpendicular event in the ACE spacecraft data sets, and compute various turbulent observed values such as the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy in the upstream and downstream of the shock. We also calculate the error associated with each turbulent observed value, and fit the observed values by a least square method and use a Fourier series fitting function. We find that the theoretical results are in reasonable agreement with observations. The energy in turbulent fluctuations is enhanced and the correlation length is approximately constant at the shock. Similarly, the normalized cross helicity increases across a perpendicular shock, and decreases across a parallel shock.

Particle acceleration and reconnection in the solar wind

An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized quasi-2D small-scale magnetic island reconnection processes. An advection-diffusion transport equation for a nearly isotropic particle distribution describes particle transport and energization in a region of interacting magnetic islands [1; 2]. The dominant charged particle energization processes are 1) the electric field induced by quasi-2D magnetic island merging, and 2) magnetic island contraction. The acceleration of charged particles in a “sea of magnetic islands” in a super-Alfvenic flow, and the energization of particles by combined diffusive shock acceleration (DSA) and downstream magnetic island reconnection processes are discussed.

The Modeling of Pickup Ion or Energetic Particle Mediated Plasmas

Suprathermal energetic particles, such as solar energetic particles (SEPs) in the inner heliosphere and pickup ions (PUIs) in the outer heliosphere and the very local interstellar medium, often form a thermodynamically dominant component in their various environments. In the supersonic solar wind beyond > 10 AU, in the inner heliosheath (IHS), and in the very local interstellar medium (VLISM), PUIs do not equilibrate collisionally with the background plasma. Similarly, SEPs do not equilibrate collisionally with the background solar wind in the inner heliosphere. In the absence of equilibration between plasma components, a separate coupled plasma description for the energetic particles is necessary. Using a collisionless Chapman-Enskog expansion, we derive a closed system of multi-component equations for a plasma comprised of thermal protons and electrons, and suprathermal particles (SEPs, PUIs). The energetic particles contribute an isotropic scalar pressure to leading order, a collisionless heat flux at the next order, and a collisionless stress tensor at the second-order. The collisionless heat conduction and viscosity in the multi-fluid description results from a nonisotropic energetic particle distribution. A simpler single-fluid MHD-like system of equations with distinct equations of state for both the background plasma and the suprathermal particles is derived. We note briefly potential pitfalls that can emerge in the numerical modeling of collisionless plasma flows that contain a dynamically important energetic particle component.

Turbulence transport within the Heliosphere

This work continues the investigation of turbulence transport throughout the supersonic solar wind initiated in Zank et al 1996 [27] and Zank et al 2012 [20]. [20] developed a system of six coupled transport equations that describe the transport of energy corresponding to forward propagating (g) and backward propagating modes (f), the residual energy (ED), and the correlation lengths corresponding to forward propagating modes (λ−), backward propagating modes (λ+), and the correlation length (λD) for residual energy. These models can be applied to both sub-Alfvenic (such as the lower corona) and super-Alfvenic (e.g., supersonic solar wind and inner heliosheath) flows. The correlation lengths calculated from our model are in good agreement with those observed. The evolution of related parameters is also calculated from 0.29 AU to 5 AU.