An introductory guide to fluid models with anisotropic temperatures Part 1 -- CGL description and collisionless fluid hierarchy

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modeling turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the CGL fluid model in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius (FLR) corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the 4th-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the "normal" closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the "normal" closure, and beyond the 4th-order moment, Landau fluid closures are required.Comment: Improved version, accepted to JPP Lecture Notes. Some parts were shortened and some parts were expanded. The text now contains Conclusion

Diffusive Shock Acceleration and Reconnection Acceleration Processes

Shock waves, as shown by simulations and observations, can generate high levels of downstream vortical turbulence, including magnetic islands. We consider a combination of diffusive shock acceleration (DSA) and downstream magnetic-island-reconnection-related processes as an energization mechanism for charged particles. Observations of electron and ion distributions downstream of interplanetary shocks and the heliospheric termination shock (HTS) are frequently inconsistent with the predictions of classical DSA. We utilize a recently developed transport theory for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets. Particle energization associated with the anti-reconnection electric field, a consequence of magnetic island merging, and magnetic island contraction, are considered. For the former only, we find that (i) the spectrum is a hard power law in particle speed, and (ii) the downstream solution is constant. For downstream plasmoid contraction only, (i) the accelerated spectrum is a hard power law in particle speed; (ii) the particle intensity for a given energy peaks downstream of the shock, and the distance to the peak location increases with increasing particle energy, and (iii) the particle intensity amplification for a particular particle energy, f(x,c/c_0)/f(0,c/c_0), is not 1, as predicted by DSA, but increases with increasing particle energy. The general solution combines both the reconnection-induced electric field and plasmoid contraction. The observed energetic particle intensity profile observed by Voyager 2 downstream of the HTS appears to support a particle acceleration mechanism that combines both DSA and magnetic-island-reconnection-related processes

No Evidence for Critical Balance in Field-aligned Alfvénic Solar Wind Turbulence

The properties of Alfvenic solar wind turbulence have been studied for decades using spacecraft measurements. In particular, the observation of spectral anisotropy of magnetic fluctuations has stimulated the development of several phenomenological models, one of the most popular being critical balance. However, the experimental validation of these models is intrinsically difficult because of the one-dimensional nature of the measurements provided by spacecraft instrumentation. In this work, a thorough search is performed in the Wind spacecraft database to extract samples of field-aligned fast solar wind, which allow the precise estimation of the parallel spectral properties of the magnetic fluctuations, and of their intermittency. Hilbert spectral analysis is used, in order to eliminate the possible role of nonstationarity and large-scale structures. Our results indicate that the spectral anisotropy predicted by the critical balance theory is not observed in the selected database, thus questioning the validity of the critical balance in the solar wind turbulence. A stochastic process characterized by a -5/3 spectral scaling, which is not necessarily attributed to usual turbulence, as indicated by the absence of intermittency, is indeed observed in the analyzed data samples

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-Alfvénic (such as the lower corona) and super-Alfvénic (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. <P /

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-Alfvénic flow, and the energization of particles by combined diffusive shock acceleration (DSA) and downstream magnetic island reconnection processes are discussed

Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

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Turbulent Transport in a Three-dimensional Solar Wind

Turbulence in the solar wind can play essential roles in the heating of coronal and solar wind plasma and the acceleration of the solar wind and energetic particles. Turbulence sources are not well understood and thought to be partly enhanced by interaction with the large-scale inhomogeneity of the solar wind and the interplanetary magnetic field and/or transported from the solar corona. To investigate the interaction with background inhomogeneity and the turbulence sources, we have developed a new 3D MHD model that includes the transport and dissipation of turbulence using the theoretical model of Zank et al. We solve for the temporal and spatial evolution of three moments or variables, the energy in the forward and backward fluctuating modes and the residual energy and their three corresponding correlation lengths. The transport model is coupled to our 3D model of the inhomogeneous solar wind. We present results of the coupled solar wind-turbulence model assuming a simple tilted dipole magnetic configuration that mimics solar minimum conditions, together with several comparative intermediate cases. By considering eight possible solar wind and turbulence source configurations, we show that the large-scale solar wind and IMF inhomogeneity and the strength of the turbulence sources significantly affect the distribution of turbulence in the heliosphere within 6 au. We compare the predicted turbulence distribution results from a complete solar minimum model with in situ measurements made by the Helios and Ulysses spacecraft, finding that the synthetic profiles of the turbulence intensities show reasonable agreement with observations

Theory and Transport of Nearly Incompressible Magnetohydrodynamics Turbulence. III. Evolution of Power Anistropy in Magnetic Field Fluctuations throughout the Heliosphere

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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 Alfvén velocity to describe the transport of low-frequency turbulence for any inhomogeneous flows, including sub-Alfvénic coronal flows, and super-Alfvénic 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-Alfvénic solar wind flows from 0.29 to 100 AU without the Alfvén 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 ϕ = 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. <P /