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

Abstract

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.

arXiv commentImproved version, accepted to JPP Lecture Notes. Some parts were shortened and some parts were expanded. The text now contains Conclusions

References in corpus (23)

• Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas
• Kappa distributions: theory and applications in space plasmas
• Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind
• The Protogalactic Origin for Cosmic Magnetic Fields
• Energy transfer, pressure tensor and heating of kinetic plasma
• The power-law spectra of energetic particles during multi-island magnetic reconnection
• Fluid description of multi-component solar partially ionized plasma
• New insight into short wavelength solar wind fluctuations from Vlasov theory
• Pressure anisotropy and small spatial scales induced by velocity shear
• A nonlinear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma
• A Landau fluid model for warm collisionless plasmas
• Fluidization of collisionless plasma turbulence
• Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas
• Numerical simulations of quiet Sun magnetic fields seeded by Biermann battery
• The parametric instability of Alfvén waves: effects of temperature anisotropy
• New closures for more precise modeling of Landau damping in the fluid framework
• Fluid simulations of plasma turbulence at ion scales: comparison with Vlasov-Maxwell simulations
• On the parallel and oblique firehose instability in fluid models
• Nonlinear firehose relaxation and constant-B field fluctuations
• Reduction of compressibility and parallel transfer by Landau damping in turbulent magnetized plasmas
• "Magneto-elastic" waves in an anisotropic magnetised plasma
• Wave instabilities of a collisionless plasma in fluid approximation
• Comparison of linear modes in kinetic plasma models

Cited by in corpus (22)

• Energy Dissipation and Entropy in Collisionless Plasma
• Generalized Fluid Models of the Braginskii Type
• Bridging hybrid- and full-kinetic models with Landau-fluid electrons: I. 2D magnetic reconnection
• Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: toward linking energy cascade and instabilities
• A Measurement of the Effective Mean-Free-Path of Solar Wind Protons
• Mixing the solar wind proton and electron scales. Theory and 2D-PIC simulations of firehose instability
• Particle-In-Cell simulations of the parallel proton firehose instability influenced by the electron temperature anisotropy in solar wind conditions
• Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
• Electron Heat Flux in the Solar Wind: Generalized Approaches to Fluid Transport with a Variety of Skewed Velocity Distributions
• Simulations of the Biermann battery mechanism in two-fluid partially ionised plasmas
• Magnetic Energy Conversion in MHD: Curvature Relaxation and Perpendicular Expansion of Magnetic Fields
• A non-local fluid closure for modeling cyclotron resonance in collisionless magnetized plasmas
• Enhancement of the non-resonant streaming instability by particle collisions
• Action Principles and Conservation Laws for Chew-Goldberger-Low Anisotropic Plasmas
• Critical comparison of collisionless fluid models: Nonlinear simulations of parallel firehose instability
• Fast magneto-acoustic waves in the solar chromosphere: Comparison of single-fluid and two-fluid approximations
• Electron neural closure for turbulent magnetosheath simulations: energy channels
• Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions
• Interplay between the non-resonant streaming instability and self-generated pressure anisotropies
• A conserved thermo-mechanic invariant in extended fluid description of collisionless plasmas
• Well-posedness for moving interfaces in anisotropic plasmas
• The Machine Learning Approach to Moment Closure Relations for Plasma: A Review