Extended hydrodynamical models for plasmas (original) (raw)
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General moment system for plasma physics based on minimum entropy principle
Kinetic & Related Models, 2015
In plasma physics domain, the electrons transport can be described from kinetic and hydrodynamical models. Both methods present disadvantages and thus cannot be considered in practical computations for Inertial Confinement Fusion (ICF). That is why we propose in this paper a new model which is intermediate between these two descriptions. More precisely, the derivation of such models is based on an angular closure in the phase space and retains only the energy of particles as a kinetic variable. The closure of the moment system is obtained from a minimum entropy principle. The resulting continuous model is proved to satisfy fundamental properties. Moreover the model is discretized w.r.t the energy variable and the semi-discretized scheme is shown to satisfy conservation properties and entropy decay.
Fluid Moments in the Reduced Model for Plasmas with Large Flow Velocity
Plasma and Fusion Research, 2011
Representation of particle fluid moments in terms of fluid moments in the modified guiding-centre model for flowing plasmas with large E × B velocity [N. Miyato et al., J. Phys. Soc. Jpn. 78, 104501 (2009)] is derived from the formal exact representation by a perturbative expansion in the subsonic flow case. It is similar to that in the standard gyrokinetic model in the long wavelength limit, except it has an additional flow term. The flow term has no effect on the representation for particle density, leading to the same representation as the standard one formally. In the conventional guiding-centre models for flowing plasmas, on the other hand, the representation for particle density is different from the standard one. This is due to the difference in the transformation for the guiding-centre position. Although the exact representation usually used in the standard gyrokinetic model has a different form from that in the modified guiding-centre case, correspondence between the two models is shown by considering the alternative form of exact representation in the standard gyrokinetic case. The representation for particle density is also obtained from the single particle Lagrangian by a variational method which is used to derive the representation in the transonic case.
The zero-electron-mass limit in the hydrodynamic model for plasmas
Nonlinear Analysis-theory Methods & Applications, 2010
The limit of the vanishing ratio of the electron mass to the ion mass in the isentropic transient Euler–Poisson equations with periodic boundary conditions is proved. The equations consist of the balance laws for the electron density and current density for a given ion density, coupled to the Poisson equation for the electrostatic potential. The limit is related to the low-Mach-number limit of Klainerman and Majda. In particular, the limit velocity satisfies the incompressible Euler equations with damping. The difference to the zero-Mach-number limit comes from the electrostatic potential which needs to be controlled. This is done by a reformulation of the equations in terms of the enthalpy, higher-order energy estimates and a careful use of the Poisson equation.
Non-Extensive Transport Equations in Magnetized Plasmas
arXiv: Plasma Physics, 2018
In this work we introduce, for the first time, as far as we know, a complete self-consist kinetic model for collisional transport in the nonextensive statistics, i.e., the generalization of the ordinary Maxwell-Boltmzann statistics according to the Tsallis entropy. Starting only from the definition of this entropy, we derive the kinetic model, find its solutions for the electrons in a strongly magnetized plasmas, and calculate the respective transport coefficients in order to set the closed fluid equations. The results are further applied to model heat transport in space plasmas and the cold pulse phenomenon in magnetic confined plasmas.
Plasma thermal transport with a generalized 8-moment distribution function
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Moment equations that model plasma transport require an ansatz distribution function to close the system of equations. The resulting transport is sensitive to the specific closure used, and several options have been proposed in the literature. Two different 8-moment distribution functions can be generalized to form a single-parameter family of distribution functions. The transport coefficients resulting from this generalized distribution function can be expressed in terms of this free parameter. This provides the flexibility of matching the 8-moment model to some validating result at a given magnetization value, such as Braginskii's transport, or the more recent results of Davies et al. [Phys. Plasma, 28, 012305 (2021)]. This process can be thought of as a solution for the 8-moment distribution function that matches the value of a transport coefficient given by a Chapman–Enskog expansion while retaining the improved physical properties, such as finite propagation speeds and time...
Reports in Advances of Physical Sciences
Plasma dynamics have been studied extensively and there is a fair amount of understanding where the scientific community has reached at. However, there is still a very big gap in completely explaining plasma physics at the classical as well as the quantum level. The dynamics of plasma from an entropic approach are not very well understood or explained. There is too much chaos to account for and even a small deviation in terms of perturbations of any kind makes a sizeable difference. This study is based on the entropic approach where we take a model independent classical plasma. Then we apply Langevin equations and Fokker–Planck equations to explain the entropy generated and entropy produced. Then we study various conditions in which we apply an electric field and a magnetic field and understand the various trends in entropy changes. When we apply the electric field and the magnetic fields independently of each other and together in the plasma model, we see that there is a very impor...
A Maxwell formulation for the equations of a plasma
2012
In light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid equations of motion may be reformulated as a set of Maxwell equations. This analogy has been explored in the literature for incompressible turbulent flow and compressible flow but has not been widely explored in relation to plasmas. This letter introduces the analogous fluid Maxwell equations and formulates a set of Maxwell equations for a plasma in terms of the species canonical vorticity and its cross product with the species velocity. The form of the source terms is presented and the magnetohydrodynamic (MHD) limit restores the typical variety of MHD waves.
Toward a realistic macroscopic parametrization of space plasmas with regularized κ-distributions
Astronomy & Astrophysics, 2020
So-called κ-distributions are widely invoked in the analysis of nonequilibrium plasmas from space, although a general macroscopic parametrization as known for Maxwellian plasmas near thermal equilibrium is prevented by the diverging moments of order l ≥ 2κ − 1. To overcome this critical limitation, recently novel regularized κ-distributions (RK) have been introduced, including various anisotropic models with well-defined moments for any value of κ > 0. In this paper, we present an evaluation of the pressure and heat flux of electron populations, as provided by moments of isotropic and anisotropic RKs for conditions typically encountered in the solar wind. We obtained finite values even for low values of κ < 3/2, for which the pressure and heat flux moments of standard κ-distributions are not defined. These results were also contrasted with the macroscopic parameters obtained for Maxwellian populations, which show a significant underestimation especially if an important supra...
Fluid dynamics of out of equilibrium boost invariant plasmas
Physics Letters B, 2018
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.