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Dirk H Rischke - One of the best experts on this subject based on the ideXlab platform.
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nonresistive dissipative magnetohydrodynamics from the boltzmann equation in the 14 moment approximation
Physical Review D, 2018Co-Authors: Gabriel S Denicol, E Molnar, Harri Niemi, Xuguang Huang, Gustavo Monteiro, Jorge Noronha, Dirk H RischkeAbstract:We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like Particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be non-resistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-Particle Distribution Function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.
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closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the boltzmann equation
Physical Review D, 2016Co-Authors: E Molnar, Harri Niemi, Dirk H RischkeAbstract:In Molnar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-Particle Distribution Function. In this paper we make a particular choice for this Distribution Function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.
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derivation of anisotropic dissipative fluid dynamics from the boltzmann equation
Physical Review D, 2016Co-Authors: E Molnar, Harri Niemi, Dirk H RischkeAbstract:Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-Particle Distribution Function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-Particle Distribution Function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-Particle Distribution Function, ${\stackrel{^}{f}}_{0\mathbf{k}}$, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-Particle Distribution Function from ${\stackrel{^}{f}}_{0\mathbf{k}}$. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.
E Molnar - One of the best experts on this subject based on the ideXlab platform.
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nonresistive dissipative magnetohydrodynamics from the boltzmann equation in the 14 moment approximation
Physical Review D, 2018Co-Authors: Gabriel S Denicol, E Molnar, Harri Niemi, Xuguang Huang, Gustavo Monteiro, Jorge Noronha, Dirk H RischkeAbstract:We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like Particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be non-resistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-Particle Distribution Function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.
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closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the boltzmann equation
Physical Review D, 2016Co-Authors: E Molnar, Harri Niemi, Dirk H RischkeAbstract:In Molnar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-Particle Distribution Function. In this paper we make a particular choice for this Distribution Function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.
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derivation of anisotropic dissipative fluid dynamics from the boltzmann equation
Physical Review D, 2016Co-Authors: E Molnar, Harri Niemi, Dirk H RischkeAbstract:Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-Particle Distribution Function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-Particle Distribution Function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-Particle Distribution Function, ${\stackrel{^}{f}}_{0\mathbf{k}}$, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-Particle Distribution Function from ${\stackrel{^}{f}}_{0\mathbf{k}}$. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.
A V Artemyev - One of the best experts on this subject based on the ideXlab platform.
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Kinetic equation for nonlinear wave-Particle interaction: Solution properties and asymptotic dynamics
Physica D: Nonlinear Phenomena, 2019Co-Authors: A V Artemyev, Anatoly Neishtadt, Alexei VasilievAbstract:Abstract We consider a kinetic equation describing evolution of the Particle Distribution Function in a system with nonlinear wave-Particle interactions (trappings into resonance and nonlinear scatterings). We study properties of its solutions and show that the only stationary solution is a constant, and that all solutions with smooth initial conditions tend to a constant as time grows. The resulting flattening of the Distribution Function in the domain of nonlinear interactions is similar to one described by the quasi-linear plasma theory, but the Distribution evolves much faster. The results are confirmed numerically for a model problem.
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probabilistic approach to nonlinear wave Particle resonant interaction
Physical Review E, 2017Co-Authors: Anatoly Neishtadt, A V Artemyev, A A Vasiliev, Didier MourenasAbstract:In this paper we provide a theoretical model describing the evolution of the charged-Particle Distribution Function in a system with nonlinear wave-Particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual Particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the Particle Distribution. In this equation, effects of charged-Particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-Particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
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Kinetic equation for nonlinear resonant wave-Particle interaction
Physics of Plasmas, 2016Co-Authors: A V Artemyev, Anatoly Neishtadt, Alexei Vasiliev, Didier MourenasAbstract:We investigate the nonlinear resonant wave-Particle interactions including the effects of Particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of Particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-Particle interaction into a kinetic equation for the Particle Distribution Function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of Particle momentum Distribution due to Particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test Particle simulations.
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Approximate analytical solutions for the trapped electron Distribution due to quasi-linear diffusion by whistler mode waves
Journal of Geophysical Research Space Physics, 2014Co-Authors: Didier Mourenas, A V Artemyev, V KrasnoselskikhAbstract:The Distribution of trapped energetic electrons inside the Earth’s radiation belts is the focus of intense studies aiming at better describing the evolution of the space environment in the presence of various disturbances induced by the solar wind or by an enhanced lightning activity. Such studies are usually performed by means of comparisons with full numerical simulations solving the Fokker-Planck quasi-linear diffusion equation for the Particle Distribution Function. Here we present for the first time approximate but realistic analytical solutions for the electron Distribution, which are shown to be in good agreement with exact numerical solutions in situations where resonant scattering of energetic electrons by whistler mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet time Distributions are well recovered, as well as the evolution of energized relativistic electron Distributions during disturbed geomagnetic conditions. It is further shown that careful comparisons between the analytical solutions and measured Distributions may allow to infer important bounce- and drift-averaged wave characteristics (such as wave amplitude). It could also help to improve the global understanding of underlying physical phenomena.
Harri Niemi - One of the best experts on this subject based on the ideXlab platform.
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nonresistive dissipative magnetohydrodynamics from the boltzmann equation in the 14 moment approximation
Physical Review D, 2018Co-Authors: Gabriel S Denicol, E Molnar, Harri Niemi, Xuguang Huang, Gustavo Monteiro, Jorge Noronha, Dirk H RischkeAbstract:We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like Particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be non-resistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-Particle Distribution Function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.
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closing the equations of motion of anisotropic fluid dynamics by a judicious choice of a moment of the boltzmann equation
Physical Review D, 2016Co-Authors: E Molnar, Harri Niemi, Dirk H RischkeAbstract:In Molnar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-Particle Distribution Function. In this paper we make a particular choice for this Distribution Function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.
-
derivation of anisotropic dissipative fluid dynamics from the boltzmann equation
Physical Review D, 2016Co-Authors: E Molnar, Harri Niemi, Dirk H RischkeAbstract:Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-Particle Distribution Function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-Particle Distribution Function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-Particle Distribution Function, ${\stackrel{^}{f}}_{0\mathbf{k}}$, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-Particle Distribution Function from ${\stackrel{^}{f}}_{0\mathbf{k}}$. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.
Didier Mourenas - One of the best experts on this subject based on the ideXlab platform.
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probabilistic approach to nonlinear wave Particle resonant interaction
Physical Review E, 2017Co-Authors: Anatoly Neishtadt, A V Artemyev, A A Vasiliev, Didier MourenasAbstract:In this paper we provide a theoretical model describing the evolution of the charged-Particle Distribution Function in a system with nonlinear wave-Particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual Particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the Particle Distribution. In this equation, effects of charged-Particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-Particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
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Kinetic equation for nonlinear resonant wave-Particle interaction
Physics of Plasmas, 2016Co-Authors: A V Artemyev, Anatoly Neishtadt, Alexei Vasiliev, Didier MourenasAbstract:We investigate the nonlinear resonant wave-Particle interactions including the effects of Particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of Particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-Particle interaction into a kinetic equation for the Particle Distribution Function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of Particle momentum Distribution due to Particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test Particle simulations.
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Approximate analytical solutions for the trapped electron Distribution due to quasi-linear diffusion by whistler mode waves
Journal of Geophysical Research Space Physics, 2014Co-Authors: Didier Mourenas, A V Artemyev, V KrasnoselskikhAbstract:The Distribution of trapped energetic electrons inside the Earth’s radiation belts is the focus of intense studies aiming at better describing the evolution of the space environment in the presence of various disturbances induced by the solar wind or by an enhanced lightning activity. Such studies are usually performed by means of comparisons with full numerical simulations solving the Fokker-Planck quasi-linear diffusion equation for the Particle Distribution Function. Here we present for the first time approximate but realistic analytical solutions for the electron Distribution, which are shown to be in good agreement with exact numerical solutions in situations where resonant scattering of energetic electrons by whistler mode hiss, lightning-generated or chorus waves, is the dominant process. Quiet time Distributions are well recovered, as well as the evolution of energized relativistic electron Distributions during disturbed geomagnetic conditions. It is further shown that careful comparisons between the analytical solutions and measured Distributions may allow to infer important bounce- and drift-averaged wave characteristics (such as wave amplitude). It could also help to improve the global understanding of underlying physical phenomena.