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Fluids
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Modelling of Plasma Flow
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Modelling of Plasma Flow

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (1 September 2019) | Viewed by 32283

Special Issue Editors

Dr. Alain Ghizzo

E-Mail Website
Guest Editor
Institut Jean Lamour, CNRS UMR 7198, University of Lorraine, BP 239 F-54506 Vandoeuvre les Nancy, France
Interests: modelling of Vlasov plasmas; nonlinear phenomena; laser–plasma interaction; plasma turbulence
Dr. Daniele Del Sarto

E-Mail Website
Guest Editor
Institut Jean Lamour, CNRS UMR 7198, University of Lorraine, BP 239 F-54506 Vandoeuvre les Nancy, France
Interests: mathematical modelling of kinetic and fluid plasmas; MHD plasma instabilities; laser–plasma instabilities; magnetic reconnection; nonlinear phenomena

Special Issue Information

Dear Colleagues,

Plasmas, gazes of charged particles displaying a collective behavior and interacting with electromagnetic fields, due to their large number of constituents, provide the most frequently-encountered example in the universe of diluted continuous systems with multi-scale properties. The typical lack of collisions, for which they differ from classical gazes, highlights the importance of kinetic effects in the processes they are involved in, often far from thermodynamical equilibrium. Nevertheless, their collective behavior as continuous systems is well described by fluid-type equations: Either hydrodynamic-type equations for the large scale particle response to electromagnetic fields, i.e., the magnetohydrodynamic or multi-fluid plasma descriptions for the fluid moments of the distribution functions, or as continuity equations for the particle density in the phase-space, i.e., the Vlasov transport equation and its reduced models.

In both frameworks, the modelling of “plasma flows” plays a dominant role in the description of collective processes, such as instabilities, turbulence, transport processes, topological conservations and vortex dynamics, which may involve both magnetohydrodynamic-type vortices or “phase–space vortices” describing populations of trapped particles, dragged by the Hamiltonian flow.

On the other hand, remarkable advancements in plasma physics have considerably expanded the selection of available analytical tools and computational techniques, which may be applied to the study of nonlinear phenomena. These tools have brought great benefits to several applications in the physics of fluids, including the study of flow transition and thus of turbulence, both in the physical space and in the phase-space. Today, the numerical simulation of plasmas, which continues to be explored through the development and the use of both fluid and kinetic models, provides a range of challenges for computational scientists including those involved in the area of fluid dynamics. Fluid and plasma communities, indeed, share common algorithmic needs and similar computational and scientific methodologies.

The aim of this Special Issue is to collect a wide variety of papers which have as their unifying theme the modelling of plasma flows and of their associated instabilities or turbulence, as well as the use of analytical tools for the description of plasma processes that can be of interest to the physics of classical fluids. In order to grant accessibility to a wide audience, we intend to place a strong emphasis on the pedagogical presentation of subjects which may be relevant to the physics of laser plasma interaction, of magnetically confined plasmas fusion and astrophysical plasmas.

Dr. Alain Ghizzo
Dr. Daniele Del Sarto
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fluid and kinetic modelling in plasmas
  • plasma turbulence
  • laser-plasma interaction
  • magnetized plasmas

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Published Papers (9 papers)

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15 pages, 3000 KiB  
Article
Energy Transport by Kelvin-Helmholtz Instability at the Magnetopause
by Francesco Palermo
Fluids 2019, 4(4), 189; https://doi.org/10.3390/fluids4040189 - 1 Nov 2019
Cited by 2 | Viewed by 3523
Abstract
By means of the formation of vortices in the nonlinear phase, the Kelvin Helmholtz instability is able to redistribute the flux of energy of the solar wind that flows parallel to the magnetopause. The energy transport associated with the Kelvin Helmholtz instability contributes [...] Read more.
By means of the formation of vortices in the nonlinear phase, the Kelvin Helmholtz instability is able to redistribute the flux of energy of the solar wind that flows parallel to the magnetopause. The energy transport associated with the Kelvin Helmholtz instability contributes significantly to the magnetosphere and magnetosheath dynamics, in particular at the flanks of the magnetopause where the presence of a magnetic field perpendicular to the velocity flow does not inhibit the instability development. By means of a 2D two-fluid simulation code, the behavior of the Kelvin Helmholtz instability is investigated in the presence of typical conditions observed at the magnetopause. In particular, the energy penetration in the magnetosphere is studied as a function of an important parameter such as the solar wind velocity. The influence of the density jump at the magnetopause is also discussed. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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11 pages, 3213 KiB  
Article
Influence of Toroidal Flow on Stationary Density of Collisionless Plasmas
by Elias Laribi, Shun Ogawa, Guilhem Dif-Pradalier, Alexei Vasiliev, Xavier Garbet and Xavier Leoncini
Fluids 2019, 4(3), 172; https://doi.org/10.3390/fluids4030172 - 16 Sep 2019
Cited by 1 | Viewed by 2515
Abstract
Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal [...] Read more.
Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal (poloidal) flow in the plasma can ensure radial confinement, while the presence of a longitudinal (toroidal) flow can enhance greatly the confinement. Moreover in the global physically reasonable situation, we find that no unstable point can emerge in the effective integrable Hamiltonian of the individual particles, hinting at some stability of the confinement when considering a toroidal geometry in the large aspect ratio limit. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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19 pages, 463 KiB  
Article
Energy Transfer in Incompressible Magnetohydrodynamics: The Filtered Approach
by Jesse T. Coburn and Luca Sorriso-Valvo
Fluids 2019, 4(3), 163; https://doi.org/10.3390/fluids4030163 - 2 Sep 2019
Cited by 2 | Viewed by 2164
Abstract
We develop incompressible magnetohydrodynamic (IMHD) energy budget equations with a spatial filtering kernel and estimate the scaling of the structure functions. The Politano-Pouquet law is recovered as an upper bound on the scale-to-scale energy transfer. The primary result of this work is the [...] Read more.
We develop incompressible magnetohydrodynamic (IMHD) energy budget equations with a spatial filtering kernel and estimate the scaling of the structure functions. The Politano-Pouquet law is recovered as an upper bound on the scale-to-scale energy transfer. The primary result of this work is the relation of the scaling of IMHD invariants. It can be produced by hypothesizing a scale-independent energy transfer rate. These results have relevance in plasma regimes where the approximations of IMHD are justified. We measure structure functions with solar wind data and find support for the relations. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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13 pages, 2767 KiB  
Article
Laser-Plasma Accelerated Protons: Energy Increase in Gas-Mixtures Using High Mass Number Atomic Species
by Tadzio Levato, Leonardo V. Goncalves and Vincenzo Giannini
Fluids 2019, 4(3), 150; https://doi.org/10.3390/fluids4030150 - 8 Aug 2019
Cited by 6 | Viewed by 3757
Abstract
The idea of using a gas-mixture comprising atoms with a high mass number in order to increase proton energies in laser induced plasma acceleration at critical density is investigated by means of 2D PIC (Particle-In-Cell) simulations. Comparing and discussing the case of a [...] Read more.
The idea of using a gas-mixture comprising atoms with a high mass number in order to increase proton energies in laser induced plasma acceleration at critical density is investigated by means of 2D PIC (Particle-In-Cell) simulations. Comparing and discussing the case of a pure hydrogen plasma and that of a plasma containing higher mass number species with a small percentage of hydrogen, we demonstrate that the mixture enhances the energies of the accelerated protons. We also show that using a gas-mixture introduces the possibility of using the densities ratio in order to change the relative acceleration of the species. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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45 pages, 9360 KiB  
Article
Turbulence and Microprocesses in Inhomogeneous Solar Wind Plasmas
by Catherine Krafft, Alexander S. Volokitin and Gaëtan Gauthier
Fluids 2019, 4(2), 69; https://doi.org/10.3390/fluids4020069 - 11 Apr 2019
Cited by 7 | Viewed by 3151
Abstract
The random density fluctuations observed in the solar wind plasma crucially influence on the Langmuir wave turbulence generated by energetic electron beams ejected during solar bursts. Those are powerful phenomena consisting of a chain of successive processes leading ultimately to strong electromagnetic emissions. [...] Read more.
The random density fluctuations observed in the solar wind plasma crucially influence on the Langmuir wave turbulence generated by energetic electron beams ejected during solar bursts. Those are powerful phenomena consisting of a chain of successive processes leading ultimately to strong electromagnetic emissions. The small-scale processes governing the interactions between the waves, the beams and the inhomogeneous plasmas need to be studied to explain such macroscopic phenomena. Moreover, the complexity induced by the plasma irregularities requires to find new approaches and modelling. Therefore theoretical and numerical tools were built to describe the Langmuir wave turbulence and the beam’s dynamics in inhomogeneous plasmas, in the form of a self-consistent Hamiltonian model including a fluid description for the plasma and a kinetic approach for the beam. On this basis, numerical simulations were performed in order to shed light on the impact of the density fluctuations on the beam dynamics, the electromagnetic wave radiation, the generation of Langmuir wave turbulence, the waves’ coupling and decay phenomena involving Langmuir and low frequency waves, the acceleration of beam electrons, their diffusion mechanisms, the modulation of the Langmuir waveforms and the statistical properties of the radiated fields’ distributions. The paper presents the main results obtained in the form of a review. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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11 pages, 463 KiB  
Article
On the Fractional Diffusion-Advection Equation for Fluids and Plasmas
by Gaetano Zimbardo and Silvia Perri
Fluids 2019, 4(2), 62; https://doi.org/10.3390/fluids4020062 - 1 Apr 2019
Cited by 7 | Viewed by 3687
Abstract
The problem of studying anomalous superdiffusive transport by means of fractional transport equations is considered. We concentrate on the case when an advection flow is present (since this corresponds to many actual plasma configurations), as well as on the case when a boundary [...] Read more.
The problem of studying anomalous superdiffusive transport by means of fractional transport equations is considered. We concentrate on the case when an advection flow is present (since this corresponds to many actual plasma configurations), as well as on the case when a boundary is also present. We propose that the presence of a boundary can be taken into account by adopting the Caputo fractional derivatives for the side of the boundary (here, the left side), while the Riemann-Liouville derivative is used for the unbounded side (here, the right side). These derivatives are used to write the fractional diffusion–advection equation. We look for solutions in the steady-state case, as such solutions are of practical interest for comparison with observations both in laboratory and astrophysical plasmas. It is shown that the solutions in the completely asymmetric cases have the form of Mittag-Leffler functions in the case of the left fractional contribution, and the form of an exponential decay in the case of the right fractional contribution. Possible applications to space plasmas are discussed. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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17 pages, 1668 KiB  
Article
Tokamak Edge Plasma Turbulence Interaction with Magnetic X-Point in 3D Global Simulations
by Davide Galassi, Guido Ciraolo, Patrick Tamain, Hugo Bufferand, Philippe Ghendrih, Nicolas Nace and Eric Serre
Fluids 2019, 4(1), 50; https://doi.org/10.3390/fluids4010050 - 15 Mar 2019
Cited by 14 | Viewed by 4297
Abstract
Turbulence in the edge plasma of a tokamak is a key actor in the determination of the confinement properties. The divertor configuration seems to be beneficial for confinement, suggesting an effect on turbulence of the particular magnetic geometry introduced by the X-point. Simulations [...] Read more.
Turbulence in the edge plasma of a tokamak is a key actor in the determination of the confinement properties. The divertor configuration seems to be beneficial for confinement, suggesting an effect on turbulence of the particular magnetic geometry introduced by the X-point. Simulations with the 3D fluid turbulence code TOKAM3X are performed here to evaluate the impact of a diverted configuration on turbulence in the edge plasma, in an isothermal framework. The presence of the X-point is found, locally, to affect both the shape of turbulent structures and the amplitude of fluctuations, in qualitative agreement with recent experimental observations. In particular, a quiescent region is found in the divertor scrape-off layer (SOL), close to the separatrix. Globally, a mild transport barrier spontaneously forms in the closed flux surfaces region near the separatrix, differently from simulations in limiter configuration. The effect of turbulence-driven Reynolds stress on the formation of the barrier is found to be weak by dedicated simulations, while turbulence damping around the X-point seems to globally reduce turbulent transport on the whole flux surface. The magnetic shear is thus pointed out as a possible element that contributes to the formation of edge transport barriers. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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16 pages, 1184 KiB  
Article
1-D Modeling of the Screw-Pinch Plasma in PROTO-SPHERA
by Paolo Buratti, Brunello Tirozzi, Franco Alladio and Paolo Micozzi
Fluids 2019, 4(1), 42; https://doi.org/10.3390/fluids4010042 - 7 Mar 2019
Cited by 1 | Viewed by 3321
Abstract
A simple steady-state model for a 3-species mixture (ions, electrons, and neutrals) in a screw-pinch plasma configuration is developed. The model is applied to the central plasma column of the PROTO-SPHERA experiment. Degree of ionization, azimuthal current density, and azimuthal ion velocity are [...] Read more.
A simple steady-state model for a 3-species mixture (ions, electrons, and neutrals) in a screw-pinch plasma configuration is developed. The model is applied to the central plasma column of the PROTO-SPHERA experiment. Degree of ionization, azimuthal current density, and azimuthal ion velocity are calculated. Full ionization is found at plasma temperatures above 1.5 eV, with neutrals confined in an outer shell where radial plasma flow develops and drives both azimuthal current and azimuthal flow. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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19 pages, 1045 KiB  
Tutorial
Subcritical Instabilities in Neutral Fluids and Plasmas
by Maxime Lesur, Julien Médina, Makoto Sasaki and Akihiro Shimizu
Fluids 2018, 3(4), 89; https://doi.org/10.3390/fluids3040089 - 2 Nov 2018
Cited by 4 | Viewed by 4378
Abstract
In neutral fluids and plasmas, the analysis of perturbations often starts with an inventory of linearly unstable modes. Then, the nonlinear steady-state is analyzed or predicted based on these linear modes. A crude analogy would be to base the study of a chair [...] Read more.
In neutral fluids and plasmas, the analysis of perturbations often starts with an inventory of linearly unstable modes. Then, the nonlinear steady-state is analyzed or predicted based on these linear modes. A crude analogy would be to base the study of a chair on how it responds to infinitesimaly small perturbations. One would conclude that the chair is stable at all frequencies, and cannot fall down. Of course, a chair falls down if subjected to finite-amplitude perturbations. Similarly, waves and wave-like structures in neutral fluids and plasmas can be triggered even though they are linearly stable. These subcritical instabilities are dormant until an interaction, a drive, a forcing, or random noise pushes their amplitude above some threshold. Investigating their onset conditions requires nonlinear calculations. Subcritical instabilities are ubiquitous in neutral fluids and plasmas. In plasmas, subcritical instabilities have been investigated based on analytical models and numerical simulations since the 1960s. More recently, they have been measured in laboratory and space plasmas, albeit not always directly. The topic could benefit from the much longer and richer history of subcritical instability and transition to subcritical turbulence in neutral fluids. In this tutorial introduction, we describe the fundamental aspects of subcritical instabilities in plasmas, based on systems of increasing complexity, from simple examples of a point-mass in a potential well or a box on a table, to turbulence and instabilities in neutral fluids, and finally, to modern applications in magnetized toroidal fusion plasmas. Full article
(This article belongs to the Special Issue Modelling of Plasma Flow)
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