Response to “Comment on ‘On higher-order corrections to gyrokinetic Vlasov–Poisson equations in the long wavelength limit’” [Phys. Plasmas 16, 124701 (2009)]

Lee, W. W.; Kolesnikov, R. A.

doi:10.1063/1.3272154

Cited by 3 publications

(10 citation statements)

References 5 publications

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“…From a variational point of view, the reduced polarization density (11) is defined from the reduced Hamiltonian H as…”

Section: B Top-down Variational Approachmentioning

confidence: 99%

“…which was considered by Lee and Kolesnikov [9,11]. Lastly, we compare the nonlinear gyrocenter polarization density (55) with the oscillation-center polarization density (30).…”

Section: Variational Derivationmentioning

confidence: 99%

“…For a general drift-particle orbit in a strong magnetic field, the reduced polarization density (11) is defined to lowest order [7] as…”

Section: A Bottom-up Push-forward Approachmentioning

confidence: 99%

“…While standard nonlinear gyrokinetic theory retains only the first-order (linear) gyrocenter polarization in its gyrokinetic Poisson equation (in the form of a quasineutrality equation used to determine the electrostatic potential through ion polarization effects), it was recently argued by Parra and Catto [8] that the standard gyrokinetic quasineutrality equation could not be used to find the electrostatic potential in the long-wavelength limit without the introduction of additional nonlinear physics. The ensuing debate [9][10][11] concerning the nature of these high-order effects motivates the present work, which hopes to introduce new light into this important topic.…”

Section: Introductionmentioning

confidence: 99%

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Beyond linear gyrocenter polarization in gyrokinetic theory

Brizard

2013

Physics of Plasmas

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The concept of polarization in gyrokinetic theory is clarified and generalized to include contributions from the guiding-center (zeroth-order) polarization as well as the nonlinear (second-order) gyrocenter polarization. The guiding-center polarization, which appears as the antecedent (zeroth-order) of the standard linear (first-order) gyrocenter polarization, is obtained from a modified guiding-center transformation. The nonlinear gyrocenter polarization is derived either variationally from the third-order gyrocenter Hamiltonian or directly by gyrocenter push-forward method.Comment: 11 pages, 1 figur

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“…From a variational point of view, the reduced polarization density (11) is defined from the reduced Hamiltonian H as…”

Section: B Top-down Variational Approachmentioning

confidence: 99%

“…which was considered by Lee and Kolesnikov [9,11]. Lastly, we compare the nonlinear gyrocenter polarization density (55) with the oscillation-center polarization density (30).…”

Section: Variational Derivationmentioning

confidence: 99%

“…For a general drift-particle orbit in a strong magnetic field, the reduced polarization density (11) is defined to lowest order [7] as…”

Section: A Bottom-up Push-forward Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Beyond linear gyrocenter polarization in gyrokinetic theory

Brizard

2013

Physics of Plasmas

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“…Then, instead of developing gyrokinetic codes for the edge, it will be greatly advantageous to develop a generalization of the fluid theory in order to include kinetic effects in very simple fluid models. Indeed, one of the main advantages of using fluid equations is the simplicity of the models in comparison to the fact that even after 30 years of research some researchers do not agree about the validity of the gyrokinetic equations (Parra & Catto 2008; Lee & Kolesnikov 2009 a , b ; Parra & Catto 2009).…”

Section: Introductionmentioning

confidence: 99%

Generalized fluid theory including non-Maxwellian kinetic effects

Izacard

2017

J. Plasma Phys.

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The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasma come mainly from the use of very CPU-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker-Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g., the INMDF [O. Izacard, Phys. Plasmas 23, 082504 (2016) Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas]). One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter, or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. The results shown here could draw the breaking of some unsolved understandings of the turbulence.

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Consequence of head‐on collision and double‐layer soliton with linear analysis in multi‐component dusty plasmas

Imon,

Alam

2023

Contrib. Plasma Phys

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The unmagnetized multicomponent collisional dusty plasmas have been considered to investigate the consequence of head‐on collision of dust‐ion‐acoustic waves (DIAWs) with nonlinear characteristic analysis of DIAWs and collisionless plasmas have been considered for studying the production of double layer (DL). The plasma system consists of positively charged ion fluid, negatively charged cold dust fluid, thermal electrons, q‐nonextensive electrons, and immobile background neutral particles. The extended Poincaré‐Lighthill‐Kuo (ePLK) method has been used to derive two‐sided damped Korteweg–De Vries (dKdV) equations and the reductive perturbation method has been used to derive modified KdV (mKdV) equation and the standard Gardner equation (SGE). Linear dispersion relation is derived using linear perturbation technique. The nonlinear propagation of DIA Gardner solitons (DIAGSs) and double layers (DLs) as well as phase shifts have been investigated for the effects of the concerned parameters. It is found that the DIA soliton structures are significantly modified by the species densities, dust mass, and superextensive parameter. The rarefactive dip shape solitary Gardner solitons become produced for the effects of concerned parameters and the positive (negative) DLs become produced in the range of () for the effect of temperatures on the species. The superextensive and the subextensive parameters of electrons significantly affect the DL soliton structures.

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Response to “Comment on ‘On higher-order corrections to gyrokinetic Vlasov–Poisson equations in the long wavelength limit’” [Phys. Plasmas 16, 124701 (2009)]

Cited by 3 publications

References 5 publications

Beyond linear gyrocenter polarization in gyrokinetic theory

Beyond linear gyrocenter polarization in gyrokinetic theory

Generalized fluid theory including non-Maxwellian kinetic effects

Consequence of head‐on collision and double‐layer soliton with linear analysis in multi‐component dusty plasmas

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