Kinetic water-bag model of global collisional drift waves and ion temperature gradient instabilities in cylindrical geometry

Gravier, Etienne; Plaut, Emmanuel

doi:10.1063/1.4799814

Cited by 5 publications

(11 citation statements)

References 24 publications

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“…If we now look only at waterbag distribution functions, the requirement for C 1 becomes [f, δC 1 /δf ] = 0 for all f given by Eq. (12), and hence is less restrictive. This leads to the creation of an additional invariant, e.g.,v 1 .…”

Section: {Fmentioning

confidence: 99%

“…In this section, we demonstrate the usefulness of the new thermodynamical variables for linking the water-bag and fluid models by considering the three water-bag distribution function, whose expression is given by Eq. (12) for N = 3. A three water-bag model is equivalent to a Hamiltonian fluid model with four fluid moments.…”

Section: Three Water-bag Modelmentioning

confidence: 99%

“…Such a distribution function, whose expression is given by Eq. (12) with N = 2, is represented in Fig. 2.…”

Section: B Two Water-bag Model: Introduction Of the Thermodynamical mentioning

confidence: 99%

“…( 1), other representations of the distribution function can be used to decrease the complexity of the initial problem. In this paper we consider a general water-bag model [6][7][8] , which has also been used, e.g., in gyrokinetics [9][10][11][12] . In one dimension, this projection is obtained by replacing the distribution function with a piecewise constant function in the velocity v such that…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

et al. 2015

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Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N -field fluid models is proposed.

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Section: {Fmentioning

confidence: 99%

Section: Three Water-bag Modelmentioning

confidence: 99%

“…Such a distribution function, whose expression is given by Eq. (12) with N = 2, is represented in Fig. 2.…”

Section: B Two Water-bag Model: Introduction Of the Thermodynamical mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

et al. 2015

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“…Water-bag distribution functions can be considered as piecewise constant approximations of smooth distribution functions and were used, for instance, in the context of gyrokinetic theory [131][132][133][134]. An important feature of the water-bag distribution functions is that they provide a weak solution of the Vlasov-Ampère system (281)- (282) if and only if the velocity…”

Section: A Four-moment Model Derived From the Vlasov-ampère Systemmentioning

confidence: 99%

Hamiltonian closures in fluid models for plasmas

Tassi

2017

Eur. Phys. J. D

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This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models.Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and connections with previously discussed fluid models are pointed out.

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Drift waves and ion temperature gradient instabilities in the large linear device SPEKTRE

Gravier,

Brochard,

Lesur

et al. 2024

Physics of Plasmas

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The objective of this work is to linearly investigate the plasma instabilities that will be observed in the linear SPEKTRE device, currently being assembled at Institut Jean Lamour. Two configurations are considered. In the first configuration, the magnetic field is set to 0.1 T with no ion temperature gradient (ITG), resulting in the observation of only collisional drift waves (DW). In the second configuration, the magnetic field is set to 0.44 T, and ions can be heated using an ion cyclotron radiofrequency heating (ICRH) system to establish an ITG. Under these conditions, two major types of instabilities may be observed: collisional DW and ITG instabilities. ITG instabilities become more unstable than DW when the ratio of the characteristic lengths of the ion temperature to ion density profiles η=ΩT*/Ωn*>2.6. The observation of such a transition between the two types of instabilities will be possible on this machine using the ICRH system. The azimuthal mode number m of the most unstable mode is significantly larger for helium plasma compared to argon plasma. Furthermore, for the plasma parameters considered in both configurations, a fluid model is often sufficient to accurately describe DW, while a kinetic model is required to accurately describe ITG instabilities. There is a 30% difference between the ITG instability growth rates predicted by the fluid model and those predicted by the kinetic model.

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Kinetic water-bag model of global collisional drift waves and ion temperature gradient instabilities in cylindrical geometry

Cited by 5 publications

References 24 publications

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

Hamiltonian closures in fluid models for plasmas

Drift waves and ion temperature gradient instabilities in the large linear device SPEKTRE

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