Physique des plasmas (Vol. II)

Delcroix, J. L.; Bers, A.

doi:10.1051/978-2-7598-0286-9

Cited by 43 publications

(27 citation statements)

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“…Note that the dimensional constant in front of ( 10) is (r 0 v 2 th ) 2 . The Rutherford cross-section (10) presents two singularities of very different nature: -first, the kinetic collision kernel, |v − v * | −3 , is singular as v − v * → 0. It is classical that kinetic singularities are well tractable from the mathematical point of view if they are locally integrable, see for instance the wellknown paper of DiPerna and Lions [14].…”

Section: Preliminary Discussionmentioning

confidence: 99%

“…Justifications for this screening assumption can be found in many physical textbooks on plasma physics, as [5,10]; from the mathematical point of view we are still far from understanding it. The screening will result in a less important role of collisions with a high impact parameter, therefore a less important role of grazing collisions.…”

Section: Preliminary Discussionmentioning

confidence: 99%

“…In 1936, Landau, as part of his important works in plasma physics, established the kinetic equation which is now called after him, modelling the behavior of a dilute plasma interacting through binary collisions. Since then, this equation has been widely in use in plasma physics, see for instance [5,8,10,20,27] and references therein. In this paper we shall present what we believe to be an important advance in the problem of rigorously justifying Landau's approximation.…”

Section: Introduction: Binary Collisions In Plasmasmentioning

confidence: 99%

“…when particles are separated by distances much larger than the so-called Debye (or screening) length. The screening effect may be induced by the presence of two species of particles with opposite charges: typically, the presence of ions constitutes a background of positive charge which screens the interaction of electrons at large distances [5,10]. Some half-heuristic, half-rigorous arguments suggest to model the interaction between charged particles by the so-called Debye (or Yukawa) potential, e −r/λ D /(4πε 0 r), where λ D is the Debye length, rather than by the "bare" Coulomb potential 1/(4πε 0 r).…”

Section: Introduction: Binary Collisions In Plasmasmentioning

confidence: 99%

“…The proportionality factor is the so-called Coulomb logarithm: essentially, it is log(λ D /r 0 ). We refer to [20] for Landau's original argument, to [5,10,28] for more physical background, and to [9] for a slightly more mathematically oriented presentation. Also a variant of Landau's argument can be found in [33].…”

Section: Introduction: Binary Collisions In Plasmasmentioning

confidence: 99%

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Sur l'approximation de Landau en physique des plasmas

Reynaud¹

2004

Annales de l'Institut Henri Poincare (C) Non Linear Analysis

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This paper studies the approximation of the Boltzmann equation by the Landau equation in a regime when grazing collisions prevail. While all previous results in the subject were limited to the spatially homogeneous case, here we manage to cover the general, space-dependent situation, assuming only basic physical estimates of finite mass, energy, entropy and entropy production. The proofs are based on the recent results and methods introduced previously in [R. Alexandre, C. Villani, Comm. Pure Appl. Math. 55 (1) (2002) 30-70] by both authors, and the entropy production smoothing effects established in [R. Alexandre et al., Arch. Rational Mech. Anal. 152 (4) (2000) 327-355]. We are able to treat realistic singularities of Coulomb type, and approximations of the Debye cut. However, our method only works for finite-time intervals, while the Landau equation is supposed to describe long-time corrections to the Vlasov-Poisson equation. If the mean-field interaction is neglected, then our results apply to physically relevant situations after a time rescaling. RésuméNous étudions l'approximation de l'équation de Boltzmann par l'équation de Landau quand les collisions rasantes sont dominantes. Alors que tous les résultats connus auparavant en la matière concernaient le cas spatialement homogène, ici nous parvenons à couvrir le cas général, spatialement inhomogène, supposant seulement des estimations a priori physiquement réalistes portant sur la masse, l'énergie, l'entropie et la production d'entropie. Les preuves reposent sur les résultats et méthodes mis au point récemment par les auteurs dans [R. Alexandre, C. Villani, Comm. Pure Appl. Math. 55 (1) (2002) 30-70], et sur les effets de régularisation par production d'entropie établis dans [R. Alexandre et al., Arch. Rational Mech. Anal. 152 (4) (2000) 327-355]. Nos résultats couvrent certaines singularités physiquement réalistes de type coulombien, et des approximations de la coupure de Debye. Cependant, nos résultats s'appliquent sur un intervalle de temps fini, alors que l'équation de Landau est censée décrire les corrections en temps grand de l'équation de Vlasov-Poisson. Si le terme d'interaction de champ moyen est négligé, nos résultats s'appliquent à des situations physiquement réalistes après un changement d'échelle de temps.

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Section: Preliminary Discussionmentioning

confidence: 99%

Section: Preliminary Discussionmentioning

confidence: 99%

Section: Introduction: Binary Collisions In Plasmasmentioning

confidence: 99%

Section: Introduction: Binary Collisions In Plasmasmentioning

confidence: 99%

Section: Introduction: Binary Collisions In Plasmasmentioning

confidence: 99%

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Sur l'approximation de Landau en physique des plasmas

Reynaud¹

2004

Annales de l'Institut Henri Poincare (C) Non Linear Analysis

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Modeling and characterization of microwave breakdown at atmospheric pressure in OMUX filters

Frigui

Bila

Baillargeat

et al. 2013

Int J RF and Microwave Comp Aid Eng

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For output multiplexer (OMUX) filters placed in telecommunication satellites, microwave breakdown happens in an involuntary and undesirable way during tests at atmospheric pressure. This avalanche phenomenon is due to exponential growth of the electronic density caused by thermoelectronic emission under strong electromagnetic field magnitude. In this paper, our objective is to model and characterize experimentally multipole OMUX filters composed with coupled cavities. For identifying the element responsible for the breakdown, the electric field is calculated within each cavity and each iris. In order to characterize the breakdown phenomenon, we proposed an experimental test bench and we measured the power, both at the input and at the output of the filter. The article details the theoretical breakdown prediction and the experimental setup for such a structure. V C 2013Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:46-54, 2014.

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