Dynamics of Ionized Media

Gasiorowicz, S.; Neuman, Maurice; Riddell, Robert J.

doi:10.1103/physrev.101.922

Cited by 78 publications

(57 citation statements)

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“…Faster particles show reduced, asymmetric screening, for which an analytic solution cannot be obtained, but numerical solutions have been published by a number of authors (Wang et al 1981, Decyk 1987, Ellis et al 2011. Several authors have used the Holtsmark distribution for the distant interactions (Chandrasekhar et al 1943, Gasiorowicz et al 1956), which describes the electric field due to a completely random distribution of stationary point charges. This diverges, so an upper cut-off has to be introduced.…”

Section: Scatteringmentioning

confidence: 99%

Theory of fast electron transport for fast ignition

et al. 2014

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Abstract. Fast Ignition Inertial Confinement Fusion is a variant of inertial fusion in which DT fuel is first compressed to high density and then ignited by a relativistic electron beam generated by a fast (< 20 ps) ultra-intense laser pulse, which is usually brought in to the dense plasma via the inclusion of a re-entrant cone. The transport of this beam from the cone apex into the dense fuel is a critical part of this scheme, as it can strongly influence the overall energetics. Here we review progress in the theory and numerical simulation of fast electron transport in the context of Fast Ignition. Important aspects of the basic plasma physics, descriptions of the numerical methods used, a review of ignition-scale simulations, and a survey of schemes for controlling the propagation of fast electrons are included. Considerable progress has taken place in this area, but the development of a robust, high-gain FI 'point design' is still an ongoing challenge.

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Section: Scatteringmentioning

confidence: 99%

Theory of fast electron transport for fast ignition

et al. 2014

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“…Each theory has a difficulty in describing the scales of the order of d. The mean-field approach cannot describe the graininess of these scales, and the Rutherford picture cannot describe the simultaneous "collisions" with several particles. Even for scales smaller than d, the Rutherford collision is modified due to the fluctuating electric field of the other particles in the Debye sphere [73]. Using the more relevant description for scales smaller than d [110] and the one for the larger scales [73], the corresponding contributions to transport turn out to be of the same order of magnitude.…”

Section: A Limited Capabilities Of Modelsmentioning

confidence: 62%

“…Using the more relevant description for scales smaller than d [110] and the one for the larger scales [73], the corresponding contributions to transport turn out to be of the same order of magnitude. Furthermore, if one accepts to cross the "validity border" d, and one performs the final integration on the whole range of scales [λ ma , λ D ] for either theory, the two results are found to agree [73,110].…”

Section: A Limited Capabilities Of Modelsmentioning

confidence: 78%

“…Historically two groups at UC Berkeley's Radiation Laboratory derived at almost the same time a Fokker-Planck equation describing "collisions" in non magnetized plasmas and quoted each other results in their respective papers: one by Gasiorowicz, Neuman and Riddell [73] and a year later one by Rosenbluth, MacDonald and Judd [110]. The first group of authors dealt with the mean-field part of the interaction by using perturbation theory in electric field amplitude.…”

Section: A Limited Capabilities Of Modelsmentioning

confidence: 99%

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How to Face the Complexity of Plasmas?

Escande

2013

Nonlinear Systems and Complexity

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This paper has two main parts. The first part is subjective and aims at favoring a brainstorming in the plasma community. It discusses the present theoretical description of plasmas, with a focus on hot weakly collisional plasmas. It comprises two sub-parts. The first one deals with the present status of this description. In particular, most models used in plasma physics are shown to have feet of clay, there is no strict hierarchy between them, and a principle of simplicity dominates the modeling activity. At any moment the description of plasma complexity is provisional and results from a collective and somewhat unconscious process. The second sub-part considers possible methodological improvements, some of them specific to plasma physics, some others of possible interest for other fields of science. The proposals for improving the present situation go along the following lines: improving the way papers are structured and the way scientific quality is assessed in the referral process, developing new data bases, stimulating the scientific discussion of published results, diversifying the way results are made available, assessing more quality than quantity, making available an incompressible time for creative thinking and non purpose-oriented research. Some possible improvements for teaching are also indicated. The suggested improvement of the structure of papers would be for each paper to have a "claim section" summarizing the main results and their most relevant connection to previous literature. One of the ideas put forward is that modern nonlinear dynamics and chaos might help revisiting and unifying the overall presentation of plasma physics.The second part of this chapter is devoted to one instance where this idea has been developed for three decades: the description of Langmuir wave-electron interaction in one-dimensional plasmas by a finite dimensional Hamiltonian. This part is more specialized, and is written like a classical scientific paper. This Hamiltonian approach enables recovering Vlasovian linear theory with a mechanical understanding. The quasilinear description of the weak warm beam is discussed, and it is shown that self-consistency vanishes when the plateau forms in the tail distribution function. This leads to consider the various diffusive regimes of the dynamics of particles in a frozen spectrum of waves with random phases. A recent numerical simulation showed that diffusion is quasilinear when the plateau sets in, and that the variation of the phase of a given wave with time is almost non fluctuating for random realizations of the initial wave phases. This led to new analytical calculations of the average behavior of the self-consistent dynamics when the initial wave phases are random. Using Picard iteration technique, they confirm numerical results, and exhibit a spontaneous emission of spatial inhomogeneities.Non quia difficilia sunt, non audemus, sed quia non audemus, difficilia sunt. It is not because things are difficult that we do not dare, it is because we do not dare that things a...

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“…Chandrasekhar (1942Chandrasekhar ( , 1943a derived a Fokker-Planck equation by considering gravitational encounters in an infinite homogeneous system of stars. The derivation of the diffusion and friction coefficients was simplified by Cohen, Spitzer & Routly (1950); Gasiorowicz, Neuman & Riddell (1956) ;Rosenbluth, MacDonald & Judd (1957). The general kinetic equation for inhomogeneous stellar systems was derived by Gilbert (1968); this is rigorous and based on a systematic 1/N expansion of the BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) equations of non-equilibrium statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

Stellar dynamics around a massive black hole – II. Resonant relaxation

Sridhar

Touma

2016

Mon. Not. R. Astron. Soc.

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We present a first-principles theory of Resonant Relaxation (RR) of a low mass stellar system orbiting a more massive black hole (MBH). We first extend the kinetic theory of Gilbert (1968) to include the Keplerian field of a black hole of mass M • . Specializing to a Keplerian stellar system of mass M ≪ M • , we use the orbit-averaging method of Sridhar & Touma (2015; Paper I) to derive a kinetic equation for RR. This describes the collisional evolution of a system of N ≫ 1 Gaussian Rings in a reduced 5-dim space, under the combined actions of self-gravity, 1 PN and 1.5 PN relativistic effects of the MBH and an arbitrary external potential. In general geometries RR is driven by both apsidal and nodal resonances, so the distinction between scalar-RR and vector-RR disappears. The system passes through a sequence of quasi-steady secular collisionless equilibria, driven by irreversible 2-Ring correlations that accrue through gravitational interactions, both direct and collective. This correlation function is related to a 'wake function', which is the linear response of the system to the perturbation of a chosen Ring. The wake function is easier to appreciate, and satisfies a simpler equation, than the correlation function. We discuss general implications for the interplay of secular dynamics and nonequilibrium statistical mechanics in the evolution of Keplerian stellar systems toward secular thermodynamic equilibria, and set the stage for applications to the RR of axisymmetric discs in Paper III.

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Dynamics of Ionized Media

Cited by 78 publications

References 5 publications

Theory of fast electron transport for fast ignition

Theory of fast electron transport for fast ignition

How to Face the Complexity of Plasmas?

Stellar dynamics around a massive black hole – II. Resonant relaxation

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