A moment method for calculating the transport of energetic charged particles in hot plasmas

Haldy, P.A.; Ligou, J.

doi:10.1088/0029-5515/17/6/009

Cited by 27 publications

(7 citation statements)

References 8 publications

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“…As discussed in Ref. [4], the values of the electron and ion coloumb logarithms will be different for such a problem. Therefore, we have calculated and applied a correction factor of 2.75 In Ai, g In /ii in this problem to give the correct ion stopping power.…”

Section: Spherical Geometry Benchnark Problemmentioning

confidence: 97%

“…In much of the early work such as that developed for modeling magnetic mirror devices ( 11, the spatial dependence was only included via a bounce-average approximation. More recent methods which specifically account for spatial effects include the modified multigroup flux-limited diffusion scheme of Corman et al 121; the LSN treatment of the equations of mass and energy transport by Antai and Lee [3 1, the modified moment method of Haldy and Ligou [4], and the integral particle tracking techniques of Moses 151. However, most of these schemes involve the introduction of substantial approximations into the Fokker-Planck equation in order to arrive at a set of equations that are amenable to numerical solutions.…”

Section: Intro~uc770nmentioning

confidence: 99%

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A discrete ordinates solution of the Fokker-Planck equation characterizing charged particle transport

Mehlhorn

Duderstadt

1980

Journal of Computational Physics

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A formalism for obtaining a discrete ordinates solution of the time and space-dependent Fokker-Planck equation governing the transport of charged particles in multispecie plasmas is developed. In the absence of macroscopic electromagnetic fields and assuming isotropic Rosenbluth potentials, the Fokker-Planck equation is solved for a test particle distribution; both angular dispersion and velocity diffusion are accounted for. Difference relations are obtained and a series of validation problems are discussed. The conservation of both particles and energy are continuously monitored. In addition to providing the single-particle distribution function J(r, ,u, v, t), spatially dependent energy deposition profiles are calculated. Comparisons with reported energy deposition profiles for a central source of 35MeV alpha particles in a spherical D-T plasma are made and are found to be in good agreement.

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Section: Spherical Geometry Benchnark Problemmentioning

confidence: 97%

Section: Intro~uc770nmentioning

confidence: 99%

A discrete ordinates solution of the Fokker-Planck equation characterizing charged particle transport

Mehlhorn

Duderstadt

1980

Journal of Computational Physics

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“…Several simplified methods compatible with hydrodynamic codes have been developed. Haldy and Ligou [8] apply the moment method to model ion energy deposition in a hot and dense homogeneous plasma, but only a stationary case has been considered. A variety of methods based on diffusion models applied to charged-particle transport problems have also been developed.…”

Section: Purpose Of the Studymentioning

confidence: 99%

Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma

Peigney¹,

Larroche²,

Tikhonchuk³

2014

Journal of Computational Physics

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We present an ion kinetic model describing the ignition and burn of the deuterium-tritium fuel of inertial fusion targets. The analysis of the underlying physical model enables us to develop efficient numerical methods to simulate the creation, transport and collisional relaxation of fusion reaction products (α-particles) at a kinetic level. A twoenergy-scale approach leads to a self-consistent modeling of the coupling between suprathermal α-particles and the thermal bulk of the imploding plasma. This method provides an accurate numerical treatment of energy deposition and transport processes involving suprathermal particles. The numerical tools presented here are validated against known analytical results. This enables us to investigate the potential role of ion kinetic effects on the physics of ignition and thermonuclear burn in inertial confinement fusion schemes.Keywords: Fokker-Planck equation, fusion reactions, kinetic effects, inertial confinement fusion plasma, suprathermal particles, multi-scale coupling, explicit schemes Purpose of the studyInertial confinement fusion (ICF) is a process of energy production obtained from the nuclear fusion reaction between deuterium (D) and tritium (T) ions. It is a promising and abundant energy source for future power plants. The fusion reactions D + T → α + n + 17.56 MeV take place in a hot and dense plasma compressed and heated by intense laser radiation. The thermonuclear burn of the deuterium-tritium (DT) fuel is supported by energetic α-particles, which are created by fusion reactions at the energy 3.52 MeV. Those suprathermal particles subsequently transfer their energy to the fresh fuel through Coulomb collisions.In the case of Inertial Confinement Fusion [1, 2], a spherical DT shell is compressed to densities of the order of a few hundred g/cc by the ablation pressure. Fusion reactions start in a central zone characterized by a density ρ ∼ 50 g.cm −3 and a high "ignition" temperature T ≈ 7 − 10 keV. The surrounding shell is 10 times colder than the hot spot (T ≈ 0.7 keV). The density of the central "hot spot" is such that the mean free path λ α of fast α-particles is roughly equal to the hot spot radius R [3]. This allows the self-heating of the hot spot fuel which serves as a spark that subsequently burns the surrounding colder and denser shell.The design of ICF targets and the interpretation of ICF experiments rely on numerical simulations based on hydrodynamic Lagrangian codes where kinetic effects are only considered as corrections included in the transport coefficients [1,2]. The fluid description is relevant if the mean free path of plasma particles, namely electrons and ions, is smaller than the characteristic length scale. Although this condition is reasonably fulfilled during the implosion stage, it does not apply to fast particles, in particular to fusion products near the ignition threshold. Thus, an accurate kinetic modeling is required.The purpose of the present work is to propose an ion-kinetic description of suprathermal fusion products,...

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“…Despite such problems, many authors have studied the problem of electron transport in one spatial dimension using the method of discrete ordinates. The multigroup diffusion method of Corman et al [19], the moments technique of Haldy and Ligaou [20], the LSN method of Antal and Lee [21], and the integral tracking technique of Moses [22] are some well-known methods of one-dimensional electron transport. Melhorn and Duderstadt [23] modified blhe TIMEX [24] We have developed 1301 a numerical algorithm extending the technique as used by Wienke [26] to two spatial dimensions.…”

Section: Introductionmentioning

confidence: 99%

A Spatial Characteristic Scheme for Multigroup Discrete Ordinates Electron Energy Deposition in Two Dimensions

Datta

Ray

1993

Physica Status Solidi (b)

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Energy deposition calculations are performed due to an incident source of electrons in rectangular slab geometry using the method of discrete ordinates for directions and the multigroup treatment in energy. Using the restricted stopping power formalism to distinguish between large energy loss collisions (catastrophic) and small energy loss collisions (continuous), coupled with a second-order differencing scheme in energy, an improved model of electron energy loss is incorporated in our computational model. Results are presented for isotropic and normal incident sources and compared with available results.

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A moment method for calculating the transport of energetic charged particles in hot plasmas

Cited by 27 publications

References 8 publications

A discrete ordinates solution of the Fokker-Planck equation characterizing charged particle transport

A discrete ordinates solution of the Fokker-Planck equation characterizing charged particle transport

Fokker–Planck kinetic modeling of suprathermal α -particles in a fusion plasma

A Spatial Characteristic Scheme for Multigroup Discrete Ordinates Electron Energy Deposition in Two Dimensions

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