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

Mehlhorn, T. A.; Duderstadt, James J.

doi:10.1016/0021-9991(80)90013-3

Cited by 21 publications

(3 citation statements)

References 11 publications

(7 reference statements)

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“…The alpha-particle loses energy to the plasma along its path length. We can calculate the alpha-particle loss energy through following equation [22]: Fig. 6 The stopping range of deuterons in terms of initial deuterons energy at different temperatures for a DT, b D 3 He fuels with q = 300 g cm -3 .…”

Section: The Fraction Of Power Deposited By Alpha Particlesmentioning

confidence: 99%

Determination of Fundamental Parameters for Fast Ignition Using Deuteron Beam in DT and D3He Fuels

2015

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Fast ignition is studied in the pre-compressed DT and D 3 He fuels at uniform density 300 g cm -3 using deuteron beam with considering Maxwellian energy distribution. Total stopping power and range of deuterons are computed by calculating the stopping power contribution of field electrons and ions as a function of initial deuterons energy and temperature in both fuels. Also, the fraction of power deposited by alpha particles is determined. In addition, bonus energy and total deposition energy due to the additional fusion reactions obtained from injection of energetic deuterons into DT and D 3 He fuels are calculated. The contribution of average produced extra energy by deuteron beam-target fusion for DT fuel is more than D 3 He fuel. This research indicates that deuteron beam has some advantages over its other competitors.

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Section: The Fraction Of Power Deposited By Alpha Particlesmentioning

confidence: 99%

Determination of Fundamental Parameters for Fast Ignition Using Deuteron Beam in DT and D3He Fuels

2015

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“…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. In a recent paper [31] the numerical algorithm using the method of characteristics has been extended with considerable success in studying the energy deposition in aluminium for an isotropic source of electrons.…”

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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“…They are based on the determination of the angular flux of suprathermal particles at a set of discrete directions, each one associated with a quadrature weight [14,15,16]. Although they are more accurate than diffusion methods and can be extended to highly anisotropic particle distribution functions, the weakly collisional limit is not described accurately and the thermalization process is treated approximately with the same strategy as in Monte Carlo methods.…”

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

Cited by 21 publications

References 11 publications

Determination of Fundamental Parameters for Fast Ignition Using Deuteron Beam in DT and D3He Fuels

Determination of Fundamental Parameters for Fast Ignition Using Deuteron Beam in DT and D3He Fuels

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

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

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