Multi-group diffusion of energetic charged particles

Corman, E.G.; Loewe, W.E.; Cooper, G.E.; Winslow, A.M.

doi:10.1088/0029-5515/15/3/003

Cited by 77 publications

(48 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This hypothesis does not hold for a typical ICF target near ignition. Corman et al [9] derive a multi-group diffusion model from the Fokker-Planck equation to describe fast ion transport in a fusion plasma. However, they introduce heuristically a flux limiter in order to prevent unphysical behavior when particle flux approaches the free-streaming limit.…”

Section: Purpose Of the Studymentioning

confidence: 99%

“…In the one-dimensional spherical problem considered here, the electron energy density W e is governed by the following conservation equation : (9) where κ e is Spitzer's thermal conductivity [19] in the presence of several ion species (see also [7] and Appendix in [20]), the collision time τ e j has been defined in Eq. (5) where α is replaced by the considered ion species j.…”

Section: Dealing With Electronsmentioning

confidence: 99%

See 1 more Smart Citation

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

Peigney¹,

Larroche²,

Tikhonchuk³

2014

Journal of Computational Physics

View full text Add to dashboard Cite

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,...

show abstract

Section: Purpose Of the Studymentioning

confidence: 99%

Section: Dealing With Electronsmentioning

confidence: 99%

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

Peigney¹,

Larroche²,

Tikhonchuk³

2014

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…This problem was first spelled out and solved to leading order by Landau and then Spitzer in the context of electron-ion temperature equilibration, and later by Corman et al for the charged particle stopping power [3,4,5].…”

Section: The Bps Formalismmentioning

confidence: 99%

The energy partitioning of non-thermal particles in a plasma: the Coulomb logarithm revisited

Singleton¹,

Brown²

2008

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated exactly to leading and next-to-leading accuracy in the plasma density by Brown, Preston, and Singleton (BPS). Since the calculational techniques of BPS might be unfamiliar to some, and since the same methodology can also be used for other energy transport phenomena, we will review the main ideas behind the calculation. BPS used their stopping power calculation to derive a Fokker-Planck equation, also accurate to leading and next-to-leading orders, and we will also review this. We use this Fokker-Planck equation to compute the electronion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion -more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fractional energy loss to electrons and ions as accurately as possible, as this could have implications for the Laser Mégajoule (LMJ) facility in France and the National Ignition Facility (NIF) in the United States. The traditional method by which one calculates the electron-ion energy splitting of a charged particle traversing a plasma involves integrating the stopping power dE/dx. However, as the charged particle slows down and becomes thermalized into the background plasma, this method of calculating the electron-ion energy splitting breaks down. As a result, the method suffers a systematic error of order T /E 0 , where T is the plasma temperature and E 0 is the initial energy of the charged particle. In the case of DT fusion, for example, this can lead to uncertainties as high as 10% or so. The formalism presented here is designed to account for the thermalization process, and in contrast, it provides results that are near-exact.

show abstract

“…(74)(75)(76)(77) Again, this is strictly applied in the rest frame of the moving fluid or material. While somewhat artificial, this prescription works well in many applications.…”

Section: Flux Limited Diffusionmentioning

confidence: 99%

“…While somewhat artificial, this prescription works well in many applications. (23,29,(70)(71)(72)(73)(74)(75)(76)(77) Fick's law is recast in terms of a flux limiter, A, which enforces the streaming limit, and collapses to the diffusion limit in proper circumstance, enforcing the condition,…”

Section: Flux Limited Diffusionmentioning

confidence: 99%

Transport equations in moving material Part I: Neutrons and photons

Wienke

2005

Progress in Nuclear Energy

View full text Add to dashboard Cite

Multi-group diffusion of energetic charged particles

Cited by 77 publications

References 9 publications

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

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

The energy partitioning of non-thermal particles in a plasma: the Coulomb logarithm revisited

Transport equations in moving material Part I: Neutrons and photons

Contact Info

Product

Resources

About