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Review of the First Charged-Particle Transport Coefficient Comparison Workshop

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 Added by Paul Grabowski
 Publication date 2020
  fields Physics
and research's language is English




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We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4-6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron-ion coupling, inter-ion diffusion, ion viscosity, and charged particle stopping powers. Here, we give general background on Coulomb coupling and computational expense, review where some transport coefficients appear in hydrodynamic equations, and present the submitted data. Large variations are found when either the relevant Coulomb coupling parameter is large or computational expense causes difficulties. Understanding the general accuracy and uncertainty associated with such transport coefficients is important for quantifying errors in hydrodynamic simulations of inertial confinement fusion and high-energy density experiments.



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We report on the results of the 10th Non-LTE code comparison workshop, which was held at the University of San Diego campus November 28 through December 1, 2017. Non-equilibrium collisional-radiative models predict the electronic state populations and attendant emission and absorption characteristics of hot, dense matter and are used to help design and diagnose high-energy-density experiments. At this workshop, fifteen codes from eleven institutions contributed results for steady-state and time-dependent neon, aluminum, silicon, and chlorine cases relevant to a variety of high-density experimental and radiation-driven astrophysical systems. This report focuses on differences in the predictions from codes with different internal structure, completeness, density effects, and rate fidelity and the impact of those differences on hot, dense plasma diagnostics.
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The Spatial Parallel Diffusion Coefficient (SPDC) is one of the important quantities describing energetic charged particle transport. There are three different definitions for the SPDC, i.e., the Displacement Variance definition $kappa_{zz}^{DV}=lim_{trightarrow t_{infty}}dsigma^2/(2dt)$, the Ficks Law definition $kappa_{zz}^{FL}=J/X$ with $X=partial{F}/partial{z}$, and the TGK formula definition $kappa_{zz}^{TGK}=int_0^{infty}dt langle v_z(t)v_z(0) rangle$. For constant mean magnetic field, the three different definitions of the SPDC give the same result. However, for focusing field it is demonstrated that the results of the different definitions are not the same. In this paper, from the Fokker-Planck equation we find that different methods, e.g., the general Fourier expansion and perturbation theory, can give the different Equations of the Isotropic Distribution Function (EIDFs). But it is shown that one EIDF can be transformed into another by some Derivative Iterative Operations (DIOs). If one definition of the SPDC is invariant for the DIOs, it is clear that the definition is also an invariance for different EIDFs, therewith it is an invariant quantity for the different Derivation Methods of EIDF (DMEs). For the focusing field we suggest that the TGK definition $kappa_{zz}^{TGK}$ is only the approximate formula, and the Ficks Law definition $kappa_{zz}^{FL}$ is not invariant to some DIOs. However, at least for the special condition, in this paper we show that the definition $kappa_{zz}^{DV}$ is the invariant quantity to the kinds of the DIOs. Therefore, for spatially varying field the displacement variance definition $kappa_{zz}^{DV}$, rather than the Ficks law definition $kappa_{zz}^{FL}$ and TGK formula definition $kappa_{zz}^{TGK}$, is the most appropriate definition of the SPDCs.
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The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial approach, is proposed for periodically modulated experiments, within the context of the standard advection-diffusion model where these issues are related to the vanishing of the determinant of a 2x2 matrix. This sheds light on the accuracy of calculations with transport codes, and provides a path for a more precise assessment of the profiles and of the related uncertainty.
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