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Title: Application of diffusion theory to neutral atom transport in fusion plasmas

Abstract

It is found that energy dependent diffusion theory provides excellent accuracy in the modelling of transport of neutral atoms in fusion plasmas. Two reasons in particular explain the good accuracy. First, while the plasma is optically thick for low energy neutrals, it is optically thin for high energy neutrals and diffusion theory with Marshak boundary conditions gives accurate results for an optically thin medium even for small values of 'c', the ratio of the scattering to the total cross section. Second, the effective value of 'c' at low energy becomes very close to one due to the down-scattering via collisions of high energy neutrals. The first reason is proven both computationally and theoretically by solving the transport equation in a power series in 'c' and the diffusion equation with 'general' Marshak boundary conditions. The second reason is established numerically by comparing the results from a one-dimensional, general geometry, multigroup diffusion theory code, written for this purpose, with the results obtained using the transport code ANISN.

Authors:
; ;
Publication Date:
Research Org.:
California Univ., Los Angeles (USA). Dept. of Mechanical, Aerospace and Nuclear Engineering
OSTI Identifier:
5628647
Report Number(s):
UCLA/PPG-902
ON: DE86010913
DOE Contract Number:
AS03-80ER52062
Resource Type:
Technical Report
Resource Relation:
Other Information: Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PLASMA; TRANSPORT THEORY; PLASMA DRIFT; ATOMS; BOUNDARY CONDITIONS; CROSS SECTIONS; DIFFUSION; SCATTERING; 700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)

Citation Formats

Hasan, M.Z., Conn, R.W., and Pomraning, G.C. Application of diffusion theory to neutral atom transport in fusion plasmas. United States: N. p., 1986. Web. doi:10.2172/5628647.
Hasan, M.Z., Conn, R.W., & Pomraning, G.C. Application of diffusion theory to neutral atom transport in fusion plasmas. United States. doi:10.2172/5628647.
Hasan, M.Z., Conn, R.W., and Pomraning, G.C. 1986. "Application of diffusion theory to neutral atom transport in fusion plasmas". United States. doi:10.2172/5628647. https://www.osti.gov/servlets/purl/5628647.
@article{osti_5628647,
title = {Application of diffusion theory to neutral atom transport in fusion plasmas},
author = {Hasan, M.Z. and Conn, R.W. and Pomraning, G.C.},
abstractNote = {It is found that energy dependent diffusion theory provides excellent accuracy in the modelling of transport of neutral atoms in fusion plasmas. Two reasons in particular explain the good accuracy. First, while the plasma is optically thick for low energy neutrals, it is optically thin for high energy neutrals and diffusion theory with Marshak boundary conditions gives accurate results for an optically thin medium even for small values of 'c', the ratio of the scattering to the total cross section. Second, the effective value of 'c' at low energy becomes very close to one due to the down-scattering via collisions of high energy neutrals. The first reason is proven both computationally and theoretically by solving the transport equation in a power series in 'c' and the diffusion equation with 'general' Marshak boundary conditions. The second reason is established numerically by comparing the results from a one-dimensional, general geometry, multigroup diffusion theory code, written for this purpose, with the results obtained using the transport code ANISN.},
doi = {10.2172/5628647},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1986,
month = 5
}

Technical Report:

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  • Solution of the energy dependent diffusion equation in two dimensions is formulated by multigroup approximation of the energy variable and general triangular mesh, finite element discretization of the spatial domain. Finite element formulation is done by Galerkin's method. Based on this formulation, a two-dimensional multigroup finite element diffusion theory code, FENAT, has been developed for the transport of neutral atoms in fusion plasmas. FENAT solves the multigroup diffusion equation in X-Y cartesian and R-Z cylindrical/toroidal geometries. Use of the finite element method allows solution of problems in which the plasma cross-section has an arbitrary shape. The accuracy of FENAT hasmore » been verified by comparing results to those obtained using the two-dimensional discrete ordinate transport theory code, DOT-4.3. Results of application of FENAT to the transport of limiter-originated neutral atoms in a tokamak fusion machine are presented.« less
  • FENAT solves the two-dimensional energy dependent diffusion equation in Cartesian (X-Y) and cylindrical/toroidal (R-Z) coordinates. The boundary conditions allowed are: vacuum, reflection, albedo and surface source. The energy variable is treated by multigroup method. The resulting multigroup diffusion equation is solved by finite element Galerkin's method with triangular element discretization of the spatial domain. The algebraic matrix equation is solved by the direct method of Crout variation of Gauss' elimination. Dynamic memory allocation has been used so that the maximum problem size is limited by the size of active core storage of the machine. When necessary, the global matrix ismore » stored in a binary disk file. FENAT is particularly suitable for the transport of neutral atoms in fusion plasmas.« less
  • It is shown that the widely held view that diffusion theory can not provide good accuracy for the transport of neutral particles in fusion plasmas is misplaced. In fact, it is shown that multigroup diffusion theory gives quite good accuracy as compared to the transport theory. The reasons for this are elaborated and some of the physical and theoretical reasons which make the multigroup diffusion theory provide good accuracy are explained. Energy dependence must be taken into consideration to obtain a realistic neutral atom distribution in fusion plasmas. There are two reasons for this; presence of either is enough tomore » necessitate an energy dependent treatment. First, the plasma temperature varies spatially, and second, the ratio of charge-exchange to total plasma-neutral interaction cross section (c) is not close to one. A computer code to solve the one-dimensional multigroup diffusion theory in general geometry (slab, cylindrical and spherical) has been written for use on Cray computers, and its results are compared with those from the one-dimensional transport code ANISN to support the above finding. A fast, compact and versatile two-dimensional finite element multigroup diffusion theory code, FINAT, in X-Y and R-Z cylindrical/toroidal geometries has been written for use on CRAY computers. This code has been compared with the two dimensional transport code DOT-4.3. The accuracy is very good, and FENAT runs much faster compared even to DOT-4.3 which is a finite difference code.« less
  • Solution of the energy-dependent diffusion equation in two dimensions is formulated by multigroup approximation of the energy variable and general triangular mesh, finite element discretization of the spatial domain. Finite element formulation is done by Galerkin's method. Based on this formulation, a two-dimensional multigroup finite element diffusion theory code, FENAT, has been developed for the transport of neutral atoms in fusion plasmas. FENAT solves the multigroup diffusion equation in X--Y cartesian and R--Z cylindrical/toroidal geometries. Use of the finite element method allows solution of problems in which the plasma cross section has an arbitrary shape. The accuracy of FENAT hasmore » been verified by comparing results to those obtained using the two-dimensional discrete ordinate transport theory code, DOT-4.3. Results of application of FENAT to the transport of limiter-originated neutral atoms in a tokamak fusion machine are presented. copyright 1987 Academic Press, Inc.« less
  • A neoclassical theory for momentum transport by collisional ions in a tokamak plasma with strong NBI and strong rotation is developed. A consistently ordered hierarchy of approximations to the kinetic equation are derived and solved to obtain expressions for particle flows, the radial electric field, poloidal asymmetries in density and potential, and the radial flux of toroidal angular momentum and the associated torque that acts to damp toroidal rotation. Upon decomposing the first-order distribution function into gyroangle-dependent and gyroangle-averaged components, neoclassical gyroviscosity is recovered from the former, and a new rotational viscosity of a collisional origin is recovered from themore » latter. The same viscosity coefficient and functional form is obtained for both types of viscosity. The magnitude and scaling with plasma parameters of the associated momentum damping rate has previously been demonstrated to be in agreement with a number of rotation experiments in tokamaks.« less