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 downscattering 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 onedimensional, 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/PPG902
ON: DE86010913
 DOE Contract Number:
 AS0380ER52062
 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 KineticsTheoretical (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 downscattering 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 onedimensional, 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
}

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 twodimensional 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 XY cartesian and RZ cylindrical/toroidal geometries. Use of the finite element method allows solution of problems in which the plasma crosssection has an arbitrary shape. The accuracy of FENAT hasmore »

User's manual for FENAT: a twodimensional multigroup diffusion theory Finite Element Neutral Atom Transport code
FENAT solves the twodimensional energy dependent diffusion equation in Cartesian (XY) and cylindrical/toroidal (RZ) 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 » 
Application of diffusion theory to the transport of neutral particles in fusion plasmas
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 » 
Twodimensional finite element multigroup diffusion theory for neutral atom transport in plasmas
Solution of the energydependent 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 twodimensional 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 XY cartesian and RZ 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 » 
Neoclassical theory of momentum transport by collisional ions in stronglyrotating tokamak plasmas with unbalanced neutralbeam injection
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 firstorder distribution function into gyroangledependent and gyroangleaveraged components, neoclassical gyroviscosity is recovered from the former, and a new rotational viscosity of a collisional origin is recovered from themore »