1. FPI Code

2. 1D-2Fluids code

3. The FPI Code, The Fluid Code and the Hybrid Iterations

4. BABOUM Code

5. DEGAS Code: Divertor Neutral Gas Transport Code

I.  FPI Code (FORTRAN Program):

Z. Abou-Assaleh, J. P. Matte, and T. W. Johnston. Université du Québec, Institut National de la recherche Scientifique, (INRS - Énergie et Matériaux), Québec, Canada. 1987-1993.  

>>> The FPI code (Fokker-Planck International), advances the Vlasov-Fokker-Planck equation for the electron distribution function in time. Electron-electron, electron-ion, and electron-neutral collisions are included. The code is one-dimensional in space and two-dimensional in velocity space. The ions and the neutral particles are considered as a fluid in the code.  

II.  1D-2Fluids code (FROTRAN program):

Z. Abou-Assaleh, J. P. Matte, and T. W. Johnston. Université du Québec, Institut National de la recherche Scientifique, (INRS - Énergie et Matériaux), Québec, Canada. 1988-1993.  

>>> The fluid code is one-dimensional, two-fluid code. Recycling, Ionisation, excitation and charge exchange of the neutral atoms are included in this code. The code advanced in time the following equations: Continuity, Momentum balance, Electron and Ion Energy Balance, including the heat flux limiter.

III.  The FPI Code, The Fluid Code and the Hybrid Iterations:

Z. Abou-Assaleh, J. P. Matte, and T. W. Johnston. Université du Québec, Institut National de la recherche Scientifique, (INRS - Énergie et Matériaux), Québec, Canada. 1989-1993.

>>> The electron kinetic code "Fokker-Planck International FPI" used previously for transport modelling relevant to laser-plasma problems, has been modified and used to simulate transport and recycling of the edge plasmas in the divertor near the neutralizer plate in tokamaks. In addition to the previous features, such as Fokker-Planck e-e and e-i coulomb collisions, transport, cold ion motion, and a self-consistent electric field, the code now accounts for ionization, excitation, finite ion temperature, recycling, neutral motion, and a new boundary condition at the plate sheath edge. The new boundary condition at the plate sheath edge permeate of pre sheath simulation (which is in our interest) without the necessity of including the very small sheath region in the simulations.  Ions and neutrals are treated as fluids. As one might expect, this full code is very expensive to run, having very fast (electron) and very slow (ion motion) time scales. We therefore developed a two-fluid ambipolar code with electron heat flow obtained from usual flux limited coefficients on the thermal transport.  We alternate both the fluid and FPI codes, using the FPI code to correct the fluid code's temperature and local heat transport, while using the fluid code for ion dynamics.  We thus arrive at an equilibrium completely consistent with electron kinetics but at a tiny fraction of the cost of doing so with the FPI code alone.  Two models were used for simulating the divertor plasma with high recycling.  

In the first model we assumed that the neutral particle has a fixed and uniform distribution in the divertor chamber near the plate.  In the second model we assumed that must of the ions which arrived at the plate are reflected as neutral particles with fixed velocity.  The FPI and the fluid equilibrium solutions of both model for the neutral particles show that the profiles of Te, qe, Sexc, and Sion calculated from the fluid code do not agree with those of the FPI code.  The electron distribution function calculated from the FPI code is not Maxwellian especially near the plate.  From this we conclude that the nonlocal effect in the divertor electron plasma is very strong, therefore the classical theory of the electron heat flux does not work very well in the edge plasma near the plate in tokamaks.  

REFERENCES

Z. Abou-Assaleh, J.P. Matte, T.W. Johnston and R. Marchand, "Fokker-Planck Modelling of Edge Plasma Near the Neutralizer Plate in a Tokamak". Contrib. Plasma Phys. 32 (1992) 3/4, 268-272.

Z. Abou-Assaleh, J.P. Matte, T.W. Johnston and R. Marchand, "Fokker-Planck Modelling of Edge Plasma Near the Neutralizer Plate in a Tokamak". Contrib. Plasma Phys. 32 (1992) 3/4, 268-272.

Z. Abou-Assaleh, Ph.D. Dissertation, 1991. Université du Québec, Institut National de la recherche Scientifique, (INRS - Énergie et Matériaux), Québec, Canada.

R. Marchand, Z. Abou-Assaleh and J.P. Matte, "Nonlocal Fluxes at a Plasma Sheath". Phys. Fluids B, Vol. 2, No. 6, 1247, June 1990.

Z. Abou-Assaleh, R. Marchand, J.P. Matte, T.W. Johnston and K.J. Parbhakar, "Kinetic Modelling of Plasma Near the Neutralizer Plate in a Tokamak Divertor". Contrib. Plasma Phys. 30 (1990) 1, 37-43.

J.H. Rogers, J.S. De Groot, Z. Abou-Assaleh, J.P. Matte, T.W. Johnston and M.D. Rosen, "Electron Heat Transport in a Steep Temperature Gradient". Phys. Fluids B. Vol. 1, No. 4, 741, April 1989.

IV.  BABOUM Code:

(INRS - Énergie et Matériaux), Québec, Canada.

The code BABOUM is a fortran program which generates a Monte Carlo simulation of the effects of rapid atoms or ions impinging on a solid.  the following quantities will be calculated^**:

> Depth profile of implanted atoms or ions.

> Coefficient of backscattering, as well as angular, energy and charge distribution of backscattered particle.

> Depth profile of irradiation damage.

> Sputtering coefficient, as well as angular, energy and charge distribution of sputtered atoms.

** For more information about the BABOUM code see the internal reports:  TV RI 231e Avril 1987, Tokamak de Varennes, "CODES NUMERIQUE POUR LE Tokamak DE VARENNES".  V. Fuchs, G. Leclair, H.D. Pacher, Editeurs.

V.  DEGAS Code: Divertor Neutral Gas Transport Code: 

REFERENCES

"Neutral Paricle Transport", D.B. Heifetz. Physics of Plasma-Wall Interaction in Controlled Fusion, Ed. by D.E. Post and R. Behrisch (Plenum Press 1984).

A Monte-Carlo Model of Neutral-Particle Transport in Divertor Plasmas. D. Heifetz, D. Post, M. Petravic, J. Weisheit, and G. Bateman, Journal of Computational Physics 46, 309-327 (192).  

DEGAS User's Guide 2/13/87