M. Petravic

A Monte-Carlo model of neutral-particle transport in diverted plasmas

The transport of neutral atoms and molecules in the edge and divertor regions of fusion experiments has been calculated using Monte-Carlo techniques. The deuterium, tritium, and helium atoms are produced by recombination at the walls. The relevant collision processes of charge exchange, ionization, and dissociation between the neutrals and the flowing plasma electrons and ions are included, along with wall-reflection models. General two-dimensional wall and plasma geometries are treated in a flexible manner so that varied configurations can be easily studied. The algorithm uses a pseudocollision method. Splitting with Russian roulette, suppression of absorption, and efficient scoring techniques are used to reduce the variance. The resulting code is sufficiently fast and compact to be incorporated into iterative treatments of plasma dynamics requiring numerous neutral profiles. The calculation yields the neutral gas densities, pressures, fluxes, ionization rates, momentum-transfer rates, energy-transfer rates, and wall-sputtering rates. Applications have included modeling of proposed INTOR/FED poloidal divertor designs and other experimental devices.

An analytic one-dimensional divertor model with neutral sources

Abstract Divertor operation with high-density, low-temperature plasmas near the neutralizer plate offers the possibility of impurity control for high-power, long-pulse fusion experiments. Such plasmas can be produced by intense neutral recycling near the neutralizer plate. To complement large scale computational modeling of such divertors, we have developed a simple analytic model to describe this divertor regime. Continuity equations for neutral atom and plasma transport are analytically solved in a one-dimensional model, and the role of recycling is examined. The results are parametrized in a dimensionless form and compared with both theoretical and experimental results.

An ILUCG algorithm which minimizes in the euclidean norm

This paper presents an algorithm which solves sparse systems of linear equations of the form Ax =y, where A is non-symmetric, by the Incomplete LU Decomposition-Conjugate Gradient (ILUCG) method. The algorithm minimizes the error in the Euclidean norm ‖xi − x‖2 , where xi is the solution vector after the ith iteration and x the exact solution vector. The results of a test on one real problem indicate that the algorithm is likely to be competitive with the best existing algorithms of its type.

Models for poloidal divertors

Recent progress in models for poloidal divertors has both helped to explain current divertor experiments and contributed significantly to design efforts for future large tokamak (INTOR, etc.) divertor systems. These models range in sophistication from zero-dimensional treatments and dimensional analysis to two-dimensional models for plasma and neutral particle transport which include a wide variety of atomic and molecular processes as well as detailed treatments of the plasma-wall interaction. This paper presents a brief review of some of these models, describing the physics and approximations involved in each model. We discuss the wide variety of physics necessary for a comprehensive description of poloidal divertors. To illustrate the progress in models for poloidal divertors, we discuss some of our recent work as typical examples of the kinds of calculations being done.

Recent progress in the tokamak edge modeling

Abstract Tokamak edge modeling, with a particular emphasis on divertors, was reviewed in detail in 1982. At that time the emphasis was on the qualitative behavior of the scrape-off plasma and the atomic processes involved in the neutral-plasma interaction. While no detailed comparisons with the experiments were available, the data nevertheless showed all the basic features of the cool high-density regime predicted by the models. The two most important modeling developments of 1983 were the introduction of accurate magnetic geometries and the inclusion of impurity transport in the plasma equations. This made possible detailed comparisons with the PDX and ASDEX experiments which on the one hand showed remarkable agreement while on the other hand pointed to new areas of uncertainty, i.e., the plasma-wall and neutral-wall interactions. In another development, the scrape-off models are beginning to be linked to the main plasma transport in order to provide better boundary conditions for the main plasma models, and in particular to model limiters. The fully two-dimensional plasma flow models should be particularly useful in this area.

INTOR divertor in a realistic 2-D geometry

Abstract The INTOR divertor operation has so far been modeled only in a simplified rectangular geometry, which omitted some of the important features of the actual INTOR divertor. Recently, the PLANET plasma transport code upgrades have allowed us to model the open magnetic geometry of the INTOR divertor realistically, in particular, with regard to the trapped neutral gas region between the two separatrices and the open geometry. The effect of this neutral gas build-up on the plasma density, temperature, and the energy loss has been examined. The neutral hydrogen interaction with the plasma, and the interaction of the resulting charge-exchange neutrals with the walls is discussed. The power flux profiles at the plates were computed under the assumption of constant radial transport coefficients. It was found that the change in these profiles from the x- point to the plates is due mostly to the compression in the poloidal magnetic field. The heat loads on the neutralizer plate and first wall have been characterized, and the erosion of the divertor walls and the neutralizer plates is discussed.

Orthogonal grid construction for modeling of transport in tokamaks

Abstract A simple method has been developed for numerically constructing orthogonal grids based on the tokamak poloidal flux surfaces. The poloidal flux surfaces form -a natural set of coordinate lines for the study of transport in the tokamak scrape-off region, since the energy transport there is mostly along the field lines contained within the flux surfaces. For a study of both the poloidal and perpendicular (radial) transport, a two-dimensional, preferably orthogonal, mesh is required. The need for a new mesh generating code arose from the requirements of the particular topology produced by the zeros in the poloidal field (x-points) and the consequent problems with the numbering of the mesh.

Scrape-off layer modeling using coupled plasma and neutral transport codes

An effort is made to refine the neutral transport model used in the B2 edge plasma code by coupling it to the DEGAS Monte Carlo code. Results are discussed for a simulation of a high recycling divertor. It appears that on the order of 100 iterations between the two codes are required to achieve a converged solution. However, the amount of computer time used in the DEGAS simulations is large, making complete runs impractical for design purposes. On the other hand, the differences in the resulting plasma parameters when compared to the B2 analytic neutrals model indicate that it would be worthwhile to explore techniques for speeding up the coupled system of codes.

Calculations of neutral transport in the PDX divertor

Abstract Neutral particle transport during a typical beam-heated PDX diverted discharge was modeled using the multidimensional code DEGAS. Plasma parameters were taken from probe measurements, and were assumed not to change during the calculations. A realistic plasma/divertor geometry was included in the model, along with a simple particle recycling scheme. Calculated results were compared with the experimentally measured neutral pressures. Without any pumping in the device, the computed pressures were found to be higher than those measured by a factor of approximately two. Introducing a simple pumping model for wall absorption, wherein 10% of the absorbed neutral particles were assumed not to desorb, reduced the calculated pressures to about the measured values. However the pressure was observed to monotonically increase during the discharge, whereas the model results peaked in mid-discharge. One possible explanation of the disagreement is that the saturation of the device walls increases during the discharge, so that the fraction of particles pumped decreases with time. Reduction of the permanently absorbed fraction from 10 to 4% during the course of the discharge caused the calculated pressure to monotonically increase.

A computational study of operating regimes for poloidal divertors

We have identified three theoretical operating regimes for poloidal divertors. These regimes are determined by the geometry of the divertor and the input energy and particle fluxes, and are characterized by the divertor plasma density and temperature. A fully self-consistent two-dimensional model for the plasma and neutral atom and molecule transport [1,2] was used to study poloidal divertor operation. Extensions of our previous calculations [2] important to this study were the inclusion of parallel electron and ion thermal conduction. We find that the key physics in divertor operation is the neutral recycling near the neutralizer plate. This can be parametrized by R = ΓpΓ0, the ratio of particle flux striking the neutralizer plate to the particle flux entering the divertor. Values of R ~ 1 can be produced by large pumping rates near the neutralizer plates resulting in low neutral recycling and a high temperature, low density divertor plasma. By decreasing the pumping near the neutralizer plate, R can be raised to an intermediate value of 5–10, the plasma temperature lowered by the same factor, and the density raised by a factor of 10–30. In this regime, escape of the neutrals back to the main plasma is virtually blocked. By further restricting the pumping, R can be raised to twenty or more, thereby lowering the temperature by a factor of twenty or more and raising the density by a factor of ninety or more. Such high density regimes have been observed on D-III [3] and appear to offer the most promise for impurity control and particle control on large reactor experiments such as INTOR or FED. In this paper, we explore the range 3 < R < 16.