D.E. Post

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.

Attainment of high confinement in neutral beam heated divertor discharges in the PDX tokamak

Abstract The PDX divertor configuration has recently been converted from an open to a closed geometry to inhibit the return of neutral gas from the divertor region to the main chamber. Since then, operation in a regime with high energy confinement in neutral beam heated discharges (ASDEX H-mode) has been routine over a wide range of operating conditions. These H-mode discharges are characterized by a sudden drop in divertor density and H α emission and a spontaneous rise in main chamber plasma density during neutral beam injection. The confinement time is found to scale nearly linearly with plasma current, but can be degraded due either to the presence of edge instabilities or heavy gas puffing. Detailed Thomson scattering temperature profiles show high values of T c near the plasma edge (∼ 450 eV) with sharp radial gradients (∼ 400 eV/cm) near the separatrix. Density profiles are broad and also exhibit steep gradients close to the separatrix.

Baldur: A one-dimensional plasma transport code

Abstract A version of the BALDUR plasma transport code which calculates the evolution of plasma parameters is documented. This version uses an MHD equilibrium which can be approximated by concentric circular flux surfaces. Transport of up to six species of ionized particles, of electron and ion energy, and of poloidal magnetic field is computed. A wide variety of source terms are calculated including those due to neutral gas, fusion and auxiliary heating. The code is primarily designed for modelling tokamak plasmas.

Survey of atomic processes in edge plasmas

A review of the most important reactions of atomic and molecular hydrogen with the fusion edge plasma electrons and ions is presented. An appropriate characterization of the considered collision processes, useful in plasma edge studies (evaluated cross sections, reaction rates, energy gain/loss per collision, etc.) has been performed. While a complete survey of atomic physics of fusion edge plasmas will be given elsewhere shortly, we demonstrate here the relevance of the atomic collision processes for describing the physical state of edge plasmas and understanding the energy balance in cool divertor plasmas. It is found that the excited neutral species play an important role in the low-temperature, high-density plasmas.

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.

Particle fueling and impurity control in PDX

Abstract Fueling requirements and impurity levels in neutral-beam-heated discharges in the PDX tokamak have been compared for plasmas formed with conventional graphite rail limiters, a particle scoop limiter, and an open or closed poloidal divertor. Gas flows necessary to obtain a given density are highest for diverted discharges and lowest for the scoop limiter. Hydrogen pellet injection provides an efficient alternative fueling technique, and a multiple pellet injector has produced high density discharges for an absorbed neutral beam power of up to 600 kW, above which higher speeds or more massive pellets are required for penetration to the plasma core. Power balance studies indicate that 30–40% of the total input power is radiated while ~15% is absorbed by the limiting surface, except in the open divertor case, where 60% flows to the neutralizer plate. In all operating configurations, Z eff usually rises at the onset of neutral beam injection. Both open divertor pl;asmas and those formed on a well conditioned water-cooled limiter have Z eff ⪅ 2 at the end of neutral injection. A definitive comparison of divertors and limiters for impurity control purposes requires longer beam pulses or higher power levels than available on present machines.

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.

Two-dimensional fluid simulations of the ITER SOL plasma

Abstract Simulations of scrape-off layer plasmas in ITER have been performed using a 2-d fluid model with a set of perpendicular energy and particle transport coefficients matching those determined in a limited number of experiments on presently operating tokamaks. These simulations include single- and double-null magnetic configurations, and ignited and driven operation. Predictions are made of divertor power loading, density scrape-off length, effective core/edge recycling coefficient, and divertor sheath electron temperature.

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.