D.B. Heifetz

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.

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.

Plasma-material interactions in TFTR

This paper presents a summary of plasma-material interactions which influence the operation of TFTR with high current (≤ 2.2 MA) ohmically heated, and high-power (∼ 10 MW) neutral-beam heated plasmas. The conditioning procedures which are applied routinely to the first-wall hardware are reviewed. Fueling characteristics during gas, pellet, and neutral-beam fueling are described. Recycling coefficients near unity are observed for most gas fueled discharges. Gas fueled discharges after helium discharge conditioning of the toroidal bumper limiter, and discharges fueled by neutral beams and pellets, show R<1. In the vicinity of the gas fueled density limit (at ne = 5–6 × 1019 m−3) values of Zeff are ≦1.5. Increases in Zeff of ≦1 have been observed with neutral beam heating of 10 MW. The primary low Z impurity is carbon with concentrations decreasing from ∼10% to <1% with increasing ne. Oxygen densities tend to increase with ne, and at the ohmic plasma density limit oxygen and carbon concentrations are comparable. Chromium getter experiments and He2+/D+ plasma comparisons indicate that the limiter is the primary source of carbon and that the vessel wall is a significant source of the oxygen impurity. Metallic impurities, consisting of the vacuum vessel metals (Ni, Fe, Cr) have significant (∼10−4 ne) concentrations only at low plasma densities (ne <1019 m−3). The primary source of metallic impurities is most likely ion sputtering from metals deposited on the carbon limiter surface.

Initial limiter and getter operation in TFTR

Abstract During the recent ohmic heating experiments on TFTR, the movable limiter array, preliminary inner bumper limiter, and prototype ZrAl alloy bulk getter surface pumping system were brought into operation. This paper summarizes the operational experience and plasma characteristics obtained with these components. The near-term upgrades of these systems are also discussed.

The density dependence of neutral hydrogen density and neutral hydrogen emission from PLT

The efflux of atoms with energies greater than 10 eV from tokamaks results primarily from charge exchange. This flux is useful as a diagnostic of plasma properties such as particle transport, particle confinement, power balance, neutral density, and ion temperature. This flux also contributes to plasma contamination by sputtering of impurities from walls and limiters. We have measured the efflux of neutral hydrogen in the energy range from 10 to 2000 eV as a function of plasma parameters in the steady-state portion of ohmically heated discharges in PLT. Results have been obtained both near the main plasma limiter and far away from it. These data serve as a benchmark for comparing atomic emission during auxiliary heating and current drive. We find that the main parameter which affects the efflux is the plasma density. The total energy-integrated efflux, Γ, rises rapidly with ne to Γ = 4 × 1015cm−2s−1 at ne = 1 × 1013cm−3, and then falls a factor of 2–4. The total efflux is then relatively constant with ne up to ne ≈ 6 × 1013cm−3. The average energy of the efflux rises from 180 eV at ne = 1012 cm−3 to 500 eV at ne = 1013 cm−3. It then decreases to approximately 150 eV at ne = 2 × 1013cm−3, and drops slightly more to 100 eV at ne ≈ 6 × 1013cm−3. Using the measured dΓ/dEdΩ spectra, electron temperature, and electron density as inputs and consistency checks, the ion temperature profiles and 3-dimensional neutral density profiles are calculated using the DEGAS code. From these calculations the particle confinement time, impurity generation by sputtering, and contribution of ions and charge-exchange neutrals to the power balance are evaluated as a function of electron density. The importance of the limiter to recycling at high densities is clearly demonstrated. The ratio of the ion flux onto the limiter versus the ion flux onto the wall goes from 4.8 at ne = 1.8 × 1012cm−3 to 6.3 at ne = 1 × 1013cm−3, and to 24.1 at ne = 5.5 × 1013cm−3.

An advanced pump limiter experiment of large toroidal extent — ALT II

Abstract Concepts for an advanced pump limiter experiment able to exhaust 5–10% of the plasma particle flux and remove 200 W/cm 2 of heat flux on the limiter face are developed and analyzed. An axisymmetric toroidal belt limiter has a compound curvature blade with edges that extend one particle e-folding distance into the scrape-off layer plasma. Approximately 30% of the plasma efflux flows in a gap between the bottom of the limiter blade and the top of either a structural floor, a plenum box or a liner. Neutralizer/deflector plates are located in discrete pairs at each pumping duct and are designed to optimally scatter neutralized particles into the pump ducts. An alternative design consists of a central toroidal spine beneath the blade which scatters plasma as neutral gas into a plenum box. For application to the TEXTOR tokamak with 1.5 MW of ICRF heating and 2.6 MW of 50 keV neutral beam injection, detailed analysis shows that an average heat flux is approximately 200 W/cm 2 and that the localized collector plate design is about five times more efficient than the spinal design for particle removal.

Tritium inventory and permeation in TFTR

Abstract The control of tritium in TFTR has both important safety and environmental implications. Current modelling techniques allow realistic predictions of the tritium inventory in and permeation through in-torus components. The source of the tritium was computed using a three-dimensional description of the neutral particle flux on the TFTR vacuum vessel wall from the neutral transport code DEGAS, under plasma conditions modelled with the one-dimensional transport code BALDUR. The movable limiter (graphite) was modelled using an extension of the Local Mixing Model for hydrogen retention and isotope exchange. In particular, the calculations consider the inventory and recycling for the movable limiters (which are expected to experience transient temperatures up to 2000°C) as well as the bumper limiters and protective plates which will remain somewhat cooler. Transient effects in the bulk graphite limiter and in the stainless steel wall were modelled using the DIFFUSE code with materials parameters taken from the most recent literature. It appears that for the expected material properties, specifically the hydrogen recombination constant measured in a clean TFTR environment, and operating scenario, there will be essentially no tritium permeation through the stainless steel walls or bellows and less than 0.1 kCi of tritium inventory in the stainless steel first wall. The limiters may contain as much as 5 kCi of tritium.

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.

Total backscattering of keV light ions from solids at oblique and grazing incidence

The particle and energy reflection coefficients of light keV ions from heavy random targets have been calculated analytically and by TRIM computer simulation. Analytical results have been found by two different approaches: on the basis of small-angle multiple scattering theory of Remizovich et al., in the case of glancing angles of incidence, and by applying the single collision model, in the case of nearly perpendicular incidence. Electronic stopping is assumed velocity proportional and the scattering determined by Thomas-Fermi interaction. The agreement between analytical results and TRIM data in a wide range of angles of incidence is satisfactory for ∈ 0 ≳5, where ∈ 0 is Lindhards energy parameter.