T.D. Rognlien

A fully implicit, time dependent 2-D fluid code for modeling tokamak edge plasmas

A fully implicit, time dependent 2-D fluid code is described that models the edge plasma region of a tokamak with a divertor or limiter. Equations solved are for particle continuity, parallel momentum, electron energy, ion energy, electrostatic potential, and neutral gas diffusion. We include the effects of parallel currents and cross-field drifts so that divertor biasing can be investigated. The core plasma is poloidally periodic, and the inner and outer private flux regions are properly connected. An implicit method-of-lines scheme is used to advance the variables in time utilizing the Krylov technique which does not require explicit formation or solution of the Jacobian matrix. However, for good performance, the problem needs to be preconditioned; a numerically generated Jacobian is used for this stage. The Jacobian can also be used to obtain the steady state solution by standard Newton iteration. Results are presented on the effects of biasing and parallel currents for DIII-D single-null parameters, and showing the time dependent heat flux on the divertor plate.

Low-to-high confinement transition simulations in divertor geometry

Recent results are presented for turbulence in tokamak boundary plasmas and its relationship to the low-to-high confinement (L–H) transition in a realistic divertor geometry. These results are obtained from a three-dimensional (3D) nonlocal electromagnetic turbulence code, which models the boundary plasma using fluid equations for plasma vorticity, density, electron and ion temperatures and parallel momenta. With sources added in the core-edge region and sinks in the scrape-off layer (SOL), the code follows the self-consistent profile evolution together with turbulence. Under DIII-D [Luxon et al., International Conference on Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1986), p. 159] tokamak L-mode conditions, the dominant source of turbulence is pressure-gradient-driven resistive X-point modes. These modes are electromagnetic and curvature-driven at the outside mid-plane region but become electrostatic near X-points due to magnetic shear and collisionality. Cl...

Dust-Particle Transport in Tokamak Edge Plasmas

Dust particulates in the size range of 10nm–100μm are found in all fusion devices. Such dust can be generated during tokamak operation due to strong plasma∕material-surface interactions. Some recent experiments and theoretical estimates indicate that dust particles can provide an important source of impurities in the tokamak plasma. Moreover, dust can be a serious threat to the safety of next-step fusion devices. In this paper, recent experimental observations on dust in fusion devices are reviewed. A physical model for dust transport simulation and a newly developed code DUSTT are discussed. The DUSTT code incorporates both dust dynamics due to comprehensive dust-plasma interactions as well as the effects of dust heating, charging, and evaporation. The code tracks test dust particles in realistic plasma backgrounds as provided by edge-plasma transport codes. The results are presented for dust transport in current and next-step tokamaks. The effect of dust on divertor plasma profiles and core plasma conta...

Plasma?surface interaction, scrape-off layer and divertor physics: implications for ITER

Recent research in scrape-off layer (SOL) and divertor physics is reviewed; new and existing data from a variety of experiments have been used to make cross-experiment comparisons with implications for further research and ITER. Studies of the region near the separatrix have addressed the relationship of profiles to turbulence as well as the scaling of the parallel power flow. Enhanced low-field side radial transport is implicated as driving parallel flows to the inboard side. The medium-n nature of edge localized modes (ELMs) has been elucidated and new measurements have determined that they carry ~10?20% of the ELM energy to the far SOL with implications for ITER limiters and the upper divertor. The predicted divertor power loads for ITER disruptions are reduced while those to main chamber plasma facing components (PFCs) increase. Disruption mitigation through massive gas puffing is successful at reducing PFC heat loads. New estimates of ITER tritium retention have shown tile sides to play a significant role; tritium cleanup may be necessary every few days to weeks. ITERs use of mixed materials gives rise to a reduction of surface melting temperatures and chemical sputtering. Advances in modelling of the ITER divertor and flows have enhanced the capability to match experimental data and predict ITER performance.

Two-dimensional electric fields and drifts near the magnetic separatrix in divertor tokamaks

A two-dimensional calculation is presented for the transport of plasma in the edge region of a divertor tokamak solving continuity, momentum, and energy balance fluid equations. The model uses classical processes of parallel transport along the magnetic field and cross-field drifts together with anomalous radial diffusion, including perpendicular ion viscosity. The self-consistent electrostatic potential is calculated on both sides of the magnetic separatrix via quasineutrality and current continuity. Outside the separatrix, the model extends to material divertor plates where the incident plasma is recycled as neutral gas and where the plate sheath and parallel currents dominate the potential structure. Inside the separatrix, various radial current terms—from anomalous viscosity, collisional damping, inertia, and ∇B drifts—contribute to determining the potential. The model rigorously enforces cancellation of gyroviscous and magnetization terms from the transport equations. The results emphasize the import...

The magnetic field structure of a snowflake divertor

The snowflake divertor exploits a tokamak geometry in which the poloidal magnetic field null approaches second order; the name stems from the characteristic hexagonal, snowflakelike shape of the separatrix for an exact second-order null. The proximity of the poloidal field structure to that of a second-order null substantially modifies edge magnetic properties compared to the standard X-point geometry (with a first-order null); this, in turn, affects the edge plasma behavior. Modifications include: (1) The flux expansion near the null-point becomes 2–3 times larger. (2) The connection length between the equatorial plane and divertor plate increases. (3) Magnetic shear just inside the separatrix becomes much larger. (4) In the open-field-line region, the squeezing of the flux-tubes near the null-point increases, thereby causing stronger decoupling of the plasma turbulence in the divertor legs and in the main scrape-off layer. These effects can be used to reduce the power load on the divertor plates and/or ...

Transition from Pastukhov to collisional confinement in a magnetic and electrostatic well

It is shown that the Pastukhov formula for charged particle confinement in a combined magnetic and electrostatic well becomes invalid when the mean free path, reduced by the mirror ratio, is of the order of the system length. A smooth transition is made to a collisional confinement time based on a completely filled loss cone which gets depleted only at the end of the system. A Monte Carlo computer code is used to study the transition regime, and it shows that a good model is to add the analytic Pastukhov and collisional confinement times.

Kinetic effects in tokamak scrape-off layer plasmas

The short mean-free path expansion used in fluid modeling of scrape-off layer plasmas is often violated for typical discharge parameters, especially by the superthermal particles, which carry most of the heat flux. Thus, the tail of the distribution function can strongly depart from Maxwellian due to nonlocal mean-free path effects, which can modify plasma transport, impurity radiation, and plasma–neutral gas interactions. These nonlocal effects become particularly pronounced for detached plasma conditions that are characterized by sharp gradients in the plasma parameters along the magnetic field. These problems are being addressed by developing one spatial dimension and two velocity variables, fully kinetic, collisional, and time-dependent particle-in-cell code, W1 [Contrib. Plasma Phys. 34, 436 (1994)], and its parallel-computer version, PW1 [Contrib. Plasma Phys. 34, 424 (1996)]. Comparisons are made with the Fokker–Planck code ALLA [Phys. Plasmas 3, 1634 (1996)] and with experimental results. Kinetic ...

Simulation of experimentally achieved DIII‐D detached plasmas using the UEDGE code

The introduction of a divertor Thomson scattering system in DIII‐D [J. Luxon et al., International Conference on Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1986), p. 159] has enabled accurate determination of the plasma properties in the divertor region. Two plasma regimes are identified: detached and attached. The electron temperature in the detached regime is about 2 eV, much lower than 5–10 eV determined earlier. Fluid models of the DIII‐D scrape‐off layer plasma successfully reproduce many of the features of these two regimes, including the boundaries for transition between them. Detailed comparison between the results obtained from the fluid models and experiment suggest the models underestimate the spatial extent of the low‐temperature region associated with the detached plasma mode. Low‐temperature atomic physics processes that are not included in the present models may account for this discrepancy.

Plasma–surface interaction issues of an all-metal ITER

We assess key plasma surface interaction issues of an all-metal plasma facing component (PFC) system for ITER, in particular a tungsten divertor surface, and a beryllium or tungsten first wall. Such a system eliminates problems with carbon divertor erosion and T/C codeposition, and for an all-tungsten system would better extrapolate to post-ITER devices. The issues studied are sputtering, transport, and formation of mixed surface layers, tritium codeposition, core plasma contamination, ELM response, and He on W irradiation effects. Code package OMEGA computes PFC sputtering erosion/redeposition in an ITER full power D-T plasma edge regime with convective transport. The HEIGHTS package analyzes divertor plasma transient response. PISCES and other data are used with code results to assess PFC performance. Predicted outer wall sputter erosion rates are acceptable for Be (0.3 nm/s) or bare (stainless steel/Fe) wall (0.05 nm/s) for the low duty factor ITER, and are very low (0.002 nm/s) for W. Most wall-sputtered Be is redeposited on the wall itself or baffle region, with about 10% transported to the divertor target. T/Be codeposition in redeposited wall material could be significant (~2 gT per 400 s ITER pulse). Core plasma contamination potential from wall sputtering appears acceptable for Be (~2%), and negligible for W (or Fe) due to near-surface ionization of sputtered W (Fe) atoms and subsequent strong redeposition. A tungsten divertor likewise appears acceptable from the self-sputtering and plasma contamination standpoints, and would have negligible T/W codeposition. Be can grow on/near the strike point region of a W divertor, but for the predicted maximum surface temperature of ~800°C, deleterious Be/W alloy formation may be avoided. ELMs are a serious challenge to the divertor, but this is true for all materials. We identify acceptable ELM parameters for W. We conclude that an all-metal PFC system is likely a much better choice for ITER D-T operation than a system using carbon, but critical R&D issues remain, e.g., in areas of transient surface erosion (of all materials), W surface integrity with energetic He etc. bombardment, and in predictive plasma/surface interaction modeling generally. Steps are suggested to ameliorate problems and reduce uncertainties, e.g., via a 300 or 400°C baking capability for T/Be reduction, and using a deposited tungsten first wall test section.