M.E. Rensink

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.

Divertor heat flux reduction by D2 injection in DIII-D

D{sub 2} gas injected into ELMing H-mode discharges in DIII-D reduced total integrated heat flux to the divertor by {approximately}2{times} and peak heat flux by {approximately}5{times}, with only modest degradation to plasma stored energy. Steady gas injection without particle pumping results in eventual degradation in stored energy. The initial reduction in peak heat flux at the divertor tiles may be primarily due to the increase in radiated power from the X-point/divertor region. The eventual formation of a high density region near the X-point appears to play a role in momentum (and energy) transfer from the flux surfaces near the outboard strike point to flux surfaces farther out into the scrapeoff. This may also contribute to further reduction in peak heat flux.

Collisional loss of electrostatically confined species in a magnetic mirror

The basic problem of particle end-loss in a magnetic mirror field with an electrostatic confining potential is considered. The analytic treatments of Pastukhov and Chernin and Rosenbluth have been generalized to apply to any electrostatically confined species in a multi-species plasma, and the Pastukhov analysis has been extended to apply to arbitrary magnetic-field profiles (instead of square-well). The analytic results are compared with results obtained from one-and two-dimensional Fokker-Planck codes. In particular the scaling with potential, mirror ratio, and effective charge is considered. The closest agreement (within 20%) is between the 2-D Fokker-Planck and generalized Pastukhov results.

Interactions between Liquid-Wall Vapor and Edge Plasmas

Abstract The use of liquid walls for fusion reactors could help solve problems associated with material erosion from high plasma heat-loads and neutronic activation of structures. A key issue analyzed here is the influx of impurity ions to the core plasma from the vapor of liquid side-walls. Numerical 2D transport simulations are performed for a slab geometry which approximates the edge region of a reactor-size tokamak. Both lithium vapor (from Li or Sn–Li walls) and fluorine vapor (from Flibe walls) are considered for hydrogen edge-plasmas in the high- and low-recycling regimes. It is found that the minimum influx is from lithium with a low-recycling hydrogen plasma, and the maximum influx occurs for fluorine with a high-recycling hydrogen plasma.

UEDGE and DEGAS modeling of the DIII-D scrape-off layer plasma☆

This paper presents work to develop benchmarked theoretical models of scrape-off-layer (SOL) characteristics in diverted tokamaks by comparing shot simulations using the UEDGE plasma fluid and DEGAS neutral transport codes to measurements of the DIII-D SOL plasma. The experimental data include the radial profiles of n{sub e} T{sub e}, and T{sub i}, the divertor exhaust power, the intensity of H{sub {alpha}} emission, and profiles of the radiated power. A very simple model of the anomalous perpendicular transport rates produces consistency between the calculated and measured radial profiles of the divertor power, and of the midplane densities and temperatures. Experimentally, the measured exhaust power is now 80--90% of the input power. The simulated peak power on the outer leg of the divertor floor is now within 20% of the measured power. Various sensitivities of these comparisons to model assumptions are described. Finally, these benchmarked models have been used to examine the effects of various baffle configurations for the Radiative Divertor Upgrade in DIII-D.

Development of a radiative divertor for DIII-D

Abstract We have used experiments and modeling to develop a new radiative divertor configuration for DIII-D. Gas puffing experiments with the existing open divertor have shown the creation of a localized (∼ 10 cm diameter) radiation zone which results in substantial reduction (3–10) in the divertor heat flux while τ E remains ∼ 2 times ITER-89P scaling. However, n e increases with D 2 puffing, and Z eff increases with neon puffing. Divertor structures are required to minimize the effects on the core plasma. The UEDGE fluid code, benchmarked with DIII-D data, and the DEGAS neutrals transport code are used to estimate the effectiveness of divertor configurations; slots reduce the core ionization more than baffles. The overall divertor shape is set by confinement studies which indicate that high triangularity (δ ≈ 0.8) is important for high τ E VH-modes. Results from engineering feasibility studies, including diagnostic access, will be presented.

Techniques and results of tokamak-edge simulation

This paper describes recent development of the UEDGE code in three important areas. (1) Non-orthogonal grids allow accurate treatment of experimental geometries in which divertor plates intersect flux surfaces at oblique angles. (2) Radating impurities are included by means of one or more continuity equations that describe transport and sources, and sinks due to ionization and recombination processes. (3) Advanced iterative methods that reduce storage and execution time allow us to find fully converged solutions of larger problems (i.e., finer grids). Sample calculations are presented to illustrate these development.

A design study for an advanced divertor for DIII-D and ITER: the radiative slot divertor

Reduction of the divertor heat load is an important issue for future tokamaks, particularly during the technology phase of ITER. We discuss a conceptual design for one type of advanced divertor: the radiative slot divertor. The goal of this divertor configuration is to enhance the radiation in the divertor region and thereby reduce the heat load at the strike points. At the same time, any effects on the core plasma must be minimized. Proof-of-principle experiments to enhance the radiation in the DIII-D divertor have been performed both with deuterium and impurity injection. We compare several computer models with results from these experiments to predict performance and thereby guide designs of radiative divertors for future machines. We have estimated impurity radiation using calculations of the background plasma with a two-dimensional fluid code (B2 or LEDGE) coupled with models of impurity radiation. The DEGAS code has been used to estimate hydrogenic transport, charge exchange and radiation losses. Estimates of impurity transport are provided by 11/1-dimensional models and calculations of impurity frictional-force terms. These model, results are in qualitative agreement with the ∼1 MW reduction of measured divertor power in DIII-D during divertor impurity puffing experiments. Specific designs, including engineering details, for applications to DIII-D and ITER will be discussed.

Simulation of the Effect of Plasma Flows in DIII-D, JET, and JT-60U

Abstract The results of 2D fluid plasma simulations of the ion flow in the boundary plasma of DIII-D, JET, and JT-60U are reported. The model includes the effects of drifts and of impurity radiation using a multi-species model of intrinsic carbon impurities. Drift effects are important in determining the primary and impurity ion fluxes in the SOL and the private region, with E × B drifts dominant. Simulated parallel velocities are consistent with experimental measurement on the high field side of JT-60U, where the parallel flow is determined by ion sources. Simulated parallel velocities are significantly less than seen in experiment at the outer midplane of JT-60U, and at the top of JET where the flow is sensitive to poloidal variations of the turbulence driven transport, suggesting the velocity in these regions is determined by transport. Parallel flows are reversed by changing the direction of the ion ∇ B drift relative to the X -point.

Radial transport calculations for tandem mirrors

The existence of a non-axisymmetric magnetic field in the transition regions between the central cell and end-plugs of a tandem mirror device can lead to significant radial transport of central-cell ions. Self-consistent calculation of the consequences of this non-ambipolar process requires the solution of a highly non-linear charge balance equation for the ambipolar potential. In this paper, radial transport in tandem mirrors is studied, with particular emphasis on the charge balance equation and its consequences. A time-dependent radial transport code is presented. Simulations of the Tandem Mirror Experiment (TMX) are performed. Generally, good agreement between code and experiment is obtained. The phenomenon of quenching of radial transport is analysed and demonstrated numerically.