R.D. Stambaugh

Reconstruction of current profile parameters and plasma shapes in tokamaks

An efficient method is given to reconstruct the current profile parameters, the plasma shape, and a current profile consistent with the magnetohydrodynamic equilibrium constraint from external magnetic measurements, based on a Picard iteration approach which approximately conserves the measurements. Computational efforts are reduced by parametrizing the current profile linearly in terms of a number of physical parameters. Results of detailed comparative calculations and a sensitivity study are described. Illustrative calculations to reconstruct the current profiles and plasma shapes in ohmically and auxiliarily heated Doublet III plasmas are given which show many interesting features of the current profiles.

Principal physics developments evaluated in the ITER design review

As part of the ITER Design Review and in response to the issues identified by the Science and Technology Advisory Committee, the ITER physics requirements were reviewed and as appropriate updated. The focus of this paper will be on recent work affecting the ITER design with special emphasis on topics affecting near-term procurement arrangements. This paper will describe results on: design sensitivity studies, poloidal field coil requirements, vertical stability, effect of toroidal field ripple on thermal confinement, material choice and heat load requirements for plasma-facing components, edge localized modes control, resistive wall mode control, disruptions and disruption mitigation.

Separation of bar betap and ℓi in tokamaks of non-circular cross-section

Integral relations for the average poloidal beta p and the plasma internal inductance li are derived from the magnetohydrodynamic (MHD) equilibrium equation for an axisymmetric torus. The volume-dependent parameters that appear depend only weakly on the actual current density distribution inside the plasma and can be evaluated approximately, given the plasma shape and boundary poloidal magnetic field. In practice, these can be accurately and efficiently obtained for both diverted and limited plasmas from measured external poloidal magnetic field and flux values by approximating the plasma current distribution using a few filaments or distributed sources. For a tokamak plasma with a non-circular cross-section of sufficient elongation, p and li can then be approximately determined separately. This is demonstrated for analytic equilibria of known shape as well as for actual Doublet III (D-III) plasmas for which p and li have been determined by using other methods. Results of a sensitivity study are described.

The Spherical Tokamak Path to Fusion Power

AbstractThe low-aspect-ratio tokamak or spherical torus (ST) approach offers the two key elements needed to enable magnetic confinement fusion to make the transition from a government-funded research program to the commercial marketplace: a low-cost, low-power, small-size market entry vehicle and a strong economy of scale in larger devices. Within the ST concept, a very small device (A = 1.4, major radius ~1 m, similar size to the DIII-D tokamak) could be built that would produce ~800 MW(thermal), 200 MW(net electric) and would have a gain, defined as QPLANT = (gross electric power/recirculating power), of ~2. Such a device would have all the operating systems and features of a power plant and would therefore be acceptable as a pilot plant, even though the cost of electricity would not be competitive. The ratio of fusion power to copper toroidal field (TF) coil dissipation rises quickly with device size (like R3 to R4, depending on what is held constant) and can lead to 4-GW(thermal) power plants with QPL...

H-mode energy confinement scaling from the DIII-D and JET tokamaks

Neutral beam heated H-mode DIII-D and JET expanded boundary divertor discharges were examined to study the parametric dependence of the thermal energy confinement on the plasma current, plasma size and neutral beam power. Single-null discharges in both machines were examined during the ELM-free phase (ELM stands for edge localized mode) to extract information about the intrinsic H-mode thermal energy confinement time τth. A power law dependence of ELM-free thermal energy confinement was assumed, with the result that for Bτ ≈ 2.2 T and κ = 1.8, τth = C Ip1.03±0.07 PL−0.46±0.06 L1.48±0.09. The size dependence of τth is described by the linear dimension L since the determination of the individual dependences on the minor and major radii is precluded by the similar aspect ratio of the two machines. For this representation of τth (units of s, MA, MW and m), when L is the plasma major radius, C = 0.106 ± 0.011, and when L is the plasma minor radius, C = 0.441 ± 0.044. A dimensionally correct version of the scaling, consistent with the constraints of a collisional high beta model, is τth∝ Ip1.06 PL−0.45 L1.40 ne0.07 Bτ0.06. These results indicate that, within the experimental error, the empirical scaling and the dimensionally correct scaling are the same.

Energy confinement properties of H-mode discharges in the DIII-D tokamak

Neutral beam heated DIII-D expanded boundary divertor discharges have exhibited ASDEX-like H-mode behaviour over a wide parameter range. The deuterium H-mode energy confinement of 120 ms remained near the Ohmic value for up to 6 MW of neutral beam heating, where it was 2-2.5 times higher than the L-mode value at a plasma current of 1 MA. The hydrogen and helium H-mode energy confinement times were similar and substantially below the deuterium H-mode confinement time. The H-mode confinement times decreased with increasing neutral beam power and were only 30% better than the L-mode confinement times at 5 MW. In an H-mode with a mixture of hydrogen and deuterium ([H]/[H+D] 40%), the confinement time was in between the values obtained in the pure hydrogen and deuterium cases, increased linearly with plasma current for q95 > 3.2, and decreased with increasing neutral beam power. The confinement quality in these plasmas was 85 ms per MA at a heating power of 5.6 MW. The lower energy confinement in the non-deuterium H-modes and the degradation of energy confinement with neutral beam power were both accompanied by an increase in the edge localized mode (ELM) amplitude and frequency. The changing ELM characteristics make a determination of the intrinsic isotopic and neutral beam effect on confinement difficult. For values of BT < 0.9 T and q95 < 3, the confinement quality in the deuterium and hydrogen/deuterium H-modes deteriorated to values near the L-mode level. This deterioration in energy confinement was not related to operation at high beta but instead appears to be due to a combined action between sawteeth and ELMs that becomes more pronounced at low q and low BT. L-mode energy confinement was independent of ion species and in good agreement with Kaye-Goldston scaling. Odajima-Shimomura scaling disagreed with the present L-mode τE data in terms of isotopic mass dependence; their prediction for the hydrogen L-mode exceeds the present measurements by a factor of two.

Fusion Nuclear Science Facility Candidates

Abstract To move to a fusion DEMO power plant after ITER, a Fusion Nuclear Science Facility (FNSF) is needed in addition to ITER and research in operating tokamaks and those under construction. The FNSF will enable research on how to utilize and deal with the products of fusion reactions, addressing such issues as how to extract the energy from neutrons and alpha particles into high-temperature process heat streams to be either used directly or converted to electricity, how to make tritium from the neutrons and lithium, how to deal with the effects of the neutrons on the blanket structures, and how to manage the first wall surface erosion caused by the alpha particle heat appearing as low-energy plasma fluxes to those surfaces. Two candidates for the FNSF are considered in this paper: normal and low aspect ratio copper magnet tokamaks. The methods of selecting optimum machine design points versus aspect ratio are fully presented. The two options are compared and contrasted; both options appear viable.

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.

A fusion development facility on the critical path to fusion energy

A fusion development facility (FDF) based on the tokamak approach with normal conducting magnetic field coils is presented. FDF is envisioned as a facility with the dual objective of carrying forward advanced tokamak (AT) physics and enabling the development of fusion energy applications. AT physics enables the design of a compact steady-state machine of moderate gain that can provide the neutron fluence required for FDFs nuclear science development objective. A compact device offers a uniquely viable path for research and development in closing the fusion fuel cycle because of the demand to consume only a moderate quantity of the limited supply of tritium fuel before the technology is in hand for breeding tritium.

Confinement and stability of VH mode discharges in the DIII-D Tokamak

A regime of very high confinement (VH-mode) has been observed in neutral beam-heated deuterium discharges in the DIII-D tokamak with thermal energy confinement times up to [approx]3.6 times that predicted by the ITER-89P L-mode scaling and 2 times that predicted by ELM-free H-mode thermal confinement scalings. This high confinement has led to increased plasma performance, n[sub D] (0)T[sub i](0)[tau][sub E] = 2 [times] 10[sup 20] m[sup [minus]3] keV sec with I[sub p] = 1.6 MA, B[sub T] = 2.1 T, Z[sub eff] [le] 2. Detailed transport analysis shows a correspondence between the large decrease in thermal diffusivity in the region 0.75 [le] [rho] [le] 0.9 and the development of a strong shear in the radial electric field in the same region. This suggests that stabilization of turbulence by sheared E [times] B flow is responsible for the improved confinement in VH-mode. A substantial fraction of the edge plasma entering the second regime of stability may also contribute to the increase in confinement. The duration of the VH-mode phase has been lengthened by feedback controlling the input power to limit plasma beta.