% % FN: modified 5/00 for sendin to review % % ast5. -RLM % % Note use of the rotating package (pages and ) % \documentclass[12pt,twoside]{article} \usepackage{aries_art} \usepackage{ariesref} \usepackage{epsfig} \usepackage{cite} \usepackage{xspace} \hyphenation{ARIES-ST} \hyphenation{ARIES-RS} \hyphenation{DIII-D} \newcommand{\N}{\phantom{-}} \newcommand{\Z}{\phantom{0}} \newcommand{\D}{\phantom{.0}} \newcommand{\DT}{\hbox{D--T}\xspace} \newcommand{\DD}{\hbox{D--D}\xspace} \newcommand{\DHe}{\hbox{D--$^3$He}\xspace} \newcommand{\SdegC}{$\,^\circ$C\xspace} \newcommand{\AST}{\hbox{ARIES-ST}\xspace} \newcommand{\AI}{\hbox{ARIES-I}\xspace} \newcommand{\X}{\times} \newcommand{\NB}{Nb$_3$Sn} \begin{document} \title{\bf ARIES-ST DESIGN POINT SELECTION} \author{Ronald L. Miller\\ Fusion Energy Research Program, University of California, San Diego, CA \\ and the ARIES Team } \date{} \maketitle \begin{abstract} The spherical tokamak (ST) regime of low-aspect-ratio tokamak operation has provided an opportunity to consider a 1,000-MWe(net) \DT power plant conceptual design, designated ARIES-ST. Physics attributes include high beta ($\sim 50\%$) together with high bootstrap current contribution ($\sim 95\%$). Neutral-beam current drive ($\sim 28$~MW) supports steady-state operation. The plasma aspect ratio was selected to be $A \simeq 1.6$ leading to the choice of major plasma toroidal radius, $R_T=3.2$~m and plasma half-width, $a=2.0$~m. The usual engineering considerations of providing an efficient thermal power cycle (gross efficiency $\simeq 45\%$), while handling first-wall ($\sim 1$~MW/m$^2$) and divertor-plate ($\sim 5$~MW/m$^2$) surface heat fluxes, leads to 14-MeV neutron wall loads near 4.1~MW/m$^2$ (average) and 5.6~MW/m$^2$ (peak at outboard mid-plane) in a dual (PbLi and He) coolant system. The water-cooled toroidal-field-coil (TFC) centerpost is protected by a 20-cm (inboard) shield that does not breed tritium. Joule dissipation in the TFC system provides the major contribution to the plant recirculating power; specifically, Cu centerpost (222~MW), Al outboard shell (47~MW), Cu leads (27~MW), and power supplies (33~MW). The overall plant recirculating power fraction is an uncomfortable 34\%. For a plant capacity factor $\sim 76\%$, consistent with earlier ARIES studies, the COE is projected to be $\sim 84$~mill/kWeh (1992 constant dollars), using similar unit-cost assumptions and some passive-safety cost credits. Inclusion of additional credits for advanced, low-unit-cost manufacturing based on plasma spray and related techniques (as applied to the TFC centerpost and outboard TFC shell only) lowers this COE estimate to $\sim 79$~mill/kWeh. \end{abstract} \newpage \section{Introduction} \label{s-1} Interest in the spherical tokamak (or spherical torus, ST) concept~\cite{Pen95a} is motivated by the potential for high-beta ($\beta \equiv$ ratio of plasma pressure to confining magnetic-field pressure) operation with high self-generated bootstrap-current fractions, $f_{BC} \simeq 1$. The emerging physics basis~\cite{Gry98}, together with an engineering embodiment of the fusion power core (FPC) of the ST allows a conceptual projection of a 1,000~MWe(net)-class, deuterium-tritium (\DT) fueled, central-station electric power plant. As is the case with most conceptual fusion power-plant projections, a plasma physics model is coordinated with an engineering embodiment of the FPC sufficient to establish a power flow model in the context of a central-station power cycle. A cost estimate is projected and used as a figure-of-merit in trade studies meant to steer the design in optimal directions and resolve certain configurational decisions and subsystem choices. The present work builds upon earlier consideration of a Low-Aspect-Ratio (LAR) candidate considered in the STARLITE study~\cite{Sta97}. A previous, comprehensive study~\cite{Mil86} of this concept assumed physics and current-drive characteristics prior to the availability of the emerging database. The primary tool for the integration of physics, engineering, and costing aspects of magnetic-fusion power-plant is the ARIES Systems Code (ASC). Some features of the profile-averaged (0-dimensional), steady-state power-balance model used in the ASC are summarized in the next section as prelude to the engineering characterization of the ST fusion power core (FPC). A description of the ST power-plant design space leads to the selection of a reference design point, which was subjected to more detailed analysis by the ARIES Team. Results of some sensitivity studies are presented to highlight the key cost drivers. \section{Physics Aspects} \label{s-2} {\bf Plasma Equilibrium.} The ST plasma equilibrium has been examined separately~\cite{Jardin00} with a view toward maximizing the available beta (ratio of plasma pressure to confining magnetic-field pressure). This examination has produced a series of discrete cases representing three values of plasma toroidal aspect ratio, $A$, in the range of interest. The $\beta$ value has been found to scale as the inverse square root of $A$. Three values of $A$ (1.4, 1.6, and 1.8) illustrate the physics performance of the ST. The $A=1.6$ case was identified as ``near optimum'' with the other cases acting as bracketing outliers. The $A=1.6$ case itself was considered at three levels: 1) high-beta (including ``squareness'' in the plasma shaping, as with the other aspect-ratio cases), 2) a reference case (without squareness, consistent with modeled poloidal-field-coil performance) at somewhat lower beta, and 3) a subcase with no stabilizing wall, forced to use lower plasma elongation, resulting in lower beta. Relative to the conventional tokamak plasma at typically higher aspect ratio, the ST plasma accesses higher values of normalized beta, $\beta_N$, due to the favorable impact of increased magnetic shear in the edge plasma and the suppression of ballooning modes~\cite{Jardin00}. {\bf Plasma Profiles.} The following forms are assumed for the minor-radial density profiles for all species, the temperature profile for all thermal species, and the toroidal current-density profile: % \begin{eqnarray} \label{e-1} n(x) & = & (n_o - n_s)(1 - x)^{\alpha_n} + n_s\:, \\ \label{e-2} T(x) & = & T_o(1 - x)^{\alpha_T}\:, \\ \label{e-3} j_\phi(x) & = & j_o(1 - x)^{\alpha_J} \:; \end{eqnarray} % where $x\equiv (r/r_p)^2$ and the $\alpha$s are fitting constants. A non-zero edge density, $n_s$, is included to lower the peak heat flux and plasma temperature at the divertor plate, but the presence of this density pedestal has been found to lower the efficiency of RF current drive. The profile inputs to the ASC for \AST\ designs at representative values of plasma aspect ratio, $A \equiv R_T/a_p$, are summarized in \hbox{Table~\ref{t-1}} ($R_T$ is the major toroidal plasma radius and $a_p$ is the plasma half-width in the equatorial plane). These cases span a range of plasma aspect ratio $1.4 < A \equiv R_T/a_p < 1.8$ of interest to the present study. This range is somewhat higher than the the $A = 1.25$ case considered in the STARLITE study~\cite{Sta97}. As will be seen below, the $A = 1.6$ case is the reference \AST\ choice. Difficulties in incorporating a poloidal-field-coil (PFC) set that provides the higher-order ``squareness'' contribution to plasma shaping were identified, so this variant was dropped. The case with no stabilizing wall was found to provide insufficient plasma beta and was also not emphasized. % {\bf Plasma Beta.} The plasma-surface-averaged poloidal magnetic field, \hbox{$B_{\theta} \equiv \bar B_{\theta}(r_{p})$}, is produced by the plasma toroidal current, $I_\phi$, and is given by % \begin{eqnarray} \label{e-4} B_{\theta} & = & \frac{\oint B_{\theta} \, d\ell}{\oint \, d\ell} \: = \: \frac{\mu_{o} I_{\phi}}{2\pi a_p S} \: , \end{eqnarray} % where $\mu_o = 4\pi \times 10^{-7}$ H/m is the permeability of vacuum. The toroidal magnetic field, produced by external toroidal-field (TF) coils, provides the primary confining field for the plasma pressure, $p$, in a tokamak. The on-axis toroidal magnetic-field strength is \hbox{$B_\phi(R_T) \equiv B_{\phi o}$}, the toroidal beta is \hbox{$\beta \equiv 2\mu_o p/B^2_{\phi o}$}, and the poloidal beta is \hbox{$\beta_{\theta} \equiv 2\mu_o p/B^2_{\theta}$}. The plasma-edge safety factor, $q$, is approximated by % \begin{eqnarray} \label{e-5} q & = & \frac{2\pi}{\mu_0} C_q \, \frac{a_p\, B_{\phi o}}{I_\phi} \, \frac{\epsilon}{\left(1 - \epsilon^2\right)^2} \, S^2 \: , \end{eqnarray} % where the coefficient \hbox{$C_q \equiv C_q(\epsilon\beta_\theta, q) \approx 1$}. The plasma shape factor, $S$, represents the ratio of the length of the perimeter of the shaped (including elongation, triangularity, squareness) plasma to the perimeter of a circular plasma with the same value of $a_p$. The value of S is dominated by elongation, $\kappa$, such that \hbox{$S\approx (1 + \kappa^2)/2$}. The inputs to the ASC equilibrium model are derived from equilibrium and stability results, and are summarized in \hbox{Table~\ref{t-2}}. From this set of physics results, the intermediate $A = 1.6$ case was selected to provide representative performance. The reference (final) \AST\ case does not invoke ``squareness'' in the plasma shaping, such that the value of beta is somewhat reduced. Wall stabilization of certain potential instabilities is invoked to raise the level of accessible beta values. Operation at some stand-off from the beta limit (here 90\%) is invoked to reduce the probability of plasma disruptions, seen as an important operational concern for tokamaks, generally. {\bf Power Balance.} The plasma particle- and power-balance module used in the ASC is based on the zero-dimensional (0-D), steady-state MakNTAU\cite{Wer89,Wer91} code. The model used in this module is summarized in this subsection with a detailed description given in Ref.~\cite{Wer89}. Profile effects are included in the model through radial averages over the profiles given by \hbox{Eqns.~(\ref{e-1})-~(\ref{e-3})}. The steady-state, zero-dimensional ion and electron power balance equations, written in terms of power density, are given by % \begin{eqnarray} \label{e-6} p_{CP_{i}} + p_{H_{i}} & = & p_{TR_{i}} + p_{ie}\:, \\ \label{e-7} p_{CP_{e}} + p_{H_{e}} + p_\Omega + p_{ie} & = & p_{TR_{e}} + p_{BR} + p_{CY} + p_{LINE}\:. \end{eqnarray} % The charged-particle fusion-product power density, $p_{CP}$, is calculated by summing over \DHe, \DD, and \DT fusion reactions. The power density deposited in the ions and electrons, $p_{CP_{i}}$ and $p_{CP_{e}}$, respectively, (assuming a specified prompt loss fraction) is calculated through a time integral of the slowing down rate of a test particle against the background ions over the time for the test particle to thermalize. The heating power densities provided by sources external to the plasma are % \begin{eqnarray} \label{e-8} p_{H_{i}} & = & {p_{CP} \over Q_{p}}f_{H_{i}}\:, \\ \label{e-9} p_{H_{e}} & = & {p_{CP} \over Q_{p}}(1 - f_{H_{i}})\:. \end{eqnarray} % The fractional heating power going to the ions, $f_{H_{i}}$, and the plasma gain, $Q_p\equiv P_{CP}/P_H$, are input from other plasma engineering modules. The term that partitions energy between the ions and electrons is given by $p_{ie}$. The transport energy losses are characterized by ion and electron energy confinement times: % \begin{eqnarray} \label{e-10} p_{TR_{i}} & = & \frac{3}{2}k n_i~T_i/\tau_{E_{i}} \:, \\ \label{e-11} p_{TR_{e}} & = & \frac{3}{2}k n_e~T_e/\tau_{E_{e}} \:. \end{eqnarray} % where \hbox{$k=1.6021 \times 10^{-19}$~J/eV}. The total transport energy confinement time is given by % \begin{eqnarray} \label{e-12} \tau_E & = & \frac{n_iT_i + n_eT_e} {(n_{i}T_{i}/\tau_{E_{i}}) + (n_{e}T_{e}/ \tau_{E_{e}})}\:, \end{eqnarray} % and a ratio of $\tau_{Ei}/\tau_{Ee} =1$ is assumed. The plasma-energy confinement time expressed in terms of the net heating power, \hbox{$P_{TR} \simeq P_{PH}(1-f_{RAD})$}, is % \begin{eqnarray} \label{e-13} \tau_E & = & \frac{W_p}{P_{PH} \left(1 - f_{RAD}\right)} \: . \end{eqnarray} % The ASC uses the particle- and power-balance calculations to establish the appropriate ion constituent fractions and the corresponding values of the Lawson parameter, $n_i \tau_E$, and $\tau_E$. Once $\tau_E$ is known, a comparison can be made to any of a number of proposed empirical scaling laws~\cite{Ite89,Uck89}. It should be emphasized that a scaling law is not needed to derive any of the ARIES design points; $\tau_E$ is determined from the specification of $P_E$ and $Q_p$ that is set by the power requirements of the current-drive system. The value of $\tau_E$ required for a design point is compared to the various empirical scaling laws by means of a confinement multiplier, \hbox{$H_j \equiv \tau_E/\tau^j_E$}, where the superscript $j$ denotes the particular scaling of interest. The standard scaling law used for comparison is the ITER-89P scaling~\cite{Pos90} and is given by % \begin{eqnarray} \label{e-14} \tau^{89P}_E & = & \frac{3.8033\X 10^{-6} I_\phi^{0.85} n_e^{0.1} B_{\phi 0}^{0.2} a^{0.3} R_T^{1.2} \kappa_\X^{0.5} A_i^{0.5}} {[P_{PH} (1-f_{RAD})]^{0.5}} \: , \end{eqnarray} % where $A_i$ is the atomic mass (2.5 for a nominal 50:50 fuel mixture of either \DT or \DHe). Bremsstrahlung provides the dominant plasma radiation loss channel, with cyclotron radiation being relatively small at the high betas and low magnetic-field strengths characteristic of the \AST. The plasma-core radiation fraction is given by % \begin{eqnarray} \label{e-15} f_{RAD} & \equiv & \frac{p_{BR} + p_{CY}}{p_{CP} + p_{H} + p_\Omega} \: . \end{eqnarray} % The core radiation fraction for the \AST\ plasma at \hbox{$T \simeq 16$~keV} with \hbox{$Z_{eff} \simeq 2$}, including the addition of Kr impurity, is $f_{RAD} \simeq 0.3$). {\bf Current Drive.} A neutral beam (NB) system provides steady-state current drive (CD) for the \AST\ with a beam energy, $E_B = 120$~keV. For purposes of the ASC, a scaling of NBCD efficiency, represented by $\gamma_B$, was developed~\cite{Mau99} for the ranges: $1.6 < Z_{eff} < 2.2$ and $8 < T_{e0} < 24$~keV. The figure-of-merit, $\gamma_B$, improves as $Z_{eff}$ increases and as central electron temperature, $T_{e0}$, increases. Efficient CD performance tends to favor higher plasma temperature, at the reduction of plasma density and fusion power density. The \AST\ benefits from a high bootstrap current fraction, $f_bc \simeq 0.95$. {\bf Operating Space.} Plasma operating contour (POPCON) plots have been generated for the \AST\ using the several empirical scaling relations. The results assuming the ITER-89P relation are shown in \hbox{Fig.~\ref{f-1}}. Thermally stable operation near $T_{i} \simeq 16$~keV is suggested by result; other scaling relations might shift this zone. A start-up trajectory from initially low values of density and temperature with an auxiliary heating input of $\sim 50$~MW is suggested by this operating space. The chord-averaged electron density relative to the Greenwald density limit is $\overline{n_e}/n_{GR} \simeq 0.75$ for the \AST. \section{Engineering Aspects} \label{s-3} A number of engineering considerations are incorporated into the ASC models of the ARIES-ST; these considerations interact with the plasma physics aspects to characterize the Fusion Power Core (FPC) and provide the basis for cost projections. Adequate tritium breeding is obtained from the outboard blanket provided that the Li in the LiPb eutectic is enriched to 60\% $^6$Li. {\bf Geometric Considerations.} To begin with, several geometric invariants related to the physics cases of {\hbox{Table~\ref{t-2}} (above) are summarized in {\hbox{Table~\ref{t-3}}. These results supercede those found in Table 2 of \hbox{Ref.~\cite{Mil97}}. A tight plasma aspect ratio can be expected to restrict the inboard radial build with several adverse consequences. These effects include a small-radius centerpost with high(er) current density and Joule dissipation as well as elimination of an inboard tritium-breeding blanket in favor of a thin shield. High plasma elongation increases the length of the centerpost and increases Joule dissipation. High plasma triangularity restricts the possibility of increasing the radius (flaring) the centerpost away from the plasma mid-plane to reduce current density and Joule dissipation. The peak-to-average ratio of the 14-MeV neutron wall varies slowly among the several combinations of $A$ and $\kappa$. The peak neutron wall load, occurring at the outboard (OB) mid-plane, is used to gauge the in-service lifetime of the first-wall and blanket structures. The ARIES-ST first-wall/blanket structural fluence lifetime, $\tau_{max}$, is taken to be 18MWa/m$^2$, corresponding to $\sim 200$~dpa, a value lower than the 20~MWa/m$^2$ used for the STARLITE LAR case~\cite{Sta97}. {\bf Toroidal and Poloidal Coils.} Rather than a set of discreet toroidal-field coils (TFCs) typically seen in conventional tokamaks, the \AST\ uses a water-cooled monolithic centerpost (CP) made from Cu alloy. The systems-level characterization of the CP is at the level of previous models~\cite{Sne89,Sta98}. The outboard return conductor is configured as a 0.70-m Al shell, rather than as discreet TFCs. The TFC components are operated as near-room-temperature resistive elements. The CP, at 110 \SdegC, has a resistivity of 2.64E-08 ohm-m and the Al outboard shell, at 65 \SdegC, has a resistivity of 2.64E-08 ohm-m. The conductor fractions of both components are 85 \%. Massive Cu-alloy TFC current leads attach to the TFC outboard shell near the equatorial plane and provide a heat sink under accident conditions. In normal operation, the Joule dissipation in these leads is $\sim 22$~MW. The TFC leads are sized using the scaling summarized in \hbox{Fig.~\ref{f-4}}. It is assumed that the TFC power supplies have internal dissipation consistent with a voltage drop equal to 1 Volt, resulting in an additional $\sim 33$~MW of dissipation as a component of recirculating power. The low-temperature superconducting (LTS) poloidal-field coils (PFCs) are located inside the TFC shell in the low-field \AST. This positioning improves the coupling to the plasma for purposes of shaping. The \AST\ does not have an ohmic-heating coil set due to the lack of space at low aspect ratio. {\bf Shielding Considerations.} The ARIES-ST uses a He-cooled steel inboard shield to capture useful thermal power, reduce the damage-induced resistivity growth of the Cu-alloy CP conductor, and aid in the meeting of shallow-burial (Class-C) waste-disposal criteria for the activated and expendable centerpost (CP). In a sense, a thicker CP conductor occupying the same annular space provides a measure of self-shielding of the CP core, but does not contribute to the power conversion cycle and adds to the radioactive waste stream. As shown in \hbox{Fig.~\ref{f-2}}, a bare (unshielded) CP would typically experience a $\sim 14\%$ increase in resistive dissipation for an exposure of 20 MWa/m$^{2}$ compared to $\sim 7\%$ increase for a CP protected by a 0.30-m-thick inboard shield/manifold. Damage to the CP occurs in an outer annular region with a thickness of a few tens of centimeters corresponding to a few neutron mean free paths; a radial an axial integration gives a volumetric average and a time average for the service life, $\tau$, is used to represent the degraded performance terminated by CP replacement at $\sim 3$ full power years (FPY). The plant capacity factor, $p_{f}$, of course, characterizes the number of FPYs accumulated per calendar year (CY). Pending a more detailed availability and maintenance study, a nominal value, $p_{f} \simeq 0.76$, is assumed in the COE projections. {\bf Power Flow.} The power flow, as modeled in the ASC, is illustrated in \hbox{Fig.~\ref{f-3}} for \AST. Given a stipulated target for the net electric-power output, $P_E$, the thermal-power output, $P_{TH}$, is determined for a nominal value of the thermal conversion efficiency, $\eta_{TH}$, such that \hbox{$P_E = \eta_{TH} (1-\epsilon) P_{TH}$}, where \hbox{$\epsilon = 1/Q_E$} is the recirculating power fraction and \hbox{$Q_E \equiv P_{ET}/P_C$} is the engineering $Q$-value. The gross electric-power output is \hbox{$P_{ET} = \eta_{TH} P_{TH}$}. A fraction $f_{AUX}=0.04$ of $P_{ET}$ ($P_{AUX} = f_{AUX} P_{ET}$) is allocated for auxiliary functions. A fraction $f_{pump}$ of $P_{ET}$ (\hbox{$P_{pump} = f_{pump} P_{ET}$}) is allocated for primary-loop pumping power. The engineering gain, $Q_E$, can be written as % \begin{eqnarray} \label{e-16} Q_E & = & \frac{1}{\epsilon} \: = \: \eta_{TH} \: \frac{M_N \, P_N + P_{CP} + P_{H} + P_{\Omega} + 0.90 \, P_{pump}} {P_{TFC} + P_{AUX} + P_{pump} + \left(P_{CD}+P_{AH}\right)/ \eta_{CD}} \: . \end{eqnarray} % The gross thermal conversion efficiency, $\eta_{TH}$, is 45\% for the \AST. The neutron energy multiplication, $M_N$, is found from neutronics modeling to be $\sim 1.11$ and is used to determine the useful thermal power, $P_{TH}$, recovered from the blanket, divertors, and high-temperature shields. It is assumed that \hbox{$0.98\, P_{pump}$} is recoverable as useful thermal power in the primary coolant loop. \section{Systems Assessment} \label{s-4} The role of systems analysis for the \AST\ power plant is to identify high-leverage parameters affecting the conceptual design. Representative values for parameters of the fusion power core (FPC) that minimize the projected cost-of-electricity (COE) are identified with reasonable self-consistency. {\bf Systems Models.} The plasma equilibrium ({\it e.g.}, magnetic topology, $\beta$, {\it etc.}), current-drive, and other physics models are based upon the analyses of the equilibrium provided by the Physics effort. Together with the approximate engineering models, the \AST\ fusion power core is characterized in sufficient detail to provide a conceptual design. A cost breakdown structure (CBS) provides the basis for a direct cost estimate, consistent with previous ARIES and other studies. Scaling estimates for building volumes and other balance of plant (BOP) items are used. The ASC costing algorithms limit the capacity of a single turbine to 1,360~MWe. For the same target electrical output of 1.0 GWe(net) as previous ARIES designs, the gross electrical power, $P_{ET}$, of the ARIES-ST exceeds this threshold, requiring two turbine-generator sets at reduced capacity. Extrapolation of the single-turbine scaling to larger units (consistent with large, recent fission plants) results in the savings of $\sim 3$~mill/kWeh in the COE values reported here. Space constraints preclude a full exposition of the cost database here. Unit costs for the FPC components are derived from recent ARIES studies. Since the \AST\ coil configuration is unconventional, it is appropriate to report the coil costing basis in {\hbox{Table~\ref{t-4}}. Using consensus financial assumptions, total capital costs are calculated and the Cost of Electricity (COE, mill/kWeh) is projected. Assumptions include a plant factor, $p_f \simeq 0.76$, and a six-year construction lead time. All costs are reported in 1992 dollars. The base configuration of the \AST\ fusion power core (FPC) is shown in \hbox{Fig.~\ref{f-5}}. The inboard first wall conforms to a flux surface and serves as a limiter to the plasma surface inboard of the null. Vertical space is provided above the null for a divertor chamber that captures the plasma exhaust from the outboard plasma surface. The centerpost cross section expands above the equatorial plane as allowed by the first wall and inboard shield to provide maximum shaping of the centerpost conductor in order to reduce coil current density and Joule dissipation. The \AST\ CP is not up-down symmetric; the flaring of the upper end has been incorporated into the Al outboard shell to allow a lowering of the CP separate from the other FPC components. This tapered CP is not trapped by the inboard shield annulus. {\bf Design Survey.} The most basic design parameter is the physical size of the tokamak. Typically, the ASC determines the plasma minor radius that minimizes the cost of electricity (COE) for a specified plasma aspect ratio and ion temperature with an internal scan of minor radius. The COE for the \AST\ might be expected to display a minimum in minor radius resulting from the trade-off of maximizing the Fusion Power Core (FPC) mass power density (MPD) and of maximizing the engineering gain ($1/\epsilon$, where $\epsilon$ is the recirculating power fraction). Decreasing the plasma minor radius decreases the blanket, shield, and coil masses and increases the MPD. For an ST-based power plant, the centerpost dissipation dominates the recirculating-power losses that determine the engineering gain. Decreasing the plasma minor radius increases the ohmic dissipation in the resistive TF coils, because the centerpost cross-sectional area decreases with decreasing plasma minor radius, and the centerpost resistance and ohmic dissipation then increase. Determination of a self-consistent PFC configuration may inhibit the realization of this minimum-COE design point. For the fixed plasma aspect ratio, $A \equiv R_T/a_p$, cases of Tables 1-3, plasma minor radius, $a_p$, is used by the ASC as a marching variable. Results are summarized in \hbox{Fig.~\ref{f-6}}. {\bf Design Point Determination.} The selection of the \AST\ design point is summarized in the results of \hbox{Fig.~\ref{f-7}}. The resolution of the plasma-aspect-ratio cases is coarse such that it is not practical to identify minimum-COE performance in the vicinity of $A = 1.6$, which is taken as the baseline case. The reference \AST\ major plasma radius was taken to be $R_T = 3.2$ m. Summary lists of parameters for the reference design used in the systems analysis are given in Tables~\ref{t-5} through \ref{t-7}. This final design point superceeds the interim results of Refs.~\cite{Mil98,Mil99a,Mil99b}. The confinement-time enhancement factors, $H$, reported in Table~\ref{t-5} are calculated from empirical scaling relations derived from a database emphasizing conventional tokamaks. Since not enough information is available to characterize a ST-specific transport scaling, the $H$ factors reported here should be considered suggestive only. Level of Safety Assurance (LSA) factors have been used to give credit to fusion systems for improvements related to passive safety~\cite{Hol88}. Nuclear systems without such credits reflect N-stamp costs consistent with present fission power plants (LSA = 4). At the other end of this scale, LSA = 1 represents non-nuclear (fossil) costs. ARIES-ST has been designated to achieve LSA = 2. The COE values for the four LSA cases are summarized in \hbox{Table~\ref{t-8}} assuming conventional unit costs and again in \hbox{Table~\ref{t-9}}, assuming the low-unit-cost advanced manufacturing~\cite{Wag99} is applied to the Cu TF centerpost and outboard Al TF shell. These large components would be fabricated on-site. The periodic need for replacement centerposts implies the regular fabrication of these items. {\bf Sensitivities.} The sensitivity of the $A = 1.6$ \AST\ projected COE to the assumed thickness of the inboard shield, $\Delta_{Si}$, is illustrated in \hbox{Fig.~\ref{f-8}}. Not shown in these results is the increased resistivity growth for shields thinner than the reference case ($\Delta_{Si} = 0.20$ m) that would increase the Joule dissipation and penalize the COE. The sensitivity of the $A = 1.6$ \AST\ projected COE to average first-wall 14-MeV neutron wall load is illustrated in \hbox{Fig.~\ref{f-9}}. For fixed net electrical power output, $P_E = 1.0$ GWe, higher (lower) wall loads occur as the FPC size is reduced (increased). The trade-off between recirculating power and mass power density results in a nearly flat COE. {\bf Superconducting TFC.} The \AST\ study concentrated on the resistive TFC embodiment. The conventional wisdom has been that for ST systems with tight plasma aspect ratio, $A$, there would be insufficient space on the inboard side to provide adequate shielding (1-1.5 m) of the inboard TFC legs, assuming conventional low-temperature-superconductor (LTS) TFCs. The ASC was not able to ``run to completion'' and solve for a self-consistent FPC in this range of inboard shield thicknesses. At about 0.5 m, however, a case was found that is generally consistent with this conventional wisdom. Despite the fact that there is the possibility of trading the additional direct cost of a LTS TFC against the costs associated with recirculating power in the resistive system, even this optimistic LTS ST is seen to be less competitive than the range of resistive STs shown in \hbox{Fig.~\ref{f-10}}. The large LTS-ST FPC is also noted to be incompatible with the \AST\ vertical maintenance scheme. No engineering attention was applied to this LTS ST case. \section{Summary and Conclusions} \label{s-5} Work on the \AST\ extends the preliminary assessment of the low-aspect-ratio case considered in the STARLITE Study for a 1-GWe(net) \AST. The interaction of engineering considerations with a broader set of physics cases suggests consideration of a plasma aspect ratio near $A = 1.6$, in part to accommodate a thin inboard shield. Joule dissipation on the resistive TF-coil results in an uncomfortably large recirculating power fraction. The application of advanced, low-unit-cost manufacturing techniques seems particularly well suited to the TF-coil centerpost and outer TF-coil shell to help offset the costs associated with high recirculating power. Access to higher beta would allow additional performance improvements. \section*{Acknowledgments} \label{s-6} This work was supported by the US Department of Energy, Office of Fusion Energy Sciences. Useful discussions with C. G. Bathke (LANL) and K. A. Werley (LANL) are acknowledged gratefully. %FIGURES... \clearpage \begin{figure} \centerline{\epsfig{file=ast-3-01.ps,height=5in}} \vskip0.75in \caption[fig-1] {ARIES-ST Plasma Operating Contour (POPCON) diagram. Solid contours indicate auxiliary heating power,$P_{AUX}$, in increments of 10~MW until ``ignition'' ($P_{AUX} = 0$) at the dashed contours.} \label{f-1} \end{figure} % \begin{figure} \centerline{\epsfig{file=ast-3-02.ps,height=5in}} \vskip0.75in \caption[fig-2] {Dependence of typical ST centerpost (CP) resistive power dissipation growth due to neutron-induced damage/transmutation (resistivity growth) and current profile redistribution as a function of exposure for representative cases (straight {\it versus} flared and bare {\it versus} shielded). } \label{f-2} \end{figure} % \begin{figure}[p] \centerline{\epsfig{file=ast-3-03.ps,width=6in}} \vskip0.75in \caption[fig-3] {Overall \AST\ power-flow diagram used in the ASC. Values of powers are given in~MW. Minor differences between the entries on this figure and those of Tables 5,6 may exist.} \label{f-3} \end{figure} % \begin{figure}[p] \centerline{\epsfig{file=ast-3-04.ps,height=5in}} \vskip0.75in \caption[fig-4] {Power-dissipation and mass trade-off of the \AST\ TF-coil resistive leads, comparing aluminum to the reference copper case.} \label{f-4} \end{figure} % \begin{figure}[p] \centerline{\hskip 2.in \epsfig{file=ast-3-05.ps,height=6in}} \caption[fig-5] {Elevation view of the \AST\ fusion power core.} \label{f-5} \end{figure} \begin{figure}[p] \centerline{\epsfig{file=ast-3-06.ps,height=5in}} \caption[fig-6] {Projected Cost of Electricity (COE) as a function of major toroidal radius, $R_T$, for 1-GWe(net) ARIES-ST power plants with plasma aspect ratio, $A = R_T/a_p$, invoking advanced (``low-cost'') manufacturing techniques {\it cf.} Ref.~\cite{Wag99}. The reference ARIES-ST with $A = 1.6$ and $R_T = 3.2$ m is indicated by the open circle. The smallest accessible value of $R_T$ with slightly reduced COE and higher power density and higher wall loads is indicated by the open triangle.} \label{f-6} \end{figure} \begin{figure}[p] \centerline{\epsfig{file=ast-3-07.ps,height=5in}} \caption[fig-7] {Projected Cost of Electricity (COE) as a function of major toroidal radius, $R_T$, for 1-GWe(net) ARIES-ST power plants with plasma aspect ratio, $A = 1.6$, comparing the impact of conventional (``conv'') unit costs for the toroidal-field-coil system with advanced (``low'') manufacturing techniques {\it cf.} Ref.~\cite{Wag99}. The reference ARIES-ST with $R_T = 3.2$ m is indicated by the open circle.} \label{f-7} \end{figure} \begin{figure}[p] \centerline{\epsfig{file=ast-3-08.ps,height=5in}} \caption[fig-8] {Sensitivity of the projected Cost of Electricity (COE) of the 1-GWe(net) ARIES-ST power plant with plasma aspect ratio, $A = 1.6$ to the thickness of the inboard shield, $\Delta_{Si}$. The penalty of additional neutron-damage-induced CP resistivity growth is not included for the thinner shields. The reference ARIES-ST with $\Delta_{Si} = 0.20$ m is indicated by the open square.} \label{f-8} \end{figure} \begin{figure}[p] \centerline{\epsfig{file=ast-3-09.ps,height=5in}} \caption[fig-9] {Sensitivity of the projected Cost of Electricity (COE) of the 1-GWe(net) ARIES-ST power plant with plasma aspect ratio, $A = 1.6$ to the average first-wall neutron load, $I_w (MW/m^2)$. The reference ARIES-ST at $R_T = 3.20$ m is indicated by the open square.} \label{f-9} \end{figure} \begin{figure}[p] \centerline{\epsfig{file=ast-3-10.ps,height=5in}} \caption[fig-10] {Comparison of an optimistic, thin-inboard-shield ST power plant with $A = 1.6$ using low-temperature superconducting (LTS) toroidal-field-coil technology, indicated by the diamond, with the resistive-coil ARIES-ST design window.} \label{f-10} \end{figure} %TABLES... \clearpage \begin{table} \caption{} \centering{\bf Plasma Radial Profile Inputs to the ASC$^{\ast}$} \vspace{1.0cm} \renewcommand{\arraystretch} {1.30} \begin{tabular} {l c c c c c}\hline Aspect ratio, $A \equiv R_T/a_p$ & 1.4 &\multicolumn{3}{c}{1.6} & 1.8 \\ \cline{3-5} Footnote: & (a) & (a) & (b) & (c) & (a) \\ \hline \\ Peak-to-average pressure, $p_0/p(=n_0T_0/nT)$ & 1.373 & 1.385 & 1.404 & 2.004 & 1.390 \\ Peak-to-average density, $n_0/n$ & 1.218 & 1.220 & 1.230 & 1.803 & 1.222 \\ Separatrix-to-average density, $n_s/n$ & 0.05 & 0.05 & 0.05 & 0.05 & 0.05 \\ \\ \hline \multicolumn{6}{l}{$^{\ast}$ Corresponding to cases summarized in Table 2.}\\ \multicolumn{6}{l}{$^{(a)}$ High-beta series, including ``squareness'' in plasma shaping.}\\ \multicolumn{6}{l}{$^{(b)}$ Final beta case, without ``squareness''.}\\ \multicolumn{6}{l}{$^{(c)}$ No stabilizing wall.}\\ \end{tabular} \label{t-1} \end{table} \begin{table} \caption{} \centering{\bf Plasma Equilibrium Inputs to the ASC} \vspace{1.0cm} \renewcommand{\arraystretch} {1.30} \begin{tabular} {l c c c c c}\hline $A \equiv R_T/a_p$ & 1.4 &\multicolumn{3}{c}{1.6} & 1.8 \\ \cline{3-5} Footnote: & (a) & (a) & (b) & (c) & (a) \\ \hline %\hline \hspace{1.75 truein} & \hspace{1.75 truein} & \hspace{.75 truein} & %\hspace{1.75 truein} \hspace{.75 truein}\\ Plasma elongation, $\kappa_\times$ & 3.60 & 3.40 & 3.40 & 3.10 & 3.20 \\ Plasma triangularity, $\delta_\times$ & 0.644 & 0.644 & 0.644 & 0.720& 0.644 \\ On-axis safety factor, $q_o$ & 4.51 & 4.48 & 4.33 & 1.76 & 4.53 \\ Edge safety factor, $q$ &18.19 &10.65 &10.97 &22.21 & 7.84 \\ Circularized safety factor, $q_\ast$ & 2.97 & 2.73 & 2.87 & 3.14 & 2.63 \\ $\beta_N$ (\%) & 8.830 & 8.350 & 8.200 & 5.600& 7.830 \\ Toroidal beta, $\beta$ & 0.741 & 0.601 & 0.560 & 0.296& 0.465 \\ Toroidal beta, $\beta$$^{(d)}$ & 0.667 & 0.541 & 0.504 & 0.266& 0.419 \\ Poloidal beta, $\beta_\theta$$^{(d)}$ & 1.653 & 1.694 & 1.697 & 1.266& 1.668 \\ Stability parameter, $\epsilon\beta_\theta$ & 1.181 & 1.059 & 1.061 & 0.791& 0.927 \\ Bootstrap-current fraction, $f_{bc}$ & $\sim$1& $\sim$1 & $\sim$1 & 0.9 & $\sim$1 \cr %Troyon coefficient, $C_T$ (Tm/MA) & & & & & \\ %Scaling coefficient, $C_q$ & & & & & \\ $I_{TF}/I_{p}$ & 0.835 & 1.111 & 1.172 & 1.515& 1.516 \\ \\ \hline \multicolumn{6}{l}{$^{(a)}$ High-beta series, including ``squareness'' in plasma shaping.}\\ \multicolumn{6}{l}{$^{(b)}$ Final beta case, without ``squareness''.}\\ \multicolumn{6}{l}{$^{(c)}$ No stabilizing wall.}\\ \multicolumn{6}{l}{$^{(d)}$ Including disruption-avoidance margin (0.9).}\\ \end{tabular} \label{t-2} \end{table} \clearpage \begin{table}[p] \caption{} \centering{\bf ARIES-ST Engineering Invariants} \vspace{1.0cm} \renewcommand{\arraystretch} {1.30} \begin{tabular} {l c c c c c}\hline $A \equiv R_T/a_p$ & 1.4 &\multicolumn{3}{c}{1.6} & 1.8 \\ \cline{3-5} Footnote & (a) & (a) & (b) & (c) & (a) \\ \hline %\hline \hspace{1.75 truein} & \hspace{1.75 truein} & \hspace{.75 truein} & %\hspace{1.75 truein} \hspace{.75 truein}\\ Plasma elongation, $\kappa_\times$ & 3.60 & 3.40 & 3.40 & 3.10 & 3.20 \\ Plasma triangularity, $\delta_\times$ & 0.644 & 0.644 & 0.644 & 0.720 & 0.644 \\ %Toroidal beta, $\beta$ & 0.741 & 0.601 & 0.560 & 0.296 & 0.465 \\ $I_{TFC}/I_{p}$ & 0.835 & 1.111 & 1.172 & 1.515 & 1.516 \\ Neutron wall load (NWL)$^{\ast}$: & & & & & \\ \quad IB peak/Tot. avg. NWL & 0.871 & 0.887 & 0.891 & 0.933 & 0.901 \\ \quad OB peak/Tot. avg. NWL, $\hat I_w$/$I_w$ & 1.361 & 1.370 & 1.380 & 1.514 & 1.379 \\ \quad IB norm. avg. NWL & 0.584 & 0.611 & 0.613 & 0.600 & 0.639 \\ \quad IB avg./IB peak NWL & 0.670 & 0.689 & 0.688 & 0.643 & 0.709 \\ \quad OB norm. avg. NWL & 1.083 & 1.100 & 1.101 & 1.108 & 1.111 \\ \quad OB avg./OB peak NWL & 0.795 & 0.803 & 0.797 & 0.731 & 0.807 \\ \\ \hline \multicolumn{6}{l}{$^{(a)}$ High-beta series, including ``squareness'' in plasma shaping.}\\ \multicolumn{6}{l}{$^{(b)}$ Final beta case, without ``squareness''.}\\ \multicolumn{6}{l}{$^{(c)}$ No stabilizing wall.}\\ \multicolumn{6}{l}{$^{\ast}$ Inboard (IB) and outboard (OB) peaks occur at respective equatorial mid-planes.}\\ \end{tabular} \label{t-3} \end{table} \clearpage \begin{table}[p] \caption{} \centering{\bf Magnet-System Unit Costs (1992 \$)} \vspace{1.0cm} \renewcommand{\arraystretch}{1.3} \begin{tabular}{l c c}\hline Component & Mass Density & Unit Cost \\ & (kg/m$^3$) & (\$/kg)\\ \hline \\ Low-Temp. Superconductors (LTS)$^{(a,b)}$: \\ \quad Bi & 7,500 & 103.0 \\ \quad Ternary \NB\ & 7,500 & \Z97.8 \\ \quad \NB\ & 7,500 & \phantom{$^{(c)}$}\Z92.7$^{(c)}$ \\ \quad NbTi & 7,500 & \phantom{$^{(c)}$}\Z82.8$^{(c)}$ \\ Resistive Coils: \\ \quad Resistive Cu$^{(d,e)}$& 7,300 & \Z65.4 \\ \quad ARIES-ST Cu centerpost(CP)$^{(f)}$ & 7,565 & 7.05 \\ \quad ARIES-ST Al outer TFC shell$^{(f)}$ & 2,295 & 5.52 \\ \\ \hline \multicolumn{3}{l}{\parbox{5in}{$^{(a)}$ Compare with 6,462-7,108 $\,kg/m^{3}$ and $39-35 \, \$/kg$ for TFCs and 7,900 $\,kg/m^{3}$ and $62 \, \$/kg$ for PFCs, {\it cf.} STARFIRE~\cite{Bak80}.}}\\ \multicolumn{3}{l}{$^{(b)}$ Compare with 7,900 $\,kg/m^{3}$ and $111 \, \$/kg$, {\it cf.} GENEROMAK~\cite{Del88a}.}\\ \multicolumn{3}{l}{$^{(c)}$ Refs.~\cite{Tho88,Mil88,Bro89}.}\\ \multicolumn{3}{l}{$^{(d)}$ {\it cf.} TITAN~\cite{Naj90}.}\\ \multicolumn{3}{l}{$^{(e)}$ Compare with 7,900 $\,kg/m^{3}$ and $62 \, \$/kg$, {\it cf.} GENEROMAK~\cite{Del88a}.}\\ \multicolumn{3}{l}{$^{(f)}$ Ref.~\cite{Wag99}.}\\ \end{tabular} \label{t-4} \end{table} % \begin{table}[p] \caption{} \centering {\bf ARIES-ST Power-Plant Physics Parameters} \vspace{0.5cm} {\small \renewcommand{\arraystretch}{0.83} \begin{tabular}{l @{\hspace{1.0 truecm}} c} \hline \\ Plasma major toroidal radius, $R_T\rm (m)$ & 3.20\\ Plasma minor radius, $a_p\rm (m)$ & 2.00\\ Plasma vertical elongation: & \\ \quad $\kappa_\times$ & 3.40\\ \quad $\kappa_{95}$ & 3.75\\ Plasma triangularity: & \\ \quad $\delta_\times$ & 0.64\\ \quad $\delta_{95}$ & 0.67\\ Plasma aspect ratio, $A=R_T/a_p$ & 1.60\\ On-axis safety factor, $q_0$ & 4.33\\ Circularized safety factor, $q_\ast$ & 2.87\\ Plasma-edge safety factor, $q$ & 10.97\\ Troyon coefficient, $C_T$ (Tm/MA) & 0.07\\ Plasma beta, $\beta$ & 0.50\\ Plasma poloidal beta, $\beta_p$ & 1.70\\ Stability parameter, $\epsilon\beta_p$ & 1.06\\ Peak-to-average density, $n_0/n$ & 1.23\\ Peak-to-average temperature, $T_0/T$ & 1.14\\ normalized edge density, $n_E/n$ & 0.05\\ Ion temperature, $T_i\rm (keV)$ & 16.00\\ Electron temperature, $T_e\rm (keV)$ & 16.47\\ Ion density, $n_i(10^{20}/{\rm m}^3)$ & 1.41\\ Electron density, $n_e(10^{20}/{\rm m}^3)$ & 1.58\\ Particle-to-energy confinement time ratio, $\tau_p/\tau_E$ & 1.00\\ Ion-to-electron energy confinement time ratio, $\tau_{Ei}/\tau_{Ee}$& 1.00\\ Lawson parameter, $n_i\tau_E(10^{20}{\rm s}/{\rm m}^3)$ & 3.02\\ ITER-89P scaling~\cite{Pos90} multiplier, $H_{89P}$ & 3.00\\ ITER-98H scaling multiplier, $H_{98H}$ & 1.47\\ On-axis toroidal field, $B_{\phi 0}\rm (T)$ & 2.08\\ Radiation fraction, $f_{RAD}$ & 0.30\\ Plasma current, $I_p\rm (MA)$ & 28.49\\ Bootstrap-current fraction, $f_{BC}$ & 0.96\\ Current-drive power to plasma, $P_{CD}\rm (MW)$ & 27.79\\ Charge period, $\tau_C$ (h) & 0.00\\ Ramp/Quench period, $\tau_R/\tau_Q$ (s) & 0.00\\ Ignition period, $\tau_I$ (s) & 0.00\\ Burn period, $\tau_B$ (h) &664.80\\ Current-drive efficiencies: & \\ \quad $I_{EX}/P_{CD} (mA/W)$ & 43.42\\ \quad $\gamma (10^{20} A/W$-$m^2)$ & 5.22\\ \\ \hline \end{tabular} } \label{t-5} \end{table} \clearpage \begin{table}[p] \caption{} \centering {\bf ARIES-ST Power-Plant Engineering Parameters} \vspace{0.5cm} {\small \renewcommand{\arraystretch}{0.90} \begin{tabular}{l @{\hspace{2.0 truecm}} c } \hline \\ Field at TF coil, $B_{\phi c}\rm (T)$ & 7.43\\ centerpost resistive losses (MW) &\D\Z222 \\ Total TF resistive losses (MW) &\D\Z329 \\ %TF-coil stress (MPa) & 0.00\\ TF-coil current density, $j_{TF}$ (MA/m$^2$) & 7.77\\ Magnetic-field energy, $W_B$ (GJ) & 17.86\\ Total specific energy, $W_B/M_c$ (MJ/tonne) & 4.67\\ Fusion power, $P_F$ (GW) & 2.98\\ Neutron power, $P_N$ (GW) & 2.38\\ Average neutron wall load, $I_w$ (MW/m$^2$) & 4.10\\ Peak neutron wall load, $\hat I_w$ (MW/m$^2$) & 5.58\\ Neutron fluence life-FW/B, $I_w\tau$ (MW yr/m$^2$) & 18.00\\ %Neutron fluence life protection/extension factor-R/M & 0.00\\ Average blanket energy multiplication & 1.12\\ Average first-wall heat flux, $q_w(MW/m^2)$ & 0.33\\ Blanket power density, $P_{TH}/V_{BLK}$ (MW/m$^3$) & 4.78\\ Current-drive system efficiency, $\eta_{CD}$ & 0.68\\ Thermal conversion efficiency, $\eta_{TH}$ & 0.45\\ Thermal power, $\hat P_{TH}$ (GWth) & 3.37\\ %\quad peak, $\hat P_{TH}$ & 3.37\\ %\quad average, $P_{TH}$ & 3.37\\ Auxiliary site power, $P_{AUX}$ (MW) & 60.78\\ Primary loop pumping power (MW) & 91.18\\ Gross electrical power, $P_{ET}\rm (GWe)$ & 1.52\\ Net electrical power, $P_E\rm (GWe)$ & 1.00\\ Recirculating-power fraction, $\epsilon = 1/Q_E$ & 0.34\\ Plasma gain, $Q_p=P_F/P_{CD}$ &108.05\\ Engineering gain, $Q_E$ & 2.93\\ Net plant efficiency, $\eta_p = \eta_{TH} (1 - \epsilon)$ & 0.30\\ Plant capacity factor, $p_f$ & 0.76\\ Masses (tonne):&\\ \quad First wall & \D\Z\Z13 \\ \quad Blanket and reflector & \D\Z814 \\ \quad Shield & \Z2,545 \\ \quad TF coils & \Z2,904 \\ \quad PF coils & \D\Z919 \\ \quad PF-coil spares & 0 \\ \quad Fusion power core & \Z8,613 \\ Mass power density, MPD (kWe/tonne) & 54.97\\ Level of Safety Assurance, LSA & 2\\ \\ \hline \end{tabular} } \label{t-6} \end{table} \clearpage \begin{table}[p] \caption{} \centering {\bf ARIES-ST Power-Plant Economic Parameters (1992 \$)} \vspace{0.5cm} {\small \renewcommand{\arraystretch}{0.8} \begin{tabular}{l l @{\hspace{1.cm}} c} \hline Acct.\ No. & Account Title & Million Dollars \\ \hline \\ 20. & Land and land rights & \D\Z10.6\\ 21. & Structures and site facilities & \D370.8\\ 22. & Reactor plant equipment &1,224.1\\ 22.1.1 & \ \ First wall, Blanket, and Reflector & \D\Z50.2\\ 22.1.2 & \ \ Shield &\D113.1\\ 22.1.3 & \ \ Magnets &\D102.6\\ 22.1.3.1& \ \ \ TF-coil set & \D\Z16.0\\ 22.1.3.3& \ \ \ PF coils & \D\Z72.3\\ 22.1.4 & \ \ Supplemental heating systems &\D212.5\\ 22.1.5 & \ \ Primary structure and support & \D\Z37.4\\ 22.1.6 & \ \ Reactor vacuum systems & \D\Z48.1\\ 22.1.7 & \ \ Power supplies & \D\Z71.6\\ 22.1.8 & \ \ Impurity control (Divertor) & \D\Z\Z8.8\\ 22.1.9 & \ \ Direct energy conversion system & \D\Z\Z0.0\\ 22.1.10 & \ \ ECRH breakdown system & \D\Z\Z4.4\\ 22.1 & \ \ Reactor equipment &\D648.7\\ 22.2 & Main Heat Transfer and Transport &\D358.1\\ 22.[3-7]& \ \ Other &\\ 23. & Turbine plant equipment &\D339.6\\ 24. & Electric plant equipment &\D125.4\\ 25. & Miscellaneous plant equipment & \D\Z77.9\\ 26. & Heat rejection system & \D\Z64.3\\ 27. & Special materials &\D108.9\\ 90. & Total direct cost &2,321.7\\ 91. & Construction services and equipment &\D278.6\\ 92. & Home office engineering and services &\D120.7\\ 93. & Field office engineering and services &\D139.3\\ 94. & Owner's costs &\D429.1\\ 96. & Project contingency &\D555.1\\ 97. & Interest during construction (IDC) &\D635.1\\ 98. & Escalation during construction (EDC) & \D\Z\Z0.\D \\ 99. & Total capital cost &4,479.7\\ \\ & & \underline{Constant dollars} \\ % keep [90] etc in {} or LATEX will screw up. {[90]} & Unit direct cost, UDC (\$/kWe) &2,321.7\\ {[94]} & Unit base cost, UBC (\$/kWe) &3,289.4\\ {[99]} & Unit total cost, UTC (\$/kWe) &3,844.5\\ \\ & Capital return (mill/kWeh) & \Z65.04\\ {[40-47,51]} & O\&M (1.4\%) (mill/kWeh) & \Z\Z9.28\\ {[50]} & Blanket replacement (mill/kWeh) & \Z\Z3.71\\ & Decommissioning (mill/kWeh) & \Z\Z0.50\\ {[02]} & Fuel (mill/kWeh) & \Z\Z0.05\\ & (LSA=2) Cost of Electricity, COE (mill/kWeh) & \Z78.57\\ \\ \hline \end{tabular} } \label{t-7} \end{table} \clearpage \begin{table}[p] \caption{} \centering{\bf ARIES-ST (A = 1.6) with Conventional Unit Costing} \vspace{1.0cm} \renewcommand{\arraystretch} {1.20} \begin{tabular} {l c c c c}\hline LSA$^{(a)}$ rating: & 4 & 3 &{\bf 2}& 1 \\ \hline Capital return & 78.20 & 71.57 & 69.66 & 58.57 \\ O\&M & 10.91 & 10.09 & 9.28 & 7.64 \\ SCR & 4.48 & 4.40 & 4.17 & 3.85 \\ Fuel & 0.05 & 0.05 & 0.05 & 0.05 \\ Decommissioning & 1.00 & 0.75 & 0.50 & 0.25 \\ Total COE (mill/kWeh)$^{(b)}$& 94.63 & 86.86 & 83.65 & 70.36 \\ \\ \hline \multicolumn{5}{l}{$^{(a)}$ Level of Safety Assurance, {\it cf.} Ref.~\cite{Hol88}.}\\ \multicolumn{5}{l}{$^{(b)}$ Constant 1992 dollars.}\\ \end{tabular} \label{t-8} \end{table} % \begin{table}[p] \caption{} \centering{\bf ARIES-ST (A = 1.6) with Advanced (Low) Unit Costing$^{(a)}$} \vspace{1.0cm} \renewcommand{\arraystretch} {1.20} \begin{tabular} {l c c c c}\hline LSA$^{(b)}$ rating: & 4 & 3 &{\bf 2}& 1 \\ \hline Capital return & 73.02 & 66.63 & 65.04 & 54.34 \\ O\&M & 10.91 & 10.09 & 9.28 & 7.64 \\ SCR & 3.98 & 3.91 & 3.71 & 3.42 \\ Fuel & 0.05 & 0.05 & 0.05 & 0.05 \\ Decommissioning & 1.00 & 0.75 & 0.50 & 0.25 \\ Total COE (mill/kWeh)$^{(c)}$& 88.97 & 81.43 & 78.57 & 65.69 \\ \\ \hline \multicolumn{5}{l}{$^{(a)}$ {\it cf.} Ref.~\cite{Wag99}.}\\ \multicolumn{5}{l}{$^{(b)}$ Level of Safety Assurance, {\it cf.} Ref.~\cite{Hol88}.}\\ \multicolumn{5}{l}{$^{(c)}$ Constant 1992 dollars.}\\ \end{tabular} \label{t-9} \end{table} % \clearpage \begin{thebibliography}{99} \bibitem{Pen95a} Y.-K.~M.~Peng, {\it et al.}, ``Physics Progress Toward Compact Tokamak Reactors with Normal Conducting Toroidal Field Coils,'' {\it Plasma Physics and Controlled Nuclear Fusion Research 1994}, (IAEA 1995) {\bf 2}, 643. \bibitem{Gry98} M.~Gryaznevich, {\it et al.}, ``Achievement of Record $\beta$ in the START Spherical Tokamak,'' {\it Phys. 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