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\begin{document}

\title{\bf 3. SYSTEMS ANALYSIS}
\author{
\autlist{}{Ronald L. Miller}{}
}
\date{ }
\maketitle

\begin{titlepage}
{%\baselineskip=1.8ex
\tableofcontents
}
\end{titlepage}

\setcounter{chapter}{2}
\setcounter{page}{1}

\chapter{SYSTEMS ANALYSIS}

\section{INTRODUCTION}
\label{s-3-1}

The SPPS Systems Activity integrates physics, engineering, and costing models
to identify potentially attractive stellarator power-plant design points for
further detailed analysis.  Additionally, trade and parametric studies
establish key sensitivities of the stellarator approach.

The objective of the Systems Activity is to study and determine systematically
plant operating parameters through economic analysis and optimization of the
power station, with an emphasis placed on the performance of the fusion power
core (FPC). The FPC includes the plasma chamber, first wall, divertor, blanket,
shield, coils, and associated structure.  A reference design point is chosen to
meet overall design goals of the SPPS, such as minimal cost of electricity
(COE) and high mass power density (MPD, defined as the ratio of
net-electric-power output to the mass of the FPC). Trade-off and sensitivity
studies are performed to establish and characterize the design window for
optimal magnetic fusion power plants. Results and constraints from more
detailed modeling and engineering design efforts are fed back and integrated
into the systems model.  The systems code is, therefore, used as a tool in the
iterative conceptual engineering-design process.  The Systems Analysis approach
used for the SPPS is consistent with the recent ARIES~\cite{ARIES4} and
PULSAR~\cite{PULSAR} tokamak conceptual designs, although the SPPS level of
effort is smaller than that of the tokamak studies.

The ARIES Systems Code (ASC), described in detail in Ref.~\cite{ARIES4},
was modified for use in the SPPS; the modified version is denoted
``ASC$^{\star}$'' in this report. Typically, the projected cost of electricity
(COE, mill/kWeh) is used as a object function to be minimized.
Certain descriptive material is recapitulated here from the corresponding
section of Ref.~\cite{ARIES4}.  Some explanations relating to the cost
models and assumptions that may be unfamiliar to the stellarator
community are retained here for their tutorial value.
New material, particularly that reporting code modifications from
ASC to ASC$^{\star}$, appropriate to present stellarator applications,
is also included.

Section~\ref{s-3-2} summarizes the plasma, FPC, power plant, and costing models
that are used in the ASC$^{\star}$.  The reference SPPS design point, based on
the Modular Helias-like Heliac (MHH), is reported in \hbox{Sec.~\ref{s-3-3}}.
Results~\cite{Lyo94} dating from an early phase of the SPPS for a Compact
Torsatron (CT) have not been brought up to date using the final ASC$^{\star}$
costing groundrules, but those results are thought to remain generally
comparable.  The results of parametric and sensitivity studies about the
SPPS/MHH reference design point are discussed in \hbox{Sec.~\ref{s-3-4}}.
Conclusions drawn from this work are summarized in \hbox{Sec.~\ref{s-3-5}}.  An
Appendix to this report contains a more comprehensive listing of physics,
engineering, and economic parameters and results produced by the ASC$^{\star}$
for the SPPS/MHH.

\section{MODELS AND METHODS}
\label{s-3-2}

The SPPS systems studies activity integrates physics, engineering, and costing
models to identify potentially attractive deuterium-tritium magnetic-fusion
power-plant design points for further detailed analysis.  Additionally, trade
and parametric studies establish key sensitivities of the stellarator approach
and help sort through the several competing variants.  Where appropriate,
assumptions, models, and materials choices in common with the recent
ARIES~\cite{ARIES4} and PULSAR~\cite{PULSAR} tokamak power plant studies are
employed to facilitate meaningful comparisons.

\subsection{Plasma Engineering}
\label{s-3-2-1}

The ASC$^{\star}$ model for plasma engineering is a steady-state,
point-plasma (zero-di\-men\-sion\-al) model that is adjusted to simulate
two-dimensional profile effects.  Features of this model are discussed
in this subsection.  The SPPS/MHH deuterium-tritium (DT) plasma
would operate at (or slightly below) ignition, heated primarily by the
fusion-product alpha particles.

\subsubsection{Preliminaries}
\label{s-3-2-1-1}

\paragraph{Plasma Geometry.}

\begin{figure}[p]
\centerline{\psfig{file=spps-3-2-1-a.ps,height=3.25in,bbllx=108pt,bblly=225pt,%
            bburx=450pt,bbury=558pt,clip=} \hfil
            \psfig{file=spps-3-2-1-b.ps,height=3.25in,bbllx=108pt,bblly=225pt,%
            bburx=450pt,bbury=558pt,clip=} }
%\vskip +0.01truecm
\centerline{\psfig{file=spps-3-2-1-c.ps,height=3.25in,bbllx=108pt,bblly=225pt,%
            bburx=450pt,bbury=558pt,clip=} \hfil
            \psfig{file=spps-3-2-1-d.ps,height=3.25in,bbllx=108pt,bblly=225pt,%
            bburx=450pt,bbury=558pt,clip=} }
\caption[f-3-2-1]
{Schematic elevation views of the SPPS/MHH plasma outer (last closed) flux
surface (dashed line at $\rho=0$), modular-coil centroid (outer solid line at
$\rho=1$), and intermediate phantom surfaces ($\delta\rho=0.1$) for the
four-field-period MHH0103 case~\cite{Rom94} scaled to a major toroidal radius,
$R_T=13.95$~m at several toroidal locations denoted by the angle, $\phi$.  The
view at $\phi=90^\circ$ returns to that at $\phi=0^\circ$ to define the
periodicity of the configuration.  See Fig.~3.2-2 for representative
three-dimensional views of the plasma surface.}
\label{f-3-2-1}
\end{figure}

The SPPS/MHH plasma geometry incorporates a non-planar-axis, quasi-toroidal
plasma column with a periodic, but variable cross section~\cite{Rom94}.
Representative elevation views at selected toroidal positions along a field
period are illustrated in \hbox{Fig.~\ref{f-3-2-1}}.  Anticipating the baseline
SPPS/MHH baseline design point, the MHH0103 configuration has been scaled to a
major toroidal radius, $R_T=13.95$~m, denoted by the ``+'' symbol.  The
crescent-shaped plasma cross section is at the largest major toroidal radius at
the position, $\phi=0^\circ$, corresponding to the MHH corner.  The last closed
plasma flux surface is indicated by the dashed line.  The outermost solid
contour denotes the centroid of the modular coil as projected into the $\phi =
constant$ plane.  The actual coil dimension is determined by the required
on-axis magnetic-field strength and a nominal coil current density, as
discussed below.  Intermediate conformal contours are indicated by the
remaining solid lines; the innermost solid line need not indicate the position
of the first wall.  These contours are suggestive of the nested blanket and
shield geometries that must be accomodated, together with the divertor, in the
SPPS/MHH configuration.  The available standoff distance between the plasma
surface and the coil centroid shrinks as the major radius is reduced, thus
inhibiting reductions in fusion power core size and access to the higher-power
density operating regime.

As a simplification for purposes of the ASC$^{\star}$, the effective toroidal
plasma geometry is described by the equivalent major toroidal radius, $R_T$,
and minor plasma radius, $a_p$ ({\it i.e.}, half width of the minor plasma
diameter at the mid-plane), and vertical half height, $b$, defining the
elongation, $\kappa_\times = b/a_p$.  The plasma aspect ratio is \hbox{$A
\equiv R_T/a_p = 1/\epsilon$}.  The average plasma cross-sectional area is
given by
%
\begin{eqnarray}
 A_p & = & \pi a_p^2 \kappa_\times \: \: \equiv \: \: \pi r_p^2 \: ,
\label{e-4-2-1}
\end{eqnarray}
%
where $r_p$ is the circularized (average) plasma radius.  The corresponding
effective major toroidal radius of the centroid of the plasma cross section is
$R_T$ for the MHH.  The plasma aspect ratio is \hbox{$A \equiv R_T/a_p =
1/\epsilon$} in the usual tokamak parlance, or \hbox{$A^{\star} \equiv
R_T/r_p$} for the MHH.  The plasma volume is conveniently given by \hbox{$V_p
\equiv 2\pi R_T A_p$}. Then,
%
\begin{eqnarray}
 V_p & = & 2\pi^2 \, R_T \, a_p^2 \, \kappa_\times  \: .
\label{e-4-2-2}
\end{eqnarray}
%
The actual geometrical quantities derived from separate numerical
calculations~\cite{Rom94} are calibrated by the simplified ASC$^{\star}$
approximations.  Results are summarized in Table~\ref{t-3-2-1}.  While the
primary goal of the approximation in matching the plasma volume has been met,
it is not possible to recover simultaneously the large plasma surface area of
the MHH plasma.  Thus, the first-wall neutron wall load is overestimated by the
approximate model (see Sec.~5.3.2).

\begin{table}[t]
\caption{}
\centering{\bf SPPS/MHH Plasma Geometry$^{(a)}$}
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.3}
\begin{tabular} {l c}\hline \\
Plasma major `toroidal' radius, $R_T$ (m) & 13.95 \\
Plasma half-width, $a_{p}$  (m) & 1.155 \\
Plasma aspect ratio ({\it cf.}, tokamak), $A \equiv R_T/a_{p}$ & 12.08 \\
Plasma elongation, $\kappa_{\times}$ & 2.0 \\
Circularized (average) plasma radius, $r_{p}$ (m) & 1.633 \\
Plasma aspect ratio, $A^{\star} \equiv R_T/r_{p}$ & 8.54 \\
Average plasma cross-sectional area, $A_{p}$ (m$^2$) & 8.38$^{(b)}$ \\
Plasma volume, $V_{p}$ (m$^3$) & 734.7 \\
First-wall surface area$^{(c)}$, $A_{FW}$ (m$^2$) & 1,171 \\
\\ \hline
\multicolumn{2}{l}{$^{(a)}$ {\it cf.}, Ref.~\cite{Rom94}.}\\
\multicolumn{2}{l}{$^{(b)}$ Compare with MHH0103 value of 8.39~$m^2$.}\\
\multicolumn{2}{l}{$^{(c)}$ Compare with MHH0103 plasma-surface area
 of 1,233~$m^2$.}\\
\end{tabular}
\label{t-3-2-1}
\end{table}

\paragraph{Thermal Plasma Constituency.}

The same temperature profile, $T_i(r)$, is assumed to describe all background
ions. Therefore, the total ion density, $n_i$, the electron density, $n_e$
(assuming charge neutrality), and the effective ionic charge, $Z_{eff}$, are
obtained by summing over the ion species.  Calculation of the average $Z$ and
$Z^2$ of impurity species assumes coronal equilibrium.

The plasma ion and electron densities are denoted by $n_i$ and $n_e$,
respectively. Local charge neutrality requires that
%
\begin{eqnarray}
 n_e(r) = {\displaystyle\sum_j} \, n_j(r) Z_j \:,
\label{e-4-2-3}
\end{eqnarray}
%
where the summation is over all ion species ({\it i.e.}, fuel, fusion products,
and impurities). The effective plasma charge is defined as
%
\begin{eqnarray}
 Z_{eff} & = & \frac{\displaystyle\sum_j n_jZ_j^2}{\displaystyle\sum_j n_jZ_j}
 \: ,
\label{e-4-2-4}
\end{eqnarray}
%
and the effective square of the plasma charge is defined as
%
\begin{eqnarray}
 Z_{eff}^2&=& \frac{\displaystyle\sum_j n_jZ_j^3}{n_eZ_{eff}}
 \: .
\label{e-4-2-5}
\end{eqnarray}
%
The Maxwellian plasma ion population consists of deuterium (D) and tritium (T)
as the primary fuel species; fusion-product $\alpha$-particles ($^4$He), proton
(p), and helium-3 ($^3$He); and assumed impurities (1\%~O).  The concentration
of each ion species (other than oxygen) \hbox{$f_j \equiv n_j/n_i$} is
calculated with the continuity equations described below.  For the baseline
SPPS/MHH design point, \hbox{$f_{D} \simeq 0.470$}, \hbox{$f_{T} \simeq
0.471$}, and \hbox{$f_{{^3}He} \simeq 0.047$} to yield \hbox{$Z_{eff} \simeq
1.59$}.

\paragraph{Radial Plasma Profiles.}
The following general forms are assumed for the density profile for all
species, the temperature profile for all thermal species, and the
toroidal current-density profile:
%
\begin{eqnarray}
\label{e-4-2-6}
n(x) & = & (n_o - n_s)(1 - x)^{\alpha_n} + n_s\:, \\
\label{e-4-2-7}
T(x) & = & T_o(1 - x)^{\alpha_T}\:, \\
\label{e-4-2-8}
j_\phi(x) & = & j_o(1 - x)^{\alpha_J} \:;
\end{eqnarray}
%
where $x\equiv (r/r_p)^2$ and the $\alpha_n$, $\alpha_T$, and $\alpha_J$ are
fitting constants that are adjusted to fit reference radial profiles.  With no
net plasma current in the stellarator, \hbox{Eq.~(\ref{e-4-2-8})} is of
interest only for tokamak applications.  A non-zero edge-plasma density, $n_s$,
is included to lower the peak heat flux and plasma temperature at the divertor
plate.  Approximating the plasma as a circular cylinder with concentric flux
surfaces, profile form factors are calculated for all terms.

The volume-averaged current density, plasma density, temperature, and
density-weighted volume-averaged temperature are defined, respectively, as
follows:
%
\begin{eqnarray}
\label{e-4-2-9}
 j_\phi & \equiv & \frac{I_\phi}{A_p} \: ,  \\
\label{e-4-2-10}
 n      & \equiv & \frac{2 \pi}{A_p} {\,} \int^{r_p}_0 n(r) {\,} rdr
  \: ,  \\
\label{e-4-2-11}
 \bar{T} & \equiv & \frac{2 \pi}{A_p} {\,} \int^{r_p}_0 T(r) {\,} rdr
  \: ,  \\
\label{e-4-2-12}
 T       & \equiv & \frac{2 \pi}{n {\,} A_p} {\,}
  \int^{r_p}_0 T(r) {\,} n(r) {\,} rdr \: ,
\end{eqnarray}
%
where $I_\phi$ is the toroidal plasma current, of no interest for
stellarator applications.  These integrations yield
%
\begin{eqnarray}
\label{e-4-2-13}
 \frac{n}{n_o} & = & \frac{1}{1+\alpha_n(1-n_s/n)} \: , \\
\label{e-4-2-14}
 \frac{\bar{T}}{T_o} & = & \frac{1}{1+\alpha_T} \: ,  \\
\label{e-4-2-15}
 \frac{T}{T_o} & = & \frac{1+\alpha_n\{1-\alpha_Tn_s/[n(1+\alpha_T)]\}}
   {1+\alpha_n+\alpha_T} \: .
\end{eqnarray}
%
Equilibrium and stability considerations dictate the pressure profile,
\hbox{$p(r)[\propto n(r)T(r)]$}, consistent with the magnetohydrodynamic (MHD)
properties of the configuration.  The simplified one-dimensional density and
temperature profiles used herein are required to reproduce the peak-to-average
values of the pressure and density that are obtained from the more detailed
calculations of equilibrium and stability, as discussed in Sec.~2.

\begin{figure}[b]
\centerline{\psfig{file=spps-3-2-2.ps,height=4.5in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=593pt,clip=}}
\caption[f-3-2-2]
{Density, $n(x)$, temperature, $T(x)$, and pressure, $p(x)$, radial profiles,
where $x \equiv r/r_{p}$, used in the ASC$^{\star}$ for the MHH.
See \hbox{Table~\ref{t-3-2-2}} for more profile information.}
\label{f-3-2-2}
\end{figure}

\begin{table}[p]
\caption{}
\centering{\bf Profile Inputs$^{(a)}$ to the ASC and ASC$^{\star}$
and Other Profile Information}
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.3}
\begin{tabular} {l c c c}\hline
Parameter             & \AI\ & \AIIoIV\ & SPPS/MHH \\
\hline \\
Peak-to-average pressure, $p_0/p(=n_0T_0/nT)$ &2.47&\fbox{2.97}& 3.09 \\
Peak-to-average density, $n_0/n$ & 1.30 &\fbox{1.12}& 1.99 \\
Peak-to-average temperature,$^{(b)}$ $T_0/T$ & 1.90 & 2.65 & 1.55 \\
Peak-to-average temperature,$^{(c)}$ $T_0/{\bar T}$ & 2.10 & 2.84 & 2.10 \\
Separatrix-to-average density, $n_s/n$ &\fbox{0.70}&\fbox{0.45}
&\fbox{0.01}\\
Density profile exponent, $\alpha_n$ &\fbox{1.00}& 0.22
&\fbox{1.00}\\
Temperature profile exponent, $\alpha_T$ &\fbox{1.10}& 1.84
&\fbox{1.10}\\
Pressure profile exponent, $\alpha_p$ & 2.10 & 1.97 & 2.10 \\
Current-density profile exponent, $\alpha_J$ & 3.48 & 2.55 & NA \\
Profile form factors$^{(d)}$, $g_{k}$: & & & \\
-- Fusion reactions: & & & \\
\quad $g_{DT}$                 & 1.081 & 1.369 & 1.924 \\
\quad $g_{DDn}$                & 1.327 & 1.718 & 1.941 \\
\quad $g_{DDp}$                & 1.327 & 1.655 & 1.915 \\
\quad $g_{D^{3}He}$            & ---   & 5.876 & 3.364 \\
-- Bremsstrahlung radiation: & & & \\
\quad $g_{BR}$                 & 1.050 & 0.941 & 1.396 \\
\\ \hline
\multicolumn{4}{l}{$^{(a)}$ Input values are boxed.}\\
\multicolumn{4}{l}{$^{(b)}$ The density-weighted, volume-averaged
temperature.}\\
\multicolumn{4}{l}{$^{(c)}$ The volume-averaged temperature.}\\
\multicolumn{4}{l}{$^{(d)}$ As described in Sec.~\ref{s-3-2-1-2}.}\\
\end{tabular}
\label{t-3-2-2}
\end{table}

Representative radial plasma profiles for the SPPS/MHH are illustrated in
\hbox{Fig.~\ref{f-3-2-2}}, and profile inputs to the ASC$^{\star}$ are
summarized in \hbox{Table~\ref{t-3-2-2}}.  The improved performance of the
\AIIoIV~\cite{ARIES4} gaseous divertor permited a lower density pedestal than
was used for \AI~\cite{ARIES1} to allow penetration of lower-hybrid (LH)
current drive into the edge plasma region.  In the absence of detailed
information regarding the implications and consequences of stellarator edge
performance, the edge-density pedestal for the SPPS/MHH case was suppressed.
This issue should be revisited in any future studies with a view toward
developing a self-consistent picture of the core plasma and the scrape-off
layer (SOL) in interaction with the divertor as the impurity-control system.
The issue of the possible advantage or need of a radiating mantle to spread
power over the entire first-wall surface area, sparing the divertor surfaces
was not explored during the present study.

\paragraph{Plasma Beta.}

The magnetic field produced by external coils provides the confining field in
stellarators for the plasma pressure, $p$.  The on-axis toroidal magnetic-field
strength is \hbox{$B(R_T) \equiv B_{o}$}, the toroidal beta is \hbox{$\beta
\equiv 2\mu_o \/B^2_{o}$}, where $\mu_o \equiv 4\pi\X 10^{-7}$~H/m is the
permeability of free space.  The beta value of the reference SPPS/MHH
configuration is taken to be 5\% (see Sec.~2).

The fractional beta supported by athermal fusion products, $f_{\beta H}$,
is calculated by integrating over their slowing-down distributions.
The relationship between the thermal plasma pressure and the total beta
is given by 
%
\begin{eqnarray}
\label{e-4-2-16}
 \beta(1 - f_{\beta H}-f_{\beta B}) & = &
  \frac{2\mu_ok_B(n_iT_i + n _eT_e)}{B^2_{\phi o}}\:,
\end{eqnarray}
%
where \hbox{$f_{\beta B}$} is the fractional beta introduced by any
neutral beams (not used for the SPPS/MHH, such that $f_{\beta B} = 0$).
For the SPPS/MHH, the value of \hbox{$f_{\beta H} \simeq 0.06$}.

The inputs to the ASC$^{\star}$ equilibrium model are derived from detailed
equilibrium and stability calculations (Sec.~2).  It would be desirable to
have a representative scaling relation for $\beta$ as a function of plasma
aspect ratio, $A$, radial profile parameters, {\it etc.}, in order to exercise
the optimization capabilities of the ASC$^{\star}$.  Such a relation was not
available for the SPPS, thus limiting the study to the characterization of
the MHH to a representative, but not globally optimized, case.

\subsubsection{Particle and Power Balance}
\label{s-3-2-1-2}

The plasma particle- and power-balance module used in the ASC$^{\star}$ is
based on the zero-dimensional (0-D), steady-state
MakNTAU~\cite{ARIES4,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{Eqs.~(\ref{e-4-2-6})-(\ref{e-4-2-8})}
above.

\paragraph{Profile Averaging.}

A volume-averaged power density is denoted by $p_k$ and, assuming toroidal
symmetry, is defined as
%
\begin{eqnarray}
\label{e-4-2-17}
 p_k & \equiv & \frac{2 \pi}{A_p} \int^{r_p}_0 p_k(j(r), n(r), T(r)) rdr \: ;
\end{eqnarray}
%
where the subscript $k$ denotes a power generation or loss process ({\it e.g.},
fusion, radiation, or ohmic-heating).  The volume-averaged power density can be
written as a product of a profile-form factor, $g_k$, that contains the profile
information and a ``mean'' power density that is evaluated at the average
plasma parameters, {\it i.e.},
%
\begin{eqnarray}
\label{e-4-2-18}
 p_k & = & g_k \, p_k(j_\phi, n, T) \: .
\end{eqnarray}
%
The profile-form factor is then defined as
%
\begin{eqnarray}
\label{e-4-2-19}
 g_k & \equiv & \frac{2 \pi}{p_k(j_\phi, n, T) \, A_p} \, \int^{r_p}_0
   p_k\left(j(r), n(r), T(r)\right) \, rdr \: .
\end{eqnarray}
%
The total power is then given by
%
\begin{eqnarray}
\label{e-4-2-20}
 P_k & \equiv & V_p p_k \: .
\end{eqnarray}

\begin{table}[t]
\caption{}
\centering{\bf Dominant Fusion Reactions }
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.2}
\begin{tabular} {l @{\hspace{1.cm}} l c}\hline
 $k$   & \multicolumn{1}{c}{Reaction} & $Q_k$ (MeV/fusion) \\
\hline \\
 DT & $D + T \rightarrow n + {^4}He $ & 17.586  \\
 DD & $D + D \rightarrow p + T    $ & {\Z} 4.032  \\
    & $D + D \rightarrow n + {^3}He $ & {\Z} 3.267 \\
 D ${^3}$He  & $D + {^3}He \rightarrow p + {^4}He $ & 18.341 \\
\\ \hline
\end{tabular}
\label{t-3-2-3}
\end{table}
%
Several fusion reactions, dominated by $T(d,n){^4}He$ at $T\simeq 10$~keV,
would occur in the MHH plasma and are summarized on \hbox{Table~\ref{t-3-2-3}}.
Using the definition of the profile form factor, the average fusion power
density for the $k^{th}$ reaction is given by
%
\begin{eqnarray}
\label{e-4-2-21}
 p_{Fk} & = & g_k \, n_l n_m \, \langle \sigma v \rangle_{k} \, Q_k \: ,
\end{eqnarray}
%
where \hbox{$\langle \sigma v \rangle_k$} is the Maxwellian-averaged fusion
reactivity that is evaluated at the density-weighted, volume-averaged ion
temperature, and $g_k$ is the fusion-power profile-form factor.  The
volume-averaged plasma ion density, $n_{i}$, has several fuel-ion constituents
denoted by separate subscripts ({\it e.g.}, $l$, $m$, {\it etc.}), which
participate in the various possible fusion reactions.  The values of
\hbox{$\langle \sigma v \rangle_k$} are obtained using R-matrix
fits~\cite{Bos92}.  The ion-temperature dependence of \hbox{$\langle \sigma v
\rangle_k$} is illustrated in \hbox{Fig.~\ref{f-3-2-3}}.
%
\begin{figure}[b]
\centerline{\psfig{file=spps-3-2-3.ps,height=4.in,bbllx=116pt,bblly=224pt,%
            bburx=444pt,bbury=582pt,clip=}}
\caption[f-3-2-3]
{Temperature-dependent Maxwellian-averaged fusion reactivity, 
\hbox{$ \langle \sigma v \rangle_k$}, for the various reactions
listed in \hbox{Table~\ref{t-3-2-3}} that are appropriate to SPPS/MHH.}
\label{f-3-2-3}
\end{figure}

The results of the profile averaging of the fusion reactivity are used in the
other plasma engineering modules. For example, the average-fusion-reaction-rate
density that is used in the particle-balance model is given by
%
\begin{eqnarray}
\label{e-4-2-22}
      R_{lm} & = & g_k \, n_l n_m \, \langle \sigma v \rangle_{k} \: .
\end{eqnarray}
%
Additionally, the charged-particle fusion-product power density in
the power-balance model
is related to the fusion power density in \hbox{Eq.~(\ref{e-4-2-21})} by
%
\begin{eqnarray}
\label{e-4-2-23}
      p_{CP} & = & (1-f_p) \, \sum_k \frac{P_{Fk}f_{CP}}{V_p} \: ;
\end{eqnarray}
%
where $f_p$ is the prompt fusion-product loss, $f_{CP}$ is the fraction of the
fusion power carried by charged fusion products, and the sum is over the $k$
reaction given in \hbox{Table~\ref{t-3-2-3}}.

The tritium-fuel source rate, $S_T$, in steady state balances the sum of the
tritium burnup and loss rate, \hbox{$L_T = f_tn_i/\tau_p$}.  Another plasma
parameter that uses the profile-form factor for fusion reactions is the tritium
burnup fraction, $f_B$, for DT systems and it is given by
%
\begin{eqnarray}
\label{e-4-2-21d}
 f_B & \equiv & \frac{S_{T}-L_{T}}{S_{T}} \approx \left[ 1 + \frac{1}
  {g_{DT} \, f_D \, \langle\sigma v \rangle_{DT} \, n_i \, \tau_E
  \, \left( \tau_p / \tau_E \right)} \right]^{-1} \:\: .
\end{eqnarray}
%
where \hbox{$\langle\sigma v \rangle_{DT} \gg \langle\sigma v \rangle_{DD}$} is
assumed.  The particle confinement time, $\tau_p$, is specified by a factor (4
for the SPPS/MHH) multiplied by the energy confinement time, $tau_E$.  For the
reference SPPS/MHH design, \hbox{$f_B \simeq 0.095$}, and the Lawson
confinement parameter is \hbox{$n_i\tau_E\simeq 2.55\X 10^{20}$~s/m$^3$}.

\paragraph{Particle Balance.}  

Assuming all ion species have the same particle confinement time, $\tau_p$, the
ion continuity equations are given by
%
\begin{eqnarray}
\label{e-4-2-25}
 \frac{n_\alpha}{\tau_p} & = & R_{\rm DT} + R_{\rm D ^3He} \:, \\
\label{e-4-2-26}
 \frac{n_{\rm P}}{\tau_p} & = & R_{\rm D ^3He} + R_{\rm DDP} \:,  \\
\label{e-4-2-27}
 \frac{n_{\rm\,^3\!He}}{\tau_p} & = & -R_{\rm D\,^3\!He} + R_{\rm DDN} +
  \phi_{\rm\,^3\!He} S \: , \\
\label{e-4-2-28}
 \frac{n_{\rm T}}{\tau_p} & = & -R_{\rm DT} + R_{\rm DDP} + 
  \phi_{\rm T}S \: , \\
\label{e-4-2-29}
 \frac{n_{\rm D}}{\tau_p}&=& - R_{\rm DT} - R_{\rm D\,^3\!He} - 2~R_{\rm DDP} -
  2R_{\rm DDN} + \phi_{\rm D}S \: ,
\end{eqnarray}
%
where $R_{ij}$ is the fusion reaction rate per unit volume between species $i$
and $j$ \hbox{[Eq.~(\ref{e-4-2-22})]}, $S$ is the total particle fueling rate
per unit volume, and $\phi_j$ is the fractional composition of the fuel with
\hbox{$\phi_{\rm\,^3\!He} + \phi_{\rm T} + \phi_{\rm D} = 1$}.  The values of
$\phi_{\rm D}$ and $\phi_{\rm T}$, as well as the $\tau_p/\tau_{E_{e}}$ ratio,
are input to the ASC$^{\star}$.  It was assumed that $\tau_p/\tau_{E_{e}}=4$.
The issue of recycling of fuel ions or fusion-product alpha particles across
the interface between the plasma edge and the scrape-off layer has not been
examined in detail.

An optimal 50:50 fuel mixture ($\phi_{\rm D} \simeq \phi_{\rm T} \simeq 0.5$)
was used for the SPPS/MHH.  The value of $\tau_p/\tau_{E_{e}}=4$ gives a
fractional burnup of $\sim$10\%; a higher burnup fraction would provide a lower
tritium inventory.  These $\tau_p/\tau_{E_{e}}$ values were not forced to be
self-consistent with either the assumed density and temperature profiles or any
particle and energy transport models.

\paragraph{Power Balance.}

The steady-state, zero-dimensional ion and electron power balance equations,
written in terms of power density, are given by
%
\begin{eqnarray}
\label{e-4-2-30}
 p_{CP_{i}} + p_{H_{i}} & = & p_{TR_{i}} + p_{ie}\:, \\
\label{e-4-2-31}
 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 $D^{3}$He, DD, and DT fusion reactions
\hbox{[Eq.~(\ref{e-4-2-23})]}.  The power density deposited in the ions and
electrons, $p_{CP_{i}}$ and $p_{CP_{e}}$, respectively, (assuming a specified
prompt loss fraction, which is the same for all charged-particle fusion
products) 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~\cite{Kam75}.

The heating power densities provided by sources external to the plasma are
%
\begin{eqnarray}
\label{e-4-2-32}
p_{H_{i}} & = & {p_{CP} \over Q_{p}}f_{H_{i}}\:, \\
\label{e-4-2-33}
p_{H_{e}} & = & {p_{CP} \over Q_{p}}(1 - f_{H_{i}})\:.
\end{eqnarray}
%
The fractional heating power going to the ions, $f_{H_{i}}$, is additional
information provided with the heating power, and the plasma gain, $Q_p\equiv
P_{CP}/P_H$, is a result of the convergence loop fixing the net electrical
power.  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 as follows:
%
\begin{eqnarray}
\label{e-4-2-34}
p_{TR_{i}} & = & \frac{3}{2}k_B n_i~T_i/\tau_{E_{i}} \:, \\
\label{e-4-2-35}
p_{TR_{e}} & = & \frac{3}{2}k_B n_e~T_e/\tau_{E_{e}} \:.
\end{eqnarray}
%
where $k_B$ is the Boltzmann constant ($1.602\X 10^{-19}$~J/eV).
The total transport energy confinement time is given by
%
\begin{eqnarray}
\label{e-4-2-36}
 \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 $\tau_{Ei}/\tau_{Ee}=1$ 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-4-2-37}
 \tau_E & = & \frac{W_p}{P_{PH} \left(1 - f_{RAD}\right)} \: ;
\end{eqnarray}
%
where $W_p$ is the total plasma kinetic energy, including the suprathermal
fusion-product energy and any neutral-beam energy.  The ASC$^{\star}$ 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.  It should be emphasized
that a scaling law is not used to derive any of the \A\ or SPPS design points;
$\tau_E$ is determined from the specification of net electrical power and $Q_p$
that is determined self-consistently with the power requirements of the
(tokamak) current-drive system.  The value of $\tau_E$ required for a design
point can be compared to the various empirical scaling laws by means of a
confinement multiplier, \hbox{$H_j\equiv\tau_E/\tau^j_E$}, where the subscript
and superscript $j$ denotes the particular scaling of interest.

Stellarator plasma energy confinement is seen to improve with density,
magnetic-field strength, and volume, but degrades with input power; enhanced
(H-mode) confinement has been observed in two devices.  The global (L-mode)
energy confinement time, $\tau_{E}$, is given by (for example) the
Lackner-Gottardi relation~\cite{Lac90,Wel91}
%
\begin{eqnarray}
\label{e-4-2-38}
 \tau_{E}^{L-G} = 6.77 \times 10^{-10} R_T a_{p}^{2} \bar{n}^{0.6}
 B_{0}^{0.8} P^{-0.6} {\ib}^{0.4} \: ,
\end{eqnarray}
%
where $R_T$~(m) is the major toroidal radius, $a_{p}$~(m) is the average
plasma minor radius, $\bar{n}$~(10$^{20}$~m$^{-3})$ is the line-averaged plasma
density, $B_{0}$~(T) is the on-axis magnetic-field strength, $P$~(MW) is the
heating power, and ${\ib}$ is the rotational transform ({\it i.e.}, the inverse
of the tokamak safety factor, $q$).  A possible enhancement factor, $H$,
relative to \hbox{Eq.~(\ref{e-4-2-38})} is monitored ({\it i.e.}, $H \simeq 2$
for H mode).  Subsequent to the termination of technical work on the SPPS, a
new International Stellarator Scaling (ISS95) has been proposed~\cite{Str96}.

The radiation-loss channels for plasmas operating at temperatures above a few
keV are Bremsstrahlung and cyclotron radiation. Impurities at these high
temperatures are fully stripped of electrons and produce little line
radiation. Impurities enhance plasma radiation by increasing the effective
plasma charge.  The electron-ion and electron-electron Bremsstrahlung local
power density is given by~\cite{Mcn82}
%
\begin{eqnarray}
\label{e-4-2-39}
 p_{BR} & = & 5.35\X 10^{-43} n^2_e Z_{eff} T_e^{\frac{1}{2}}
  \, \left[ 1 + 1.55\X 10^{-3} \, T_e +
 7.15\X 10^{-6} \, T^2_e \right. \nonumber \\
  &  & + \left. 4.14\X 10^{-3} \, \frac{T_e}{ Z_{eff}}
 + 0.071\,\frac{Z_{eff}^2}{T_e^{\frac{1}{2}}}\right] \: ,
\end{eqnarray}
%
which includes a correction for relativistic effects and uses the definitions
of effective plasma charge and the effective square of the plasma charge given
in \hbox{Eqs.~(\ref{e-4-2-4})} and \hbox{(\ref{e-4-2-5})}, respectively.

The cyclotron radiation global-power density, $p_{CY}$, for the SPPS/MHH is a
relatively small loss, due to the modest magnetic field strength and reflective
first-wall surface.  Cyclotron radiation losses are a function of the effective
first-wall reflectivity for cyclotron radiation, $R_{CY}$, which includes the
effects of both reflection from the first wall and absorption in first-wall
holes.  The first-wall surface hole fraction for the SPPS/MHH is \hbox{$f_H
\simeq 0.10$}, accounting promarily for the divertor channel openings.  The
cyclotron power lost through the divertor channels and other (smaller) holes in
the first wall of the SPPS/MHH is about 2~MW.

The plasma-core radiation fraction is given by
%
\begin{eqnarray}
\label{e-4-2-40}
f_{RAD} & \equiv & \frac{p_{BR} + p_{CY}}{p_{CP} + p_{H} + 
p_\Omega} \: .
\end{eqnarray}
%
The value of $f_{RAD}$ for a DT plasma at \hbox{$T \simeq 20$~keV} with
\hbox{$Z_{ eff}\simeq 1.5$} and a highly reflective \hbox{($P_{CY} \simeq 0$)}
first wall is \hbox{$\simeq 0.5$}, but drops below $0.2$ at \hbox{$T\simeq
10$~keV}.  The value for the SPPS/MHH reference case is $f_{RAD}=0.21$.

No detailed calculations of the performance of the SPPS/MHH divertor system
where performed.  Relative to the \A\ tokamaks, the SPPS/MHH is expected to
have fairly straightforward heat-removal rquirements.  Attempts to improve upon
the baseline SPPS/MHH case by increasing the power density can be expected to
increase the loads on the high-heat flux surfaces.  Any future, more detailed
study should address this issue with greater care insofar as it may become
performance limiting.

\subsection{Power Plant Engineering}
\label{s-3-2-2}

The ASC$^{\star}$ model for reactor engineering characterizes the first wall,
blanket, shield, coils, current-drive, and impurity-control hardware
to provide the basis for the direct cost estimate of the FPC.
Additionally, the plant power balance is modeled to size
the balance-of-plant (BOP) requirements of the electric generating station.

\begin{table}[b]
\caption{}
\centering{\bf SPPS/MHH Inboard Radial Build}
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.3}
\begin{tabular} {l @{\hspace{3.0truecm}} c}\hline \\
SOL thickness, $\delta_s$ (m)& 0.15  \\
First wall:        &                  \\
\quad coating      & none             \\
\quad composition  & 30\% V5Cr5Ti, 70\% Li \\
\quad thickness (m)& 0.014            \\
Gap thickness (m)  & 0.               \\
Blanket:           &                  \\
\quad composition  & 10\% V5Cr5Ti,  90\% Li  \\
\quad thickness (m)&  0.350           \\
Gap thickness (m)  &  0.020           \\
Shield:            &                  \\
\quad composition  & 15\% V5Cr5Ti, 5\% Li,   \\
                   & 80\% Tenelon   \\
\quad thickness (m)&  0.800           \\
Gap thickness (m)  &  0.020           \\
Cryostat (m)       &  0.100              \\
Total thickness, $\delta_i$ (m) & 1.454  \\
\\ \hline
\end{tabular}
\label{t-3-2-4}
\end{table}

The radial build of the SPPS/MHH configuration is summarized in
Table~\ref{t-3-2-4}, consistent with the more detailed discussion found in
Sec.~5.  In common with the \AII\ design, liquid-Li serves as both breeder and
coolant and V5Cr5Ti serves as the structural material for the SPPS/MHH.  The
scale of the FPC for the MHH is to a large extent set by the restrictive
inboard standoff as it interacts with the the necessity of protection of the
coils from radiation damage.

The thermal-hydraulic properties of the liquid-metal blanket
suggest~\cite{ARIES4} an adequate limit on the peak neutron wall load ($\leq
10.4$~MW/m$^2$), which is not encountered by typical SPPS/MHH design points,
because of the interaction between the choice of plasma aspect ratio,
plasma-coil standoff distance, design power level, {\it etc.}.  The V-alloy
coolant channels are assumed to be coated with an insulator ({\it e.g.}, CaO)
to nullify the MHD contribution to the Li-coolant pumping power.

\subsubsection{Magnetic Coils}
\label{s-3-2-2-1}

The stellarator magnetic configuration is provided entirely by the external
coil set.  The specialized MHH coil configuration incorporates a nonplanar axis
with four toroidal field periods, as illustrated in \hbox{Fig.~3.2-1}.  Details
of the coil internals are described in Sec.~4.  For purposes of the
ASC$^{\star}$, a homogenized characterization provides information regarding
the coil masses and costs.  The coil cross-sectional area is determined by the
required magnetic field strength and a nominal overall coil current density of
30~MA/m$^2$.  The homogenized coil mass density is taken to be 7,500~kg/m$^3$,
ignoring variations in the structure-to-conductor ratio that can be expected
across a parametric scan.  The unit coil cost is taken to be a constant
98~\$/kg, again ignoring expected dependancies, but including certain credits.
This is the same unit coil cost used in the \A\ studies; no penalty for
out-of-plane winding or other `complications' attributed to the MHH
configuration having been assessed.  A limit on peak magnetic field strength at
the coil windings was set at $\sim$14.5~T, lower than the 16-T limit imposed in
the \AIIoIV\ cases.  There is no convenient, general relationship describing
the location of the peak coil field or scaling corresponding to the $1/R$
dependance of the toroidal-field strength in a standard tokamak.  Thus, the MHH
reference configuration can be scaled only in a restricted sense.

The ASC$^{\star}$ includes models for continuous helical coils, consistent with
the Large Helical Device (LHD)~\cite{Fuj96}, presently under construction in
Japan, or other proposed Compact-Torsatron (CT) configurations~\cite{Lyo94}.
These models were not exercised in the course of the SPPS to perform a
comparative assessment of modern stellarator configurations, as was done for an
earlier study~\cite{Mil83}.

\subsubsection{Thermal Cycle}
\label{s-3-2-2-2}

The power recovered by the thermal cycle is divided into that deposited in the
blanket, $P^B_{TH}$, and that delivered to the divertor, $P^D_{TH}$.  The
efficiency of converting the thermal blanket power to electricity is denoted by
$\eta^B_{TH}$. The thermal-conversion efficiency for the divertor-coolant loop
is denoted by $\eta^D_{TH}$, in order to model the case of a compound system
(typically \hbox{$\eta^D_{TH} < \eta^B_{TH}$}) or the extreme case where the
divertor power, $P^D$, is dumped to the environment as low-grade (waste) heat
(\hbox{$\eta^D_{TH} \simeq 0$}). The power-to-wall area weighted-average
thermal-conversion efficiency is defined as
%
\begin{eqnarray}
\label{e-4-2-41}
 \eta_{TH} & = & \frac{\eta^B_{TH}\, P^B_{TH}+\eta^D_{TH}\, P^D_{TH}}{P^B_{TH}
  +P^D_{TH}} \: ,
\end{eqnarray}
%
where
%
\begin{eqnarray}
\label{e-4-2-42}
 P^B_{TH} & = & f_{RAD} \, (1-f_D) \, (1-f_{DC}) \,
  (P_{CP}+P_{H}+P_\Omega) + M_N^{DT} \, P_N^{DT} + M_N^{DD} \, P_N^{DD}
  \: ; \hspace{1.5cm} \\
\label{e-4-2-43}
 P^D_{TH} & = & \left( 1 - f_{RAD} + f_{RAD} \, f_D \, (1-f_{DC}) \right) \,
  (P_{CP}+P_{H}+P_\Omega) \: .
\end{eqnarray}
%
In the above expressions, $f_{RAD}$ is the core plasma-radiation fraction and
is given by \hbox{Eqs.~(\ref{e-4-2-40})}; \hbox{$f_D \equiv A_D/A_{FW}$} is the
fraction of the first-wall surface area devoted to the divertor plate surfaces;
$f_{DC}$ is the fraction of the radiated power recovered for direct collection
($f_{DC}=0$ for all \A\ designs); \hbox{$P_{CP}$} is the charged-particle
fusion power; and \hbox{$M_N^{DT}$} and \hbox{$M_N^{DD}$} are the blanket
neutron-energy multiplications for $14$-Mev DT and $2.5$-MeV DD neutrons,
respectively. To avoid the design complication of two separate coolant
circuits, the blanket and divertor use the same coolant inlet and outlet
temperatures and pressures to yield \hbox{$\eta^D_{TH} = \eta^B_{T H} =
\eta_{TH}$}. The thermal-cycle parameters used for the \A\ and SPPS/MHH designs
are given in \hbox{Table~\ref{t-3-2-5}}.  The low-activation SiC blankets of
\AI\ and -IV result in the lowest energy multiplication for $14$-MeV DT
neutrons of the \A\ designs.  However, the He-cooled \AI\ and -IV designs have
the highest thermal-conversion efficiencies.

\begin{table}[tb]
\caption{}
\centering{\bf Thermal-Cycle Parameters of SPPS and 
ARIES Designs~\cite{ARIES1, ARIES4}}
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.2}
\begin{tabular} {l c c c c}\hline
            & \AI\ & \AII\ & \AIV\ & SPPS/MHH \\
\hline \\
Divertor coverage, $f_D\equiv A_D/A_{FW}$  & 0.25 & 0.15 & 0.15 & 0.15 \\
Neutron Energy multiplication: \\
\quad 14-Mev, $M_N^{DT}$                   & 1.30 & 1.38 & 1.23 & 1.40 \\
\quad 2.5-Mev, $M_N^{DD}$                  & 4.20 & 3.70 & 4.27 & 3.70 \\
Thermal conversion efficiency, $\eta_{TH}$ & 0.49 & 0.46 & 0.49 & 0.46 \\
Pumping power fraction, $f_{PMP}$          & 0.05 & 0.01 & 0.05 & 0.01 \\
\\ \hline
\end{tabular}
\label{t-3-2-5}
\end{table}
%

\begin{figure}[b]
\centerline{\psfig{file=spps-3-2-4.ps,height=3.4in,bbllx=36pt,bblly=202pt,%
            bburx=573pt,bbury=616pt,clip=}}
\caption[f-3-2-4]
{Overall power-flow diagram used in the ASC$^{\star}$ for the SPPS/MHH.  Values
of powers are given in MW and are for the 1,000-MWe reference design.  Powers
with a superscript ``$\ast$'' denote discarded, low-grade heat.}
\label{f-3-2-4}
\end{figure}

The power flow, as modeled in the ASC$^{\star}$, is shown in
\hbox{Fig.~\ref{f-3-2-4}} for the SPPS/MHH.  Given a stipulated target for the
net-electrical-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{$Q_E
\equiv P_{ET}/(P_{ET}-P_E)$} is the engineering gain. The gross electrical
power 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. From \hbox{Table~\ref{t-3-2-5}}, the
gas-cooled \AI\ and -IV designs require five times the pumping power of the
liquid-cooled \AII\ and SPPS/MHH designs. It is assumed that \hbox{$0.98\,
P_{pump}$} is recoverable as thermal power usable in the primary coolant loop;
\hbox{$0.9\, P_{pump}$} was assumed in \AI\null~\cite{ARIES1}.  The engineering
gain, $Q_E$, can be written as
%
\begin{eqnarray}
\label{e-4-2-44}
 Q_E & = & \frac{1}{\epsilon} \: = \: \eta_{TH} \:
  \frac{M_N \, P_N + P_{CP} + P_{H} + P_{\Omega} + 0.98 \, P_{pump}}
  {P_{AUX} + P_{pump} + \left(P_{CD}+P_{AH}\right)/ \eta_{CD}} \: .
\end{eqnarray}
%
The ratio of fusion power to external heating power is the plasma
gain, \hbox{$Q_p \equiv P_F/P_H$}.  For the SPPS/MHH, $Q_p \simeq 1,700$,
consistent with a small external heating power (20~MW) to
provide control at a steady-state operating point set slightly below ignition.

\subsubsection{Neutron Wall Load}
\label{s-3-2-2-3}

The average neutron first-wall load, \hbox{$P_N/A_w=I_w$}, is given by
%
\begin{eqnarray}
\label{e-4-2-45}
 I_w & = & \frac{0.8 \, P_F^{DT}+0.336 \, P_F^{DD}}
{4\pi^2 \, R_T \, r_w} \: .
\end{eqnarray}
%
A plasma filling fraction, \hbox{$x \equiv r_p/r_w$}, is calculated based on
the assumed scrape-off layer thickness, \hbox{$\delta_s = r_w - r_p$}, taken to
be 0.15~m for the SPPS/MHH.  The poloidal distribution of the neutron wall load
is calculated internal to the ASC$^{\star}$, as is shown in
\hbox{Fig.~\ref{f-3-2-5}}, corresponding to, but not representative of the
actual 3-D MHH geometry, the results of the NEWLIT (tokamak) code~\cite{Att85}.
Assuming toroidal symmetry, a three-dimensional neutron source (also shown in
\hbox{Fig.~\ref{f-3-2-5}}) is constructed from the volumes of the simulated
flux surfaces and the radial profile of the neutron power density.  The neutron
wall load is calculated from approximate three-dimensional integrals over the
source volume that has an unobstructed view of the wall, as determined by ray
tracing.  This calculation is repeated to construct the poloidal distribution
of the neutron wall load that is shown in \hbox{Fig.~\ref{f-3-2-5}}.  Limiting
values of peak neutron wall load ${\hat I_w} \geq 10.4$~MW/m$^2$ for \AII\ or
${\hat I_w} \geq 5.8$~MW/m$^2$ for \AIV\ were rejected for thermal-hydraulic
reasons~\cite{ARIES4}, but the former limit is not approached by the SPPS/MHH
design using comparable self-cooled Li technology.  The peak (local) neutron
wall load, together with the assumed material fluence life, sets the service
life of the module for purposes of scheduled changeout.

\begin{figure}[p]
\centerline{\hspace{2.cm}
            \psfig{file=spps-3-2-5.ps,width=7.5in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=583pt,clip=}}
\caption[f-3-2-5]
{Schematic poloidal distribution of the neutron wall load for the SPPS/MHH,
idealized consistent with the ASC$^{\star}$ model, and not representative of
any actual vertical cut through the MHH configuration.  Also shown are the
simulated flux surfaces used to construct the neutron source, the surface
representing the first wall, and the neutron source in the equatorial plane as
a function of major radius.  Under these assumptions, the peak-to-average
neutron wall load is $\hat I_w/I_w=1.79$.  }
\label{f-3-2-5}
\end{figure}

\clearpage

\subsubsection{Fusion-Power-Core Mass}
\label{s-3-2-2-4}

The total FPC mass, $M_{FPC}$, is the sum of coil, blanket, shield, and
structure component masses. The ratio $P_E/M_{FPC}$ (kWe/tonne) defines the FPC
mass power density (MPD) figure of merit. A target value of $\sim$100~kWe/tonne
has been identified as a necessary condition for a fusion power plant to be of
marginal economic interest~\cite{Con85}.  Higher power-density systems lead to
higher values of MPD, with the MPD value that minimizes COE being highly
dependent on the confinement concept~\cite{Kra94a,Kra91}.  The value obtained
for the SPPS/MHH is $~\sim$47~kWe/tonne, which raises a concern that is
somewhat mitigated in terms of its impact on the overall economics by the
favorably low value of recirculating power.  The low value of MPD is a direct
result of the MHH geometry, as well as conservative assumptions regarding
magnetic field strength, power density, and 14.1-MeV neutron wall load.  The
FPC mass is a distinguishing global characteristic, along with recirculating
power fraction, in comparing various MFE point designs.  FPC masses for several
conceptual design are summarized in \hbox{Table~\ref{t-3-2-6}}.  A
representative Helias conceptual design, HSR20~\cite{Bei95}, is also included.

\begin{table}[b]
\caption{}
\centering{\bf FPC Mass Parameter Comparison}
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.2}
\begin{tabular} {l c c c }\hline
                 & \AII~\cite{ARIES4} & HSR20~\cite{Bei95} & SPPS/MHH \\
\hline \\
Masses (ktonne): \\
\quad First Wall, Blanket, Reflector  & \Z0.43  & \Z0.55  & \Z0.25 \\
\quad Shield                          & \Z6.02  &  20.06  & \Z9.45 \\
\quad Coils:                          & \Z2.41  &  13.36  & \Z4.19 \\
\quad\quad TF coils                   & \Z1.81  \\
\quad\quad PF coils                   & \Z0.59  \\
\quad Structure                       & \Z1.23  & \Z1.10  & \Z5.36 \\
\quad Vacuum Vessel                   & \Z0.71  & \Z2.20  & \Z2.17 \\
\quad Fusion Power Core, FPC          &  10.80  &  37.27  &  21.43 \\
Mass Power Density, MPD (kWe/tonne)   &  92.6\Z &  26.5\Z &  46.7\Z \\
\\ \hline
\end{tabular}
\label{t-3-2-6}
\end{table}

\subsection{Costing}
\label{s-3-2-3}

\subsubsection{Direct Cost Database}
\label{s-3-2-3-1}

The ASC$^{\star}$ plasma and engineering models combine to provide a
characterization of MHH power plants that is adequate for conceptual cost
projections.  Despite the uncertainty in projecting the future costs of an
emerging and complex technology, a competitive cost, together with favorable
safety and environmental characteristics, remain as important considerations in
the eventual decision to commercialize fusion power~\cite{Kra94a,Kra91,Con90}.
This subsection reports the cost basis and methodology used in the SPPS.  The
ARIES/SPPS cost data base as used in the ASC$^{\star}$ is summarized on
\hbox{Table~\ref{t-3-2-7}}.  The direct-cost account entries, $C_i$, are
obtained by applying relevant (installed) unit-cost estimates ({\it e.g.,}
\$/W, \$/kg, \$/m$^3$) to the calculated usage of these items in the conceptual
design, such that \hbox{$C_i (\$) = u_i (\$/{\rm unit}) X_i$ (unit)}.  A
learning-curve or mass-production credit is taken for a ``tenth-of-a-kind''
commercial reactor installation, consistent with U.S.\ fusion-reactor
design-community practice.  The SPPS study, like STARFIRE~\cite{Bak80} and most
other U.S.  fusion-reactor designs reported in the last decade, assumes FPC
unit costs consistent with these learning-curve~\cite{Hir64,Arg90} credits,
rather than ``first-of-a-kind'' unit costs (including R\&D) appropriate for the
International Thermonuclear Experimental Reactor (ITER)~\cite{Ite96}.  A ``80\%
learning curve'' ({\it {\it i.e.},} 0.80 progress ratio, $p$), as used for the
ARIES tokamaks and the SPPS/MHH, represents the expectation~\cite{Tho88}, that
each doubling of production represents a \hbox{$p\simeq$ 0.8} reduction in unit
costs. A ``tenth-of-a-kind'' reactor represents, nominally, $\sim$3.3 doublings
of production or \hbox{$p^{(ln 10/ln 2)}\simeq 50\%$} cost reduction relative
to ``first-of-a-kind'' FPC costs.  Of course, actual production experience
varies~\cite{Arg90}.  Learning credits are not applied to BOP items, consistent
with mature industrial production in which the learning credits have already
been wrung out.  For similar reasons, a 94\% learning curve is recommended for
advanced fission cost estimates~\cite{Del93}.  Because of the larger leverage
of the stellarator FPC cost, relative to a tokamak, a more conservative
learning-curve credit, as recommended in Ref.~\cite{Hen96}, would tend to
penalize the stellarator preferentially.

\begin{table}[p]
\caption{}
\centering
{\bf Summary of ASC/ASC$^{\star}$ Cost Data Base$^{(a,b,c)}$}
\vspace{1.0cm}
\renewcommand{\arraystretch}{0.96}
\begin{tabular}{l l l }\hline
Acct. No. & \multicolumn{1}{c}{Account Title} &
                \multicolumn{1}{c}{Cost (M\$, 1992)} \\
\hline
 & \hbox to 3.00 truein{\hfil} & \hbox to 2.25 truein{\hfil} \\
{\bf 20.} & {\bf Land and Land Rights} & 10.44 \\
\\
{\bf 21.} & {\bf Structures and Site Facilities} \\
21.1      & Site improvements and facilities & 18.44 \\
21.2      & Reactor building$^{(c)}$ & $77.1 \, (V_{RB}/80,000)^{0.62}$ \\
21.3      & Turbine building & $28.67 \, (P_{ET}/1200)^{0.75} + 5.72$ \\
21.4      & Cooling structures & $11.67 \, (P_{ET}/1000)^{0.3}$ \\
21.5      & Power supply and energy storage bldg. & 14.98 \\
21.6      & Miscellaneous buildings & 125.10 \\
21.7      & Ventilation stack & 2.96 \\
\\
{\bf 22.} & {\bf Reactor Plant Equipment (RPE)} \\
22.1      & Reactor equipment \\
22.1.1    & First Wall/Blanket/Reflector: \\
          & \ \ Breeding material: & Table 2.2-VIII of Ref.~\cite{ARIES4} \\
          & \ \ \ \ Liquid metal (LM): PbLi$^{(d,e)}$
                         & (see Acct.~\ 26.1.) \\
          & \ \ \ \ \phantom{Liquid metal (LM):} Li$^{(d,f)}$
                         & (see Acct.~\ 26.1.) \\
          & \ \ \ \ Water solution: LiNO$_3$$^{(d,g)}$
                      & ($12.81 f_{6_{Li}} + 4.02) \, \X 10^{-3} \, M$ \\
          & \ \ Blanket and first-wall structure
 & Table 2.2-VIII of Ref.~\cite{ARIES4} \\
          & \ \ Be multiplier$^{(g)}$ & Table 2.2-IX of Ref.~\cite{ARIES4} \\
22.1.2    & \ \ Shield
 & Tables 2.2-VIII \& 2.2-IX of Ref.~\cite{ARIES4} \\
22.1.3    & \ \ Magnet coils: \\
          & \ \ \ \ Superconducting    & Table 2.2-XI of Ref.~\cite{ARIES4} \\
          & \ \ \ \ Resistive Cu       & Table 2.2-XI of Ref.~\cite{ARIES4} \\
22.1.4    & \ \ Supplemental heating systems
                              & Table 2.2-XII of Ref.~\cite{ARIES4} \\
22.1.5    & \ \ Primary structure and support & $0.1840 \, V_{STR}$
\\
22.1.6    & \ \ Reactor vacuum system
                    & $0.024\, M_{VAC}^{(f)} + 4.09$ (kg/d) \\
\\
\end{tabular}
\label{t-3-2-7}
\end{table}

\begin{table}[p]
\centering
{\bf Table~\ref{t-3-2-7} (Cont'd)}
\vspace{1.0cm}
\renewcommand{\arraystretch}{1.0}
\begin{tabular}{l l l }\hline
Acct. No. & \multicolumn{1}{c}{Account Title} &
                \multicolumn{1}{c}{Cost (M\$, 1992)} \\
\hline
 & \hbox to 3.00 truein{\hfil} & \hbox to 2.25 truein{\hfil} \\
22.1.7    & \multicolumn{2}{l}{\ \ Power supply (switching, energy 
storage):} \\
          & \ \ \ \ Superconducting PF coils & 485.2~\$/(kVA)$^{0.8}$ \\
          & \ \ \ \ Resistive-Cu coils       & 30.33~\$/kVA \\
          & \ \ \ \ Superconducting TF coils & 60.66~\$/kVA \\
          & \ \ \ \ IBC$^{(f)}$              & 60.66~\$/kVA \\
          & \ \ \ \ OFCD$^{(f,g)}$            & 60.66~\$/kVA \\
          & \ \ \ \ Other                    & 1.64 \\
          & \ \ TF IBC busbars$^{(f)}$       & 4.96 \\
          & \ \ DF IBC busbars$^{(f)}$       & 2.66 \\
22.1.8    & \ \ Impurity control system      \\
           & \ \ \ TITAN                          & $0.108 \, A_{DIV}$ \\
           & \ \ \ ARIES                          & $0.073 \, A_{DIV}$ \\
22.1.9    & \ \ Direct energy conversion
 & Table 2.2-XIII of Ref.~\cite{ARIES4}$^{(h)}$ \\
22.1.10   & \ \ ECRH breakdown system        & 2.60 \\
22.2      & Main heat-transfer system: \\
22.2.1    & \ \ Primary coolant$^{(i)}$: \\
          & \ \ \ \ Li$^{(f)}$, PbLi, He
             & $233.9 \, (P_{TH}/3500)^{0.55}$ \\
          & \ \ \ \ OC, H$_2$O$^{(g)}$
             & $\Z75.0 \, (P_{TH}/3500)^{0.55}$ \\
22.2.2    & \ \ Intermediate coolant system
             & $\Z40.6 \, (P_{TH}/3500)^{0.55}$ \\
22.2.3    & \ \ Secondary coolant system
             & $\Z75.0 \, (P_{TH}/3500)^{0.55}$ \\
22.3      & Auxiliary cooling systems & $1.10\X 10^{-3} \, P_{TH}$ \\
22.4      & Radioactive waste treatment & $1.96\X 10^{-3} \, P_{TH}$
\\
22.5      & Fuel handling and storage \\
22.5.1    & \ \ Pellet injectors & 6.07 M\$~each $\X 2$ \\
22.5.2    & \ \ Fuel processing system & 0.82~(g/d)$^{0.7}$ \\
22.5.3    & \ \ Fuel storage  & 6.07 \\
22.5.4    & \ \ Atmospheric tritium recovery & 
0.33~(m$^3$/h)$^{0.6}$ \\
22.5.5    & \ \ Water detritiation system: \\
          & \ \ \ \ TITAN-I, \AI\  & 8.18 \\
          & \ \ \ \ TITAN-II & 229 \\
22.6      & Other reactor plant equipment & $1.78\X 10^{-3} \,
P_{TH}$ \\
22.7      & Instrumentation and control & 38.29 \\
\\
\end{tabular}
\end{table}

\begin{table}[p]
\centering
{\bf Table~\ref{t-3-2-7} (Cont'd)}
\vspace{1.0cm}
\renewcommand{\arraystretch}{0.96}
\begin{tabular}{l l l }\hline
Acct. No. & \multicolumn{1}{c}{Account Title} &
                \multicolumn{1}{c}{Cost (M\$, 1992)} \\
\hline
 & \hbox to 3.00 truein{\hfil} & \hbox to 2.25 truein{\hfil} \\
{\bf 23.} & {\bf Turbine Plant Equipment$^{(i)}$} \\
          & \ \ \ OC, H$_{2}$O &$ 254.4 \Z (P_{ET}/1200)^{0.83}$ \\
          & \ \ \ Li, PbLi &$ 240.3 \Z (P_{ET}/1200)^{0.83}$ \\
          & \ \ \ He &$ 205.5 \Z (P_{ET}/1200)^{0.7}$ \\
23.1      & Turbine generators & \\
23.2      & Main steam system & \\
23.3      & Heat rejection systems & \\
23.4      & Condensing system & \\
23.5      & Feed heating system & \\
23.6      & Other turbine plant equipment & \\
23.7      & Instrumentation and control & \\
\\
{\bf 24.} & {\bf Electric Plant Equipment$^{(i)}$} &$ 126.4 \Z
(P_{ET}/1200)^{0.49}$ \\
24.1      & Switchgear & \\
24.2      & Station service equipment & \\
24.3      & Switchboards & \\
24.4      & Protective equipment & \\
24.5      & Electrical structures and wiring containers & \\
24.6      & Power and control wiring & \\
24.7      & Electrical lighting & \\
\\
{\bf 25.}  & {\bf Miscellaneous Plant Equipment$^{(i)}$} &$ 60.5 \Z
(P_{ET}/1200)^{0.59}
$
\\

25.1      & Transportation and lifting equipment & \\
25.2      & Air and water service systems & \\
25.3      & Communications equipment & \\
25.4      & Furnishings and fixtures & \\
\\
{\bf 26.} & {\bf Special Materials} \\
26.1      & Reactor LM coolant/breeder:$^{(d)}$ \\
          & \ \ PbLi$^{(e)}$ & $(12.81 f_{^6Li} + 4.02) \X 10^{-3}
M_{LM}$
\\
          & \ \ Li$^{(f)}$   & $(1233 f_{^6Li} + 61.2) \X 10^{-3} M_{LM}$
\\
26.4      & Other & 0.41 \\
26.5      & Reactor-building cover gas $^{(f,j)}$ & 0.21 \\
\end{tabular}
\end{table}

\begin{table}[p]
\centering
{\bf Table~\ref{t-3-2-7} (Cont'd)}
\vspace{1.0cm}
\renewcommand{\arraystretch}{0.92}
\begin{tabular}{l l c }\hline
Acct. No. & \multicolumn{1}{c}{Account Title} &
                \multicolumn{1}{c}{Cost (M\$, 1992)} \\
\hline
 & \hbox to 3.00 truein{\hfil} & \hbox to 2.25 truein{\hfil} \\
{\bf 90.} & {\bf Total Direct Cost (TDC)} & \\
\\
{\bf 91.} & {\bf Construction Services and Equipment} & 
Table~\ref{t-3-2-8} \\
\\
{\bf 92.} & {\bf Home Office Engineering and Services} & 
Table~\ref{t-3-2-8} \\
\\
{\bf 93.} & {\bf Field Office Engineering and Services} 
& Table~\ref{t-3-2-8} \\
\\
{\bf 94.} & {\bf Owner's Cost} & Table~\ref{t-3-2-8} \\
\\
{\bf 95.} & {\bf Process Contingency} & Table~\ref{t-3-2-8} \\
\\
{\bf 96.} & {\bf Project Contingency} & Table~\ref{t-3-2-8} \\
\\
{\bf 97.} & {\bf Interest during Construction (IDC)} 
& Table~\ref{t-3-2-10} \\
\\
{\bf 98.} & {\bf Escalation during Construction (EDC)} & 
Table~\ref{t-3-2-10} \\
\\
{\bf 99.} & {\bf Total Capital Cost (TCC)} \\
\\
\hline
\multicolumn{3}{l}{$^{(a)}$  Adapted from Table 2.3-VII of
Ref.~\cite{ARIES1} and Table 2.2-XV of Ref.~\cite{ARIES4}.}\\
\multicolumn{3}{l}{$^{(b)}$ Installed cost (LSA~=~4), including
future learning credits for a tenth-of-a-kind plant.}\\
\multicolumn{3}{l}{$^{(c)}$  Gross electrical power, $P_{ET}$,
net electrical power, $P_{E}$, and total thermal power, $P_{TH}$,}\\
\multicolumn{3}{l}{\phantom{$^{(c)}$} are given in MW. Volumetric
$V$~(m$^3$)
or corresponding mass $M$~(tonne) unit costs}\\
\multicolumn{3}{l}{\phantom{$^{(c)}$} for the FPC and
related items are given as follows:}\\
\multicolumn{3}{l}{\phantom{$^{(c)}$}
\ \ Reactor building, $V_{RB} = 4 \, (R_T + r_s + 9)^2 (f_z r_s) + 
1.50\X 10^5$
+ 150 \hbox{$P_{CD}^{NBI}$};} \\
\multicolumn{3}{l}{\phantom{$^{(c)}$}
\ \ Blanket, $M_{BL}$ ; Shield, $M_{SHD}$;}\\
\multicolumn{3}{l}{\phantom{$^{(c)}$}
\ \ Magnet coils, $M_C$; Structure, $V_{STR}$; 
Vacuum tank,
$M_{VAC}$;}\\
\multicolumn{3}{l}{\phantom{$^{(c)}$}
\ \ Divertor-plate surface area, $A_{DIV}$ (m$^2$).}\\
\multicolumn{3}{l}{$^{(d)}$ Liquid metal, $M_{LM}$ (tonne):\ $^6$Li 
enriched,
$0.075 < f_{^6Li} < 0.90$~\cite{Bad82}.}\\
\multicolumn{3}{l}{$^{(e)}$ Applicable to CRFPR~\cite{Kra86} and
MARS~\cite{Log84}. }\\
\multicolumn{3}{l}{$^{(f)}$ Applicable to \TI\ ~\cite{TITAN}. }\\
\multicolumn{3}{l}{$^{(g)}$ Applicable to \TII\ ~\cite{TITAN}. }\\
\multicolumn{3}{l}{$^{(h)}$ 0.32 \$/W for \AIIIF\ ~\cite{ARIES3} case only. }\\
\multicolumn{3}{l}{$^{(i)}$ Ref.~\cite{Del89c}. }\\
\multicolumn{3}{l}{$^{(j)}$ Applicable to \AI\ ~\cite{ARIES1}. }\\
\end{tabular}
%\label{t-3-2-7}
\end{table}

The cost data base consists of cost scaling relationships of the general
form
%
\begin{eqnarray}
\label{e-4-2-46}
 C_j \, (\$) & = & c_j \, (X_j)^{e_j} \: ,
\end{eqnarray}
%
where $X$ can be either a descriptive variable ({\it e.g.,} power, mass,
volume) or a scaled variable, $X_j/X_{REF}$, related to a reference value,
$X_{REF}$ of $X_j$, and $e_j$ is an appropriate scaling exponent (usually
\hbox{$0 < e_j < 1$}). \hbox{Equation~(\ref{e-4-2-46})} can be rewritten in the
form
%
\begin{eqnarray}
\label{e-4-2-47}
 C_j & = & \frac{c_j \, (X_j)^{1-e_j}\ (X_j)^{e_j}}{(X_j)^{1 - e_j}}
  \: = \: \left[ \frac{c_j}{(X_j)^{1-e_j}}\right] \, X_j \: ,
\end{eqnarray}
%
which allows the definition of a (variable) unit cost
%
\begin{eqnarray}
\label{e-4-2-48}
 u_j & = & \frac{c_j}{(X_j)^{1-e_j}} \: ,
\end{eqnarray}
%
and is a dependent function of the descriptive variable, $X_j$, itself.  While
the cost accounting scheme allows for detailed cost breakdowns (to four
levels), only a two-level subset of items is estimated and reported explicitly
for their conceptual reactor design.  The cost scaling exponents, $e_j$, used
for the ARIES series and the SPPS are typically consistent with those of the
U.S.\ fission-reactor experience~\cite{Del88b} and represent the inclusion of
quality-control costs associated with nuclear-safety-grade (N-stamped)
components.

Minimal effort was devoted to architectural/engineering (AE) issues relating to
the SPPS/MHH plant layout, as well as building design and costing.  The
reactor-building elevation and plan views depicted on p.~20-95 to 20-98 of the
STARFIRE report~\cite{Bak80} are considered relevant to ARIES-tokamak and
SPPS/MHH applications.  The MFE reactor building is a (large) rectangular
ribbed-box structure subdivided into a reactor hall and a ``process-module
room'' containing the primary coolant loop and other support systems.  The
reactor-building reinforced-concrete walls and roof have a thickness of 1.5~m
for seismic, tornado-missile, and radiation-shielding reasons; the building is
steel-lined to contain tritium.  The interior layout assumes fully remote
maintenance and contains a 600-tonne-capacity overhead bridge crane.  The floor
of the reactor hall and process-module room is at grade level, supported by a
16-m high subgrade structure and pipe chase.  The volume of the process-module
room is retained as a fixed contribution of $1.5\X 10^{5}$ ~m$^{3}$, to which
is added a 15\% increment for an intermediate coolant loop (ARIES-II and
SPPS/MHH), to which is added volume for neutral-beam injection (NBI, ARIES-III
only), based on the scaling $V_{NBI}=150P_{NBI}$, where $V_{NBI}$ is in
m$^{-3}$ and $P_{NBI}$ (MW) is the NBI power.  The reactor hall scales with the
size of the FPC envelope and has differing peripheral and overhead clearance
requirements based on the choice of either horizontal or vertical remote
maintenance.  Horizontal maintenance is adopted for the SPPS/MHH.  The reactor
building volumes, $V_{RB}$, for ARIES-I, -II, -III, and -IV are $1.96\X
10^{5}$, $2.18\X 10^{5}$, $2.30\X 10^{5}$, and $2.03\X 10^{5}$~$m^{3}$,
respectively.  The corresponding building volume for the SPPS/MHH is $2.33\X
10^{5}$~$m^{3}$.  Other buildings are taken to be fixed costs ({\it cf.},
STARFIRE~\cite{Bak80}), including 14.98~M\$ for the power-supply building, and
124.62~M\$ for miscellaneous buildings (including 87.77~M\$ for the hot-cell
building).  The cost of the Turbine building (TB) is scaled~\cite{Mil93} by
$C_{21.3}=C_{TB}$ (M\$) $=28.67(P_{ET}/1,200)^{0.75}+5.72$, where the second
term represents ``fixed'' building services and architectural costs ({\it cf.},
STARFIRE~\cite{Bak80}).

\subsubsection{LSA Credits}
\label{s-3-2-3-2}

Potential cost savings derived from the substitution of conventional
(non-nuclear) components, as well as the elimination of certain active safety
systems or other excess components~\cite{Bru91,Mot93}, under the condition of
demonstrable inherent safety are significant, but controversial~\cite{Mar93}.
Cost differentials between fission and coal plants reflect both quality
assurance requirements and distinct considerations related to extreme loads
({\it e.g.}, seismic, missiles, {\it etc.})~\cite{Ste84}.  Investment
protection considerations may inhibit taking full advantage of possible
credits. Cost credits represent both the simplifications resulting from the
elimination of active safety systems as well as the assumed reduction in costs
associated with the quality assurance requirements mandated in the U.~S. by
Appendix B of 10CFR50 [{\it i.e.}, the substitution of conventional for
nuclear-safety-grade (N-stamped) components].  Detailed bulk-commodity and
labor costs for N-stamped {\it versus} conventional construction are described
in Sec.~2.3 of Ref.~\cite{Del93}.  The safety assurance credit factors used for
the \AI\ study ({\it cf.} \hbox{Table 2.3-VI} of Ref.~\cite{ARIES1}) have been
superseded for the present study by a new set of credits associated with the
various Levels of Safety Assurance (LSA)~\cite{Pie86,Hol89,Del90c}, which
provide progressive discounts relative to nuclear-safety-grade (LSA~=~4) costs
to credit passive safety down to conventional (LSA~=~1, coal plant) costs for
certain cost subaccounts.  Following Piet~\cite{Pie86} and ESECOM~\cite{Hol89},
LSA~=~4 denotes active protection ({\it i.e.}, active engineered safety systems
are required); the system does not meet the minimum requirements for inherent
safety.  For LSA~=~3, safety is assured by passive mechanisms of release
limitation as long as severe violations of small-scale geometry ({\it e.g.},
large coolant pipe breaks) are avoided.  For LSA~=~2, safety is assured by
passive mechanisms as long as severe reconfiguration of large-scale geometry is
avoided.  For LSA~=~1, safety is assured by passive mechanisms of release
limitation for any accident sequence; radioactive inventories and material
properties preclude a fatal release regardless of the reactor's condition.  The
postulated LSA cost-credit factors~\cite{Del90c} are summarized in
\hbox{Table~\ref{t-3-2-8}}.

\begin{table}[p]
\caption{}
\centering
{\bf Level of Safety Assurance (LSA) Cost-Credit Factors$^{(a)}$}
\vspace{0.7cm}
\renewcommand{\arraystretch}{0.88}
\begin{tabular}{l c c c c l}\hline
\quad LSA:       & 1 & 2 & 3 & 4 & \\
\hline
 & \hspace{1.5 truecm} & \hspace{1.5 truecm} & \hspace{1.5 truecm} &
\hspace{1.5 truecm} & \\
Blanket$^{(b)}$                   & 0.90  & 0.95 & 1.0\Z & 1.0\Z & \\
Shield$^{(b)}$                    & 0.90  & 0.95 & 1.0\Z & 1.0\Z & \\
Coils$^{(b)}$                     & 0.90  & 0.95 & 1.0\Z & 1.0\Z & \\
Reactor \& hot-cell buildings     & 0.60  & 0.90 & 0.96 & 1.0\Z & \\
Other structures and improvements & 0.60  & 0.67 & 0.67 & 1.0\Z & \\
Heat transfer and transport       & $(c)$ & 1.0\Z & 1.0\Z & 1.0\Z & \\
Other Reactor Plant Equipment     & 0.85  & 0.94 & 0.94 & 1.0\Z & \\
Turbine Plant Equip. \& building  & 1.0\Z & 1.0\Z & 1.0\Z & 1.0\Z & \\
Electrical Plant Equipment        & 0.75  & 0.84 & 0.84 & 1.0\Z & \\
Miscellaneous Plant Equipment     & 0.85  & 0.90 & 0.93 & 1.0\Z & \\
Heat reject system                & 1.0\Z & 1.0\Z & 1.0\Z & 1.0\Z & \\
Land                              & 1.0\Z & 1.0\Z & 1.0\Z & 1.0\Z & \\
All other direct cost areas       & 1.0\Z & 1.0\Z & 1.0\Z & 1.0\Z & \\
Indirect costs, Acct. No.:        &   &  &  &             & \\
\quad 91. Constr. Ser. \& Equip.$^{(d)}$  & 0.113 & 0.120 & 0.128 & 
0.151 & \\
\quad 92. Home Off. Engr. \& Ser.$^{(d)}$ & 0.052 & 0.052 & 0.052 & 
0.052 & \\
\quad 93. Field Off. Engr. \& Ser.$^{(d)}$ & 0.052 & 0.060 & 0.064 & 
0.087 & \\
\quad 94. Owner's Cost$^{(e)}$ & 0.150 & 0.150 & 0.150 & 0.150 & \\
\quad 95. Process Contingency$^{(f,g)}$ &  NA   &  NA   &  NA   &  NA   
& \\
\quad 96. Project Contingency$^{(f)}$ & 0.150 & 0.173 & 0.184 & 
0.195 & \\
O\&M costs$^{(h)}$                & 0.70  & 0.85 & 0.925 & 1.0\Z & \\
D\&D allowance, $C_{D\&D}$ (mill/kWeh):        & & & & & \\
\quad nominal \$                   & 0.38 & 0.75 & 1.13 & 1.50 & \\
\quad constant \$                  & 0.25 & 0.50 & 0.75 & 1.00 & \\
\\ 
\hline
\multicolumn{6}{l}{$^{(a)}$ Multiplicative factor applied to cost
model accounts, {\it cf.} Refs.~\cite{Del89c,Del90c}, }\\
\multicolumn{6}{l}{\phantom{$^{(a)}$} superseding Table 2.3-VI of
 Ref.~\cite{ARIES1}.}\\
\multicolumn{6}{l}{$^{(b)}$ {\it cf.} Refs.~\cite{May85,Lee86,Del88a,ARIES1}.}\\
\multicolumn{6}{l}{$^{(c)}$ 0.60 for liquid metal or other cooling
system requiring an intermediate heat}\\
\multicolumn{6}{l}{\phantom{$^{(c)}$} exchanger (IHX) or a helium
or other cooling system requiring a double-}\\
\multicolumn{6}{l}{\phantom{$^{(c)}$} walled steam generator
with LSA~=~4; 0.90 otherwise.}\\
\multicolumn{6}{l}{$^{(d)}$ factor $\X\, [TDC]$}\\
\multicolumn{6}{l}{$^{(e)}$ factor $\X\, [TDC + C_{91} + C_{92} +
C_{93}]$}\\
\multicolumn{6}{l}{$^{(f)}$ factor $\X\, [TDC + C_{91} + C_{92} + C_{93}
+
C_{94}]$}\\
\multicolumn{6}{l}{$^{(g)}$ Not applied to a mature, tenth-of-a-kind
commercial plant.}\\
\multicolumn{6}{l}{$^{(h)}$ from \hbox{Eq.~(\ref{e-4-2-52})}, also see
Ref.~\cite{Del90a}.}\\
\end{tabular}
\label{t-3-2-8}
\end{table}

\subsubsection{Financial Assumptions}
\label{s-3-2-3-3}

The economic models used for the ARIES tokamaks and the SPPS/MHH are largely
consistent with updates~\cite{Del89b} made to the GENEROMAK~\cite{She86,Del88a}
models, incorporating, for example, a lowering of the federal income tax rate
from 46\% to 34\% under provisions of the U.S. Tax Reform Act of 1986.  The
discount rate influences societal choices by reflecting economic risk and
weights the present rather than future consumption.  Generally, a high discount
rate penalizes capital-intensive projects ({\it e.g.}, fusion and fission
relative to coal) and can reverse the advantages provided by lower fuel costs.
The financial parameters assumed here are consistent with those of
U.~S. utilities; industrial or Independent-Power-Producer (IPP) ownership of
the power plant results in significantly higher cost of money, as shown in
Table 3.1. of Ref.~\cite{Del93}.  The resulting impact on the COE of a typical
tokamak power plant is severe enough, as shown in Table~1 of Ref.~\cite{Mil96},
with the COE for the same plant ascribed to a non-utility generator (NUG)
projected to be 37\% -- 50\% higher.  A similar penalty is expected for a
stellarator power plant.  Thus, non-utility ownership of a capital-intensive
fusion power plant is not likely.  The economic parameters assumed in the
costing model used in the \A\ and SPPS/MHH studies are summarized in
\hbox{Table~\ref{t-3-2-9}}.

The detailed methodology for calculating the time-related cost factors is
described in \hbox{Refs.~\cite{She86}} and \cite{Ham85}.  This description
differs from the U.S.\ fusion-reactor-community standards~\cite{Sch78,Phu79}
used in the period 1980 to 1985 because a slightly different ``s-shaped''
spending profile during construction is assumed. A more precise spending
profile could be derived from a detailed construction schedule and historical
experience, as has been attempted in the past for fission systems~\cite{Aec74},
consistent with the present approximation, but such an effort is not justified
by the level of detail of the \A\ and SPPS/MHH conceptual designs.  The
reference design and construction lead time, $\tau_{c}$, for the ARIES tokamaks
and SPPS/MHH conceptual power plants is assumed to be six years, consistent
with the STARFIRE study~\cite{Bak80} and projections for advanced fission
systems that would be licensable and accepted by the public.  Such a schedule
assumes factory fabrication and timely delivery of modular FPC components.  The
critical path in the reference schedule ({\it cf.} Fig. 23-1. of
Ref.~\cite{Bak80}) is determined by construction of the reactor building and
installation of the FPC.  Development of more detailed algorithmic construction
schedules, which might be expected to penalize larger or more complex systems,
was beyond the scope of the ARIES study and the SPPS effort, as well.  Standard
assumptions regarding construction time (\hbox{$\tau_c = 6$~y}), plant capacity
factor ($p_f=0.76$), economies of scale, and operations and maintenance (O\&M)
charges are used to estimate the constant-dollar (1992) COE.  Without
developing a detailed construction schedule, the construction lead time is
taken to be six years, which is in common with the lead times of the
STARFIRE~\cite{Bak80}, MARS~\cite{Log84}, TITAN~\cite{TITAN}, and
\A~\cite{ARIES1,ARIES4} studies.

\begin{table}[p]
\caption{}
\centering{\bf Reference Economic Parameters$^{(a)}$}
\vspace{0.7cm}
\renewcommand{\arraystretch}{0.94}
\begin{tabular}{l  c}\hline
\\
Plant life (analysis period), N (yr)  & 30 \\
Plant lead (construction) time, $\tau_c$ (yr)          & \Z6 \\
Indirect and Contingency cost factors        & $^{(b)}$ \\
Factor for interest during construction, $f_{IDC}$: & \\
\quad Nominal \$              & 0.2630 \\
\quad Constant \$             & 0.1652 \\
Factor for escalation during construction, $f_{EDC}$: & \\
\quad Nominal \$              & 0.2335 \\
\quad Constant \$             & 0.0\Z\Z \\
Assumed plant capacity factor, $p_{f}$ & 76\% \\
Factor for spares$^{(c)}$, Acct. No.: & \\
\quad 21-23.98.                  & 0.02 \\
\quad 24.98.                  & 0.04 \\
\quad 25.98.                  & 0.03 \\
\quad 26.98.                  & 0.00 \\
Average cost of money$^{(d)}$, $x_{COM}$ (/yr): & \\
\quad Nominal \$   & 0.1135 \\
\quad Constant \$  & 0.0605 \\
Effective tax-adjusted cost of money (discount rate), X (/yr): & \\
\quad Nominal \$, X & 0.0957 \\
\quad Constant \$, $X_{0}$ & 0.0435 \\
Inflation rate, {\it y} (/yr) & 0.05 \\
Effective state and federal tax rate, t (/yr) & 0.3664 \\
Local property tax rate (/yr) & 0.02 \\
Tax depreciation life (yr): & \\
\quad Overall plant     & 15 \\
\quad Replaceable blankets, {\it etc.} & \Z5 \\
Fixed charge rate, FCR: & \\
\quad Nominal \$, $FCR$        & 0.1638 \\
\quad Constant \$, $FCR_{0}$   & 0.0966 \\
Interim annual replacement rate, RR (/yr) & 0.005 \\
\\ \hline
\multicolumn{2}{l}{$^{(a)}$ {\it cf.} Ref.~\cite{Del88a}, Table 3.1., as
updated ({\it cf.} Refs.~\cite{Del89b,Doe88}).}\\
\multicolumn{2}{l}{$^{(b)}$ LSA dependence 
({\it cf.} Table~\ref{t-3-2-8}.).}\\
\multicolumn{2}{l}{$^{(c)}$ {\it cf.} Ref.~\cite{Bak80}.}\\
\multicolumn{2}{l}{$^{(d)}$ Allowance for Funds Used During 
Construction (AFUDC) rate.}\\
\end{tabular}
\label{t-3-2-9}
\end{table}

\clearpage

Cost of electricity, COE (mill/kWeh), estimates are somewhat sensitive to
construction time through the time-dependent interest (for constant \$)
or interest and escalation (for nominal-dollar) factors, summarized on
Table~\ref{t-3-2-10}.  Following the discussion in Appendix D.IV of
Ref.~\cite{She86}, the factor for interest during construction, $f_{IDC}$,
is calculated for a representative construction (spending) profile, and
the factor for nominal-dollar escalation during construction,
$f_{EDC}=f_{cap}-f_{IDC}$.

\begin{table}[b]
\caption{}
\centering{\bf Time-Related Economic Factors$^{(a)}$ }
\vspace{1.0cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular} {l c c c c l}\hline
\multicolumn{1}{c}{Lead Time (yr)}
   & \multicolumn{2}{c}{Constant \$}
   & \multicolumn{2}{c}{Nominal \$} & \\
\multicolumn{1}{c} { }
 & $f_{IDC}$ & $f_{EDC} = 0$ & $f_{IDC}$ & $f_{EDC}$ & \\
\hline \\

\quad \Z3 & 0.0863  &             & 0.1624  & 0.0951  & \\
\quad \Z4 & 0.1118  &             & 0.2119  & 0.1394  & \\
\quad \Z5 & 0.1381  &             & 0.2637  & 0.1887  & \\
\quad \Z6$^{(b)}$ & 0.1652  &             & 0.3178  & 0.2436  & \\
\quad \Z7 & 0.1931  &             & 0.3743  & 0.3045  & \\
\quad \Z8 & 0.2219  &             & 0.4332  & 0.3719  & \\
\quad \Z9 & 0.2515  &             & 0.4948  & 0.4466  & \\
\quad  10 & 0.2821  &             & 0.5591  & 0.5291  & \\
\quad  11 & 0.3136  &             & 0.6263  & 0.6201  & \\
\quad  12 & 0.3460  &             & 0.6964  & 0.7206  & \\
\quad  13 & 0.3795  &             & 0.7696  & 0.8312  & \\
\quad  14 & 0.4139  &             & 0.8461  & 0.9530  & \\
\quad  15 & 0.4495  &             & 0.9261  & 1.0869  & \\
\\ \hline
\multicolumn{5}{l}{$^{(a)}$ compare with Table 22-54. of Ref.~\cite{Bak80}.}\\
\multicolumn{5}{l}{$^{(b)}$ Reference construction lead time, $\tau_{c}$.}\\
\end{tabular}
\label{t-3-2-10}
\end{table}

\subsubsection{Cost of Electricity}
\label{s-3-2-3-4}

The COE is the most important evaluation tool for optimizing and comparing with
alternative energy sources.  Both constant-1992 and nominal- or
then-current-1998 dollar analyses (consistent with the assumed six-year design
and construction lead time, $\tau_c$) are used to evaluate the projected costs.
Constant-dollar cost is defined as the cost measured in dollars that have a
general purchasing power as of some reference date, while nominal- (current or
as-spent) dollar costs include inflation~\cite{Del93}.  The projected busbar
energy cost is given by
%
\begin{eqnarray}
\label{e-4-2-49}
 \mbox{COE} & = & \frac{C_{AC} + \left(C_{O\&M} + C_{SCR}+ 
      C_F\right) (1 + y)^Y} {8760 \, P_E \, p_f} + C_{D\&D} \: ,
\end{eqnarray}
%
where COE (mill/kWeh) is Cost of electricity in constant or nominal (then-
current) dollars; $C_{AC}$ is the annual capital cost charge, equals the total
capital cost (TCC) multiplied by the fixed charge rate (FCR); $C_i$ is the cost
of account $i$; $C_{O\&M}$ is the annual operations and maintenance cost,
($C_{O\&M}=C_{40}+C_{41}+\dots+C_{47}$); $C_{SCR}$ is the annual scheduled
component-replacement cost, ($C_{SCR}=C_{50} +C_{51}$); $C_F$ is the annual
fuel costs, $C_{02}$; $y$ is the annual escalation rate; $Y$ is the
construction period (in year); $P_E$ is the net plant electrical power (MWe) or
Design Electrical Rating (DER); $p_f$ is the plant capacity factor; TDC is the
total direct cost (\hbox{TDC $= \sum^{26}_{i =20} C_i$}); $C_{IDC}$ is the
interest during construction (\hbox{$C_{97} = f_{IDC} \,$TDC}, {\it cf.}
Table~\ref{t-3-2-10}); $C_{EDC}$ is the escalation during construction
(\hbox{$C_{98} = f_{EDC} \,$TDC}, {\it cf.} Table~\ref{t-3-2-10}); TCC is the
total capital cost (\hbox{TCC $= \sum^{98}_{i = 20} C_i$}); and $C_{D\&D}$ is
the decontamination and Decommissioning (waste disposal) allowance.

Because of possible erosion and neutron damage, plasma facing components and
the blanket structure are periodically replaced on a scheduled basis
independent of possible repair/replacement due to unscheduled failures.  In
this regard, these nonpermanent components are analogous to the fuel elements
in a fission reactor, leading the GENEROMAK study~\cite{Del88a,Del91} to
exclude the cost of these items from the direct cost of the FPC.  Such an
approach, while understandable and conceptually consistent with fission
industry practice, when applied to fusion systems where these items represent a
larger fraction of the cost of the FPC, leads to a misleading (in the view of
the ARIES Team) underestimate of the direct cost of the FPC.  Therefore,
following the practice of the STARFIRE~\cite{Bak80}, TITAN~\cite{TITAN}, and
ARIES~\cite{ARIES1,ARIES4} studies, such items are included in the direct
costs.  The \AI\ study~\cite{ARIES1} did not amortize the cost of
replaceable blanket sectors over their individual periods of service, as
recommended by Ref.~\cite{Del88a}.  For the recent \AIIoIV\ study~\cite{ARIES4}
and present SPPS, an appropriate calculation of the annual cost of the present
worth of the revenue requirement for the investment in components which have a
service period, $L = I_w\tau/{\hat I_w}$, that is, the neutron-fluence lifetime
divided by the peak neutron wall load.  Following Eq. (3.7) of
Ref.~\cite{Del88a}, the present worth, F, of the revenue requirements for a
unit investment that is depreciated for tax purposes over a period, T, is given
by
%
\begin{eqnarray}
\label{e-4-2-50}
 F & = &  \frac{1}{(1 - t)} \left[1 - t \sum_{n=1}^{T} \frac{d_{n}}{(1 +
  x)^{n}}\right] \: ,
\end{eqnarray}
%
where $t=0.3664$~yr$^{-1}$ is the effective tax rate, $d_{n}$ is the fraction
of the cost which is deductible for tax purposes in year $n$ after investment,
and $x = 0.1135$ is the nominal-dollar cost of money from Table~\ref{t-3-2-9}.
For the scheduled replacement items of the FPC, a $T = 5$ year depreciation
schedule is used, {\it cf.} Table 2 of Ref.~\cite{Del89b} and Table 2.6. of
Ref.~\cite{Doe88}, resulting in $F=1.272$.  Thus, the appropriate term in
\hbox{Eq.(~\ref{e-4-2-49})} becomes
%
\begin{eqnarray}
\label{e-4-2-51}
 C_{SCR} \propto (C_{21.1.1} + C_{22.1.8})CRF(X_{0},L)F(1+f_{96})/L \: ,
\end{eqnarray}
%
where the contingency cost factor, $f_{96}$, from Table~\ref{t-3-2-8} has been
included.  No additional engineering indirect costs are applied.  For an
assumed first-wall neutron fluence life \hbox{$I_w \tau = 16.4\,$MW yr/m$^2$}
at a cost-optimized peak neutron wall load of \hbox{$\hat I_w \simeq
2.11\,$MW/m$^2$} and a plant capacity factor \hbox{$p_f \simeq 0.76$}, routine
(scheduled) replacement of the first wall and blanket occurs every 7.8
full-power years or 10.2 calendar years. The cost of used (spent) blanket
disposal is assumed to be part of the decontamination and decommissioning
cost. No explicit credit has been taken for recovery/recycling of blanket
material, although this is a recognized, but perhaps minor, cost-savings
measure.

The cost of scheduled component replacement is separate from the annual
operations and maintenance charge (Acct.~40.--47., 51.). The O\&M cost was
previously estimated~\cite{Sch78,Sch79} to be $\sim$2\% of the direct cost,
assessed annually; the present projection is approximately 1.8\% of the direct
cost. The O\&M cost is scaled, together with its LSA factor from
Table~\ref{t-3-2-8}, by~\cite{Del90a}
%
\begin{eqnarray}
\label{e-4-2-52}
 C_{O\&M} \, \mbox{(M\$/y)} & = & 74.4 \, (P_E/1200)^{0.5} \: ,
\end{eqnarray}
%
for the \AIIoIV\ and SPPS/MHH studies.  This revised projection is $\sim$6\%
higher than that used for the \AI\ study~\cite{ARIES1,Del89a}.  This O\&M cost,
strictly speaking, depends on system complexity and the requirements of
regulations, security, and maintenance, such that there may, in fact, be
discernable differences between tokamaks and stellarators not identified or
credited (one way or the other) because of the use of this simplifying power
scaling.

The SPPS/MHH power plant is assumed to have a 30-yr service life and an average
plant capacity factor, $p_{f}=0.76$, corresponding to 22.8 full-power years.
At the end of the tenth and twentieth years of operation, an extended outage of
120 days is anticipated for turbine generator overhaul and concurrent
superconducting TF-coil anneal (if necessary), resulting in a contribution of 8
days to the annual scheduled downtime.  Additionally, 28 days per year are
allocated for routine scheduled outages, including the replacement of FPC
FW/blanket modules.  For unscheduled outages, 52 days per year are budgeted,
leading to a total downtime of 88 days per year, corresponding to $p_{f}=0.76$.
A detailed allocation of downtimes for maintenance and/or replacement among
subsystems has not been made.

Cost projections made for the fission industry~\cite{Del91} use a similar
capacity factor, which is a target that has been exceeded by individual plant
experience, but which is beyond the recent U.S. fission industry average of
69.3\%~\cite{How93}.  Projections as high as 90\% for the availability and 85\%
for the corresponding capacity factor of advanced (future) fission systems have
been made~\cite{Bru91}.  The capacity factor is often less than the
availability factor, reflecting regulatory restriction or load following.  The
higher complexity and size (mass) of fusion systems components may imply an
availability penalty relative to fission systems.  As seen from
\hbox{Eq.~(\ref{e-4-2-49})}, the value of $p_f$ affects the projected COE
hyperbolically.

In parametric studies, the plant capacity factor has been assumed to be
independent of the plant size ({\it i.e.}, $P_E$).  Although ambiguous
evidence~\cite{Lee90} from the fission industry exists that $p_f$ decreases
with increasing $P_{ET}$, this trend is not seen in more recent U.S. fission
experience~\cite{Bla93}.  Such an effect, if present, inhibits attempts to
exploit ``economies of scale'' by pushing to larger plant sizes as a means to
decrease COE values~\cite{Dol93}.

The fuel cost, $C_F$, of deuterium for is represented by Account~02.  The unit
cost of deuterium as $D_2$ is 3,700~\$/kg~\cite{Sch79,Bak80}; deuterium
contributes negligibly to the COE of a fusion power plant.  In the long run,
the power plant is self-sufficient in terms of tritium fuel production because
of the breeding capability of the blanket so that no specific tritium-fuel
charge is reported.  It should be recognized, however, that a significant
``hidden'' cost for tritium exists in the direct cost of the DT fueled fusion
reactor ({\it i.e.}, thicker, more complex tritium breeding blanket with
thermal-hydraulic constraints not encountered soley by heat-recovery
requirements).

\section{DESIGN POINT SELECTION}
\label{s-3-3}

The SPPS/MHH reference design is selected to meet simultaneously 1) the
geometric constraint imposed by the incorporation of a minimal blanket/shield
standoff distance into the scaleable reference MHH plasma/coil configuration,
2) a technology limit on peak magnetic field strength at the coil, and 3) a
target net electrical power output of 1,000 MWe.  The latter point is somewhat
arbitrary, but facilitates certain cost comparisons with the ARIES tokamak
power plant designs.  It should be noted that such design decisions taken at
the conceptual level might mask significant differences in performance and cost
that could arise by exploiting the unique features of one approach relative to
the other.

\subsection{Plasma Physics}
\label{s-3-3-1}

Physics parameters of the SPPS/MHH reference design are summarized in
\hbox{Table~\ref{t-3-3-1}} in comparison with those of ARIES-II~\cite{ARIES4}.
The tokamak performance optimization leads to lower plasma beta in order to
reduce the current-drive power requirement.  Thus, the MHH beta value used here
exceeds that of the tokamak.  Absent a scaling relating the beta value to
plasma aspect ratio or profile parameters, for example, the SPPS/MHH physics
parameters should be considered as representative, but not necessarily
optimized in the global context of the design point.  Operating at comparable
plasma temperatures ($\sim$10~keV), the SPPS/MHH plasma density is somewhat
lower, consistent with the lower confining magnetic field.  The plasma volumes
are comparable, but the larger plasma and first-wall surface area of the
SPPS/MHH results in a lower neutron wall load, as seen below in the comparison
of engineering parameters.  Energy confinement is similar in the two conceptual
designs.  In both cases, the radiation fraction, $f_{RAD}\simeq 0.2$, helps to
spread the surface heat flux over the entire first wall and relieve the heat
flux on the divertor plates.

\begin{table}[p]
\caption{}
\centering {\bf Physics Parameters}
\vspace{0.6cm}
\renewcommand{\arraystretch}{1.00}
\begin{tabular}{l @{\hspace{1.0 truecm}} c c}\hline
                                        & ARIES-II & SPPS/MHH  \\
\hline
Plasma major toroidal radius, $R_T$ (m)      & 5.60  & 13.95   \\
Plasma minor radius, $a_p$ (m)               & 1.40  & 1.16   \\
Plasma vertical elongation, $\kappa_\times$  & 2.03  & 2.00   \\
Plasma vertical elongation, $\kappa_{95}$    & 1.80  & (1.77) \\
Plasma triangularity, $\delta_\times$        & 0.67  & NA     \\
Plasma triangularity, $\delta_{95}$          & 0.48  & NA     \\
Plasma volume, $V_p$ (m$^3$)                 & 399   & 735    \\
Plasma aspect ratio, $A=R_T/a_p$             & 4.0   & 12.08  \\
Plasma aspect ratio, $A^{\star}=R_T/r_p$     & NA    & 8.54   \\
Circularized safety factor, $q_\ast$         & 4.6   & NA     \\
Plasma-edge safety factor, $q$               & 12.2  & NA     \\
Troyon coefficient, $C_T$ (Tm/MA)            & 0.059 & NA     \\
Plasma beta, $\beta$                         & 0.034 & 0.050  \\
Plasma poloidal beta, $\beta_\theta$         & 5.40  & NA     \\
Stability parameter, $\epsilon\beta_\theta$  & 1.35  & NA     \\
Ion temperature, $T_i$ (keV)                 & 10.0  & 10.0   \\
Electron temperature, $T_e$ (keV)            & 10.3  & 10.5   \\
Ion density, $n_i$ (10$^{20}$~m$^{-3}$)      & 2.15  & 1.31   \\
Electron density, $n_e$ (10$^{20}$~m$^{-3}$) & 2.50  & 1.46   \\
Particle-to-energy confinement time ratio, $\tau_p/\tau_E$
                                             & 9.80  & 4.00  \\
Ion-to-electron energy confinement time ratio, $\tau_{Ei}/\tau_{Ee}$
                                             & 1.0\Z & 1.0\Z \\
Lawson parameter, $n_i\tau_E$ (10$^{20}$s/m$^3$)
                                             & 2.71  & 2.55   \\
ITER-89P scaling~\cite{Pos90} multiplier, $H$  & 3.07 & NA   \\
Lackner-Gottardi~\cite{Lac90,Wel91} multiplier, $H$ & NA & 2.3 \\
On-axis toroidal field, $B_{o}$ (T)          & 7.97  & 4.94 \\
Radiation fraction, $f_{RAD}$                & 0.18  & 0.21 \\
Plasma current, $I_\phi$ (MA)                & 6.43  & $\sim$0 \\
Bootstrap-current fraction, $f_{BC}$         & 0.87  & $\sim$0 \\
Current-drive power to plasma, $P_{CD}$ (MW) & 66.1  & 0.0 \\
Current-drive efficiencies: \\
\quad $I_p/P_{CD}$ (mA/W)                    & 13.06 & NA  \\
\quad $\gamma (10^{20}$ A/W-m$^2$)           & 0.18  &  NA\\
\\ \hline
\end{tabular}
\label{t-3-3-1}
\end{table}

\subsection{Engineering}
\label{s-3-3-2}

\begin{table}[p]
\caption{}
\centering {\bf Engineering Parameters}
\vspace{0.6cm}
\renewcommand{\arraystretch}{1.00}
\begin{tabular}{l @{\hspace{1.0 truecm}} c c}\hline
                         &ARIES-II&SPPS/MHH\\
\hline \\
Field at TF coil, $B_{c}\rm (T)$&15.9&14.5\\
TF-coil stress (MPa)&633&TBD\\
TF-coil current density (MA/m$^2$)&31.6&30.0\\
Stored magnetic energy (GJ)&83$^{(a)}$&80 (est.)\\
Fusion power, $P_F$ (GW)&1.91&1.73\\
Neutron power, $P_N$ (GW)&1.53&1.38\\
Average neutron wall load, $I_w$ (MW/m$^2$) &2.90&1.18\\
Peak neutron wall load, $\hat I_w$ (MW/m$^2$) &5.08&2.11\\
Neutron fluence life, $I_w\tau$ (MW yr/m$^2$) &16.4&16.4\\
Average blanket energy multiplication &1.38&1.40\\
Average first-wall heat flux, $q_w$(MW/m$^2$)&0.31&0.29\\
Blanket power density, $P_{TH}/V_{BLK}$ (MW/m$^3$)&10.7&6.03\\
Current-drive system efficiency, $\eta_{CD}$ &0.54&NA\\
Thermal conversion efficiency, $\eta_{TH}$ &0.46&0.46\\
Thermal power, $P_{TH}\rm (GWth)$ &2.57&2.29 \\
Auxiliary site power, $P_{AUX}$ (MW)&47.3&42.2\\
Primary loop pumping power (MW)&11.8&10.5\\
Gross electrical power, $P_{ET}\rm (GWe)$&1.18&1.05\\
Net electrical power, $P_E\rm (GWe)$&1.0&1.0 \\
Recirculating power fraction, $\epsilon = 1/Q_E$ &0.15&0.052 \\
Plasma gain, $Q_p=P_F/P_{CD}$&28.9&$\sim$2000\\
Engineering gain, $Q_E$&6.49&19.28\\
Net plant efficiency, $\eta_p = \eta_{TH} (1 - \epsilon)$ &0.39&0.44\\
Plant capacity factor, $p_f$ &0.76&0.76\\
Masses (ktonne):&   \\
\quad First wall, blanket, and reflector  &0.43&0.25\\
\quad Shield      &6.02&9.45\\
\quad TF coils    &1.81&4.10\\
\quad PF coils    &0.59&NA  \\
\quad Fusion power core&10.80&21.23\\
Mass power density, MPD (kWe/tonne)&92.6&47.1\\
Level of Safety Assurance, LSA &2&2\\
\\ \hline
\multicolumn{2}{l}{$^{(a)}$ TF: 65 GJ, PF: 18 GJ}
\end{tabular}
\label{t-3-3-2}
\end{table}

Engineering parameters of the SPPS/MHH and \AII\ are summarized comparatively
in \hbox{Table~\ref{t-3-3-2}}.  The SPPS/MHH is constrained to operate at a
somewhat lower peak magnetic field strength as a concession to the
uncertainties introduced by its nonplanar coil technology.  Should this concern
be dissipated by future experience, the MHH design could be improved by access
to higher fields and correspondingly higher power density.  As it stands, the
average 14.1-MeV-neutron first-wall load is less than half that of the \AII\
tokamak at the same net electrical power output, $P_E=1.0$~GWe.  With both
devices invoking the self-cooled-Li/V blanket, the thermal conversion
efficiency is taken to be $\eta_{TH}=0.46$ in both cases.  The Level of Safety
Assurance (LSA) was set at 2 for both devices for purposes of cost credits.
Absent the tokamak current-drive power requirement, the MHH has a significantly
lower recirculating power fraction, $\epsilon$.  The cost benefit of the lower
recirculating power offsets the implied penalty of lower power density on
direct cost, as seen below.

\subsection{Costing}
\label{s-3-3-3}

For purposes of the projected Cost of Electricity (COE) calculation, both the
\AII\ and the SPPS/MHH are here taken to have the same (default) value of plant
capacity factor, $p_f \simeq 0.76$.  More detailed work in the area of
reliability, availability, amd maintenance (RAM) anaylsis might well establish
an advantage in this figure of merit for one of the two approaches.
Differences in unscheduled (forced) outages based on the different
configurations and loads are possible.  Also, differences in scheduled downtime
based on the details of the module changeout scenarios for the two devices can
be postulated.  Unfortunately, fixing the capacity factor partly decouples the
COE projection from the design and obscures some dependancies which otherwise
contribute to the identification of the `near-optimum' design.  Similarly,
assuming the same construction lead time may tilt the comparative results
somewhat.  Both the \AII\ and SPPS/MHH have been taken to have the same
construction lead time, $\tau_{c}=6$~yr, for purposes of calculating the
time-related cost ({\it i.e.}, interest during construction).  A more detailed
consideration of both systems, with a view toward developing construction
schedules, might be expected to generate some distinction resulting in a
differential cost impact.  The level of design work required to better
establish some of the factors in the COE projection often is unavailable to the
conceptual power-plant study.  Such work was beyond the scope of the present
SPPS, but should be addressed in any future work.

Comparative cost breakdowns for the \AII\ and SPPS/MHH are summarized in
\hbox{Table~\ref{t-3-3-3}}, using 1992 as the reference year.  Level of Safety
Assurance (LSA) cost credits consistent with LSA~=~2, reflecting a level of
passive safety and lower source term (relative to fission), are assumed in both
cases.  COE values for LSA~=~4 are also noted, consistent with full
nuclear-safety-grade surcharges.  The direct cost of the SPPS/MHH is found to
be slightly higher than that of the \AII\, which drives a higher total capital
cost as well as a higher projected constant-dollar COE.

\begin{table}[p]
\caption{}
\centering {\bf Economic Parameters (1992 \$)}
\vspace{0.6cm}
\renewcommand{\arraystretch}{0.8}
{\small
\begin{tabular}{l l c c}\hline
\vspace{0.2cm}
Acct.\ No. & \hfil Account Title \hfil & \AII\ & MHH \\
           &                           & \multicolumn{2}{c}{Million Dollars}\\
\hline \\
20.     & Land and land rights                   &  \Z\Z10.4 &   \Z\Z10.4\\
21.     & Structures and site facilities         &   \Z328.3 &    \Z332.8\\
22.     & Reactor plant equipment (RPE)          &    1361.8 &     1475.6\\
22.1.1  & \ \ First wall, blanket, and reflector &  \Z\Z53.8 &   \Z\Z71.5\\
22.1.2  & \ \ Shield                             &   \Z366.4 &    \Z289.8\\
22.1.3  & \ \ Magnets                            &   \Z205.8 &    \Z381.4\\
        & \ \ \ TF coils                         &   \Z159.6 &           \\
        & \ \ \ PF coils                         &  \Z\Z46.2 &           \\
22.1.4  & \ \ Supplemental heating systems       &   \Z194.3 &   \Z\Z54.2\\
22.1.5  & \ \ Primary structure and support      &  \Z\Z35.3 &    \Z149.7\\
22.1.6  & \ \ Reactor vacuum systems             &  \Z\Z51.1 &   \Z\Z85.4\\
22.1.7  & \ \ Power supplies                     &  \Z\Z55.3 &   \Z\Z55.3\\
22.1.8  & \ \ Impurity control                   & \Z\Z\Z5.4 &   \Z\Z12.0\\
22.1.9  & \ \ Direct energy conversion system    & NA        &      NA   \\
22.1.10 & \ \ ECRH breakdown system              & \Z\Z\Z4.3 &  \Z\Z\Z4.3\\
22.1    & \ \ Reactor equipment (RE)             &   \Z971.7 &     1103.6\\
22.2    & Main heat transfer and transport       &   \Z231.9 &    \Z217.8\\
23.     & Turbine plant equipment (TPE)          &   \Z279.8 &    \Z254.0\\
24.     & Electric plant equipment (EPE)         &   \Z109.5 &    \Z103.6\\
25.     & Miscellaneous plant equipment (MPE)    &  \Z\Z55.5 &   \Z\Z51.9\\
26.     & Special materials                      &  \Z\Z14.8 &   \Z\Z21.0\\
90.     & Total direct cost                      &    2160.3 &     2249.4\\
91.     & Construction services and equipment    &   \Z259.2 &    \Z269.9\\
92.     & Home office engineering and services   &   \Z112.3 &    \Z117.0\\
93.     & Field office engineering and services  &   \Z129.6 &    \Z135.0\\
94.     & Owner's costs                          &   \Z399.2 &    \Z415.7\\
96.     & Project contingency                    &   \Z516.5 &    \Z537.8\\
97.     & Interest during construction (IDC)     &   \Z590.9 &    \Z615.3\\
98.     & Escalation during construction (EDC)   & \Z\Z\Z0.\Z&  \Z\Z\Z0.\Z\\
99.     & Total capital cost                     &    4168.3 &     4340.2\\
\\
             & & \multicolumn{2}{c}{\us{Constant dollars}} \\
{[90]}       & Unit direct cost, UDC (\$/kWe)      & 2,160.4 &    2,249.4\\
{[94]}       & Unit base cost, UBC (\$/kWe)        & 3,577.4 &    3,724.8\\
{[99]}       & Unit total cost, UTC (\$/kWe)       & 4,168.4 &    4,340.2\\
\\
             & Capital return (mill/kWeh)          & 60.52   & 63.02\\
{[40-47,51]} & O\&M (mill/kWeh)                    &\Z9.16   &\Z9.16\\
{[50]}       & Blanket replacement (mill/kWeh)     & \Z3.63  &\Z1.90\\
             & Decommissioning (mill/kWeh)         &\Z0.50  &\Z0.50\\
{[02]}       & Fuel (mill/kWeh)                    & \Z0.03  &\Z0.03\\
             & Cost of electricity, COE (mill/kWeh)$^{(a)}$&  73.84  & 74.60\\
\\ \hline
\multicolumn{3}{l}{$^{(a)}$ LSA~=~2; values are 84.06 and 85.39,
 respectively, for LSA~=~4.}
\end{tabular}
}
\label{t-3-3-3}
\end{table}

At $\sim$74 mill/kWeh, it would not be possible to discriminate between the two
approaches on the basis of cost in light of the conceptual nature of the
supporting studies for each and the many remaining uncertainties.  Improvements
in both approaches leading to lower COE values are recognized as being
desireable, but difficult to achieve, given the fundamental constraints
presently understood for magnetic fusion.  The ratios of reactor equipment (RE)
to reactor plant equipment (RPE) direct costs are $RE/RPE =$ 0.71 and 0.75 for
the \AII\ and SPPS/MHH, respectively.  The ratios of RPE direct cost to the
total direct cost (TDC) are $RPE/TDC =$ 0.63 and 0.66, respectively.  The
ratios of TDC to total capital cost (TCC) are 0.52 in both cases, given the
common financial factors and (assumed) common construction time.  The tabulated
data regarding these cost components are summarized comparatively in
\hbox{Fig.~\ref{f-3-3-1}} as histograms to facilitate the comparison between
\AII\ and the SPPS/MHH, and to highlight the cost drivers.

\begin{figure}[b]
\centerline{\hspace{1.cm}
            \psfig{file=spps-3-3-1-a.ps,width=2.20in,bbllx=68pt,bblly=57pt,%
            bburx=394pt,bbury=420pt,clip=} \hfil
            \psfig{file=spps-3-3-1-b.ps,width=2.20in,bbllx=68pt,bblly=57pt,%
            bburx=394pt,bbury=420pt,clip=} \hfil
            \psfig{file=spps-3-3-1-c.ps,width=2.20in,bbllx=68pt,bblly=57pt,%
            bburx=394pt,bbury=420pt,clip=}}
\caption[f-3-3-1]
{Cost breakdown of the reactor equipment cost (left), the direct cost (middle),
and the cost of electricity (right) in 1992 \$ for the \AII\ tokamak and the
SPPS/MHH power plants.  The abbreviations used are: FW/B/R for first wall,
blanket, and reflector; HEATING for supplemental-heating and current-drive
systems; STR for primary structure and support; VAC for vacuum systems; PS for
power supply, switching and energy storage; IMP CONTRL for impurity control;
ECRH BD for ecrh breakdown system; \hbox{S\&SF} for structures and site
facilities; RPE, TPE, EPE, and MPE for reactor, turbine, electric, and
miscellaneous plant equipment, respectively; SM for special materials; CAPITAL
for capital return; O\&M for operations and maintenance; REPLACE for FW/B/R
replacement; and D\&D for decontamination and decommissioning.}
\label{f-3-3-1}
\end{figure}

\clearpage

Having created a comprehensive, albeit simplified, model integrating physics,
engineering, and cost considerations, it is hardly avoidable that it be
exercised to determine the `near-optimal' SPPS/MHH configuration, subject to
the set of constraints and assumptions described here.  Some notice should also
be taken of the unquantified considerations ({\it e.g.}, complexity, technology
extrapolation, and risk) that are also key aspects of the characterization of a
viable, competitive future energy source.  These considerations are not
generally tractable in such studies as the SPPS.

\section{PARAMETRICS AND SENSITIVITIES}
\label{s-3-4}

To establish the context for the reference SPPS/MHH reference design described
in the previous subsection, a number of parametric and sensitivity scans using
the ASC$^{\star}$ were performed.  Both physics and engineering parameters were
addressed with a view toward identifying any high-leverage factors deserving
attention in follow-on power-plant studies or emphasis in the ongoing
stellarator R\&D effort.

To illustrate the impact of physics assumptions, \hbox{Fig.~\ref{f-3-4-1}}
displays the impact of $\beta$ on the projected COE.  For this and subsequent
figures, the plasma aspect ratio is fixed such that \hbox{$A^{\star} \equiv
R_T/r_{p} \simeq 8.54$}.  The major toroidal radius, $R_T$, is used as the
independant search variable in the ASC$^{\star}$.  As $R_T$ increases, the
FPC increases in size and direct cost, leading to higher COE values as system
power density falls.  For fixed net electrical output, $P_{E}$, and fixed
thermal conversion efficiency, $\eta_{TH}$, the product $({\beta}^{2} {B}^{4}
{V}_{p})$ is a constant, with larger, lower-power-density devices allowing for
lower magnetic-field strengths at both the plasma axis and at the modular coil
windings, as monitored by $B_{c}$ (T).  The apparent incentive is to reduce the
size of the FPC while maximizing the value of $B_{c}$ up to any imposed
technology limit.  Choice of the limiting peak coil field strength, $B_{c}
\simeq 14.5 \, T$, precludes access to smaller, cheaper devices.  Higher beta
values than the 5\% reference SPPS value, allow a more compact FPC with
resultant cost reductions just as lower beta values lead to COE increases, as
shown.  With the plant capacity factor, $p_{f}$, held fixed, there is no
higher-order availability/maintenance discriminator between devices of
different size.  Similarly, there is no higher-order discriminator deriving
from different construction lead times, ${\tau}_{c}$.  A possibly important,
but unknown, physics dependancy is that of the beta value on plasma aspect
ratio, A.  In the absence of information on this issue, a parametric search
that proved to be salient in the ARIES tokamak studies could not be applied to
the present SPPS work.  The plasma temperature is fixed such that $T_{i} \simeq
T_{e} \simeq 10$ keV, neglecting variations as plasma density, $n_{i,e}$, and
confinement factor, $H$, adjust to the changing values of magentic-field
strength, $B$, and $V_{p}$ (m$^3$) to preserve the target net electrical power
output, $P_{E}$ (MWe).  The reference SPPS/MHH design point is denoted
explicitly.

\begin{figure}[t]
\centerline{\psfig{file=spps-3-4-1.ps,height=4.4in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=592pt,clip=}}
\caption[f-3-4-1]
{Dependence of MHH projected Cost of Electricity, COE, on effective major
toroidal radius, $R_T$, for the indicated values of $\beta$ and the indicated
fixed parametes.  Isoquants for several values of magnetic field strength at
the coils, $B_{c}$, are indicated by the dashed lines.  The reference SPPS/MHH
design point with $\beta=0.05$ is denoted by the open circle.}
\label{f-3-4-1}
\end{figure}

Variations in the value of net electrical output power, $P_{E}$ are shown in
\hbox{Fig.~\ref{f-3-4-2}}. The reference SPPS/MHH value is $P_{E} = 1,000 \,
MWe$, to facilitate certain direct comparisons with the ARIES and PULSAR
tokamak designs.  The economies of scale suggest lower projected COE values,
for fixed plant capacity factor, $p_{f} \simeq 0.76$, as $P_{E}$ increases.
There is no fundamental inhibition standing in the way of matching the gross
electrical output, $P_{ET} \, (MWe)$, MHH with the largest (single)
turbogenerator unit available (currently $\sim 1,350 \, MWe$ in the U.S. or
$\sim 1,500 \, MWe$ in France).  The lower recirculating power of the
stellarator, relative to the tokamak, allows the stellarator to take full
advantage of the utilization of the largest available turbogenerator.
Economies of large unit provide some incentive to develop even larger
turbogenerators, but this approach stacks another development step in the path
of fusion R$\&$D.  It is also possible to consider multiple turbogenerators of
a nominal rating driven by a large FPC, but this approach incurrs some cost
penalty and is not generally recommended.  Absent the significant current drive
recirculating power requirements of tokamak power plants, the typical
stellarator plant could be deliberatly larger than a tokamak, with some cost
benefit accruing to the stellarator.  This issue has not been exploited in the
course of the SPPS.

\begin{figure}[t]
\centerline{\psfig{file=spps-3-4-2.ps,height=4.4in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=592pt,clip=}}
\caption[f-3-4-2]
{Dependence of projected MHH Cost of Electricity, COE, on effective major
toroidal radius, $R_T$, for the indicated values of $P_{E}$ and the indicated
fixed parametes.  Isoquants for several values of magnetic field strength at
the coils, $B_{c}$, are indicated by the dashed lines.  The reference SPPS/MHH
design point with $P_{E}=1,000$~MWe is denoted by the open circle.}
\label{f-3-4-2}
\end{figure}

\clearpage

Additional consideration of the first-wall 14.1-MeV neutron wall load results
in the dotted isoquants of \hbox{Fig.~\ref{f-3-4-3}} being added as an overlay
to the results of \hbox{Fig.~\ref{f-3-4-2}}.  For the assumed fixed value of
plant capacity factor, $p_f \simeq 0.76$, there is no direct influence of the
(peak) wall load on the COE through the scheduled-componet-replacement
contribution.  Fixing the value of $p_f$ represents a (default) starting
assumption, pending further work.  Degradation of the $p_f$ at higher $P_{E}$
will inhibit access to larger plants or a technological limit on surface heat
flux or blanket power density will come into play as $P_{E}$ increases.

\begin{figure}[b]
\centerline{\psfig{file=spps-3-4-3.ps,height=4.8in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=592pt,clip=t}}
\caption[f-3-4-3]
{Dependence of MHH projected Cost of Electricity, COE, on effective major
toroidal radius, $R_T$, for the indicated values of $P_{E}$ and the indicated
fixed parametes.  Isoquants of average 14.1-MeV neutron first-wall load are
shown.  The reference MHH design point with $P_{E} = 1,000 MWe$ is denoted by
the open circle.}
\label{f-3-4-3}
\end{figure}

\clearpage

Inclusion of a reliablility, availability, and maintenance (RAM) model,
developed in the course of the PULSAR study~\cite{PULSAR}, allows
preliminary consideration of the adverse impact of higher first-wall neutron
load (with fixed fluence lifetime) on the plant capacity factor, $p_{f}$.
For each indicated value of net electrical power output, $P_{E}$, the
COE projection is shifted upward, as seen in \hbox{Fig.~\ref{f-3-4-4}},
as a result of the longer scheduled outage time to replace first-wall/blanket
modules.  This effect further inhibits consideration of larger plant sizes.

\begin{figure}[b]
\centerline{\psfig{file=spps-3-4-4.ps,height=4.8in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=592pt,clip=}}
\caption[f-3-4-4]
{Dependence of MHH projected Cost of Electricity, COE, on effective major
toroidal radius, $R_T$, for the indicated values of $P_{E}$ and the indicated
fixed parametes.  The reference MHH design point is denoted by the open
circle.}
\label{f-3-4-4}
\end{figure}

\clearpage

The reference SPPS/MHH coil technology assumes a Nb$_{3}$Sn superconductor.
For larger FPCs at the same value of net electrical power output, $P_{E}$.
the magnetic field will drop to the level at which NbTi superconductors,
with lower unit costs, are appropriate.  Such a transition does not result
a design with costs near the reference SPPS/MHH design, as shown in
\hbox{Fig.~\ref{f-3-4-5}}, insofar as the cost differential between the
conducter options is modest~\cite{ARIES4}.  The homogenized coil cost
simplification is only a preliminary convenience; a better treatment is
recommended.

\begin{figure}[b]
\centerline{\psfig{file=spps-3-4-5.ps,height=4.8in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=592pt,clip=}}
\caption[f-3-4-5]
{Dependence of MHH projected Cost of Electricity, COE, on effective
major toroidal radius, $R_T$.
  The reference
MHH design point is denoted by the open circle.}
\label{f-3-4-5}
\end{figure}

\clearpage

The economy of scale available to larger plant sizes is offset somewhat by
the lower projected plant capacity factor, $p_{f}$, attributable to longer
scheduled outages to replace first-wall/blanket sectors, as shown in
\hbox{Fig.~\ref{f-3-4-6}}.  Here, an alternative parametric space is introduced
to suggest that the plant capacity factor, $p_{f}$, and unit overnight cost,
UOC (k\$/kWe), are independant drivers of the COE.  To the extent that a
compact FPC with low UOC is correlated with higher neutron wall load, the
value of $p_{f}$ should be reduced to track a larger scheduled maintenance
downtime.  Also, higher loads and stress can be expected to result in
increased forced outages of the FPC, also resulting in lower values of $p_{f}$.

\begin{figure}[b]
\centerline{\psfig{file=spps-3-4-6.ps,height=4.8in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=590pt,clip=}}
\caption[f-3-4-6]
{MHH phase space of plant capacity factor, $p_{f}$,
 and net electrical power output, $P_{E}$.
An isoquant of $COE = 70 \, mill/kWeh$ is indicated by the dashed line.
The reference SPPS/MHH design point is denoted by the open circle.}
\label{f-3-4-6}
\end{figure}

\clearpage

The nominal SPPS/MHH construction lead time, $\tau_{c}$ was taken to be six
years, in common with the ARIES and PULSAR studies.  The coils and
blanket/shield modules for all of these plants would be expected to be factory
fabricated and shipped to the plant site and thus not constitute the critical
path in the construction schedule.  The larger FPC of the MHH results in a
larger reactor hall than is required for the tokamaks, so it might be
reasonable to consider a somewhat longer construction time.  This relative
penalty is considered a higher-order correction, beyond the scope of the
present SPPS study, but is mentioned for consideration in future work.  The
corresponding COE penalty is a few mill/kWeh per year of ``delay'', as
illustrated in \hbox{Fig.~\ref{f-3-4-7}}.  No additional dependence of the
construction lead time on the major radius has been developed.  A more detailed
construction schedule, deriving from a more detailed power plant design effort,
is required to resolve this issue.

\begin{figure}[b]
\centerline{\psfig{file=spps-3-4-7.ps,height=4.2in,bbllx=0pt,bblly=202pt,%
            bburx=468pt,bbury=590pt,clip=}}
\caption[f-3-4-7]
{Dependence of MHH projected Cost of Electricity, COE, on effective major
toroidal radius, $R_T$, for various values of costruction lead time, $\tau_{c}$
and the indicated fixed parameters.  The reference SPPS/MHH design point, with
$\tau_{c}=6$~yr, is denoted by the open circle.}
\label{f-3-4-7}
\end{figure}

\clearpage

\section{CONCLUSIONS}
\label{s-3-5}

The systems analysis work performed in the course of the SPPS provides the
basis for the conceptual design study by characterizing a plausible and
integrated point design in terms of plasma physics, engineering, and economics.
Several of the models used in the SPPS systems-code variant, ASC$^{\star}$,
must be characterized as rudimentary and deserve refinement in any future work.
While the design basis of the SPPS/MHH and the ARIES tokamak series is
comparable,
several aspects of the engineering have been improved in more recent versions
of the tokamak ASC~\cite{Bat96}, as reflected in Starlite (Demo)
candidates and the ARIES-RS (reversed shear) commercial power plant.  It was
not possible to back-fit these more recent considerations into the present
SPPS/MHH description.  Thus, the SPPS/MHH design is already somewhat
out-of-step (`obsolete' is too harsh of a characterization).  A strictly
current reconciliation of evolving approaches to economics, as summarized
in Refs.~\cite{Mil96,Hen96}, was similarly not back-fit to the SPPS/MHH.

Lacking certain scaling models, the SPPS/MHH
design point should be considered representative, rather than an optimal
configuration at the level of recent ARIES tokamak designs~\cite{Kra94b}.
The 1,000-MWe class SPPS/MHH is seen to be reasonably competitive with tokamaks
using the usual figures of merit.  The low value of recirculating power helps
to offset the disadvantages of fairly low power density.
Some of the specialized attributes of the SPPS/MHH stellarator could well be
exploited further to improve its competitive position.  The stellarator could
perhaps take advantage of economies of scale by positioning at a larger
plant size than a tokamak, the latter being more constrained by
surface-heat-load and power density considerations.

\clearpage
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\bye

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