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\begin{document}

\title{\bf 5. FUSION POWER CORE}
\author{
\autlist{Dai-Kai Sze}{Laila A. El-Guebaly}{Igor N. Sviatoslavsky}
\autlist{}{Xueren~Wang}{}
}
\date{ }
\maketitle

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

\setcounter{chapter}{4}
\setcounter{page}{1}

\chapter{FUSION POWER CORE}

\section{INTRODUCTION}
\label{s-5-1}

The performance and the safety characteristics of a power plant are usually
determined by the selection of the structural material.  This material has to
be able to withstand high temperatures and resist severe radiation damage.
After the structural material has been selected, other materials, such as
breeding material and/or coolant, can be selected to be compatible with the
structural material.  The selection of the structural material has to take the
following requirements into consideration: (1)~High temperature capability,
(2)~High radiation damage resistance, (3)~High heat flux capability, (4)~Low
near-term and long-term activation, (4)~Low after heat, (5)~Low unit cost,
and (6)~Ease of fabrication.

It can be seen that no structural material can fulfill all those requirements.
Thus, the selection of the structural material is usually a compromise
procedure trying to satisfy as many requirements as possible.
\hbox{Table~\ref{t-5-1-1}} outlines a comparison of the three possible
candidates of the structural materials.  The three materials selected are
ferritic steels, V-alloy, and SiC composite.  The score is from 1 to 3, with 3
being the best and 1 being the worst.  The total score will indicate the
attractiveness of each material for the fusion applications. The total score of
V-alloy is 19, which is much higher than that of either SiC or ferritic
steels. Thus, it is reasonable to select V-alloy as the structural material.

\begin{table}[tb]
\caption{}
\centering{\bf Structural Material Compositions} \\
\vspace{1.0cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c}
\hline
                       & Ferritic steels & V-Alloy & SiC composite \\
\hline \\
High temperature capability      & \Z1\D & \Z2\D   & \Z3\D \\
High radiation damage resistance & \Z2\D & \Z3\D
                                    & \phantom{$^{(a)}$}\Z1$^{(a)}$\D\\
High heat flux capability        & \Z1.5 & \Z3\D   & \Z1.5 \\
Low near term activation         & \Z1\D & \Z2\D   & \Z3\D \\
Low long term activation         & \Z1\D & \Z3\D   & \Z2\D \\
Low after heat                   & \Z1\D & \Z2\D   & \Z3\D \\
Low unit cost                    & \Z3\D & \Z2\D   & \Z1\D \\
Ease of fabrication              & \Z3\D & \Z2\D   & \Z1\D \\
Total score                      &  13.5 &  19\D   &  15.5 \\
\\ \hline
\multicolumn{4}{l}{$(a)$ Almost no data on radiation damage on
SiC composite.}\\
\end{tabular}
\label{t-5-1-1}
\end{table}

After V-alloy is selected as the structural material, the selection of the
coolant and breeding material follows. One of the key issues associated with
using V-alloy is that it is reactive to both hydrogen and oxygen.  Lithium is
one of the few materials which has an even stronger affinity for both hydrogen
and oxygen than vanadium. Thus, if lithium is in contact with V-alloy, both
hydrogen and oxygen will be preferentially dissolved in the lithium. This
resolves a key problem associated with using V-alloy.  Also, lithium has the
following unique characteristics: (1)~Low activation, (2)~High temperature
capability, (3)~Good heat transfer characteristics, (4)~Good tritium sink
(tritium control is not an issue), (5)~Low density.

In selecting lithium as the coolant and breeding material, the following
concerns have to be resolved: (1)~Lithium is chemically reactive with air,
water, CO$_2$, concrete, {\it etc.}  Thus, the design must prevent any
potential lithium accident. (2)~Lithium is an electric conductor.  Thus, the
follow of lithium across the magnetic field will result in large MHD pressure
drop. Any design has to take this MHD pressure drop into
consideration. (3)~Lithium is a good tritium sink.  Thus tritium recovery from
lithium is a concern.  (4)~Lithium can be corrosive to certain structural
materials, such as SiC or stainless steel.  However, the compatibility between
lithium and V-alloy is not a major concern.

To reduce the MHD pressure drop, an insulating coating is required.  This
insulating coating has to be compatible with lithium at high temperatures,
resistive to radiation damage and thermal cycling, and compatible to tritium
recovery processes.  It also has to be reliable over many years of operation.
The most promising material for the insulating coating is CaO. The development
of the insulating coating is still in an early stage, and many issues have to
be resolved.  The design of the fusion core, including MHD considerations, heat
transfer, power conversion, and tritium recovery systems are discussed in
Sec.~\ref{s-5-2}.

\clearpage

Lithium is not a good shielding material, therefore, another material is
required to provide this function.  While V-alloy is acceptable for the
shielding function, the cost of the V-alloy is high, and the volume of material
required for shielding is large.  Thus, it is not economically feasible to use
V-alloy for shielding purposes.  A low activation ferritic steel called tenelon
was selected as the shielding material due to its good neutronics properties and
low cost. The tenelon is inside a vanadium container and is not directly in
contact with lithium.  Also, the tenelon does not provide structural function.
Thus, tenelon can operate at a temperature higher than that for structural
purposes.  The use of tenelon and its neutronics importance will be discussed
in \hbox{Section~\ref{s-5-3}}. The complicated geometry of stellarator fusion
core, makes configuration and maintenance of the fusion core an essential
element of the design (Sec.~\ref{s-5-4}).

\section{POWER CORE DESIGN}
\label{s-5-2}

\subsection{Configuration}
\label{s-5-2-1}

For the SPPS power plant, a liquid metal blanket with electrically insulated
coating on the walls is selected as the reference design.  Such a choice is
consistent with the philosophy of SPPS of opting for the most favorable yet
creditable option available.  The use of the insulating coating has major
impacts on the configuration.  It allows one to develop a very attractive first
wall and blanket design by addressing mechanical, thermal hydraulic, and
neutronics requirements in the most direct and simple way rather than by trying
to minimize MHD pressure drop effects by utilizing more complex flow
configurations.  Even with an insulated wall, MHD effects associated with
turbulence suppression on heat transfer are still present.  Therefore, proper
care must be taken when the configuration is defined to avoid configurations
which create stagnation flow regions near high heat flux surfaces, negate the
effect of the insulating coating by providing current closure paths through the
liquid metal, or result in poor flow distribution.  This can be done without
compromising the simplicity or the performance of the blanket.

In choosing an insulated wall concept as the reference design, a number of
challenging MHD-related issues are eliminated.  On the other hand, the
credibility of this design is based entirely on the integrity of the insulating
coating in the blanket environment.  Several candidate ceramic
insulators~\cite{r1,r2,r3} possess the necessary resistivities to satisfy the
electrical insulating requirements.  The primary candidate at this time is
CaO~\cite{r4}.  The development of insulating coating is in the early stage.
Therefore, the choice of the insulating coating material may change as new
materials will be tested, and technical problems will be uncovered as the
testing progresses.

The proposed design has an integrated first wall and blanket.  The front part
of the shield, which has a shorter life time than the design life of the power
plant, is also an integrated part of the first wall and blanket.  The back part
of the shield is designed to be a permanent component.  A blanket module is
shown schematically in \hbox{Fig.~\ref{f-5-2-1}}.

\begin{figure}[b]
\centerline{\psfig{file=spps-5-2-01.eps,height=4.7in}}
\caption[f-5-2-1]
{Blanket assembly for SPPS power plant.}
\label{f-5-2-1}
\end{figure}

Coolant is brought into the blanket module assembly through the magnet coils by
one 25-cm and one 20-cm diameter pipes at the bottom of the assembly.  The
25-cm pipe empties into the first-wall/blanket manifold and the 20-cm pipe
empties into the shield manifold.  The tow manifolds, which have a combined
cross section of 50~cm x 50~cm, extend along the entire toroidal length of the
assembly.  Coolant ducts emanate from the manifolds, run along the poloidal
direction, and empty into identical manifolds symmetrically located at the top
half of the assembly.  Outlet pipes identical to the inlet pipes take the
coolant out of the power plant.

Figure~\ref{f-5-2-2} shows a section of the blanket by a horizontal mid-plane
of the torus.  The first wall coolant channels are rectangular ducts with a
10-mm $\X$ 50-mm cross section.  The first wall should be smooth both for ease
of fabrication and because it has some MHD related advantages.  The
disadvantage of a flat wall is the fact that the maximum material stress is
bending stress, which is usually considerably higher than a corresponding hoop
stress.  This limits either the maximum allowable coolant pressure, or the duct
dimension along the toroidal direction.  The first wall thickness of 2 mm is a
compromise between lower thermal stress and lower bending stress.  The 2 mm
given here does not include any sacrificial layer required for erosion
protection.

\begin{figure}[b]
\centerline{\psfig{file=spps-5-2-02.eps,height=4.0in}}
\caption[f-5-2-2]
{Cross-sectioned view of SPPS blanket.}
\label{f-5-2-2}
\end{figure}

The radial direction of the first wall coolant channel must be made as
small as possible because the high coolant velocity required at the
first wall coolant channel must be made as small as possible.  This is
due to the fact that the high coolant velocity required at the first
wall coolant channel results in lower average exit coolant temperature,
unless the radial dimension is made sufficiently small.  Here, a
dimension of 10 mm was thought to be a reasonable compromise between
this requirement and the virtual elimination of any possibility of the
first wall coolant channel plugging.

The coolant velocity in the blanket has to be carefully controlled.  The
design velocity in the reeding zone will decrease as the distance from
the first wall increases.  This is because the nuclear heat deposition
rate reduces as the distance from the first wall increases.  This is
also to make the coolant exit temperature from all the coolant channel
uniform, thus maximizing average coolant exit temperature and
thermodynamic efficiency.  The tailoring of the velocity to the local
deposition rate can be accomplished with ducts whose radial dimension
increases with distance from the first wall.  If additional flow control
is required, an orifice can be build into the loop to control the
coolant flow.  This ``orifice'' can be based on effects.  A possible
design is to insert a short metal inner sleeve at the inlet
manifold/coolant duct junction.  The wall thickness and the length of
those inserts are adjusted to add different MHD pressure drops along the
different parallel coolant paths.

With the configuration described here, the MHD, neutronics, and heat
transfer calculations can be proceeded.

\subsection{MHD Considerations}
\label{s-5-2-2}

For a self-cooled liquid metal blanket for a Tokamak, a key design
consideration, and often a design constraint, is the magnetohydrodynamic (MHD)
pressure drop.  Allowable blanket pressure is determined by the acceptable
mechanical stress on the first wall, and/or other blanket structural
components.  The factors determining the MHD pressure drop include flow
velocity, duct dimension, duct wall thickness, magnetic field strength, coolant
flow path length, and the electrical conductivities of the liquid metal and the
structural material.  This MHD pressure drop is proportional to the wall
thickness.  Thus, increasing the wall thickness to withstand the high blanket
pressure will increase the blanket pressure further.  Therefore, it is very
possible that the design of a self-cooled liquid metal blanket will not have an
acceptable design window, with a condition consistent with the physics
requirements~\cite{r3}.

To reduce the MHD pressure drop, one possible design approach is to disrupt the
conducting path of the eddy current within the structural wall.  Either a
laminated wall with a thin wall facing the liquid metal flow, or an insulated
coating, can enlarge the space of the design window.  A design with an
insulating coating will reduce the MHD pressure drop by a few orders of
magnitude, while the laminated wall design will only reduce the MHD pressure
drop by a factor of a few.  Thus, a design with an insulated wall will be much
more attractive.  Therefore, the R/D effort follows~\cite{r4}.  In the US
coating is developed which will be reliable within the blanket environment.
This design, with an insulated wall, allows one to develop a very attractive
first wall and blanket design by addressing mechanical, thermal hydraulic, and
neutronics requirements in the most direct and simple way rather than trying to
minimize adverse MHD pressure drop effects by utilizing more complex flow
configurations.

To compare MHD pressure drop with a conducting wall and with an insulated wall,
the following calculation clearly shows the big difference.  For a conducting
wall duct,
%
\begin{eqnarray}
\label{e-5-2-1}
  \frac{dp}{dx} & = & \frac{VB^2 t_w \sigma_w}{a}  \: ,
\end{eqnarray}
%
where $V$ is the average velocity, $B$ is the transverse magnetic field, $t_w$
is the wall thickness, and $\sigma_w$ is the wall electrical conductivity.
For an insulated wall conduct,
%
\begin{eqnarray}
\label{e-5-2-2}
 \frac{dp}{dx} & = & \frac{\sigma V B^2}{M} \: ,
\end{eqnarray}
%
where $\sigma$ is the fluid electrical conductivity  and
\hbox{$M = Ba (\sigma/\mu)^{1/2}$} is the Hartmann number.

Using the above expression with $a=5$~cm, $t_w=5$~mm, $B=11$~T, $V=1$~m/s, and
$L=1$~m ($L$ is the flow path length), the pressure drops for a conducting wall
case and insulated wall case are 12~MPa and 0.01~MPa, respectively.  This
calculation clearly shows the important effect of an insulated wall on the MHD
pressure drop.  Also, it shows the problem associated with MHD pressure drop
with a conducting wall.

A feasible insulating coating must meet the following requirements:
(1)~Thermodynamically stable at the maximum blanket temperature, (2)~Chemically
compatible with lithium and the structural material, (3)~Capable of fast
in-situ self-healing, and (4)~Sufficiently high electrical resistivity after
irradiation.

Since all the insulator materials are not perfect insulators, and the
electrical resistivity will increase after irradiation, it is important to
evaluate the MHD pressure drop in a channel with a coating which has finite
conductivity.  The electrical insulation effectiveness of the coating depends
both on the material properties and the design.
The fully developed flow pressure gradient in a duct with insulator
coating of uniform thickness $t_c$ and be derived analytically is given
by~\cite{r5},
%
\begin{eqnarray}
\label{e-5-2-3}
 \frac{dp}{dx} & = & \frac {\sigma V B^2} {1 + 
    \frac{\displaystyle \rho_c \, t_c \, M}
         {\displaystyle \rho_c \, t_c + 2b\rho \, M}}
\end{eqnarray}
%
where $\rho_c$ is the electrical conductivity of the coating material, $\rho$
is the electrical conductivity of the liquid metal, $t_c$ is the coating
thickness, $2b$ is the channel radial width, and $M$ is the Hartmann number.
Equation~\ref{e-5-2-3} shows that the key parameter is the ratio \hbox{$(\rho_c
\, t_c)/(2b\rho \, M)$}. Figure~\ref{f-5-2-3} shows the dependence of pressure
gradient on this parameter.  Two dimensional numerical analysis of MHD flow in
a rectangular duct~\cite{r6} gives similar results.  In general,
\hbox{($\rho_c \, t_c$)} should be at least an order of magnitude higher than
\hbox{$(2b\rho \, M)$}.  For present design, the value of \hbox{$\rho_c \,
t_c > 0.001$}.

\begin{figure}[b]
\centerline{\psfig{file=spps-5-2-03.eps,height=3.3in}}
\caption[f-52-3]
{MHD Pressure drop for partially insulated wall.}
\label{f-5-2-3}
\end{figure}

There are a number of candidate materials which have the potential to be used
as the insulating coating.  If the coating thickness is 10~$\mu$m, the
resistances of those materials are orders of magnitude higher than that
required by fusion. \hbox{Figure~\ref{f-5-2-4}} shows the electrical resistance
of some of the candidate materials, and the requirements for both ITER and
commercial power plants.  The leading candidate at this time is CaO.  It can be
seen that, at 600\SdegC, the resistance of the CaO coating is 7 orders of
magnitude higher than that required by a commercial power plant.  This provides
a large margin to account for the degradation by the neutron irradiation.

Figure~\ref{f-5-2-5} shows the free energy of formation of~CaO
and Li$_2$O, with different oxygen concentration in lithium~\cite{r7}.  It
can be seen that the CaO is much more stable than the Li$_2$O, with
reasonable oxygen concentration inside lithium.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-2-04.eps,height=3.7in}}
\caption[f-2-4]
{Resistance requirement for SPPS and ITER.}
\label{f-5-2-4}
\centerline{\psfig{file=spps-5-2-05.eps,height=3.7in}}
\caption[f-2-5]
{The standard free energy of formation of Li$_2$O and CaO compared with
dilute solutions of oxygen in liquid lithium.}
\label{f-5-2-5}
\end{figure}

It is clear that the research of developing coating, and its impact to
MHD pressure drop and flow distribution, is a critical R\&D issue for a
self-cooled liquid lithium blanket. The R\&D effort on this subject is
still in an early stage and many questions have to be answered.
However, the purpose of this design study is to develop an
attractive fusion core and then assess the R\&D requirements to demonstrate
this concept.  Thus, a self-cooled lithium blanket with a CaO coating is
selected as the reference design.

\subsection{Heat Transfer}
\label{s-5-2-3}

The heat transfer mechanism in a self-cooled liquid lithium blanket in a
tokamak is dominated by conduction.  Although the insulating coating reduces
the MHD pressure drop, its impact on turbulence suppression is still sufficient
to eliminate all turbulence.  Although some recent development indicates that
some form of turbulence can be initiated~\cite{r8}, its impact on heat transfer
is not clear.  If some turbulence does exist, the heat transfer mode here will
get some more conservative results.

To do heat transfer calculations, a proper blanket configuration has to be
defined. With this configuration and the heat and mass balance, the proper
velocity distribution can be calculated.  This velocity distribution, and the
heat production rates, can then be used to calculate temperature distribution
within the blanket.  By assuming the maximum temperature in the blanket is the
same as the maximum allowable temperature, the level of this temperature
distribution can be adjusted to the proper level.  This gives us the complete
temperature profile of the blanket, as well as the entrance and exit coolant
temperature, which will be used for power conversion system designs.

The blanket configuration has been described in
\hbox{Fig.~\ref{f-5-2-2}} and the nuclear heating results will be
discussed in \hbox{Sec.~\ref{s-5-3}}.  A three dimensional heat transfer
code defines~\cite{r9}) all the temperature in the blanket.  The results
of this calculation are summarized in \hbox{Table~\ref{t-5-2-1}}.

\begin{table}[t]
\caption{ }
\centering
{\bf Thermal-hydraulic Parameters for the SPPS Power Plant} \\
\vspace*{1cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l @{\hspace{1.cm}} c}
\hline \\
Total thermal power (MW)                & 2,292 \\
Coolant inlet temperature (\degC)       & 300 \\
Coolant exit temperature (\degC)        & 600 \\
Maximum structure temperature (\degC)   & 650 \\
Average neutron wall loading (MW/m$^2$) & 1.18  \\
Average surface heat load (MW/m$^2$)    & 0.29  \\
Coolant flow rate  (m$^3$/s)            & 3.6  \\
Coolant pressure drop (MPa)             & 1.4  \\
Coolant pumping power (MW)              & 7  \\
Gross thermal efficiency                & 46\% \\
Total lithium volume (m$^3$)            & 600  \\
Tritium inventory (g)                   & 130 \\
\\ \hline
\end{tabular}
\label{t-5-2-1}
\end{table}

\subsection{Power Conversion}
\label{s-5-2-4}

Fusion is capital intensive.  Therefore, in order to reduce the cost of
electricity (COE), an efficient power conversion is necessary.  Also, fusion
has rather high recirculation power fraction.  This requires a high power
conversion system to compensate for the additional power required for the
plasma and magnets.  For a Li/V design, a high coolant exit temperature is
achievable.  Therefore, a high efficiency power conversion system can be
designed.

The limitation factor of the selection of the power conversion system is
usually determined by the selection of the structural material.  Based on the
BCSS report~\cite{r10}, the maximum allowable temperature for vanadium alloy is
$\sim$650--750\SdegC.  With this temperature limit, the maximum achievable exit
coolant temperature is about 600\SdegC.  At this coolant temperature, the only
power conversion system we may consider is an advance Rankine cycle.

The selection of a power conversion cycle is a compromise between performance
and extrapolation of the existing technology.  For the SPPS design, a
sub-critical steam cycle, with two stage of reheat was selected.  The
parameters of this steam cycle are summarized in \hbox{Table~\ref{t-5-2-2}}.
The cycle efficiency is over 46\% comparing to $\sim$35\% for a PWR.

\begin{table}[t]
\caption{ }
\centering
{\bf Parameters of the SPPS Power Conversion System} \\
\vspace{1.0cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l @{\hspace{1.cm}} c}
\hline \\
Exit coolant temperature (\degC) & 610 \\
Steam Temperature (\degC)        & 566 \\
Steam pressure  (MPa)            & 31  \\
Number of re-heat                & 2 \\
Number of feed water heater      & 9 \\
Cycle heating rate (kcal/kWh)    & 145  \\
Cycle efficiency                 & 46.6\% \\
\\ \hline
\end{tabular}
\label{t-5-2-2}
\end{table}

The schematic flow diagram of the temperature in the primary loop is
shown in figure \hbox{Fig.~\ref{f-5-2-6}}, and the detailed power cycle
energy balance sheet is shown in \hbox{Fig.~\ref{f-5-2-7}}.

\begin{sidewaysfigure}[p]
\centerline{\psfig{file=spps-5-2-06.eps,angle=90,height=5.8in}}
\caption[f-5-2-6]
{Primary coolant loop for the SPPS power plant.}
\label{f-5-2-6}
\end{sidewaysfigure}

\begin{figure}[p]
\vspace{1in}
\centerline{\psfig{file=spps-5-2-07.eps,width=6.5in}}
\vspace{1in}
\caption[f-5-2-7]
{Turbine-generator cycle of the SPPS power plant.}
\label{f-5-2-7}
\end{figure}

\subsection{Tritium Recovery}
\label{s-5-2-5}

Tritium recovery from lithium is a difficult technical issue. The key problem
is that tritium has a very high solubility in lithium.  The design goal is to
reduce the tritium concentration in the lithium to $\sim$1~appm.  This
stringent design goal, and the high solubility, makes the recovery process very
difficult. At 500\SdegC, and with a tritium concentration of 1~appm, the
tritium partial pressure over lithium is only $10^{-10}$~torr. Thus, to recover
tritium from vapor phase is almost impossible.  The most logical way is to
recover tritium from the liquid phase.  Many different tritium recover
processes have been proposed~\cite{r11,r12,r13}.  The only one which has
demonstrated the possibility of recovery to the level of 1~appm is the molten
salt recovery process~\cite{r11}.  However, in this process, lithium has to be
mixed with a mixture of molten salts.  This molten salt will be carried back to
the blanket by the lithium.  The potential problems associated with corrosion
and the impact to the insulating coating are major concerns.

Recently, a cold trap process was developed by ITER design
activities~\cite{r14}.  The concept is this process is to cool the lithium to
$\sim$200\SdegC, and supersaturate the Li(H+T) in the lithium.  A similar
process was developed for the fast breeder applications to remove tritium from
sodium.  However, the hydrogen solubility in lithium is 440~appm at 200\SdegC,
far higher than the design goal of 1~appm.  This concept proposes to dissolve
additional hydrogen into lithium to about 1,000~appm.  Thus, although the
tritium concentration is only 1~appm, the total hydrogen concentration would be
more than 1,000~appm, and Li(H+T) becomes supersaturated.  Thus, Li(H+T) will
precipitate out.  This concept is almost identical to that for the breeder
program, which uses isotope effects to reduce the tritium partial pressure,
while here we use the isotope effects to reduce the tritium concentration.
Thus, the entire system was developed successfully for the fast breeder
program, and there is a high degree of confidence this process will work as
designed for fusion.

Figure~\ref{f-5-2-8} shows some early results for cold trap of
hydrogen~\cite{r15}.  One can see that the cold trap concentration is almost
identical to that of the saturation concentration.  This result was used to
reject cold trap as the tritium recovery process from lithium, because the
concentration reachable is far higher than the design goal.

Figure~\ref{f-5-2-9} shows the cold trap process.  As can be seen, protium is
added to the lithium to a concentration of 1,300~appm.  The lithium is than
cooled to the cold trap temperature of 200\SdegC, at which time Li(H+T) will
precipitate out.  This Li(H+T) is heated up to 600\SdegC to decompose the
Li(H+T) to Li and HT.  A 200\SdegC cold trap is used to remove the lithium in
the vapor phase caused by evaporation at 600\SdegC.  After this, the hydrogen
isotopes are fed to the isotope separation system to remove H from T.

Figure~\ref{f-5-2-10} shows the design of the Isotope Separation System (ISS)
for ITER~\cite{r16}.  A careful ISS design study was made, and it was concluded
that the addition protium in the blanket tritium stream has minor effects on
both the tritium inventory in the ISS and the cryogenic power requirement.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-2-08.eps,width=6.5in}}
\caption[f-2-8]
{Cold trap of impurities from lithium.}
\label{f-5-2-8}
\end{figure}

\begin{figure}[p]
\vspace{0.5in}
\centerline{\psfig{file=spps-5-2-09.eps,width=6.5in}}
\vspace{0.5in}
\caption[f-2-9]
{Cold trap of tritium from lithium.}
\label{f-5-2-9}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-2-10.eps,height=7.5in}}
\caption[f-2-10]
{Isotope Separation System (ISS) arrangement.}
\label{f-5-2-10}
\end{figure}

\section{BLANKET NEUTRONICS AND SHIELD DESIGN}
\label{s-5-3}

\subsection{Introduction}
\label{s-5-3-1}

The neutronics activities for the SPPS study include the determination of the
blanket dimensions that provide tritium self-sufficiency, radiation damage to
the structural materials, lifetime of the in-vessel components, radiation level
at the superconducting magnets, and shielding requirements for magnet
protection.  An essential input to the neutronics analysis is the neutron wall
loading distribution.  \hbox{Section~\ref{s-5-3-2}} presents the variation of
the wall loading in both toroidal and poloidal directions for the nonuniform
first wall shape of the SPPS design.  The blanket is required to breed
sufficient tritium to ensure the self-sustaining operation of the D-T fueled
stellarator.  The blanket utilizes the liquid lithium as a coolant and breeder
and the low activation vanadium alloy \hbox{V-5Cr-5Ti} as a structural
material.  \hbox{Section~\ref{s-5-3-3}} documents the details of the design
requirements for tritium breeding and the optimal blanket parameters.  The
radiation damage to the V structure of the first wall, blanket and shield and
the lifetime of the different components are covered in
\hbox{Section~\ref{s-5-3-4}}.  The shield follows the blanket and is primarily
used to protect the magnets against radiation.  Since the dimensions of the
shield directly affect the size and cost of the machine, an extensive analysis
was performed to optimize the shield composition and performance, as explained
in \hbox{Section~\ref{s-5-3-5}}.

\subsection{Neutron Wall Loading Distribution}
\label{s-5-3-2}

The average neutron wall loading can simply be calculated by dividing the
neutron power by the first wall surface area.  However, the wall loading tends
to peak at certain locations depending on the wall shape and plasma parameters.
Identifying the peaking in the wall loading is of importance in estimating the
peak radiation effect and designing an adequate radiation shield to protect the
various components of the machine.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-01.ps,height=7.4in,bbllx=72pt,bblly=124pt,%
            bburx=540pt,bbury=705pt,clip=}}
\caption [Fig-3-1]
{Cross sections of the SPPS plasma at four toroidal locations: $\phi =
0^\circ$, $22.5^\circ$, $45^\circ$, and $67.5^\circ$.  The angle is measured
from the beginning of the field period.}
\label{f-5-3-1}
\end{figure}

In SPPS, the neutron wall loading $(\Gamma)$ varies in both poloidal and
toroidal directions, unlike in tokamaks.  This variation is mainly due to the
toroidal change in the plasma shape.  \hbox{Figure~\ref{f-5-3-1}} shows 4
plasma shapes at the beginning (0$^\circ$) and middle (45$^\circ$) of a field
period and at two other locations (22.5 and 67.5$^\circ$).  The inner surface
represents the plasma boundary while the outer surface is the magnet centroid.
The first wall follows the plasma contour and the scrape off layer is 15~cm
thick.  Note that the plasma centers change radially and vertically as one
moves along the plasma axis.  The plasma is symmetric around the equatorial
plane at two locations only, 0 and 45$^\circ$.  These locations represent two
extreme cases as the lowest and highest wall loadings occur at the 0 and
45$^\circ$ cross sections, respectively.  It should be mentioned that the wall
loading at any location is mostly affected by the closely surrounding
configuration up to a distance of 1-2~m.  In fact, each field period extends
toroidally for $\sim 22$~m and at any location the shape of both plasma and
wall do not change significantly over a range of 3-4~m.  As such, a 3-D model
for the wall loading distribution is not actually required and instead 2-D
models at discrete cross sections seem to give reasonably accurate results for
the SPPS conceptual design.

\begin{table}[b]
\vspace{2.cm}		% This is just to make this figure flush bottom
\caption{}
\centering
{\bf Plasma Parameters for Two Cross Sections\\
(at the Beginning and Middle of a Field Period)}
\vspace{1cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l  @{\hspace{2cm}} c  @{\hspace{1cm}} c}
\hline
                      & 0$^\circ$ & 45$^\circ$ \\
\hline \\
R (m)                     &  17.4 & 11.7  \\
a (m)                     &  0.8  & 2.2  \\
Elongation                &  3.5  & 0.59  \\
Triangularity             &  1.57 & 0.42  \\
Neutron wall loading \\
\quad Average (MW/m$^2$)  &  1    & 1.6  \\
\quad Maximum (MW/m$^2$)  &  1.5  & 2.1  \\
\quad Minimum (MW/m$^2$)  &  0.4  & 1.0  \\
\quad Overall average (MW/m$^2$) &  \multicolumn{2}{c}{1.3}  \\
\\ \hline
\end{tabular}
\label{t-5-3-1}
\end{table}

The neutron wall loading distribution for SPPS was determined using the NEWLIT
code~\cite{Att85}.  The code assumes toroidal symmetry with a symmetric plasma
shape around the mid-plane.  The first wall, however, can take any shape.  Two
sets of calculations were performed for the two symmetric locations at 0 and
45$^\circ$.  The plasma boundary was fitted into a D-shape, neglecting the bean
shape at 0$^\circ$ plasma.  The magnetic shift is small ($< 10$~cm) and the
neutron source varies radially as $[1 - (r/a)^2]^2$.  The results are
normalized to a fusion power of 1,850~MW.  The plasma parameters for the two
symmetric locations are listed in \hbox{Table~\ref{t-5-3-1}} along with the key
results from the calculations.  The poloidal distributions of the neutron wall
loading are illustrated in \hbox{Figs.~\ref{f-5-3-2}} and~\hbox{\ref{f-5-3-3}}.
The poloidal angle is measured from the outboard mid-plane.  The results show
that the peak neutron wall loading is 2~MW/m$^2$ and occurs at the middle of
the field period.  The minimum wall loading is 0.4~MW/m$^2$ and occurs at the
beginning of the field period.  The average wall loading is 1.3~MW/m$^2$ and
thus the peaking factor is 1.5.  It should be mentioned that the final results
of the systems code indicated a slightly lower fusion power of 1,730~MW and an
average wall loading of 1.2~MW/m$^2$ meaning that the neutronics calculations
which are based on the NEWLIT results are slightly conservative.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-02.eps,height=7.5in}}
\caption
{Approximate poloidal distribution of neutron wall loading at
$\phi=0^\circ$. The $0^\circ$ and $180^\circ$ poloidal angles correspond to
the outboard and inboard sides, \hbox{respectively}.}
\label{f-5-3-2}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-03.eps,height=7.3in}}
\caption
{Approximate poloidal distribution of neutron wall loading at $\phi=45^\circ$.
The $0^\circ$ and $180^\circ$ poloidal angles correspond to the outboard and
inboard sides, \hbox{respectively}.}
\label{f-5-3-3}
\end{figure}

\subsection{Blanket Neutronics}
\label{s-5-3-3}

\subsubsection{Tritium Breeding Requirements}
\label{s-5-3-3-1}

The primary goal of the blanket design is to attain tritium self-sufficiency
that ensures the self-sustaining operation of the plant.  The requirements to
achieve this goal depend on some plasma physics parameters, several
uncertainties in the design, and the technical performance of specific fusion
core components.  To lower the breeding requirements, it is essential to
increase the T burn-up in the plasma, ensure extremely low T losses, achieve
low T inventory in all subsystems, and require high reliability and fix rate
for the T processing systems.  It appears that with the existing technology, a
system with negligible T leak can be achieved to guarantee a safe and reliable
design.

The tritium breeding ratio (defined as the amount of T generated in the
blanket per fusion reaction) in a self-sustained power plant must exceed
unity by a margin $G_o$.  Thus,  the required tritium breeding ratio (TBR)
can be expressed as~\cite{Abd86}:
%
\begin{eqnarray}
\label{e-5-3-1}
 {\rm TBR} & \geq & (1 + G_o) + \sqrt{\Delta_G^2 + \Delta_p^2} \: ,
\end{eqnarray}
%
where $G_o$ is the breeding margin for the reference design, $\Delta_G$ is the
uncertainty in estimating $(1+G_o)$, and $\Delta_p$ is the uncertainty due to
nuclear data, calculational methods, and geometrical models.  Here, it is
assumed that the design is well defined and no more physics or engineering
changes to the reference design are anticipated.

The breeding margin $G_0$ is necessary to mainly supply the inventory for
startup of other fusion power plants, maintain the equilibrium hold-up
inventory, provide adequate reserve storage inventory, and compensate for the
radioactive decay of T between production and use.  The T inventory depends
largely on several system parameters such as T fractional burn-up in plasma, T
thru-put to the plasma, number of days of reserve inventory, and doubling time.
The latter is defined as the time at which the T inventory in the storage is
equal to the sum of the initial T inventory required for starting a new power
plant and the minimum T inventory that must be kept in storage for continued
plant operation during interruption of any part of the tritium cycle.  Several
approaches were identified to minimize the T inventory in the fusion power core
and on-site in the storage and plasma processing facilities.  For instance, a
high T burn-up fraction of $\sim$10\% and a low T thru-put of 2.8~kg per full
power day were considered in order to lower the T inventory in the plasma
exhaust processing system.  The low T thru-put to the plasma and the short
repair time ($<$1~day) for the T processing system help reduce the reserve
storage inventory to $\sim$0.5~kg.  The equilibrium hold-up inventory in the
fusion power core (first wall structure, divertor plates, and blanket) is
estimated to be $\sim$2~kg.  On this basis, the supply inventory to start a new
power plant should be $\sim$2.5~kg.  A doubling time of 5~y seems acceptable
for the first-of-a-kind plants and it can be increased to 7--10~y for the
tenth-of-a-kind plants.

To calculate the breeding margin $G_o$, a simple model was employed that
accounts for the radioactive decay of T.  In order to have a T inventory of
3~kg at the end of a 5~y period, the blanket production rate (P) for T can be
calculated using the expression
%
\begin{eqnarray}
\label{e-5-3-2}
 N(t) & = & \frac{P}{\lambda} \, (1 - e^{-\lambda t}) ,
\end{eqnarray}
%
where $N(t)$ is the required T inventory (3~kg), $\lambda$  is the T
decay constant (0.0562~y$^{-1})$, and T is the doubling time (5~y).  In
this case, the blanket production rate necessary to supply other plants
and provide adequate inventory is estimated to be 1.9 g/day.  Using a T
thru-put of 2.2~kg/day (@ 76\% availability), the breeding margin
$G_o$ ($P$/thru-put $\times$ burn-up fraction) amounts to 0.01 for the
SPPS  reference design.

As noted, the quantity $(1+G_o)$ is a function of several plasma and
engineering components parameters that play a key role in the tritium cycle.
Based on the analysis presented in Ref.~\cite{Abd86}, the uncertainty
$\Delta_G$ associated with $(1+G_o)$ for the SPPS parameters is estimated to be
$<$4\%.  The calculated TBR is also subject to uncertainties $(\Delta_P)$ due
to approximations and/or errors in the various elements of the calculations
such as nuclear data, calculational method, and geometric representation.  The
uncertainties in the nuclear data include the uncertainties for the basic data,
data processing and representation, and tritium production cross sections for
lithium.  The largest source of uncertainty in nuclear data is that for the
basic nuclear data, which is $\sim$6\% for the Li/V blanket~\cite{You86,You91},
and the other uncertainties are small ($\sim$1\%).  The transport calculations
and the 1-D modeling of the blanket involved some geometrical approximations
and the associated error is estimated to be in the order of $\sim$3\%.  Hence,
the uncertainties in the calculational elements total to 10\% which is
significant and will have a major impact on the breeding requirements.

In this regard, the SPPS design will attain fuel self-sufficiency if the
calculated TBR is equal to or exceeds 1.12.  It should be stressed that the TBR
must be calculated for the reference design and the effects of the blanket
coverage, Li burn-up, penetrations, assembly gaps and side walls should all be
included in the computed TBR.  Also, it is of importance to point out the
potentials the blanket design might have to enhance the breeding capability
because of the possible existence of uncovered uncertainties in the system
definition.

\subsubsection{Blanket Parameters}
\label{s-5-3-3-2}

The configuration of the SPPS dictates that a simple one-dimensional
\hbox{(1-D)} model is capable of handling the SPPS geometry due to the fact
that each of the 4 field periods extends toroidally for $\sim$22~m.  Therefore,
a poloidal cylindrical model along the plasma axis can reasonably predict the
neutronics parameters within a few percent.  As mentioned earlier, provisions
were made in the tritium breeding requirements for such uncertainties in the
results.

To evaluate the impact of the blanket parameters on the tritium breeding ratio
and neutron energy multiplication, a simple poloidal cylindrical model was
developed for the ONEDANT code~\cite{Ode82} where a 1.4~cm thick first wall was
followed by a V/Li blanket of variable thickness and, then, a meter thick steel
shield.  In the analysis, natural Li was used and the blanket thickness was
gradually increased from 10 to 80~cm while the V structural content was kept
fixed at 10\% by volume.  The analysis showed that the breeding level can
effectively be controlled by adjusting the thicknesses of the blanket.
\hbox{Figure~\ref{f-5-3-4}} indicates that a 30-40~cm thick blanket should
result in an acceptable TBR, depending on the actual coverage of the blanket.

\begin{figure}[b]
\centerline{\psfig{file=spps-5-3-04.ps,height=3.6in,bbllx=25pt,bblly=152pt,%
            bburx=565pt,bbury=560pt,clip=}}
\caption  %[Fig-3-4]
{Variation of tritium breeding ratio (TBR) with blanket thickness.}
\label{f-5-3-4}
\end{figure}

The blanket surrounds the entire SPPS plasma except for the area occupied by a
few penetrations needed for plasma fueling, heating, and control.  These
penetrations cover approximately 2\% of the first wall area.  Other components
that degrade the breeding are the divertor plates/baffles and their support
structures.  They are $\sim$5~cm thick, cover 15\% of the first wall area, and
consist of 50\% V structure, 20\% Li coolant, and 30\% void.  Taking into
account the penetrations and divertor effect, the neutronics analysis indicates
that a 35~cm thick Li/V blanket will provide T self-sufficiency for the SPPS
stellarator design.  The contributions from the different components to the
breeding are given in \hbox{Table~\ref{t-5-3-2}}.  The T bred in the 5\%
Li-cooled shield is small.  Considering the 2\% loss in breeding due to
penetrations, the overall TBR amounts to 1.12.  It should be mentioned that
higher breeding can be achieved by thickening the blankets and/or enriching the
Li to 15--20\% $^6$Li.

\begin{table}[b]
\caption{ }
\centering
{\bf Tritium Breeding in the SPPS Blanket and Shield} \\
\vspace{1 cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l  c  c}
\hline
       &   first wall \& Blanket  &  Divertor Region \\
\hline \\
First wall or divertor  &  0.04   &  0.007  \\
Blanket                 &  0.91   &  0.153  \\
Shield                  &  0.027  &  0.004  \\
\\ \hline
\end{tabular}
\label{t-5-3-2}
\end{table}

The neutron energy multiplication ($M$) accounts for the nuclear energy
deposited in both blanket and shield.  The shield design will be covered in
detail later in~\hbox{Sec.~\ref{s-5-3-5}}.  However, some changes made to the
conventional shield designs are discussed here along with their impact on $M$
and the rational for these changes.  The economic analysis of a recent tokamak
design~\cite{Naj95} employing a Li/V system has indicated that the shield is
one of the most expensive components of the machine.  The shield contains 15\%
V structure which comprises more than half of the shield cost. The potential of
using less costly materials in the shield while maintaining the safety features
of the design was investigated for the SPPS.  If the V structure (300~\$/kg) is
replaced by a cheaper steel structure (35~\$/kg), the saving in the shield cost
will be significant.  This certainty will come at a cost in the power balance
since V can operate at a higher temperature (700\SdegC) compared to steel
(550\SdegC).  An attractive solution is to divide the shield into two parts:
the inner part following the blanket operates at a high temperature while the
outer part operates at a relatively lower temperature ($\sim$300\SdegC).  The
high temperature (HT) shield along with the first wall and blanket employs V
structure whereas the low temperature (LT) shield utilizes stainless steel as
the main structural material.  As the nuclear energy deposited in the LT shield
will not be recovered, the dividing boundary between the two shields will
depend on how much power could be dumped as a low grade heat without affecting
the power balance much ({\it e.g.,} 1--5\%).  It was decided to define the
HT-LT shield boundary such that 1\% of the total nuclear heating be deposited
in the LT shield.

Several calculations were performed to estimate the amount of nuclear power
deposited in the shield.  The results indicated that the 1.4~cm first wall and
the 35~cm blanket contain 62\% of the nuclear heating while the shield carries
the balance.  \hbox{Figure~\ref{f-5-3-5}} demonstrates the cumulative heating
within the shield.  The first wall, blanket, and 45~cm thick shield contain
99\% of the nuclear heating and the rest of the shield contains 1\% of the
heating.  The overall energy multiplication is estimated to be 1.4, excluding
the 1\% heating in the LT shield.  The radial distribution of the nuclear
heating needed for the thermal hydraulic analysis is illustrated in
\hbox{Fig.~\ref{f-5-3-6}} for the reference blanket and shield design.  The
peak and average heatings are listed in \hbox{Table~\ref{t-5-3-3}} for the
different components.

\begin{table}[b]
\caption{ }
\centering
{\bf Nuclear Heating in the SPPS first wall, Blanket, and Shield} \\
\vspace{1 cm}
\renewcommand{\arraystretch}{1.2}
\begin{tabular}{l  c  c}
\hline
                      & Peak$^{(a)}$     &  Average$^{(b)}$  \\
\hline \\
1.4 cm first wall     &
        \phantom{$^{(c)}$}11$^{(c)}$\Z\Z &  5.2\Z  \\
35 cm blanket         &  \Z6.7\Z         &  2.7\Z  \\
45 cm HT shield       &  \Z6.4\Z         &  1.1\Z  \\
35 cm LT B-SS shield  &  \Z0.16          &  0.02  \\
\\ \hline
\multicolumn{3}{l}{$(a)$ For 2~MW/m$^2$ peak neutron wall loading.}  \\
\multicolumn{3}{l}{$(b)$ For 1.3~MW/m$^2$ average neutron wall loading.}  \\
\multicolumn{3}{l}{$(c)$ In V structure.}
\end{tabular}
\label{t-5-3-3}
\end{table}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-05.ps,height=3.4in,bbllx=25pt,bblly=152pt,%
            bburx=565pt,bbury=560pt,clip=}}
\caption  %[Fig-3-5]
{Cumulative neutron energy multiplication for the 36.4~cm thick
first wall and blanket and various layers of the shield.}
\vspace{0.2in}
\label{f-5-3-5}
\centerline{\psfig{file=spps-5-3-06.ps,height=3.4in,bbllx=17pt,bblly=152pt,%
            bburx=565pt,bbury=565pt,clip=}}
\caption  %[Fig-3-6]
{Radial variation of nuclear heating in first wall, blanket, and shield for the
2~MW/m$^2$ peak wall loading.}
\label{f-5-3-6}
\end{figure}

\subsection{Radiation Damage and Lifetime of V Structure}
\label{s-5-3-4}

The 40~y planned operation of the SPPS with 2~MW/m$^2$ peak neutron wall
loading places some constraints on the first wall and blanket systems.  The V
structure will require frequent replacement during operation.  From the
radiation damage viewpoint, the lifetime of the V structure of the first wall,
blanket, and shield is determined by the level of swelling and embrittlement
attainable during plant operation.  The atomic displacement level has the most
impact on these neutron-induced effects in the V alloys.  The \hbox{V-5Cr-5Ti}
alloy is the candidate structural material for the stellarator design.  This
alloy seems to possess high radiation resistance to fusion neutron damage.

The lifetime of V is determined by the dpa level attainable during operation.
The criterion adopted in this study is that no more than 200 dpa is desirable.
For a peak wall loading of 2~MW/m$^2$ and a system availability of 76\%, the
200~dpa limit implies that the first wall and blanket should be replaced every
11~y and the corresponding end-of-life (EOL) fluence is 16.4~MWy/m$^2$.  The
blanket provides lifetime protection for the shield.  At the end of the plant
life (40~y), the atomic displacement at the V structure of the shield is
170~dpa which is below 200~dpa limit.  On this basis, the shield is considered
a lifetime component and does not need replacement due to radiation damage.

\subsection{Shield Design}
\label{s-5-3-5}

The main function of the shield is to protect the superconducting magnets and
keep the radiation level below the allowable limits.  In fact, these limits
have a strong impact on the characteristics of the shield, in terms of
thickness and composition.  In order to reduce the radial standoff of the SPPS,
it was essential to optimize the shield in order to reduce the overall
dimensions of the machine.  As such, a serious effort was made to optimize the
shield and the impact of the shield performance on the design was assessed with
a view to cost, complexity, and safety.

\subsubsection{Magnet Radiation Limits}
\label{s-5-3-5-1}

As the radiation adds many problems to the magnet design, sufficient shield
should be placed between the blanket and magnet to keep the radiation effects
below certain limits.  These limits are set by the magnet designers to insure
the proper performance of the TF coils.  For instance, at the end of 30 full
power years (FPY) of operation, the fast neutron fluence (E$_n>0.1$~MeV) should
not exceed $10^{23}$~n/m$^2$ to avoid degradation of the critical properties of
the Nb$_3$Sn superconductor material.  It is undesirable to subject the magnets
to a total nuclear heating above 50~kW to avoid excessively high cryogenic load
to the cryoplant.  A limit of 2~kW/m$^3$ is imposed on the peak nuclear heating
in the winding pack.  The end-of-life dose to the glass-fiber-filled (GFF)
polyimide is limited to $10^{11}$ rads to ascertain the mechanical and
electrical integrity of the insulator.  The neutron-induced atomic displacement
in the Cu stabilizer should not exceed \hbox{$6\X 10^{-3}$} dpa to avoid high
increase in the Cu electric resistivity.  It should be mentioned that the
fluence and dose limits are at least a factor of 2-3 lower than the
experimental values at which degradation of properties was observed.  Our
neutronics calculations indicate that the predominant magnet radiation limits
are the EOL fast neutron fluence and the nuclear heat load to the magnets.
Hence, the shield is optimized to primarily minimize these effects.

\subsubsection{Optimization Analysis}
\label{s-5-3-5-2}

An extensive optimization analysis was performed to design a cost-effective
high performance shield to protect the magnet against radiation.  The
optimization study involved the selection of the shielding materials,
assessment of the shielding capability of the various candidate materials,
optimization of the composition of the shield, and determination of the
thickness of the shield required to keep the radiation damage at the magnet
below the permissible level.

The analysis employed the 1-D transport code ONEDANT with the P$_3$ Legendre
expansion for the scattering cross section and the S$_8$ angular quadrature
set.  The associated 46 neutron and 21 gamma group cross section library was
derived from the ENDF/B-V evaluation.  The different components were modeled in
poloidal cylindrical geometry around the plasma axis.  All the in-vessel
components are Li cooled.  The vacuum vessel is located outside the magnets
which are enclosed in a common cryostat.  The 75.5~cm winding pack of the
magnet includes Incoloy structure, Nb$_3$Sn superconductor and conduit, Cu
stabilizer, GFF polyimide insulator, and liquid He coolant at 25\%, 15\%, 20\%,
25\%, and 15\% (by volume), respectively.  The cryostat consists of 1~cm
stainless steel dewar, 5~cm thermal insulator, 7.5~cm coil case, and 1.25~cm
electrical insulator.  The optimization analysis was carried out for an
arbitrary 2.05~m radial standoff measured from the plasma boundary to the
magnet centroid.  Leaving 15~cm for the scrape-off layer (SOL), 1.4~cm first
wall, 35~cm blanket, 2~cm blanket-shield gap, 1.5~cm shield-magnet gap, and
14.75~cm cryostat, the space available for the shield is 97.6~cm.  The
circularized plasma radius is 1.6~m and the neutron source strength is
normalized to the 2~MW/m$^2$ peak wall loading.

The optimization analysis has focused on optimizing the major factors that
influence the shield performance.  These factors are the composition of the
shield and the arrangement of materials within the shield.  A variety of shield
options was examined and the ability of various materials to protect the
magnets was assessed.  Besides V and steel, many materials have the potential
to protect the magnets.  Each material has some merits and drawbacks.  The
behavior of the shielding material may limit its use in the shield,
particularly in high radiation zones.  For example, the tungsten is known as
the best shielding material but its high decay heat and the production of the
$^{187}$W isotope cause some safety problems.  The hydrogen compounds (like
titanium hydride, zirconium hydride, boron hydride, organic coolant, water, and
polyethylene) are superior in slowing down the fast neutrons.  Nevertheless,
all hydrides decompose at high temperatures and the dissociated hydrogen
jeopardizes the integrity of the shield.  An ideal situation from the shielding
point of view is to use water, borated water (B-H$_2$O), or organic coolant
(OC) to cool the shield.  However, this would complicate the cooling system due
to the requirement for two independent primary cooling circuits.  Moreover,
water should be avoided in Li cooled systems for safety reasons.  Organic
coolants may decompose under irradiation and elevated temperatures.  Borated
materials (such as boron carbide, boron hydride, boronized carbon, and borated
water) possess remarkably high neutron absorption cross sections particularly
for low energy neutrons, a property of great importance in magnet shielding.
Among these borides, boron carbide is the best for having the combined features
of excellent shielding capability, stability under irradiation, and ease of
fabrication.  One concern regarding the borides is the tritium generated in the
boron.  To decrease the in-shield tritium inventory, the borides should be
situated close to the back of the shield.  This constraint turned out to be
beneficial since the neutron spectrum therein is relatively soft and the
neutron absorption capability of boron is high.  The lead has been known for
its good ability to reduce magnet heating by absorbing the gamma radiation.
However, lead has a few drawbacks of which one should be aware.  Lead increases
the neutron fluence (compared to steel) as it multiplies the neutrons, starts
to deform at $\sim$220\SdegC and, thus, has to be canned in a structural
material, and generates polonium, which is a safety concern.

The first set of calculations demonstrates the shielding performance of several
low activation steels.  Vanadium alloy is the primary structural material in
all shielding components and 15~vol\% structure is foreseen enough to support
the shield.  The option of using steel filler was investigated.  At the present
time, there is no structural role envisioned for the filler materials in the
shield and, therefore, a substantial cost reduction will result from the use of
such less costly fillers.  There are a few low activation steels that are
readily available to be used in fusion plants.  These are Tenelon and modified
\hbox{HT-9} (\hbox{MHT-9}).  The analysis indicates that Tenelon has the best
shielding capability as it gives the lowest magnet damage.  Furthermore, it
results in the highest neutron energy multiplication since it contains a
substantial amount of manganese (14.5~wt\%).  It is anticipated that the
combined effect of the good shielding properties, low unit cost, and high $M$
will have a positive economic impact on the overall design.  It should be
mentioned that Tenelon has a slightly higher decay heat compared to
\hbox{MHT-9}, but this does not seem to present a problem even in the event of
a loss of coolant accident.

In the second set of calculations, the composition of the LT shield was
optimized to further reduce the radiation damage at the magnet.  As mentioned
in \hbox{Sec.~\ref{s-5-3-3-2}}, the 35~cm thick blanket is followed by a 45~cm
thick HT shield then a LT shield. The Tenelon filler in the LT shield was
traded for boron carbide, borated water, organic coolant, zirconium hydride, or
tungsten carbide.  The total HT and LT shield thickness was kept fixed at
97.6~cm.  The impact on the magnet damage is illustrated in
\hbox{Figs.~\ref{f-5-3-7}} and~\ref{f-5-3-8} .  As indicated earlier, the fast
neutron fluence and the peak nuclear heating, which is an indicative for the
total heating in the magnets, are the most demanding radiation limits.
Although water is not compatible with Li, B-H$_2$O is included in the analysis
to illustrate the shielding performance of the selected materials relative to
water.  As is evident, the hydrides and WC are more effective than B$_4$C in
reducing the magnet damage.  In all cases, the damage level at the magnet is
well below the fluence and heating limits of $10^{23}$~n/m$^2$ and 2~mW/cm$^3$,
respectively.  This means the 97.6~cm thick shield over-protects the magnet and
a thinner shield is actually needed.  Keeping the optimum composition of the
various shields, the thickness was reduced from 97.6~cm to 60~cm.
\hbox{Figures~\ref{f-5-3-9}} and~\ref{f-5-3-10} indicate that 63--96~cm thick
shield is needed to meet the magnet radiation limits, depending on the shield
type.  Note that the shield thickness required to meet the fluence limit also
satisfy the heating limit except for the OC shield where the outer 1--2~cm
should be replaced by Pb shield to reduce the heating.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-07.ps,height=3.4in,bbllx=14pt,bblly=152pt,%
            bburx=562pt,bbury=571pt,clip=}}
\caption[Fig-3-7]
{Effect on fast neutron fluence at magnet of replacing the back layer of
the steel shield by more efficient shielding materials.}
\label{f-5-3-7}
\vspace{0.2in}
\centerline{\psfig{file=spps-5-3-08.ps,height=3.4in,bbllx=25pt,bblly=152pt,%
            bburx=565pt,bbury=560pt,clip=}}
\caption[Fig-3-8]
{Effect on peak nuclear heating at magnet of replacing the back layer of
the steel shield by more efficient shielding materials.}
\label{f-5-3-8}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-09.ps,height=3.4in,bbllx=14pt,bblly=152pt,%
            bburx=569pt,bbury=560pt,clip=}}
\caption[Fig-3-9]
{Variation of fast neutron fluence at magnet with thicknesses of various
shields.}
\label{f-5-3-9}
\vspace{0.2in}
\centerline{\psfig{file=spps-5-3-10.ps,height=3.4in,bbllx=10pt,bblly=152pt,%
            bburx=569pt,bbury=560pt,clip=}}
\caption[Fig-3-10]
{Variation of peak nuclear heating at magnet with thicknesses of various
shields.}
\label{f-5-3-10}
\end{figure}

\begin{table}[p]
\caption{}
\centering
{\bf Radial Thicknesses (cm) of Different Shield Options} \\
\vspace{1cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c c}
\hline
  &  \multicolumn{1}{c}{ARIES-II$^{(a)}$}
                           && \multicolumn{6}{c}{SPPS}  \\
\cline{2-2} \cline{4-9}
Shield Type   & B$_4$C &&  SS   & {\bf B-SS}$^{(b)}$
                                       & B$_4$C &  WC   &  OC & ZrH$_{1.7}$ \\

\hline \\
First wall    & \Z1.4  && \Z1.4 & \Z1.4 & \Z1.4 & \Z1.4 & \Z1.4 & \Z1.4 \\
Blanket       &  20\D  &&  35\D &  35\D &  35\D &  35\D &  35\D &  35\D \\
Reflector     &  15\D  && ---   & ---   &  ---  &  ---  &  ---  &  ---  \\
HT Shield$^{(c)}$ & 47\D && 45\D & 45\D &  45\D &  45\D &  45\D &  45\D \\
LT Shields:  \\
\quad SS/Li   &  ---   &&  42\D & ---   &  11\D &  ---  & \Z6.3 & \Z5\D \\
\quad B-SS/Li &  ---   && ---   &  35\D &  ---  &  ---  &  ---  &  ---  \\
\quad B$_4$C/SS/Li
    & \phantom{$^{(d)}$}23$^{(d)}$\D
                       && ---   & ---   &  15\D &  ---  & ---   &  ---  \\
\quad WC/SS/Li &  ---  && ---   & ---   & ---   &  22\D &  ---  &  ---  \\
\quad OC/SS   &  ---   && ---   & ---   & ---   &  ---  &  13.2 &  ---  \\
\quad Pb/SS/OC & ---   && ---   & ---   & ---   &  ---  & \Z1.5 &  ---  \\
\quad ZrH$_{1.7}/$SS/Li
              & ---    && ---   & ---   & ---   &  ---  &  ---  &  13\D \\
Vacuum Vessel &  10\D  && ---   & ---   & ---   &  ---  &  ---  &  ---  \\
Coil Case     & \Z2\D  && \Z8.5 & \Z8.5 & \Z8.5 & \Z8.5 & \Z8.5 & \Z8.5  \\

{\bf Total}$^{(d)}$
      & 118\D\Z && 132\D\Z & 125\D\Z & 116\D\Z & 112\D\Z & 111\D\Z & 108\D\Z \\
\\ \hline
\multicolumn{9}{l}{$(a)$ Inboard components operating at 3.2 MW/m$^2$.}  \\
\multicolumn{9}{l}{$(b)$ Reference Case.} \\
\multicolumn{9}{l}{$(c)$ A SS/Li/V high-temperature shield.} \\
\multicolumn{9}{l}{$(d)$ High-temperature shield.} \\
\multicolumn{9}{l}{$(e)$ Excluding gaps.}
\end{tabular}
\label{t-5-3-4}
\end{table}

\begin{table}[p]
\caption{ }
\centering
{\bf Materials Composition$^{(a)}$ for Different Shield Options} \\
\vspace{1 cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l  l}
\hline \\
First Wall  & 30\% V structure, 70\% Li coolant  \\
Li/V Blanket & 10\% V structure, 90\% Li coolant/breeder \\
HT SS/Li/V Shield
     & 15\% V structure, 5\% Li coolant, 80\% Tenelon filler \\
\\
\multicolumn{2}{l}{\bf LT SS-Based Shield:}  \\
\quad SS/Li 
    & 15\% Tenelon structure, 5\% Li coolant, 80\% Tenelon filler \\
\multicolumn{2}{l}{\bf LT B-SS-Based Shield:}  \\
\quad B-SS/Li 
    & 15\% Tenelon structure, 5\% Li coolant, 80\% B-Tenelon filler \\
\multicolumn{2}{l}{\bf LT B$_4$C-Based Shield:}\\
\quad SS/Li 
    & 15\% Tenelon structure, 5\% Li coolant, 80\% Tenelon filler \\
\quad B$_4$C/SS/Li 
    & 15\% Tenelon structure, 5\% Li coolant, 80\% B$_4$C  filler \\
\multicolumn{2}{l}{\bf LT WC-Based Shield:} \\
\quad WC/SS/Li 
    & 15\% Tenelon structure, 5\% Li coolant, 80\% WC filler \\
\multicolumn{2}{l}{\bf LT OC-Based Shield:}  \\
\quad SS/OC
 & 15\% Tenelon structure, 5\% organic coolant, 80\% Tenelon filler \\
\quad OC/SS
    & 10\% Tenelon structure, 90\% organic coolant  \\
\quad Pb/SS/OC
    & 15\% Tenelon structure, 5\% organic coolant, 80\% Pb filler \\
\multicolumn{2}{l}{\bf LT ZrH$_{1.7}$-Based Shield:} \\
\quad SS/Li
    & 15\% Tenelon  structure, 5\% Li coolant, 80\% Tenelon filler \\
\quad ZrH$_{1.7}$/SS/Li
   & 15\% Tenelon structure 5\% Li coolant, 80\% ZrH$_{1.7}$ filler \\
\\ \hline
\multicolumn{2}{l}{$(a)$ Fillers are in the form of bricks.}
\end{tabular}
\label{t-5-3-5}
\end{table}

Table~\ref{t-5-3-4} summarizes the required shield to protect the magnet for
the various options.  The shield of the \AII tokamak design~\cite{Naj95} is
listed for comparison.  The compositions of the different shields are given in
\hbox{Table~\ref{t-5-3-5}}.  It should be noticed that the HT shield contains
only Tenelon filler while the use of other materials is limited to the LT
shield where the radiation environment is less severe.  Borated Tenelon (B-SS;
3~wt\% B) is more effective than Tenelon in reducing magnet damage.  Even
though zirconium hydride and organic coolant are better shielding materials
than WC and borides, the safety related issues associated with these materials
limited their use in the SPPS design.  For instance, ZrH$_{1.7}$, which is more
stable than ZrH$_2$, will decompose at elevated temperatures ($>600$\SdegC).
Although the shield temperature can be controlled during operation to remain
below 500\SdegC, the temperature in case of a loss of coolant accident
(LOCA) will rise and certainly exceed 600\SdegC causing dissociation of
hydrogen and jeopardizing the integrity of the shield.

The organic coolant (a kerosene product commercially known as therminol 66 or
\hbox{HB-40}) decomposes under irradiation and elevated temperatures.  To
mitigate the decomposition problem, the OC is used only in the LT shield where
the temperature and radiation levels are low.  Nevertheless, the decomposition
rate is quite high.  The radiolytic decomposition rate ($R_r$ in kg/h) and
pyrolytic decomposition rate ($R_p$ in kg/h per kg of OC) can be expressed as
%
\begin{eqnarray}
  R_r & = & 0.0131 \,  \left[ \frac{100 - HB}{100-30} \right]^2 \, D \: , \\
\label{e-5-3-3}
  R_p & = &  \left[ \frac{100 - HB}{100-30} \right]^2 \, 
      e^{\displaystyle(25.73 - 180.98/{\rm RT)}} \: ,
\label{e-5-3-4}
\end{eqnarray}
%
where $HB$ is the high boiler content in wt\% (40~wt\%), $D$ is the radiation
absorbed dose in kW, $R$ is the gas constant (0.00831~kJ/K), and $T$ is the
temperature in K.  Table~\ref{t-5-3-6} summarizes the decomposition rates in
the various zones of the LT shield.  The radiolytic decomposition rate is high
whereas the pyrolytic decomposition rate is manageable at the 100\SdegC
operating temperature.  However, in the worst accident case of a LOCA in the
blanket and LOFA in the shield, the temperature may exceed 600\SdegC leading
to excessive decomposition of $>10^6$~kg/h.  Even though the OC is confined to
the low radiation outer zone, the decomposition rates are still excessive and
this excluded the use of OC in the SPPS.

\begin{table}[t]
\caption{ }
\centering
{\bf Decomposition Rates for the Organic-Coolant Shield Option}
\vspace{1 cm}
\renewcommand{\arraystretch}{1.2}
\begin{tabular}{l  c  c  c}
\hline
Low-temperature Shield              & SS/OC    &  OC/SS    & Pb/SS/OC    \\
\hline \\
Volume Content                      & 95\%/5\% & 90\%/10\% & 80\%/15\%/5\%  \\
Thickness (cm)                      &  6.3     &  13.2     &  1.5  \\
In-vessel OC volume$^{(a)}$ (m$^3$) &  4.6     &  180      &  1.2  \\
In-vessel OC mass$^{(a)}$ (tonnes)  &  5       &  200      &  1.3  \\
Absorbed dose (kW)                  &  172     &  2,400    &  5  \\
Radiolytic decomposition rate:  \\
\quad (kg/FPH)                      &  1.7     &  23       &  0.05  \\
\quad (kg/h)$^{(b)}$                &  1.3     &  18       &  0.04  \\
Pyrolytic decomposition rate @100\SdegC (kg/h)
                         &  $6\X 10^{-11}$ & $2\X 10^{-9}$ & $2\X 10^{-11}$ \\
\\ \hline
\multicolumn{3}{l}{$(a)$ Outer loop contains the same amount.}  \\
\multicolumn{3}{l}{$(b)$ Assuming 76\% availability.} \\
\end{tabular}
\label{t-5-3-6}
\end{table}

\subsubsection{Reference Shield Design}
\label{s-5-3-5-3}

The optimization analysis has indicated that borated steel and tungsten carbide
are the most promising shielding materials.  A decision was made to employ the
80~cm thick borated steel to protect the magnets of the present design
($R=14$~m).  It was found that the minimum radial distance between the plasma
and the magnet centroid is 196.2~cm and occurs at the middle of each field
period, as indicated in \hbox{Fig.~\ref{f-5-3-11}}.  This space is actually
more than what is needed for the SOL, blanket, shield, and magnet.  The
shield-magnet gap is, therefore, 8~cm wide for the reference B-SS as indicated
by the radial build shown in \hbox{Fig.~\ref{f-5-3-12}}.  This gap gets wider
as one moves in the toroidal and/or poloidal directions reaching 1.3~m at some
locations.  It should be mentioned that the B-SS is employed in the LT shield
only in order to reduce the in-shield tritium inventory.  Although a 4~cm
reduction in thickness is feasible upon employing B-SS in both HT and LT
shields, the excessive in-shield T produced at the end of the plant life
(1.080~kg) excluded this option.  The level of radiation damage at the magnet
is compiled in \hbox{Table~\ref{t-5-3-7}} for the various shield options.  All
magnet radiation limits are met and the reference B-SS shield results in the
lowest heat load to the magnet.  The 32 magnets of SPPS cover $\sim 20$\% of
the space.  For an average wall loading of 1.3~MW/m$^2$, the nuclear heating
deposited in the coil cases and winding packs amounts to 37~kW and will be
removed at a cryoplant efficiency of 310~W/W. The cryoplant load is thus 11~MW.
This corresponds to $\sim$1\% of the output power, which is acceptable.  The
radial distribution of the nuclear heating in the magnet is shown in
\hbox{Fig.~\ref{f-5-3-13}} for the reference B-SS shield design.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-11.ps,height=7.1in,bbllx=50pt,bblly=36pt,%
            bburx=519pt,bbury=650pt,clip=}}
\caption[Fig-6-3-11]	% Same as spps-2-2-5.ps
{A contour plot of the distance between the SPPS plasma boundary and coil
centroid in the $\theta-\phi$ (poloidal angle-toroidal angle) plane.  The lower
part of the picture shows the point ($\bullet$) where the spacing is smallest
(at the inboard side of the torus).}
\label{f-5-3-11}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-3-12.ps,height=7.6in,bbllx=217pt,bblly=107pt,%
            bburx=486pt,bbury=763pt,clip=}}
\caption[Fig-3-12]
{Schematic of SPPS blanket, shield, and magnet.}
\label{f-5-3-12}
\end{figure}

\begin{sidewaystable}[p]
\caption{ }
\centering
{\bf Radiation Level at Magnet for
the Various Shield Options}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{l @{\hspace{1.cm}} c c c c c c}
\hline
Shield Type         &  SS   & {\bf B-SS}$^{(a)}$
                                  & B$_4$C &  WC  &  OC  & ZrH$_{1.7}$ \\

\hline \\
Shield thickness (cm)
                    &  \Z87 &  \Z80 & \Z71 & \Z67 & \Z66 & \Z63 \\
Total thickness$^{(b)}$ (cm)
                    &   127 &   120 &  111 &  107 &  106 &  103 \\
Minimum shield-magnet gap (cm)
                    & \Z\Z2 & \Z\Z8 & \Z17 & \Z21 & \Z23 & \Z26 \\
Peak fast n fluence to Nb$_3$Sn ($10^{19}$ n/cm$^2$@30 FPY)
                    &  1    &  1    &  1   &  1   &  1   &  1  \\
Peak nuclear heating in Winding Pack  (MW/m$^3$)
                    &  1.5  &  0.8  &  0.8 &  1.4 &  1.9 & 0.9 \\
Peak dose to insulator  ($10^{10}$ rads@30 FPY)
                    &  2.4  &  1.4  &  1.6 &  2.3 &  3.4 &  1.9 \\
Peak dpa in Cu stabilizer ($10^{-3}$ dpa@30 FPY)
                    &  4.5  &  4.0  &  4.8 &  5.0 &  5.8 &  6.2 \\
Total nuclear heating (kW):  \\
\quad Coil case     &  38   &  17   &  35  &  34  &  153 &  56  \\
\quad Winding Pack  &  34   &  20   &  19  &  33  & \Z32 &  20  \\
\quad {\it Total}   &  72   &  37   &  54  &  67  &  185 &  76  \\
Cryogenic load (MW):  \\
\quad Coil case     &  12   & \Z5   &  11  &  11  &  47  &  17  \\
\quad Winding Pack  &  10   & \Z6   & \Z6  &  10  &  10  & \Z6  \\
\quad {\it Total}   &  22   &  11   &  17  &  21  &  57  &  23  \\
\\ \hline
\multicolumn{7}{l}{$(a)$ Reference Case.} \\
\multicolumn{7}{l}{$(b)$ Including First wall, blanket, high- and
low-temperature shields and gaps.} \\
\end{tabular}
\label{t-5-3-7}
\end{sidewaystable}

\begin{figure}[t]
\centerline{\psfig{file=spps-5-3-13.ps,height=3.3in,bbllx=13pt,bblly=152pt,%
            bburx=569pt,bbury=560pt,clip=}}
\caption[Fig-3-13]
{Radial distribution of nuclear heating in the magnet for the 2~MW/m$^2$
peak wall loading.}
\label{f-5-3-13}
\end{figure}

A potential improvement to the present design is to employ a more efficient
shield in order to reduce the radial standoff and thus the overall dimension of
the machine.  The most efficient shielding material is the tungsten carbide.
However, WC is heavy and expensive (65~\$/kg) and should be used only in the
critical area where the space is constrained.  As mentioned before, there is a
single critical area at the middle of each field period where the shielding
space is limited.  Utilizing WC in this region, which cover only 1\% of the
area, will allow the radial standoff to be reduced by 19~cm.  The corresponding
reduction in the major radius is estimated to be in the order of 1.5~m.  It
should be stressed that the WC used in the LT shield is subject to a relatively
low radiation level implying that the afterheat generated by W is low and will
not cause any problem in case of an accident.

\subsubsection{Thermal Analysis}
\label{s-5-3-5-4}

The thermal analysis has been performed for the HT shield to determine the size
of the Tenelon bricks used in the various layers of the shield.  The thickness
of the steel filler is needed for the safety analysis to estimate the release
fraction from the steel in case of an accident.  The HT shield is configured in
3 steel layers sandwiched between coolant channels, as illustrated in
\hbox{Fig.~\ref{f-5-3-14}}.  The V structure, steel filler, and coolant
contents amount to 15\%, 80\%, and 5\% by volume, respectively.  The V coolant
channel wall is 0.6~cm thick.  The front and back V plates of the shield are
1~cm thick each.

\begin{figure}[b]
\centerline{\psfig{file=spps-5-3-14.ps,height=3.7in,bbllx=-41pt,bblly=223pt,%
            bburx=485pt,bbury=667pt,clip=}}
\caption[Fig-3-14]
{Temperature distribution in the HT shield.}
\label{f-5-3-14}
\end{figure}

The temperature distribution was calculated for a two-dimensional ($r-\theta$)
sector of the HT shield using the finite element ANSYS code~\cite{Des92}.  The
inner and outer radii of the shield are 213~cm and 258~cm, respectively.  The
coolant is fed at the back of the shield at 350\SdegC and collected at the
front at 600\SdegC.  The front of the shield is assumed to radiate to the back
of the blanket which operates at an average temperature of 400\SdegC.  A
perfect thermal contact between the different parts of the shield is assumed.
The radial distribution of the nuclear heating in the HT shield, shown in
\hbox{Fig.~\ref{f-5-3-6}}, was renormalized to an average wall loading of
1.3~MW/m$^2$.  The temperature distribution generated by the ANSYS code is
shown in \hbox{Fig.~\ref{f-5-3-14}}.  The analysis indicates that the
thickness of the first steel layer is 9.1~cm which could be manufactured in two
pieces, 4.55~cm each.  The second and third layers are 16.8 and 11.6~cm thick,
respectively.  The maximum temperature in the first layer of the shield reaches
655\SdegC which is below the allowable limit ($<700$\SdegC) for the Tenelon
filler.  The temperature of the V structure does not exceed the 700\SdegC
limit.

\section{CONFIGURATION AND MAINTENANCE}
\label{s-5-4}

\subsection{Introduction}
\label{s-5-4-1}

This section describes the configuration and layout of the SPPS fusion
power core, the surrounding structure and its interfacing with the magnets,
the cryostats which contain the magnets, the vacuum chamber, and the
maintenance procedures for both blankets, divertors and magnets.

Modular stellarator coils differ from tokamak coils in many ways, not only in
configuration, but also in force magnitude and distribution as well.  Whereas
the toroidal field coils in tokamaks have net centering forces which are
reacted with a structural center post, the net force on the various stellarator
coils point in different directions.  These forces have both horizontal and
vertical components, which means that they have to be surrounded with structure
on all sides.  This cocoon of structure must be arranged in such a way as to
provide access to the coils for maintenance operations.

There are also differences in blanket and divertor maintenance procedures
between tokamaks and modular stellarators.  Traditionally, blanket maintenance
in tokamaks invoked radial module extraction between toroidal field (TF) coils,
or vertical extraction through access ports at the top of the vacuum
chamber~\cite{Bad75,Bak80,Spe79}.  Although, there have been proposals for
maintaining tokamak blankets by moving TF coils~\cite{Bad73}, these have since
been abandoned.  Whereas the tokamak has the luxury of several possible blanket
maintenance schemes, the modular stellarator of the SPPS configuration must
have at least some of the coils moved to provide access for blanket
maintenance.  There simply is not enough access space between coils for the
capability of blanket module extraction without coil movement, unless the
blanket is divided into very small segments, which makes it impractical.

Fortuitously, maintaining the divertor segments will not require coil movement.
This is important, particularly if the lifetime of the divertor will be shorter
than that of the blankets.  The divertor modules are concentrated in four
locations within the plasma chamber.  These are the four corners of the near
square shape of the coil assembly, when viewed from the top.  At these corners,
the legs of the coils on the outboard side are sufficiently separated as to
allow access between them for reaching the divertor segments.  It is planned to
have a large rectangular access port to be located on the outboard side of the
corner cryostat which contains the four corner coils.  Removing the blanket and
shield segments in front of the access port uncovers a large opening through
which remote manipulators can disengage and remover divertor segments.

Finally, any power-plant design must have contingency plans for replacing coils
in the event of a failure.  Since blanket maintenance requires the extraction
of 16 of the 32 coils in the SPPS system, the remaining 16 coils must also
be provided with replacement capability.  This has been provided for and will
be covered in the sections that follow.

\subsection{Overall Configuration}
\label{s-5-4-2}

\begin{figure}[b]
\centerline{\psfig{file=spps-5-4-01.ps,height=4.2in,bbllx=80pt,bblly=324pt,%
            bburx=514pt,bbury=732pt,clip=}}
\caption[f-5-4-1]	% top half of spps-3-2-1.ps, same as f-5-3-4
{Plan view of SPPS coil set.}
\label{f-5-4-1}
\end{figure}

\begin{figure}[t]
\vspace{0.6in}
\centerline{\psfig{file=spps-5-4-02.eps,width=6.2in}}
\caption[f-5-4-2]
{Side view of SPPS coil field period as viewed from outside.}
\label{f-5-4-2}
\end{figure}

The SPPS modular stellarator power plant consists of 32 twisted coils
assembled in a near square geometry when viewed from the top as shown in
{\hbox{Fig.~\ref{f-5-4-1}}}.  There are four field periods in the system, each
consisting of eight coils, however, only four of the coils have different
geometries and the other four are identical, but flipped $180^\circ$ about a
radial horizontal axis.  Each of the four different geometries will be
duplicated eight times, making fabrication simpler by virtue of a learning
curve.  The eight coils in a field period occupy one leg of the near square
assembly of the coils.  Figure~\ref{f-5-4-2} is a view of a field period as
seen from the outside looking toward the center of the fusion core.  Note that
the coils are not centered on the same plane, but have different elevation
within one field period.  The same geometry and coil placement repeats itself
in the succeeding field periods.

The magnets are housed in 12 cryostats.  The number of cryostats and the
division of coils per cryostat was arrived at from maintenance considerations
and will be discussed in a future section.  Each cryostat will have its own
vacuum system.  The magnets will be superinsulated and structural gravity
supports or reactive local supports will have intercepts at 77~K (liquid N$_2$)
to minimize heat leaks.  Intercoil supports, where the loads are transferred
from one cryostat to an adjacent one, thus going through a cold/warm/cold
interface, will also have 77~K intercepts.  The cryostats are contained within
a doughnut shaped vacuum chamber which has a nominal outer radius of 21~m and
an inner radius of 5~m, and is $\sim$18~m high.  The vacuum chamber has four
access ports located in line with the corner cryostats as shown in
{\hbox{Fig.~\ref{f-5-4-3}}} which is a top view of the vacuum chamber with the
roof and over-the-top structure removed.  It will be shown later, that by
moving out the corner cryostats radially through the access ports, makes it
possible to maintain the internal components of the plasma chamber.

\begin{figure}[p]
\vspace{0.5in}
\centerline{\psfig{file=spps-5-4-03.eps,width=6.5in}}
\vspace{0.5in}
\caption[FIG-4-3]
{View of SPPS vacuum chamber with roof and over-the-top structure removed.}
\label{f-5-4-3}
\end{figure}

The shape of the plasma in this stellarator changes in one field period from a
crescent with rounded ends to a horizontal tear drop in the middle of the
period, and then back to a crescent.  Further, the elevation of the plasma also
changes from one end of a field period to the other.  Because it was so
difficult to visualize the plasma in 3D, a model of one field period was
constructed.  Coils are shown as planar, simply to show the boundary around the
plasma chamber.  Plastic plates assembled in a radiating fashion from a central
hub hold wires strung out through them to show the shape of the plasma.  Two
photographs of the model are shown in \hbox{Fig.~\ref{f-5-4-4}}.  A top view
and a side view of the model show the variations in the shape and location of
the plasma within a single period.  The same configuration then repeats itself
within each period.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-04.eps,height=7.8in}}
\caption[Fig-4-4]
{Photographs of the SPPS plasma model.}
\label{f-5-4-4}
\end{figure}

The plasma chamber fits within the bore of the coils which means, each
cryostat has a hole going through it from one side to the other.  When all
the cryostats are assembled within the vacuum chamber, there is a
continuous channel going around the torus.  This channel contains the
radiation shield, the breeding blanket, the plasma and the divertor
modules.  The shape of this channel somewhat conforms to the shape of the
plasma.  Since the magnets constitute a large fraction of the cost of the
fusion core, their size must be minimized, and this can be accomplished
by making the blanket/shield conform to the plasma shape.  Although this
saves on the cost of the coils, it makes it more difficult to change out
blanket modules.  The cryostats butt against each other but are not sealed
to each other.  This means that the plasma chamber will communicate with
the vacuum chamber through assembly gaps between the blankets, shields
and cryostats.  Similar schemes are used in tokamak designs, although the
total pumped surface area is smaller in tokamaks, due to the smaller size
of the vacuum chamber.  Aside from the fact that it would be difficult to
make seals between adjacent cryostats, there is one more reason which
would preclude such a step, and it has to do with safety related loss of
coolant accidents (LOCA).  When a LOCA occurs, the afterheat generated
within the blanket and shield must be conducted, convected or radiated to
other cooler surrounding components.  Since in this stellarator, the plasma
chamber is entirely surrounded by cryostat walls, there are no places
where this energy can be radiated to, and conduction by itself is not
sufficient to dissipate the energy. For this reason, holes through the
cryostats will be located at strategic places which will allow afterheat
energy to be radiated to surrounding structures from the back of the
shield.  These holes will exist in places where there are sufficiently large
spaces between the coils within the cryostats and will extend from the
inner plasma channel wall to the outer cryostat perimeter.  Naturally, the
holes will be self enclosed, preserving the separate vacuum environment of
the cryostats.  Nevertheless, this makes seals between adjacent cryostats
superfluous.

\subsection{Blanket and Shield Configuration}
\label{s-5-4-3}

It was mentioned in the previous section that the blanket and shield in this
stellarator conform to the contours of the plasma.  This means that the
shape of the plasma chamber is continuously changing  from one toroidal
location to the next.  \hbox{Figure~\ref{f-5-4-5}} is a plot of the first wall
circumference as a function of toroidal angle within one field period.  It
shows the circumference changing from 14.5~m at $\phi=0$ to 12.2~m at
$\phi=45^\circ$ and back to 14.5 at $\phi=90^\circ$, a variation of
16\%.  This variation is due to the change in the plasma shape from a
vertical crescent with rounded ends at $\phi=0$ and $90^\circ$, to a
horizontal tear drop shape at $\phi=45^\circ$.  These contours are shown
in {\hbox{Fig.~\ref{f-5-4-6}}} at intervals of 8.2$^\circ$ from
$\phi=0$ to $\phi=40.9^\circ$.  Note that the plasma shape (dotted lines)
spirals counter-clockwise around the nominal major radius of the machine
at $R=13.9$~m and $Z=0$.  The last solid line in these pictures
represents the centerline of the coil at that location.
{\hbox{Figure~\ref{f-5-4-7}}} is a CAD generated picture of the plasma
surrounded by the blanket/shield, and {\hbox{Fig.~\ref{f-5-4-8}}} shows
the same picture within the bore of the coils.

\begin{figure}[b]
\centerline{\psfig{file=spps-5-4-05.eps,height=4.0in}}
\caption[Fig-4-5]
{Plot of the SPPS first wall circumference as a function of toroidal angle
within one field period.}
\label{f-5-4-5}
\end{figure}

\begin{sidewaysfigure}[p]
\centerline{\psfig{file=spps-5-4-06.eps,angle=90,height=6.0in}}
\caption[Fig-4-6]
{SPPS plasma contours at different toroidal angles.}
\label{f-5-4-6}
\end{sidewaysfigure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-07.ps,width=6.25in,bbllx=143pt,bblly=253pt,%
            bburx=517pt,bbury=621pt,clip=}}
\vspace{3.5cm}
\caption[Fig-4-7]	%	950910_SP_blanket.ps
{View of the SPPS plasma surrounded by the blanket and shield.}
\label{f-5-4-7}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-08.ps,width=6.25in,bbllx=88pt,bblly=179pt,%
            bburx=523pt,bbury=614pt,clip=}}
\vspace{3.5cm}
\caption[Fig-4-8]	%	950910_SP_blktcoil.ps
{View of the SPPS plasma surrounded by the blanket, shield, and coils.}
\label{f-5-4-8}
\end{figure}

To facilitate the maintenance of blanket/shield components, they were
subdivided every 8.2$^\circ$, making up 44 modules altogether.  Each corner
cryostat will house six modules for a total of 24, and the remaining 20 modules
are distributed, five modules each, in the four straight legs of the torus.
The modules consisting of the blanket and hot shield are subdivided each
8.2$^\circ$, to make it easier for removing them from the ends of the
cryostats.  \hbox{Figure~\ref{f-5-4-9}} is a top view of the stellarator core
with the top cover of the vacuum chamber and the over the top structure
removed.  There are 12 cryostats, four corner cryostats and eight others, two
in each straight leg of the torus.  The dotted lines define the outer limits of
the blanket/shield in two field periods.  Modular subdivision is shown in one
field period with the modules numbered from 1-11 or from $\phi=0^\circ$ to
$\phi=90^\circ$.  The first corner cryostat will house modules 42, 43, 44, 1,
2 and 3.  Note that modules 2 and 3 and on the other side, 42 and 43, actually
protrude from the corner cryostat into the adjacent ones.  This is purposely
done to aid in their replacement during maintenance, and in no way will
interfere with the radial extraction of the corner cryostat through the access
port.  \hbox{Figure~\ref{f-5-4-10}} gives the top and side views of the
blanket/removable shield of modules 1, 2 and 3 as numerated in
\hbox{Fig.~\ref{f-5-4-9}}.  The top view shows the relative location of each
module with respect to the line going through the center of a corner cryostat
which is also the start of a field period.  On the other side of the center of
the corner cryostat ({\it i.e.,} modules 42, 43 and 44) the shapes of the
modules will be the same as modules 1, 2 and 3 except that they would spiral in
the opposite direction.  Modules 4, 5 and 6 would complete the half period and
their shapes would progress to a horizontal tear shape with the blunt end
pointing toward the center of the machine.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-09.eps,width=6.5in}}
\vspace{0.8in}
\caption[Fig-4-9]
{View of the vacuum chamber with roof and over-the-top structure removed
and the blanket subdivided into numbered modules.}
\label{f-5-4-9}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-10.eps,height=7.7in}}
\caption[Fig-4-10]
{Top and side views of blanket/shield modules 1, 2 and 3.}
\label{f-5-4-10}
\end{figure}

\subsubsection{Location of Divertors within the Blanket/Shield}
\label{s-5-4-3-1}

A detailed design of the divertor plates is not within the scope of this
study.  Studies on where particles leave confinement after having been
launched at different places around the plasma have been made and are
reported elsewhere in this report.  This section describes
where the divertor plates must be located and, in a later
section, how they will be maintained.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-11.eps,height=7.3in}}
\caption[Fig-4-11]
{View of one half of the SPPS coil set, the plasma contours at
-26.5$^\circ$, 0$^\circ$ and +22.5$^\circ$, and a 3D front view of the last MHD
stable flux surface showing location of divertor plates.}
\label{f-5-4-11}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-12.eps,width=6.5in}}
\vspace{0.5in}
\caption[Fig-4-12]
{Top view of the SPPS showing the extent of divertor plate coverage.}
\label{f-5-4-12}
\end{figure}

Figure~\ref{f-5-4-11} shows one half of the SPPS coil set, the plasma contours
at -26.5$^\circ$, 0.0$^\circ$ and +22.5$^\circ$ respectively, and a 3D front
view of the plasma last MHD stable flux surface.  The divertor plates' and
baffles' locations are shown covering the pointed extremities of the plasma
contours as is also evident from the volumetric plasma picture between the
limits of $\pm 26.5^\circ$.  \hbox{Figure~\ref{f-5-4-12}} is a top view of the
fusion core showing the extent of divertor plate coverage for the upper and the
lower divertors.  Note that the upper divertor extends from -22.5$^\circ$ to
+26.5$^\circ$ while the lower divertor from -26.5$^\circ$ to +22.5$^\circ$.
What is immediately evident from these figures is that the divertor is entirely
located inside the blanket modules which are within the corner cryostat.  This
is very fortunate, in that the divertors can be replaced simultaneously with
the blanket modules.  Alternatively, if the lifetime of the divertor plates is
shorter than that of the first wall and blanket, then another scheme has been
devised for their maintenance, as described in \hbox{Sec.~\ref{s-5-4-6-2}}.

\subsection{Cryostats Configuration}
\label{s-5-4-4}

The cryostats insure that the superconducting coils are maintained near liquid
He temperature and create the barrier between the cold coils and the hot
blanket/shield components.  The coils themselves are cooled with liquid He
which is pumped through passages in the conductors.  On the outside of the coil
cases, aluminized mylar multi-layer superinsulation is wrapped which cuts down
on radiative losses, while conductive and convective losses are eliminated by
evacuating the cryostats.  The walls of the cryostats have to be able to
withstand one atmosphere of pressure during the testing phase.  Inside the
vacuum chamber during plant operation, there is no atmospheric load on the
walls.  However, the cryostat walls must be capable of transmitting forces from
the coils to external structure located in the vacuum chamber.  To minimize the
heat conducted through this structure, there will be liquid N$_2$ cooled
intercepts located on the supports.  Thus, the only heat conducted to the coils
would be that driven by the temperature difference of 77~K to 4.2~K along the
supports.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-13.eps,width=6.5in}}
\vspace{0.5in}
\caption[Fig-4-13]
{Top view of the SPPS showing coil locations in the cryostats.}
\label{f-5-4-13}
\end{figure}

As mentioned above, the stellarator coils are distributed in the various
cryostats unevenly.  There are four coils in each corner cryostat and two coils
each in the remaining cryostats (see\hbox{Figure~\ref{f-5-4-13}}).  Note that
some of the coils appear to be sharing adjacent cryostats.  That is not the
case at all.  The heavy lines outline the upper cryostat surfaces, however,
these lines do not connect the top and bottom cryostat surfaces with vertical
surfaces, but are inclined to accommodate some of the coils' excursions.  These
excursions entail a coil part going over an adjacent coil or conversely, going
beneath an adjacent coil part.  The inter-cryostat surfaces follow these
excursions such that the coils are always within their designated cryostat.
For this reason, if \hbox{Fig.~\ref{f-5-4-13}} was viewed from the bottom, the
outline of the two cryostats between the corner cryostats would switch places.
The one important aspect of the cryostats design, is that the inter-cryostat
surfaces will not prevent maintenance of the fusion core by moving cryostats.
Thus, corner cryostats can be taken out radially through the vacuum chamber
ports, and the cryostats adjacent to them, can be taken out diagonally through
the same ports.

\subsection{Structural Distribution}
\label{s-5-4-5}

This is a brief discussion of the structure distribution in the fusion power
core.  It should be made clear that this is not a structural analysis by any
means, rather it is an attempt to determine where structure will be needed; get
a first order appreciation for how much is needed: finally, to determine if the
structure can be placed in such a way that it will not interfere with normal
maintenance of the fusion core.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-14.eps,width=6.5in}}
\vspace{0.5in}
\caption[Fig-4-14]
{Top view of one half of the SPPS showing the $X$ and $Y$ force vectors
integrated around the circumference and applied at the near coil centroids.
Integrated vertical force ($Z$) vectors from coils are also shown.}
\label{f-5-4-14}
\end{figure}

Figure~\ref{f-5-4-14} is a top view of one half of the fusion core with an
overlay of the force vectors in the $X-Y$ plane as applied to the centroid of
each coil.  This is the resultant of the integrated forces around the coil in
the $X-Y$ plane.  The coils are numbered from 25--32 and from 1--8.
\hbox{Figure~\ref{f-5-4-14}} also gives the integrated vertical force
vectors for each coil.  Note that the largest forces in the $X--Y$ plane are on
coils 25, 32, 1 and 8, which are corner coils.  The protrusions from the
center-post at these locations are intended to react these forces.  Some
components of these forces will be reacted with intercoil support structure.
The next largest $X-Y$ forces are on coils 26, 31, 2 and 7, which are also
corner coils.  Here again the main thrust will be against the center-post
protrusions with small intercoil components.  The $X-Y$ forces on coils 27--30
and 3--6 have no radial components and, therefore, will not be reacted by the
center-post.  Rather, these vectors will have force components which will have
to be reacted with intercoil structure and structure on the outboard side.
This outboard side structure is shown in \hbox{Figs.~\ref{f-5-4-13}} and
\hbox{\ref{f-5-4-14}} as filling the space between access ports in the
vacuum chamber.  A piston is shown as bridging the space between the structure
and the cryostat, implying an adjustable mechanism.  Such a mechanism is needed
for two reasons: the mechanism must be capable of being retracted to make room
for the extraction of these cryostats should that become necessary, and
adjustments will be needed for coil location and force reaction when the coils
are energized.

Figure~\ref{f-5-4-14} also shows the vertical force vectors on the coils.
These forces will be reacted with over-the-top and under-the-bottom structure
connecting with the outboard side structure and the center-port structure.  The
over-the-top and under-the-bottom structure also will need adjustable piston
type mechanisms for the same reasons as the outboard side structure.

\begin{sidewaysfigure}[p]
\centerline{\psfig{file=spps-5-4-15.ps,height=8.truein,bbllx=130pt,bblly=110pt%
                   ,bburx=535pt,bbury=680pt,angle=-90,clip=}}
\caption[Fig-4-15]
{Isometric view of the SPPS Fusion Power Core showing the structural cocoon.}
\label{f-5-4-15}
\end{sidewaysfigure}

\begin{table}[p]
\caption{ }
\centering
{\bf Force Vectors on SPPS Coils}
\vspace{1 cm}
\renewcommand{\arraystretch}{1.4}
\begin{tabular}{l c c c c c c}
\hline
Coil & $F_X$ (MN) & $F_Y$ (MN) & $F_Z$ (MN) &
                                     $F_{XY}$ (MN) & Angle & $F_{Res}$ (MN) \\
\hline \\
 25  &   -109.9  &  \N316.6 &   -103.3  &  335.2  &  \N109$^\circ$ &  350  \\
 26  &   -205.9  &  \N129.7 &   -225.3  &  243.4  &  \N149$^\circ$ &  332  \\
 27  &   -133.9  &  \Z-79.9 &   -212.5  &  156.0  &   -149$^\circ$ &  264  \\
 28  & \N\Z34.3  &   -128.0 &  \Z-68.9  &  132.5  &  \Z-75$^\circ$ &  149  \\
 29  &  \N128.0  &  \Z-34.3 & \N\Z68.9  &  132.5  &  \Z-15$^\circ$ &  149  \\
 30  & \N\Z79.9  &  \N133.9 &  \N212.5  &  156.0  & \N\Z59$^\circ$ &  264  \\
 31  &   -129.7  &  \N205.9 &  \N225.3  &  243.4  &  \N122$^\circ$ &  332  \\
 32  &   -316.6  &  \N109.9 &  \N103.3  &  335.2  &  \N161$^\circ$ &  350  \\
\Z1  &   -316.6  &   -109.9 &   -103.3  &  335.2  &   -161$^\circ$ &  350  \\
\Z2  &   -129.7  &   -205.9 &   -225.3  &  243.4  &   -122$^\circ$ &  332  \\
\Z3  & \N\Z79.9  &   -133.9 &   -212.5  &  156.0  &  \Z-59$^\circ$ &  264  \\
\Z4  &  \N128.0  & \N\Z34.3 &  \Z-68.9  &  132.5  & \N\Z15$^\circ$ &  149  \\
\Z5  & \N\Z34.3  &  \N128.0 & \N\Z68.9  &  132.5  & \N\Z75$^\circ$ &  149  \\
\Z6  &   -133.9  & \N\Z79.9 &  \N212.5  &  156.0  &  \N149$^\circ$ &  264  \\
\Z7  &   -205.9  &   -129.7 &  \N225.3  &  243.4  &   -149$^\circ$ &  332  \\
\Z8  &   -109.9  &   -316.6 &  \N103.3  &  335.2  &   -109$^\circ$ &  350  \\
\\ \hline
\end{tabular}
\label{t-5-4-1}
\end{table}

The picture which emerges is that of a set of coils encased in a cocoon of
structure on all sides with the exception of the area in front of the access
ports.  \hbox{Figure~\ref{f-5-4-15}} is a CAD generated picture of this cocoon
of structure with the fusion core removed altogether.  What appears to be a
double roof is a structure which derives stiffness from an H-beam type of
configuration.  \hbox{Table~\ref{t-5-4-1}} gives the magnitude of the
integrated force vector components for the coils shown in
\hbox{Fig.~\ref{f-5-4-14}}.  The angles of the $X-Y$ vectors are measured
counter clockwise from the vertical line parallel to the $X$-axis going through
the centroid of each coil, with 0$^\circ$ taken on the outboard side.  A
negative angle indicates a clockwise measurement.  The vectors $F_X$, $F_Y$ and
$F(Z$) change signs from 25--32 and 1--8, and $F_X$ and $F_Y$ sometimes
alternate both sign and magnitude.  However $F_{XY}$ remains the same for
similar coils, and the resultant force $F_{Res}$, which is the vector summation
of $F_{XY}$ and $F_Z$ is also the same for similar coils.

Material properties used in support structure calculations are given in
\hbox{Table~\ref{t-5-4-2}}.  Most of the support structure in the coils cocoon
will be at a temperature below 473~K and for this reason the yield strength for
20\% cold worked 316~SS at 473~K is used.  The design stress is taken as 2/3 of
the yield strength, or 446~MPa.  No distinction is made between structure at
473~K or at 20~K, and since stainless steel becomes stronger at cryogenic
temperatures, these estimates of mass of the structure will be conservative.

\begin{table}[b]
%\vspace{2.cm}		% This is just to make this figure flush bottom
\caption{ }
\centering
{\bf Material Properties Used in Support Structure Calculations}
\vspace{1 cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l  l}
\hline \\
Material                   &  316 SS cold worked  \\
Average ultimate strength  &  745 MPa at 473 K  \\
Average yield strength     &  670 MPa at 473 K  \\
Modulus of elasticity      &  $1.94\X 10^5$~MPa  \\
Poisson's ratio            &  0.3  \\
Design stress              &  446 MPa at 473 K \\
\\ \hline
\end{tabular}
\label{t-5-4-2}
\end{table}

\clearpage

\subsubsection{Center post structure}
\label{s-5-4-5-1}

The formula for a ring under several equal radial forces, equally spaced, is
used for calculating the amount of structure in the center post.  The bending
moments for this case are~\cite{Roa75}:
%
\begin{eqnarray}
\label{e-5-4-1}
 M(+) & = & \frac{WR}{2} \, (\frac{1}{S} - \frac{1}{\theta} ) \: , \\
\label{e-5-4-2}
 M_{\max}(-) & =  & - \, \frac{WR}{2} \, ( \frac{1}{\theta} - \frac{C}{S} ) \: ,
\end{eqnarray}
%
where $W$ is the applied load, $R$ the radius, $\theta$ is the half angle
between loads, $S$ the sine of $\theta$ and $C$ the cosine of $\theta$.  In
this case $W=893$~MN, $R=7.5$~m, $\theta=45^\circ$, $S=0.707$ and $C=0.707$.

The maximum bending moment occurs at the point of load application and is equal
to 916~MNm, while the bending moment between loads is 470~MNm.  For maintaining
a stress of $\sim$440~MPa, the specific moment of inertia is 0.285~m$^4$/m
which is equivalent to two tier depths of 0.76~m $\X$ 0.38~m H beams.  The
height of the center post over which the radial forces are applied is 4.56~m,
thus requiring 12 levels of stacked beams.  The total length of beams is
1,030~m at a weight of 254~kg/m, for a total mass of 262~tonnes.

In addition to the radial load, the center-post is subjected to a vertical
tensile load from the $F_Z$ forces on the coils.  This load of 2,440~MN is
shared between the center-post structure and the outboard structure, thus
requiring an area of steel in tension of 2.65~m$^2$.  The cumulative thickness
of the flanges in the two tiers of H beams exceeds this area by more than a
factor of two.  The remaining part of the center-post, which amounts to another
9~m needs 2.65~m$^2$ in tension, requiring an additional mass of 179~tonnes.
This makes the total mass of the center-post equal to 441~tonnes.

\subsubsection{Outboard structure}
\label{s-5-4-5-2}

Coils 28, 29 and 4, 5 have outward radial force components equal to
$132.5\cos(15^\circ)=128$~MN each.  Assuming a build up of the same H beams
used in the center-post, over a height of 14~m and a width of 6~m, the needed
moment of inertia is 1.0~m$^4$.  It is interesting to note that the mid-plane
deflection of the structural assembly is 1.8~cm which can be corrected with the
adjustable piston mechanism.  The total outboard structural mass at all four
locations is 488~tonnes.

\subsubsection{Over the top and bottom structure}
\label{s-5-4-5-3}

Figure~\ref{f-5-4-14} shows the vertical forces $F_Z$ on the coils.  The
sum of the forces in each cycle, for example on coils 29--32, is 610~MN, and
they are cyclic.  Using the same methodology as in the previous section, the
moments of inertia needed over a span of 11.0~m for coils 29, 30, 31 and 32 are
0.12~m$^4$, 0.71~m$^4$, 0.78~m$^4$ and 0.24~m$^4$ respectively, and the total
amount of structure is 44~tonnes, 78~tonnes, 80~tonnes and 57~tonnes
respectively.  The deflections are from 1.2--1.8~cm.  The total amount of
structure to react the vertical force vectors is 4,144~tonnes.

\subsubsection{Intercoil structure}
\label{s-5-4-5-4}

Lacking the time or resources to perform an accurate determination of the
intercoil support structure, it was necessary to resort to simplifying
assumptions which were:

\begin{enumerate}
\item The coil cases for coils 31, 32, 1 and 2 overlap on the inboard
mid-plane, requiring them to be integrated together at that point with no
intercoil supports.

\item Intercoil supports are spaced at 2~m intervals along the whole
circumference of the coils to react the force  component vectors along the
locus of the coil centroids, as shown in \hbox{Fig.~\ref{f-5-4-14}}.

\item Check for buckling of support structure at points where the coils
legs are far apart.

\item Assume that the intercoil supports will be adjustable in length.
\end{enumerate}

It is important to insure that the coil deflection between supports spaced at
2~m will not be excessive.  From \hbox{Fig.~\ref{f-5-4-14}} and
\hbox{Table~\ref{t-5-4-1}}, it can be seen that the largest intercoil force
occurs between coils 30 and 31, and others of the same configuration around the
torus.  The force component directed along the locus of the coils' centroid for
coil 30 is 125~MN.  Typically, the magnetic force density from the front to the
back of the coils varies by a factor of three, and it is safe to assume that
the intercoil forces would do the same.  This means that the force on the coil
will vary from 10~MN/m at the front to 3.3~MN/m at the back.  The coil case
thickness in this design is 7.5~cm, the conductor bundle 0.51~m $\times$
0.789~m, therefore the coil case outer dimensions are 0.66~m $\times$ 0.93~m.
The moment of inertia of the coil case by itself is 0.0137~m$^4$ for bending
about an axis parallel to the large dimension.  To calculate the coil leg
deflection between supports spaced at 2~m, a built-in beam of the above moment
of inertial loaded uniformly with 10~MN/m is assumed.  The equation
is~\cite{Roa75}:
%
\begin{eqnarray}
\label{e-5-4-3}
 y & = & \frac{W\ell^4}{384 \, E \, I} \: ,
\end{eqnarray}
%
where $y$ is the deflection, $W$ is the load per unit length, $\ell$ the
distance between supports, $E$ the modulus of elasticity and $I$ the moment of
inertia.  The deflection is \hbox{$1.5\times 10^{-4}$~m} or 150$\mu$m, a
negligible value.  The shortening of the intercoil support structure itself
under load must also be taken into account.  Because the distances between coil
legs are sometimes as long as 8~m, the structure provided in compression will
become shorter even under very low stress.  For example, if the stress is only
50~MPa, an 8~m long support rod will be reduced in length by 2.0~mm, and at a
more reasonable stress of 500~MPa it will be reduced by 2~cm.  If the accuracy
of the conductor bundle location must be maintained to $10^{-4}$~m/m, this
means that the deflection of an 8~m long support can not be more than 0.8~mm
implying that the stress in the support rod can only be 20~MPa, requiring an
inordinately large amount of structure.  This is clearly unreasonable.
Furthermore, the shrinkage of steel from room to cryogenic temperatures must
also be reckoned with, exacerbating the problem even more.  An obvious solution
would be to make these long intercoil support rods adjustable.  There are
several ways for accomplishing this, but will not be a part of this study.  For
the present, these long intercoil supports are assumed to be adjustable.  Using
the method described above for spacing intercoil structure, it has been
estimated that 7.7~tonnes will be required between each coil in the corner
cryostats.  Using a 30\% safety factor the total amount of structure in the
corner cryostats is 30~tonnes.  Similarly, the total amount of intercoil
structure is determined to be 240~tonnes.

\begin{table}[t]
\caption{ }
\centering
{\bf Mass of SPPS Magnets Support Structures (tonnes)}  \\
\vspace{1 cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l  @{\hspace{2.cm}} r}
\hline \\
Coil cases     &  1,651  \\
Center-post     &  441  \\
Top and bottom &  4,144  \\
Outboard       &  488  \\
Intercoil      &  240  \\
{\it Total}    &  5313  \\
\\ \hline
\end{tabular}
\label{t-5-4-3}
\end{table}

Table~\ref{t-5-4-3} summarizes the estimated structure which supports the
magnetic forces on the coils.  This structural evaluation can be compared with
other estimates made for similar coil systems by using the virial stress, which
very simply is the ratio of the stored energy to the volume of structure used
to contain it.  If one obtains the virial stress for the conductor volume
alone, using the stored energy of 78~GJ and a volume of 400~m$^3$, it is
195~MPa.  This value for some of the Helias design designated
HSR58~\cite{Jun91} varies from 110--130~MPa.  The virial stress for the case
where all the structure is included is 59~MPa for SPPS and varies from
41--44~MPa for the HSR58 systems.  It is interesting to note that if the
assumption of adjustable intercoil supports was not made, the added structure
would have brought the virial stress closer to the values for the HSR58 system.

\subsection{Fusion-Core Maintenance}
\label{s-5-4-6}

As mentioned in the introduction, this report will deal with three aspects of
fusion-core maintenance, namely the blanket/shield, the divertor elements and
the coils.  Further, this treatise will be rudimentary in the sense that it
cannot go into great detail.  Rather, a gross assessment of the feasibility is
made consistent with the scope of the study.

The maintenance of the SPPS components depends on the capability to move the
corner cryostats containing the four corner coils.  For this reason the vacuum
chamber was designed to have access ports behind the corner cryostats.
Further, the support structure has been arranged in such a way as to leave the
access ports unobstructed.  In the following sections the maintenance
procedures for the blanket/shield components, the divertor components, and the
coils is described.

\subsubsection{Maintenance of the Blanket/Shield Components}
\label{s-5-4-6-1}

Radiation damage in the first wall and blanket components necessitates their
periodic replacement.  The peak neutron wall loading is 2~MW/m$^2$ which means
the maximum first wall fluence will reach 15~MW a/m$^2$ in 7.7 full power years
(FPY) or, at 70\% availability, 11 calendar years.  This means that the first
wall, blanket and replaceable shield will be replaced on an 11 year schedule.
One possible scenario is to replace 25\% of these components every 33 months.
Such a scheme would work out very well, since 25\% of the components can be
replaced by moving one of the corner cryostats.

Figure~\ref{f-5-4-16} is a top view of the fusion core with a corner
cryostat extracted through a vacuum vessel access port and
\hbox{Fig.~\ref{f-5-4-17}} shows several views of a free standing corner
cryostat.  There  are six blanket/shield modules that come out with the
corner cryostat.  According to the numeration in \hbox{Fig.~\ref{f-5-4-9}}
they are  modules 42--44 and 1--3.  These modules are now accessible for
extraction through the open ends of the cryostat.  Further, the modules
adjacent to the corner cryostat, namely  39--41 and 4--6 are also
accessible through the openings in the cryostats which are still in the
vacuum vessel.  Thus, 25\% of the blanket/shield
modules become accessible for replacement by virtue of the extraction of
one corner cryostat.  It is well and good to say the modules become
accessible for extraction, but how they can be extracted is still an issue.
This will be addressed in the next sections.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-16.eps,width=6.5in}}
%\vspace{0.5in}
\caption[Fig-4-16]
{Corner cryostat shown extracted from vacuum vessel.}
\label{f-5-4-16}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-17.eps,width=6.5in}}
\vspace{1in}
\caption[Fig-4-17]
{Several views of a free standing corner cryostat.}
\label{f-5-4-17}
\end{figure}

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-18.eps,width=6.5in}}
\vspace{1in}
\caption[Fig-4-18]
{Blanket/shield module no.~1 shown with outer mid-plane part removed.}
\label{f-5-4-18}
\end{figure}

Figure~\ref{f-5-4-10} shows the top and side views of modules 1, 2 and 3.  The
complimentary modules 42, 43 and 44 are identical but are twisting in the
opposite direction.  Modules 42, 43, 2 and 3 protrude from the corner cryostat,
and thus are not contained on their total perimeter.  Extracting them should be
fairly straight forward.  On the other hand, modules 44 and 1 are contained
around their perimeter and extracting them through a somewhat changing aperture
of the cryostat will be difficult.  Fortunately, the divertor access port
located at the outboard mid-plane of the corner cryostat as shown in
\hbox{Fig.~\ref{f-5-4-9}} will help out in this case.  As shown in the figure,
the outboard mid-plane portions of the blanket/shield of modules 44 and 1 are
attached to the access port and can be withdrawn radially from the cryostat.
This relieves the rear constraint on these modules and makes it possible for
them to be extracted.  The effect on modules 44 and 1 is that their outboard
mid-plane segment is missing as shown in \hbox{Fig.~\ref{f-5-4-18}}.  However,
assembled in the fusion core with the divertor access port in place, these
modules are reconstituted.

Turning to modules 4, 5, 6 and 39, 40, 41, which are within the adjacent
cryostats still inside the vacuum chamber, it can be seen that modules 4 and 41
protrude from the cryostats somewhat and are contained over a small fraction of
their outboard perimeter.  From a cursory inspection it appears that they can
be extracted with a minimum amount of manipulation.  The remaining modules 5,
6, 39 and 40 are trapped well within their respective cryostats and cannot be
extracted easily.  There are three solutions to this problem:

\begin{enumerate}

\item
Provide a larger gap between the replaceable blanket/shield for all the modules
within these adjacent cryostats.

\item
Move the adjacent cryostats out of the vacuum chamber.

\item
Divide modules 5, 6, 39 and 40 into two parts along an inclined plane passing
vertically through them.

\end{enumerate}

The first option compromises shielding and will require a redesign of the
fusion core with larger coils; not a desirable solution.  The second option is
certainly possible, since the fusion-core design has provided for the
capability of extracting these adjacent cryostats from the vacuum vessel.
However, moving cryostats is a slow and tedious operation to be resorted to
only if all other options fail.  The last option is the least intrusive and
will require the least amount of modification.  Dividing these modules into two
halves by passing vertical planes inclined several degrees from the centerline
through them will make it possible to extract each half separately.  The major
penalty is that an additional set of coolant lines needs to be disconnected,
and seems to be a small price to pay for this convenience.

Thus far, the overall processes needed for blanket/shield replacement have been
summarized.  In this section a step-by-step description of the tasks will be
given.  The initial conditions are that the plasma has been shut down, and the
coolant continued to be circulated for a period of time to dissipate the
afterheat generated by the short term activation products.  The subsequent
steps are as follows:

\begin{enumerate}

\item
The magnets are de-energized but maintained cold by not despoiling the vacuum
within the cryostats.

\item
The lithium coolant is drained into dump tanks.

\item
The vacuum chamber is brought up to one atmosphere of pressure with dry air.
Alternatively, if the containment building in which the vacuum vessel is
situated is capable of being sealed, then the cover gas could be He or dry
N$_2$.

\item
The designated access port to the vacuum vessel is unbolted and the door
removed.

\item
Any over-the-top and under-the-bottom load activators designated for the
particular corner cryostat in question are de-energized.

\item
Coolant connections joining the blanket/shield modules to external headers are
disconnected.

\item
Cryogenic coolant lines are disconnected and capped off, and electric bus-bars
are disconnected.

\item
Rails or guided runners for gas pads are located through the access port and
fixed to the floor.

\item
Compressors for activating the gas pads are connected and turned on.

\item
A mobile robot is attached to the undercarriage of the corner cryostat which
pulls out the cryostat on guided runways radially from the vacuum vessel.  The
cryostat is moved a sufficient distance as to allow roving remote handling
machines to service the blanket/shield modules both within the corner cryostat
and within the vacuum vessel.

\end{enumerate}

\noindent
After the old blanket/shield modules are replaced with new ones, and are
checked for leak tightness, the process is reversed, the fusion core
reassembled and prepared for start-up.

As mentioned before, moving the corner cryostat is no trivial task.  Aside from
its mass, which is $\sim$2,215~tonnes, this is a very delicate and precise
operation.  Returning the cryostat back into the vacuum vessel is even more
crucial, since the location of the coils must be within a tolerance of
$10^{-4}$~m/m.  This is the reason that adjustable support structure both
intercoil and otherwise is necessary.  Precise mechanical location can be
performed with the use of fiducial marks and advanced optical measuring
instruments.  However, final adjustments must be made after the system is
evacuated and the coils energized.  Fortunately, in stellarators, vacuum fields
can be established and precisely measured, before a plasma is launched.

Table~\ref{t-5-4-4} lists the masses in corner cryostats and
\hbox{Table~\ref{t-5-4-5}} gives the physical parameters of the blanket/shields
as numbered from 1--6.  Please note that module 7 is identical to 5 and 8
identical to 4, {\it etc.}  There are volume and mass values for the so called
``hot shield'' which is replaced along with the blanket, and there are values
for the ``cold shield'' which is a lifetime component.  The masses given for
the first wall, blanket and shield are with the lithium coolant drained out.

\begin{table}[p]
\caption{ }
\centering
{\bf Masses in Corner Cryostat (tonnes)} \\
\vspace{1 cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l @{\hspace{2.cm}} r}
\hline \\
Coils               &    513  \\
Intercoil structure &     30  \\
Blanket/shield      &  1,486  \\
Cryostat            &    186  \\
{\it Total}         &  2,215  \\
\\ \hline
\end{tabular}
\label{t-5-4-4}
%\end{table}

\vspace{2.cm}

%\begin{table}[b]
\caption{ }
\centering
{\bf Physical Parameters of SPPS Blanket Modules}   \\
\vspace{1 cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l  c  c  c  c  c  c}
\hline \\
\vspace{0.2cm}
Module no.: &  1   &  2     & 3     &  4     & 5     &  6  \\
First wall surface area (m$^2$)  
          & 37.31  & 36.47  & 32.43 & 27.70  & 21.88 & 21.05 \\
First wall volume (m$^3$)
          & 0.522  & 0.511  & 0.454 & 0.388  & 0.306 & 0.295 \\
Blanket volume (m$^3$)
          & 13.06  & 12.76  & 11.35 &  9.70  & 7.66  & 7.37  \\
First wall \& blanket mass$^{(a)}$ (tonnes)   	     	   	     
          & 8.922  & 8.719  & 7.754 & 6.624  & 5.23  & 5.033 \\
Hot shield volume  (m$^3$)
          & 20.5   & 19.93  & 17.82 & 14.36  & 11.89 & 11.37 \\
Hot shield mass$^{(a)}$ Li (tonnes)
          & 146.68 & 142.60 & 127.5 & 102.71 & 85.10 & 81.37 \\
Cold shield volume (m$^3$)
          & 14.27  & 13.95  & 12.40 & 10.30  & 8.35  & 8.03  \\
Cold shield mass$^{(a)}$ (tonnes)
          & 105.74 & 103.37 & 91.88 & 76.29  & 61.90 & 59.49 \\
\\ \hline
\multicolumn{7}{l}{$(a)$ Without the Li coolant.}
\end{tabular}
\label{t-5-4-5}
\end{table}

During blanket replacement it is the masses of the first wall, blanket and the
hot shield which are replaced.  For modules 1, 2 and 3 this is 155.6 tonnes,
151.3~tonnes and 135.3~tonnes respectively.  However, since module 1 has $\sim
15\%$ of it removed with the divertor access port, this makes its mass
132.3~tonnes.  This means that the heaviest module is 2 at 151.3~tonnes, and
the lightest is at 86.4~tonnes.  Module 2 is one of the easier ones to extract,
since it protrudes from the cryostat and is constrained only at its outboard
perimeter.  An overheat crane assisted with ground mounted manipulators will be
able to perform the operation.  An overhead crane will not be able to assist in
the replacement of modules 39-41 and 4-6 due to the overhang of the structural
cocoon and the roof of the vacuum vessel.  They will be entirely handled with
ground mounted manipulators working inside the vacuum vessel.

\subsubsection{Maintenance of Divertor Plates}
\label{s-5-4-6-2}

The divertor plates suffer radiation damage at the same rate as the first wall
elements and their radiation damage lifetime will be the same.  However, these
plates will be subjected to high particle fluxes, and depending on the particle
energies, can sustain high rates of erosion.  Further, because they will be
high heat flux components, they are more vulnerable to failure than the first
wall.  For this reason, a mechanism for accessing the divertor plates for
replacement, without moving any cryostats has been devised.

Figure~\ref{f-5-4-9} shows a top view of the fusion core with the vacuum vessel
and over the top structure removed.  The corner cryostat lying along the $X$
axis has dotted lines outlining an access port on its outer perimeter.
\hbox{Figure~\ref{f-5-4-17}} has several views of the corner cryostat, and the
rear view shows an access port at the mid-plane.  It is possible to locate an
access port there, because the backlegs of the coils at that point are almost
8~m apart.  The flange shown in \hbox{Fig.~\ref{f-5-4-17}} is attached to
effectively a drawer reaching through the walls of the cryostat all the way to
the blanket/shield.  The cavity through which this drawer penetrates is totally
enclosed such that the vacuum in the cryostat is unaffected.  Withdrawing this
drawer from the cryostat extracts with it that portion of the blanket/shield
attached to it which is part of module 44 and 1.  The aperture which is created
this way is 5~m in the horizontal direction and 1.8~m in the vertical
direction.  Rails can be inserted into this port on which special remote
handling machine can enter into the plasma chamber to disconnect and remove
divertor segments.

It is conceivable that this operation can be performed through the vacuum
vessel access port door using an airlock, such that the vacuum vessel can stay
evacuated.  This would enhance the process, however, at the expense of the
complication of using an airlock.

\subsubsection{Maintenance of Coils}
\label{s-5-4-6-3}

The coils in SPPS are lifetime components and should not have to be replaced.
However, should there be coil malfunction, a problem with intercoil structure,
a cryogenic leak or a cryostat vacuum leak, it would be necessary to be able to
get at all ports of the cryostats for repair or replacement.  For this reason,
the vacuum vessel and the support structure has been designed with the
capability of extracting all of the cryostats.

Figure~\ref{f-5-4-16} shows how a corner cryostat is extracted and
\hbox{Fig.~\ref{f-5-4-19}} shows how an adjacent cryostat is extracted.  The
adjacent cryostat on the other side can be extracted in the same way.  The
other three vacuum vessel ports can be used to access all of the other
cryostats providing the capability of maintaining all the coils in the fusion
core.

\begin{figure}[p]
\centerline{\psfig{file=spps-5-4-19.eps,width=6.5in}}
\caption[Fig-4-19]
{Top view of SPPS showing adjacent cryostat extracted from vacuum
vessel.}
\label{f-5-4-19}
\end{figure}

\section{SUMMARY AND CONCLUSIONS}
\label{s-5-5}

The SPPS reference blanket design is a liquid metal blanket with lithium as
coolant and breeder and vanadium alloys as structural material. It also assumed
that a suitable insulating coating ({\it e.g.,} CaO) can be developed to
significantly reduce the MHD pressure drops.  The use of the insulating coating
has major impacts on the configuration as it allows one to develop an
attractive first wall and blanket design by addressing mechanical, thermal
hydraulic, and neutronics requirements in the most direct and simple way rather
than by trying to minimize MHD pressure drop effects by utilizing more complex
flow configurations.  Because of high exit temperature of the coolant, an
advanced Rankine cycle with an efficiency of 46\% has been utilized.

The 35~cm thick blanket will provide tritium self-sufficiency for the SPPS
stellarator design.  An overall tritium breeding ratio of 1.12 seems
adequate with provisions made for the presence of penetrations and divertor
plates.  The first wall and blanket should be replaced every 11~y due to
radiation damage to the vanadium structure.  Sufficient shield is placed
behind the blanket to protect the magnets.  For a peak neutron wall loading
of 2~MW/m$^2$, the shield is 80~cm thick and is made of borated steel
filler supported by V structure.  A successful attempt was made to lower
the cost of the shield while keeping the attractive safety feature of the
design.  A potential improvement to the present design is to employ
the more efficient WC shield in the critical areas underneath magnets in
order to reduce the radial standoff and thus the overall dimensions of the
machine.

The unique advantage of the stellarator is that it can operate with a
current-less plasma, thus avoiding the whole issue of disruptions.  It does
this by having all the current carrying elements external to the plasma
which in turn complicates the coils required for confining the plasma.
This coil system makes access to the fusion core components which need
periodic replacement due to radiation damage more challenging.  Power-plant
designers working on modular stellarators have come to recognize early on
that the only way to provide access for replacing first wall, blanket and
shield components, and for maintaining the coils is by moving blocks of
coils out of the fusion core enclosure.  The best way for accomplishing this
task is left to the innovativeness of the power-plant designers.

For SPPS, it has been determined that 16 of the 32 coils have to be
displaced to provide maintenance capability for all the fusion core
components.  The coils are housed in discrete cryostats, four in corner
cryostats and two in each adjacent one.  The whole assembly of cryostats
is surrounded with a cocoon of support structure and placed within the
vacuum vessel.  The vacuum vessel has four access ports located
behind each of the corner cryostats and unobstructed by support structure.
Adjustable pistons are used for transferring loads from the coils to the
structure and for coil alignment.  Extracting one corner cryostat through a
vacuum vessel port provides access for maintaining  25\% of the internal
plasma chamber components which are divided into 44 modules, with the
heaviest one weighing $\sim$150~tonnes.  Because there are no seals
between adjacent blanket/shield modules, the plasma chamber vacuum is
shared with that of the vacuum vessel.  An access port in the rear of the
corner cryostat provides an opening for maintaining divertor segments
independently from the blanket/shield modules.  Finally, a capability is
provided for extracting all the cryostats from the vacuum vessel in the
event of a coil failure or a failure of any component within any of the
cryostats.


\clearpage
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\end{document}

\bye
