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\begin{document}

\title{\bf Superconducting Poloidal Field Magnet Engineering for the ARIES-ST}

\author{
Leslie Bromberg, S. Pourrahimi, J.H. Schultz, P. Titus  \\
MIT Plasma Science and Fusion Center \\
S. Jardin, C. Kessel, W. Reiersen\\
Princeton Plasma Physics Laboratory \\
and the ARIES team
}

\date{ }
\maketitle

\begin{abstract}
The critical issues of the poloidal systems for the \ARST design have been
presented in this paper.  Because of the large plasma current and the need of
highly shaped plasmas, the PF coils should be located inside the toroidal field
in order to reduce their current.  Even then, the divertor coils carry large
currents. The \ARST PF coils are superconducting using the internally cooled
cable-in-conduit conductor.  The peak self field in the divertor coils is about
12~T and the highest field in the non-divertor coils is about 6~T. The PF
magnets have built-in margins that are sufficient to survive disruptions
without quenching. The costing study indicates that the specific cost of the PF
system is \$80/kg.  Detailed design and trade-off studies of \ARST are
presented and remaining R\&D issues are identified.
\end{abstract}

\section{Introduction}
\label{introduction}

The \ARST reactor is a conceptual commercial reactor based on very
low aspect ratio, with small extrapolation from the present
engineering data bases~\cite{ARIESST}.

The poloidal field magnets for \ARST have several similarities to the
designs for the other ARIES
studies~\cite{ARIESone,ARIEStwo,PULSARMagnet,ARIESRS}. However, the
design is more demanding due to the much higher coil currents.  The
poloidal field currents are much larger due to the stability and
equilibrium requirements of the highly shaped, high current plasma.
The pulsing requirements of \ARST are similar to those of
\ARRS~\cite{ARIESRS} and the other previous steady-steate
studies~\cite{ARIESone,ARIEStwo}, and differ substantially from those
of \PU, where in addition to a large solenoid for inductive current
drive, there were substantial fatigue and cryogenic cooling
issues~\cite{PULSARMagnet}.

The low aspect ratio operation has substantial consequences for the
poloidal field system of the \ARST reactor design.  As mentioned
above, the plasma current is substantially larger than in tokamak
reactor designs with higher aspect ratio.  This requires a larger PF
system.  The poloidal field system, unlike the toroidal field system
in the present \ARST design, has to be made superconducting.  This is
feasible because there are no maintenance requirements that require
that the PF coils be demountable, as well as the fact that since
there is no need for a central solenoid, the PF coils can be adequately
shielded from the plasma radiation.  In addition to high plasma
current, the PF is driven by requirements on highly shaped plasmas.
This is in order to decrease the dissipation in the toroidal field
coil, which requires high plasma $\beta$, and therefore highly shaped
plasmas~\cite{ARIESSTO}.

Low aspect ratio operation has important implications on the critical
issues of the poloidal field systems.  The objectives of the PF
magnet work in \ARST are to review conventional magnet design with
conventional materials, in an application where the divertor coils
are located inside the toroidal field coils.  In addition to the
design of the divertor and ring coils, this paper presents options
for the design of the current leads to the divertor coils.  The
current leads to these coils need to travel through the toroidal
field, and therefore experience large Lorenz forces.  Methods of
minimizing the cryogenic loads to the divertor coils, by the use of
high temperature superconducting leads, are also described.

This paper also provides details on the formalism utilized by the
systems code to evaluate the options and to provide detailed
engineering calculations of the critical issues.  The cost of the PF
magnet, an item that has an impact on the cost of a tokamak reactor,
is analyzed.  Improvements on the magnet design and construction that
could result in decreased cost of the PF magnet have also been
investigated.

Material issues are described in Sec.~\ref{materials}.  The
engineering design criteria used for the PF system design for \ARST
are described in Sec.~\ref{pf_design}.  The PF scenarios are
described in Sec.~\ref{pf_scenario_section}.
Sec.~\ref{pf_eng_design} presents the engineering details of the
design.  The current leads are described in
Sec.~\ref{pfcurrentleads}.  The cost assumptions for the PF systems
are described in Sec.~\ref{pf_costing}.  The detailed bottom's-up
costing model was developed for a one-of-a-kind system, without the
benefits of 10th of a kind that the \ARST is predicated upon.  Likely
impacts of a learning curve on the costing are made at the end of
that section.

The work presented in Sec.~\ref{pf_scenario_section} to
Sec.~\ref{pf_costing} is relevant to plasmas with low ``squareness."
The impact of the the high-``squareness" on the PF design are
presented in Sec.~\ref{high_squareness}.

Section~\ref{magnet_conclusions} summarizes the results of the \ARST PF
magnet-engineering study, including remaining critical issues.

The parameters of the detailed analysis are slightly different from
those chosen for the final design point.  However, it is not expected
that the minimal variations between the case investigated and the
final design point produce significant differences in the conclusions
of this study.

\section{Materials}
\label{materials}

The materials assumed for the PF coils in this study are presently commercially
available.  Improved manufacturing techniques and reproducibility are assumed.
Incorporating these materials and improved design concepts into PF magnets
suitable for a commercial tokamak reactor is still a difficult challenge.  The
reference \ARST design uses a multifilamentary ternary \nb for the high field
divertor coils inside of the toroidal field coil, combined with NbTi ring
coils in the outer regions of the reactor.  The value of the peak field in the
poloidal field system is 15.5~T at the divertor coil, somewhat higher to that
of ITER~\cite{ITERPF}. Only isotropic structural material (such as 316~SS and
Incoloy~908) have been considered.

The superconducting materials in the design of the poloidal field
system are NbTi and Nb$_3$Sn filamentary superconductors.  High-$T_c$
materials do not meet the stipulated level of
development/commercialization assumed in this study.  Although rapid
progress is being made in developing materials and techniques to turn
HTS into practical conductors, the materials that are closest to
commercial availability today require refrigeration to 4~K and
therefore offer marginal advantages over the more developed NbTi and
\nb.

NbTi is easy to produce in multifilamentary cables and its ductility simplifies
magnet fabrication.  It has a critical temperature, \tc, of 10~K, and an upper
critical field of 14~T.  At 4.2~K, it has an operational limit of about 8~T.
Although this is not sufficient for the divertor coils, NbTi can be used in the
low-field coils of the PF.

A ternary compound \nb(Ti)~\cite{nbthreesnti} was utilized in the design for
fields higher than 8~T.  Numerous techniques exist for producing binary and
ternary \nb, and each technique attempts to provide good mixing between the Nb
and the Sn and high-temperature ($\sim 700$\SdegC) heat treatment for growth of
the superconducting phase.  Critical properties \hc, \tc, and \jc($B$)
(critical current density) vary with ternary additions and processing.

Any high-field magnet system experiences very large forces resulting from the
Lorentz interaction between the current and the magnetic field.  The choice of
options for structural materials considered in this work is limited to the
stainless steels (in particular, 316LN~\cite{STAINLESS}) and Incoloy
908~\cite{INCOLOY}.  These materials have been extensively studied for
cryogenic magnet applications.

The Incoloy has the added advantage of requiring a heat treatment that is
compatible to the heat treatment of the \nb~\cite{INCOLOY}.  material is
relatively soft prior to heat treatment, facilitating manufacturing of the
conductor, and becomes stronger with the heat treatment process.  The
disadvantage of the Incoloy 908 is its cost.  The possibility of using SS-316
was analyzed due to its larger data base and substantially reduced
cost~\cite{STAINLESS}.

The clearly superior advantage of the Incoloy 908 over 316LN is the increased
compatibility with the \nb.  This is due to comparable thermal contractions
from high temperature to 4 K~\cite{INCOLOY}. Evidence indicates increased
superconducting properties of the cable by its use.  This is the material of
choice for the conduit.

\section{Poloidal Field System Design Criteria}
\label{pf_design}

The poloidal field (PF) magnets are responsible for forming and
shaping highly elongated plasmas during the start-up, burn pulse and
shut-down.  In \ARST the divertor PF coils need to be inside of the
TF system in order to decrease the coil currents to reasonable
values.  Preliminary calculations with an external poloidal field
system required divertor coil currents about 3 times larger than
those resulting if the divertor coils are placed inside the TF coils.
Since these coils are high field and high current density, they are
designed using internally cooled, cable-in-conduit conductors of
ternary Nb$_3$Sn, as in ITER~\cite{ITERninetyeight}.  Ternary
Nb$_3$Sn is favored over binary because it has higher temperature
margins even at the lower fields.  NbTi is used in order to decrease
the cost of the large ring coils which have relatively low fields.

In \ARST, as opposed to the \PU study~\cite{PULSARMagnet}, the poloidal field
system is not designed to provide full ohmic initiation and startup, only to
provide equilibrium and shaping of the plasma during the transients and the
flat-top part of the cycle.

Design allowables for the superconducting PF magnets, similar to those assumed
during the \ARIES study, are listed in \hbox{Table~\ref{pf_allowables}} along
with suggested additional constraints on energy and power-balance criteria for
recovery from disturbances.  The \ARST PF system design follows the ITER
recommendations, with the exception that the Tresca membrane allowable stress
in the structure is 800~MPa for \ARST.  The lower tensile stress limit for ITER
is due to fatigue crack-growth limits for pulsed tokamak operation.  The \ARST
poloidal field coils are more conservative than those of \ITER as they are also
designed for energy margins \hbox{$> 0.5$~J/cm$^3$} and fractions of critical
current in the well-cooled recovery regime.

In \hbox{Table~\ref{pf_allowables}}, $f_{critical}$ is the maximum allowable
ratio of conductor current to the critical current, $f_{well-cooled~recovery}$
is the maximum ratio of conductor current to the current at the transition
point between well-cooled and ill-cooled behavior during recovery from a
disturbance, $T_{max,dump}$ is the maximum permissible temperature in the
winding pack following a coil dump (K), $T_{margin}$ is the minimum permissible
temperature difference between the local conductor temperature and the
current-sharing temperature during a scenario (K), and $E_{margin}$ is the
minimum permissible local energy margin, defined as the volumetric energy
needed to be deposited anywhere along the the conductor that would raise the
local helium reservoir temperature to the current-sharing temperature (J/cm$^3$).

Forced-flow, internally cooled cables have two recovery regimes.  In the
well-cooled regime, almost the entire local enthalpy of helium in the conduit
at constant density, between the bath temperature and the current-sharing
temperature, is available for conductor recovery.

The design approach to \ARST is such that it should be able to absorb the
losses, forces, and voltage transients from a disruption without resulting in
quenching of the PF magnets.

In order to decrease the cost of the PF system, the copper required for quench
protection is removed from the superconducting strands.  Instead, normal
conducting copper strands are co-wound with the superconducting strands.  The
amount of superconductor and stabilizer in the conductor is small compared with
the amount of copper required for quench protection.  The cost of the magnet
system can be substantially decreased by this approach.

\section{Poloidal Field Scenarios}
\label{pf_scenario_section}

Figure~\ref{ast-8-01} shows the plasma shape and the poloidal field coils for the
case of ARIES ST.  The divertor coils are internal to the TF coils,
while the rest of the equilibrium system are outside the TF coil.

For the present design, only one equilibrium in the scenario was
developed.  Therefore, the startup and shut down transients in the
poloidal field system have not been investigated, but since the
machine is steady state, the transients due to normal events should
not change the picture much, as long as coil currents during the
startup and shut-off transients do not substantially exceed their
flat-top values.  The effect of disruptions during the flat-top phase
have been calculated, both assuming current conserving and flux
conserving assumptions.  The fractions of critical current are
calculated at the flat-top point in the scenario; the effects of
strain in the superconductor are taken into account.  Critical
fractions and margins are also recalculated after disruption
simulations.

In Table~\ref{pf_currents}, the PF currents for the flat top are shown.  Since
the plasma and the PF system are up-down symmetrical, only the current for the
coils located above the midplane (Upper coils) are shown.

The PF coil geometry for the design point is described in
\hbox{Table~\ref{pf_geometry}}.  $R$ and $Z$ are the major radius and
height of the coil centroid, $R_1$ and $R_2$ are the minimum and
maximum major radii, $Z_1$ and $Z_2$ are the minimum and maximum
heights, respectively.  The plasma is up-down symmetric.

\section{Poloidal Field System Design}
\label{pf_eng_design}

The winding pack dimensions are given in Table~\ref{pf_geometry}, and
are schematically shown in Fig.~\ref{ast-8-01}.  The winding characteristics of
the PF system are described in Table~\ref{pf_winding_description}.

The conductor type of the different coils has been optimally
determined for each coil.  The higher field coils are made of ternary
tin.  The large ring coils are made of NbTi.  The number of pancakes
per coil, $n_{pancakes}$, and the number of layers in the pancakes,
$n_{layers}$, are chosen in order to set the pack current in each of
the coils to about 50 kA.  $n_{turns}$ is the number of turns in the
coil.  $D_{strand}$ is the strand diameter.  $P_w$ is the wetted
perimeter of the strands.  It has been assumed that the Resistivity
Resistance Ratio ($RRR$) is 100 for the copper stabilizer for all the
PF coils.  The filament diameter is 10 $\mu$m for the ternary tin
superconductor, and 5~$\mu$m for the NbTi.  The effective
cross-conductance length is 20~mm for all the conductors.

The helium fraction $f_{He}$ and the fraction of the strands that are
pure copper $f_{Cu,pure}$ are shown in Table~\ref{heliumfraction}.
The value of $f_{Cu,pure}$ was determined separately for each coil.
For final design, the helium fraction needs to be provided by varying
strand diameter (making some of the pure copper strands of different size
to adjust the conductor fraction).  This could also allow the
flexibility of arbitrarily selecting the pure copper strand to
superconducting strand fractions.  The cabling process needs to be
altered to satisfy this requirement.  The wetted perimeter would
increase in the case of decreasing the diameter of the pure copper
strands, increasing the conductor stability.

The coils PF3 to PF6 have large He fraction.  It is possible to
decrease the size of the coils, which will decrease the He fraction.
However, since these coils are neither critical to the engineering
nor the large He fraction has an impact on the cost, these coils were
not fully optimized.

The corresponding conductor geometry is shown in
Table~\ref{pf_winding_geometry}.  $w_{conduit}$ and $h_{conduit}$ are
the width and height of the conduit for each of the PF coils.
$A_{cu,cond}$, $A_{noncu}$, and $A_{ss,cond}$ correspond to the
copper, non-copper ({\it i.e.}, superconductor), and steel cross-
sectional areas of the conductors of each PF coil.  $A_{He,cond}$ is
the corresponding He cross-sectional area, and $A_{condenv}$ is the
overall area of the conductor.  The number of pure copper strands in
the conductor, as well as the helium fraction, are determined for
each coil separately.

The current maxima for each of the PF coils is shown in
Table~\ref{pf_maxima}.  Only one point was used in the design, and
therefore one of the extrema is 0 for all cases.  Using 50 kA current
in the coils decreases the amount of stabilizer required for quench
protection and minimizes the cost of the winding process.  Larger
currents would require more expensive bus and power supplies.  The
size of each conductor is adjusted in order to limit maximum current
in each coil to about 50 kA.

The peak values of the magnetic field in each coil are shown in
Table~\ref{pf_peakfield}.  The peak fields on the PF1 and PF2 are
above 10 T.  PF1 and PF2 are manufactured with ternary
superconductor.  PF3 through PF6 have substantially lower fields, and
they use NbTi in order to minimize the cost of the system.

As mentioned above, PF1 and PF2, U and L (upper and lower), are inside of the
toroidal field magnet.  As a consequence, the effective magnetic field on the
coils consists of the vector addition of the toroidal and the poloidal fields.
The maximum poloidal field for PF1 and PF2 are 15 and 10.3 T, respectively.  To
this, it is necessary to add the toroidal field.  For the design case, the
toroidal field is 3.7 T and 2.1 at the location of the highest poloidal fields
in PF1 and PF2, respectively.  The maximum field in PF1 and PF2 shown in
Table~\ref{pf_peakfield} refers to the maximum total field.

The performance of the PF system is shown in
Table~\ref{pf_performance}.  $f_{c}$ represents the ratio between the
superconductor current to its critical current.  The value listed in
Table~\ref{pf_performance} is the maximum value for a given coil,
after the worse location on each coil has been identified.  This
ratio should be less than about $0.7$.  $Q"_{max}$ is the critical
heat flux from the conductor to the helium bath.  $f_{tr}$ is the
ratio between the conductor current and the transition current beyond
which the critical energy (energy required to drive the
superconductor to the current sharing condition) decreases
dramatically.  $\Delta T_{head}$ is the maximum temperature excursion
between the operating temperature and the current sharing temperature
where the conductor current exceeds the critical current.  Similarly,
$E_{mar,min}$ is the energy needed to raise the temperature of the
helium bath to the current sharing temperature.  $f_{Jprot}$ is the
ratio between the actual conductor current and that resulting in a
final conductor temperature of 150~K (after a 20~kV dump).

Each of the parameters in Table~\ref{pf_performance} is calculated
along the conductor for each coil, and the entry in the Table is the
value of the extrema (maximum or minimum) that is most limiting.

\subsection{PF structural analysis}
\label{pf_struc_anal}

The average hoop, axial, and Tresca membrane stresses in the conductor conduit
were calculated at each point along the conductor in each coil, for the
flat-top conditions.

The goal of the design is for all PF magnets to be self-supporting
against tensile loads.  Obviously, the vertical loads need to be
transferred to an external structure.  In the case of PF1 and PF2,
the external structure is the TF coil.  It is necessary to allow the
poloidal field coils to move radially with respect to the TF coil,
and this is achieved by placing the PF coils in a structural box, and
using low-coefficient of friction materials at the interface, which
is at room temperature.  The radial sliding results in minimal heat
generation at the low temperature, and care must be taken to
intercept the heat before it reaches the poloidal field coil
conductor.  In order to do this, electrically insulation high thermal
conductivity radial shims are used.  These shims are made of thin
wires in the radial direction, embedded in an insulating matrix.  The
small size of the conductor minimizes AC losses.  Preliminary
calculations indicate that it is possible to remove from a 1 mm think
shim (50\% high thermal conductivity in a insulating matrix) as much
as 10 kW/m$^3$ (10 mW//cm$^3$), or about 5 W/m$^2$ (0.5 W/cm$^2$) for a
temperature increase of about 0.25 K).  The heat transfer rate is
dominated by the conduction through the high thermal conductivity
material, rather than across the thin insulating layer.  For the above
assumed conditions, the heat transported along the radial thermal shorts
is 25-50 times larger than the thermal transport across the shims.

The loads on all the PF coils are shown in Table~\ref{forcespf}.
Only one point, the long burn, was analyzed.  The forces resulting
from a current conserving disruptions (the plasma current is zero,
but the currents of the PF coils do not vary) are shown in
Table~\ref{forcespfdis}.  The current consercing case occurs when the
power supplies control fails and the coil currents are kept constant
while the plasma current vanishes.  This case is an extreme
assumption, but the results are usually conservative.


Shown in the tables are the vertical and radial forces per meter and
the net vertical force.  It is interesting to note that the loads
during current conserving disruption do not vary substantially from
those during normal operation.  It is possible that the loads in PF1
and PF2 increase during a disruption, since PF1 and PF2 are
relatively well coupled to the plasma, and their currents are in the
same direction.  The structural implications of this case was not
analyzed.

The radial loads, assuming that the coils are self-supporting, are shown in
Tables~\ref{forcespf} and \ref{forcespfdis}.  The hoop stresses in the coils,
assuming that the coils are self-supporting against the radial loads, are also
shown in both tables.  All the external coils can self-support the radial load,
even assuming that the superconductor does not share the tensile load.

The possible exception are PF1 and PF2.  The tensile hoop stresses
are high for PF1, and the radial loads in PF2 are negative, resulting
in compression of the coil, instead of tension.  Compressive forces
are difficult to support, as they could result in buckling.  The best
manner to support the loads in PF2 is to transfer them to PF1,
simultaneously reducing the tension in PF1.  The force can be
transferred using radial struts, which are loaded in compression.
The stresses in PF1 are decreased to about 400 MPa, which is a value
that can brings the PF1 loads to a value that is comparable to those
of the external coils.

The vertical forces of the internal coils, PF1 and PF2, need to be
supported by the toroidal field coil, since there is no other
structure around.  The magnetic loads dominate over the gravitational
loads.  PF1 and PF2 weigh $\sim 260$~kN and 360~kN, respectively.
Shown in the tables are the required area of struts, $A_{strut}$
needed to transfer the loads to the TF coil, when loaded to 400~MPa.
Also shown are the required strut thickness, $\delta_{strut}$,
assuming that the strut is a uniform shell located at the major
radius of the coil, and operating at a stress of 400~MPa.  The
thickness of the uniform shell strut is about 1~cm, if a single one
is used to transfer the loads from both PF1 and PF2.  The support is
not a critical issue for the design.  Neither is maintenance, since
it is assumed that the PF coils are life-time components and
therefore PF1 and PF2 can be directly attached to the aluminum shell
TF coil.

The vertical loads of the external PF coils are large.  They can be
supported by a shell-type structure.  As is the case for the internal
coils, the thickness required for the shell has been determined
assuming that the stresses in the shell are 400~MPa.  The resulting
thickness is also shown in Tables~\ref{forcespf} and
~\ref{forcespfdis}.  The negative values are used to indicate that
the respective loads result in compression of the support shell.  The
compressive loads of PF3 and PF4 add up and are about the same value
as addition of the tensile loads of PF5 and PF6.  Because of this
there is little forces that need to be carried out from the upper to
the lower sets of coil, minimizing the structure required between
PF6U and PF6L and simplifying the assembly of the system.  These
loads and resulting thicknesses have been calculated assuming normal
operation.  Off-normal load conditions may actually drive the
structural requirements.  Structural response due to off-normal
events have not been calculated.

It should be noted that the vertical loads in PF3-U to PF6-U approximately
cancel each other.  Therefore, the thickness of the shell at the midplane can
be made small, in so far as the normal and disruption cases analyzed indicate.
It is possible, if desired, to physically separate the upper coils structure
from the lower coils structure, and connect them through locks, as in the
ALCATOR-C Mod structure.  This would minimize the height of the component,
since a single unit would be more than 23 m tall.

\subsection{Current Leads}
\label{pfcurrentleads}

In \ARST the poloidal field is substantially larger than the toroidal
field at the location of the coils.  An issue that needs to be
addressed are the current leads for the PF1 and PF2 coils, which are
internal to the toroidal field coil.  These leads are the subject of
large loads due to the interaction of the current with the toroidal
magnetic field and with the self-fields.

The optimal location of the leads is limited to regions where the
loads are easily manageable.  For PF1, the leads are connected to the
coil at the outer coil midplane.  At this location, the poloidal
field is only about 2~T, mainly in the vertical direction.  The
toroidal field is around 3~T at this location.

For PF2, the location on the coil with minimum poloidal field is
located at the inner radii where it is around 8~T.  The corresponding
toroidal field is $\sim 2$~T.  The field is not much larger elsewhere
(10~T at the top, bottom and outer walls).  Joints between pancakes
should be performed at the inner radii.

Coaxial, normal conducting feed lines are used to bring the current
to the poloidal fields coils.  Using coaxial lines eliminates the net
force interacting on the leads.  However, high voltages are present,
especially during coil dumps.

The solution proposed for \ARST is similar to the current feedthrough
for the central solenoid in ALCATOR C-MOD~\cite{Montgomery}.  In this
machine, the solenoid is located within the toroidal field, at fields
approaching 17~T.  The ALCATOR C-MOD has been designed for a peak
central solenoid conductor current of about 50~kA similar to the
maximum value of the current for PF1 and PF2.  And the peak voltage,
required for fast initiation, is on the order of 20~kV, similar to
the maximum voltage in the PF system during the dump following a
quench.

By using normal conducting leads and placing the
normal-to-superconducting joint close to the PF coils, it is possible
to place an additional normal joint near the coil, facilitating
machine assembly.

High temperature superconducting leads are used to transition the
current between the normal conductor and the superconductor.  The
background field (3.5~T for PF1, 8~T for PF2) is shielded from the
high-Tc current leads, to increase the superconducting current
density and therefore minimize the required cross section area and
the associated thermal load of the superconductor.  It is possible to
shield the HTS current lead by surrounding the HTS current leads with
a high temperature superconductor monolith~\cite{Shielding}.

The HTS monolith can be made of BSCCO 2212 material, which when operating at a
temperature of 20~K has a critical current of about 10~kA/cm$^2$, relatively
independent of field~\cite{BSCCOTubes}. Therefore, a 0.5-cm thick shell of
BSCCO can shield about 1~T.  For PF1, the thickness of the monolith needs to be
about 2~cm, while for PF2 the thickness increases to 4~cm.  The HTS monolith
can be segmented in several shells, facilitating manufacturing, assembly, and
support.

Optimized HTS current leads decrease the heat leak to about 0.1~W/kA per
transition.  Since the current in the coils is about 50~kA, the heat loads per
coil associated with the current leads is 10~W, a small value~\cite{HTSLead}.

\section{Poloidal Field Costing}
\label{pf_costing}

The PF costs were determined according to the cost algorithm developed by
J. Schultz for superconducting magnet costing~\cite{Costing}.  These algorithms
are sufficiently detailed and realistic to correctly take into account the
amount of superconductor, stabilizer, structure, insulation, and the complexity
of winding and assembly.  These algorithms need to be modified to take into
account 10$^{th}$ of a kind costing, as opposed to first of a kind such as
\ITER.  This is done at the end of this section.

The cost is determined from a bottom's-up estimate, with models for
the cost of the superconductor, conductor manufacturing, assembly,
and manufacturing of the PF coils.  As many characteristics of the PF
system are analyzed as practical, including superconductor type,
number of independent pure copper strands (for quench protection),
material of the conduit, and structural material.

The costing code was used to determine the cost of the PF system in
ARIES as well as the dependence of the cost on the main design
parameters of \ARST.  Table~\ref{pf_cost_conductor} shows the cost of
the conductor for all the PF coils.  There are two coils in each set
of coils.  The number shown in this table and in the following ones
is the cost per coil.  As will be shown in the next few tables, the
cost of the strands is a small fraction (about 12\%) of the cost of
the PF coils winding pack.  Although the coils PF1 and PF2 are made
of more expensive \nb conductor, the cost is dominated by the much
larger coils PF3-PF6.  The cost of the conductor for the PF coils
about doubles when NbTi is replaced by \nb in these coils.  The ring
coils also have larger fraction of superconductor material (lower
fraction of pure copper strands).  The cost of the additional
superconductor is more than made up by the use of a cheaper
superconductor.

PF1 and PF2, made of \nb conductor, are costed assuming that the
coils are using ``react and wind" method.

The cost of the winding pack ({\it i.e.}, the actual PF assemblies)
is shown in Table~\ref{pf_cost_winding}.  The manufacturing cost of
the coils is comparable to the cost of the conductor.  Only the
fraction of the cost that is value-added experiences a learning
curve.  Learning curves have been applied to value-added items, both
in Table~\ref{pf_cost_conductor} and Table~\ref{pf_cost_winding}.
Table~\ref{pf_cost_total} shows the final cost of the coils,
including supports, engineering, and other indirect costs.  The
minimized direct cost of the PF system is, then, about \$190~M, with
a total cost (direct plus indirect) of \$290~M.  Since the mass is
about 800~tonnes, then the total cost of first of a kind PF coil
system is about \$380/kg.  This cost is substantially higher than in
the case of \PU~\cite{PULSARMagnet} or ARIES-RS~\cite{ARIESRS}.  The
cost of the PF coils with \nb are comparable per unit weight to
those in \PU, at around \$800/kg.  However, the cost of the NbTi
coils in \ARST is substantially higher than in \PU.  This is because
of the higher fields in \ARST require a higher superconductor ratio in
the winding, by about 1/3, resulting in a higher unit cost for the
coils (since it is using a higher fraction of more expensive
materials).

In the total for each entry, an additional small value for Administration and
Operating expenses has been added.  The values of engineering and contingency
are substantially larger in the methodology described in Ref.~\cite{Costing}
than what the \ARST systems study assumes.  The relevant charge for the system
code, direct charges prior to indirect charges, are shown in
Table~\ref{improvedcost} (after the effect of a learning curve has been
included).

The bottom's-up total cost scaling is shown in Table~\ref{pf_cost_scaling}.
These are total costs using first of a kind and today's technology.  These
equations are intended for a device like \ITER, a first-of-a-kind experimental
reactor.

\subsection{Learning curve effects on costs}

The ground rule adopted by the \ARIES team is that the value-added capital
costs will be observing a 75\% learning curve on the unit cost.  The cost of
value added PF tenth-of a kind component is reduced by $10^{ln(0.75)/ln(2)}
\sim 0.385$~\cite{LearningCurve}.

The costs of the strands is a small fraction of the cost of the PF coils.  The
costs of NbTi is well established.  However, it is assumed that the cost of the
Nb$_3$Sn will decrease from about \$1,000/kg to about \$250/kg, with improved
manufacturing and Q$\&$A techniques.

The costing of the PF system is shown in Table~\ref{improvedcost}.
The First of a kind costing repeats the results presented above,
in 1998 \$M dollars.  Two types of scaling are used in the table.  IM
means improved method of fabrication.  This is the case for the
strands.  LCE stands for Learning Curve Experience, and as mentioned
above, 0.385 multiplier is used.

The cost of engineering for the 10th of a kind has been arbitrarily
decreased to zero.  Clearly, the engineering will be much smaller
than for the first few, but after the problems and the process has
been identified, the need for engineering is to maintain the
processes, rather than to develop them.

The direct cost of the PF system is decreased from \$190M to \$65M.
Adding contingency and PACE, the cost increases to about \$72M, down
from \$290M.  The specific unit cost is decreased from \$380/kg for
first-of-a-kind to \$80/kg for tenth-of-a-kind.  It should be noted
that \$100/kg was used in the previous ARIES studies for performing
calculations of the PF system.

\section{PF implications of high squareness plasmas}
\label{high_squareness}

In order to obtain the large values of plasma $\beta$ used in the
study, a high value of the plasma ``squareness" is desired.  The base
case poloidal field system that has been analyzed in this paper and
in the ARIES-ST studies, generated a relatively low value of the
squareness of the plasma.  In this section, the implications of the
increased squareness on the poloidal field system are described.

Table~\ref{pf_squareness} shows the currents on the poloidal field coils for
both the high and low values of squareness.  The coils are located either at
the same height as the innermost coils (with varying radii), or are are at the
outermost radii (and varying height).  The coil loci is therefore along a
reactanular grid.  The number and location of the coil has not been optimized.
The poloidal field system with low squareness is similar to the one analyzed
previously in this paper, with divertor coils on the order to 10-15~MA, and
modest external coils.  However, the number of coils is much larger than
necessary, and has been chosen to directly compare with the case of higher
squareness, also shown in Table~\ref{pf_squareness}.  In the case of high
squareness, the current in the poloidal field system increases dramatically,
with single coil currents in some cases on the order of 40~MA.  In order to
provide for the shaping requirements, the divertor coils need to increase
susbtantially.  The current in the divertor coils (Coils 1 and 2 in
Table~\ref{pf_squareness}) are bucked by currents in the coils 3 and 4, located
closely to the divertor coils but outside the toroidal field coil.  The net
current of the coils in the upper region of the plasma does not change much
between the two cases, but the actual currents are much larger than in the case
with lower squareness.

In order to obtain the high squareness required, the case of internal PF coils
was preliminarily investigated.  The divertor coils, coils 1 and 2, have been
assumed internal in the base case.  The rest of the poloidal field system was
also brought inside the toroidal field coil.

Figure~\ref{ast-8-02} shows results from equilibrium calculation for the case of
high squareness plasma, using poloidal field coils internal to the TF
coil.

The current distribution, with only 9 coils, is given in
Table~\ref{current_hig_square}.  The height of the divertor coils has
been decreased, decreasing the distance from the coils to the plasma.
This was done to take advantage of the larger engineering current
density in the coils (that makes them smaller).  In the equilibrium
calculations, it had been assumed that the current density of these
coils could be 20~MA/m$^2$, but it was found in the detailed
engineering analysis above that the current could be increased to as
much as 30~MA/m$^2$.  The net current in the divertor coils is
smaller than in the base case with lower squareness with external
non-divertor coils.

In this section, engineering analysis of this case will be presented.  Only
condensed results will be presented.

The coil currents for the case of optimized poloidal field coils are also shown
Table~\ref{current_hig_square}.  The number of coils has not been optimized.
These results are therefore serve as a guideline, and the optimal solution may
be better.

In the design, the cross section of the coil was determined assuming
that the current density was 30~MA/m$^2$ for the divertor coils, and
50~MA/m$^2$ for the rest.  With this assumption, the fraction of
helium and the composition of the coils was determined, similar to
Table~\ref{heliumfraction}.  The performance criteria of the coils
with this helium and composition was calculated, and is shown in
Table~\ref{performance_high_square}.  This table should be compared
with Table~\ref{pf_performance} for the base case.

It should be noted that this system has high energy margins and temperature
margins.  This is a result of the large amount of helium in the system.  The
size of the coil was held constant, and the coils were filled with helium as
the metal fraction (superconductor and normal conductor) of the coil was
lowered to meet the design criteria given in Table~\ref{pf_allowables}.
Clearly, the coil cross section can be reduced by eliminating some of the
helium, but this iterative process was not completed for the case of the
internal poloidal field coils.

The effect of the toroidal field on the peak field of the poloidal field coils
is small in the case when all the poloidal field coils are inside the toroidal
field.  For the innermost divertor coils, with a peak poloidal field of 12~T,
the toroidal field is about 3~T and the total field is increased to about 12.5~T.
For the other coils, the toroidal field is even lower and only has a marginal
effect on the critical current of the superconductor.

The costing of the internal poloidal field system was also investigated.  The
first of a kind costing was decreased substantially, with a direct cost of the
poloidal field system of \$110~M, as opposed to the base case, with a direct
cost of \$190~M.  The cost of the internal poloidal field system, with a much
more aggresive shaping requirements, decreases by about a factor of 2 when the
poloidal field system is moved closer to the plasma.  Extrapolating these
savings to 10th of a kind, the cost of the poloidal field system for the
internal PF case is \$40~M.

\section{Summary and Conclusions}
\label{magnet_conclusions}

The critical issues of the poloidal systems for the \ARST design have
been presented in this paper.  The implication to the poloidal field
system due to low aspect ratio operation have been investigated by
performing a detailed analysis of one case.

A substantial difference in the requirements of \ARST PF system from
those of the \ARIES study has to do with the large plasma current and
the need of highly shaped plasmas.  The divertor coils have to be
placed inside the toroidal field in order to reduce their current.
Even then, the divertor coils carry large currents.

In order to allow for high ``squareness," required for high plasma
pressure, it is necessary to move even the non-divertor coils inside
of the toroidal field coil.  The implications of this option, which
is the final design point of the ARIES-ST study, have been briefly
described.

The PF coils are superconducting using internally cooled
cable-in-conduit conductor.  For the case of external non-divertor
coils, the peak field in the PF system is $\sim15$~T in the divertor
coils, while it is 8~T in the ring coils, mainly because of the large
self-fields in these coils.  For the case of internal non-divertor
coils, the peak self field in the divertor coils is reduced to about
12~T, while the highest field in the non-divertor coils is about 6~T.

The PF magnets have built-in margins that are sufficient to survive
disruptions without quenching, at least during the flat top.

The costing study indicates that the specific cost of the PF system
is \$80/kg.

There are outstanding issues with respect to the idea of segregating the copper
for quench protection and the superconducting strands.  These issues include
the current sharing between the different superconducting strands and current
transfer between the superconducting and normal conducting strands in the
conductor plus further understanding of the ramp-rate limitations on the CICC.

Additional work needs to be completed to address unfinished issues.  These
issues include fault conditions and their effects on the PF coil system.
Single PF coil failure, and effects of plasma disruptions on the PF system are
areas that need substantial additional work.

\clearpage

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\bibitem{INCOLOY} M.~M.~Morra, R.~G.~Ballinger, and I.~S.~Hwang, ``INCOLOY 908,
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\end{thebibliography}

\newpage

\begin{table}
\caption{}
\centering{\bf PF-magnet constraints used for \ARST design}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.15}
\begin{tabular}{l @{\hspace{2.truein}} r }
\hline\\
$V_{terminal}$ (kV)                & 20 \\
$I_{cond}$ (kA)                    & 50 \\
$B_{max}$ (T)                      & 15.5 \\
$\sigma _{Tresca~membrane}$ (MPa)  & 800 \\
$f_{critical}$                     & 0.7 \\
$T_{max,dump}$ (K)                 & 150 \\
$T_{margin}$ (K)                   & 1.0 \\
$E_{margin}$$^{(a)}$ (J/cm$^3$)    & 0.5-1.0 \\
$f_{well-cooled~recovery}$$^{(a)}$ & 0.8 \\
\\ \hline
\multicolumn{2}{l}{$^{(a)}$Suggested values.}
\end{tabular}
\label{pf_allowables}
\end{table}

\begin{table}
\caption{}
\centering{ \bf Currents in PF Coils from \ARST \\
Flat Top Used for Calculations (in MA)\\
}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.15}
\begin{tabular}{l @{\hspace{2.truein}} r  }
\hline \\
 PF1, U        &   -14.6\Z \\
 PF2, U        &   -15.5\Z \\
 PF3, U        & \N\Z8.39 \\
 PF4, U        & \N\Z8.28 \\
 PF5, U        & \N\Z6.78 \\
 PF6, U        & \N\Z3.51 \\
Plasma current &  -32\D\Z \\
\\
Flux linkage (V-s)& \N\Z61.9\\
\\ \hline
\end{tabular}
\label{pf_currents}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARES-ST PF-System Winding-Pack and Plasma Dimensions (m)}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l @{\hspace{1.cm}} c @{\hspace{1.cm}} c @{\hspace{1.cm}}
c @{\hspace{1.cm}} c @{\hspace{1.cm}} c @{\hspace{1.cm}} c }
\hline
Coil   & $R$   & $Z$     & $R_1$  & $R_2$  & $Z_1$    & $Z_2$    \\
\hline \\
PF1, U & \Z2.0 &  \N10.5 & \Z1.72 & \Z2.27 &  \N10.22 & \N10.77 \\
PF1, L & \Z2.0 &   -10.5 & \Z1.72 & \Z2.27 &   -10.77 &  -10.22 \\
PF2, U & \Z3.0 &  \N10.5 & \Z2.73 & \Z3.27 &  \N10.23 & \N10.76 \\
PF2, L & \Z3.0 &   -10.5 & \Z2.73 & \Z3.27 &   -10.76 &  -10.23 \\
PF3, U &  10.5 & \N\Z8.5 &  10.23 &  10.76 & \N\Z8.23 &  \N8.76  \\
PF3, L &  10.5 &    -8.5 &  10.23 &  10.76 &    -8.76 &   -8.23  \\
PF4, U &  10.5 & \N\Z7.5 &  10.23 &  10.76 & \N\Z7.23 &  \N7.76  \\
PF4, L &  10.5 &    -7.5 &  10.23 &  10.76 &    -7.76 &   -7.23  \\
PF5, U &  10.5 & \N\Z6.5 &  10.26 &  10.73 & \N\Z6.26 &  \N6.73  \\
PF5, L &  10.5 &    -6.5 &  10.26 &  10.73 &    -6.73 &   -6.26  \\
PF6, U &  10.5 & \N\Z5.5 &  10.32 &  10.67 & \N\Z5.32 &  \N5.67  \\
PF6, L &  10.5 &    -5.5 &  10.32 &  10.67 &    -5.67 &   -5.32  \\
\\ \hline
\end{tabular}
\label{pf_geometry}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARIES-ST Conductor Characteristics}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c}
\hline
Coil & Superonductor & $n_{pancakes}$ & $n_{layers}$ & $n_{turns}$ &
$n_{strands}$  & $D_{strand}$ (mm) & $P_w$ (m) \\
\hline \\
PF1, U,L & TernaryTin &  18  &    18  &  324 & \D675 & 1.12 & 1.99 \\
PF2, U,L & TernaryTin &  19  &    19  &  361 & \D675 & 1.02 & 1.80 \\
PF3, U,L & NbTi       &  13  &    13  &  169 & 1,125 & 1.16 & 3.41 \\
PF4, U,L & NbTi       &  13  &    13  &  169 & 1,125 & 1.11 & 3.29 \\
PF5, U,L & NbTi       &  12  &    12  &  144 & 1,125 & 1.15 & 3.40 \\
PF6, U,L & NbTi       & \Z8  &   \Z8  & \Z64 & 1,125 & 1.15 & 3.41 \\
\\ \hline
\end{tabular}
\label{pf_winding_description}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARIES-ST Conductor Composition and Helium Fraction}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l @{\hspace{1cm}} c @{\hspace{1cm}} c }
\hline
Coil      & $f_{He}$ & $f_{Cu,pure}$\\
\hline \\
PF1, U,L  &  0.2\Z   &  0.38  \\
PF2, U,L  &  0.32    &  0.63  \\
PF3, U,L  &  0.56    &  0.65  \\
PF4, U,L  &  0.56    &  0.66  \\
PF5, U,L  &  0.56    &  0.65  \\
PF6, U,L  &  0.47    &  0.70  \\
\\ \hline
\end{tabular}
\label{heliumfraction}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARIES-ST winding geometry}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c}
\hline
      & $w_{conduit}$ & $h_{conduit}$ & $A_{cu,cond}$ & $A_{noncu}$
        & $A_{ss,cond}$ & $A_{He,cond}$ & $A_{condenv}$ \\
Coil  & (mm)  &(mm)  & (mm$^2$) & (mm$^2$) & (mm$^2$) & (mm$^2$) & (mm$^2$) \\
\hline \\
PF1, U,L &  30.6   &  30.6   & 377.   &  169.6 & 322.   & 128.  & \D998. \\
PF2, U,L &  27.8   &  27.8   & 305.   & \Z69.3 & 277.   & 176.  & \D829. \\
PF3, U,L &  40.1   &  40.1   & 431.   & \Z91.6 & 501.   & 666.  & 1,691. \\
PF4, U,L &  38.7   &  38.7   & 403.   & \Z82.5 & 472.   & 618.  & 1,576. \\
PF5, U,L &  40.0   &  40.0   & 429.   & \Z91.2 & 499.   & 663.  & 1,684. \\
PF6, U,L &  40.0   &  40.0   & 533.   & \Z94.2 & 500.   & 556.  & 1,685. \\
\\ \hline
\end{tabular}
\label{pf_winding_geometry}
\end{table}

\begin{table}
\caption{}
\centering{\bf Peak Currents in PF Coils}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{@{\hspace{1cm}} l @{\hspace{1cm}} c @{\hspace{1cm}} c
@{\hspace{1cm}} }
\hline
Coil   & $I_{cond,max}$ (kA) & $I_{cond,min}$ (kA) \\
\hline \\
PF1, U & \Z0.0               &    -47.4  \\
PF2, U & \Z0.0               &    -45.1  \\
PF3, U &  50.9               &  \N\Z0.0  \\
PF4, U &  47.3               &  \N\Z0.0  \\
PF5, U &  50.6               &  \N\Z0.0  \\
PF6, U &  50.5               &  \N\Z0.0  \\
\\ \hline
\end{tabular}
\label{pf_maxima}
\end{table}

\begin{table}
\centering
\caption{}
\centering{\bf Peak Field Flux (T) on PF coils}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{@{\hspace{2.5cm}} l @{\hspace{3cm}} r@{\hspace{2.5cm}} }
\hline \\
PF1, U,L    &   15.5 \\
PF2, U,L    &   10.7 \\
PF3, U,L    &    7.8 \\
PF4, U,L    &    7.2 \\
PF5, U,L    &    6.6 \\
PF6, U,L    &    5.6 \\
\\ \hline
\end{tabular}
\label{pf_peakfield}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARIES-ST PF superconductor performance}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c }
\hline
Coil   & $f_{c}$ & $Q"_{max}$ & $f_{tr}$ & $\Delta T_{head}$
    & $E_{mar,min}$ & $f_{Jprot}$ & $E_{coil}$ \\
       &         & (W/cm$^2$) &          & (K)
    & (J/cm$^3$)    &             & (MJ) \\
\hline \\
PF1, U & 0.68 & 0.18 & 0.78 & 3.13 & 1.09 & 0.43 & 0.30  \\
PF2, U & 0.67 & 0.14 & 0.54 & 6.02 & 4.21 & 0.73 & 0.27  \\
PF3, U & 0.73 & 0.03 & 0.76 & 1.16 & 0.40 & 1.00 & 0.19  \\
PF4, U & 0.59 & 0.03 & 0.65 & 1.46 & 0.58 & 1.08 & 0.17  \\
PF5, U & 0.47 & 0.03 & 0.58 & 1.73 & 0.91 & 0.92 & 0.14  \\
PF6, U & 0.35 & 0.02 & 0.45 & 2.14 & 0.98 & 0.48 & 0.06  \\
\\ \hline
\end{tabular}
\label{pf_performance}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARIES-ST PF Superconductor Loads and Required Structure}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c }
\hline
Group   & $F_r$/m & $F_z$/m & $F_z$        & $A_{struts}$
                                                     & $\delta_{strut}$
                                                                & $\sigma_h$ \\
        & (MN/m)  & (MN/m)  &    MN        & (m$^2$) & (m)      & (MPa) \\
\hline \\
PF1, UL &  \N88.4 & \N\Z1.5 &     18.8     & \N0.047 & \N0.0037 &  571 \\
PF2, UL &   -15.3 & \N\Z2.6 &     48.4     & \N0.121 & \N0.0064 & -158\N \\
PF3, UL & \N\Z9.1 &   -21.6 & -1,427.5\N\D &  -3.569 &  -0.0541 &  343 \\
PF4, UL & \N\Z9.5 &  \Z-1.2 &  \Z-80.0\N   &  -0.200 &  -0.0030 &  364 \\
PF5, UL & \N\Z7.6 &  \N10.8 &    714.8     & \N1.787 & \N0.0271 &  354 \\
PF6, UL & \N\Z3.6 & \N\Z8.7 &    574.6     & \N1.436 & \N0.0218 &  321 \\
\\ \hline
\end{tabular}
\label{forcespf}
\end{table}

\begin{table}
\caption{}
\centering{\bf ARIES-ST PF Vertical and Radial Loads \\
During Current Conserving Disruption}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c }
\hline
Group   & $F_r$/m & $F_z$/m   & $F_z$        & $A_{struts}$
                                                       & $\delta_{strut}$
                                                                & $\sigma_h$ \\
        & (MN/m)  & (MN/m)    &    (MN)      & (m$^2$) & (m)      & (MPa)  \\
\hline \\
PF1, UL &  86.4   &   2.0     &   \Z25.6     & \N0.064 & \N0.0051 &  558 \\
PF2, UL & -17.1\N &   3.3     &   \Z62.9     & \N0.157 & \N0.0083 & -177\N \\
PF3, UL & \Z9.2   & -22.1\N\Z & -1,459.2\N\D &  -3.648 &  -0.0553 &  346 \\
PF4, UL & \Z9.6   &  -1.7\N   &   -115.1\N   &  -0.288 &  -0.0044 &  365 \\
PF5, UL & \Z7.6   &  10.4\Z   &    683.0     & \N1.707 & \N0.0259 &  353 \\
PF6, UL & \Z3.5   &   8.4     &    557.2     & \N1.393 & \N0.0211 &  315 \\
\\ \hline
\end{tabular}
\label{forcespfdis}
\end{table}

\begin{sidewaystable}
\caption{}
\centering{\bf ARIES-ST PF System Conductor Costs (in M\$)}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c c}
\hline
      &         &      &       &       &        & & Additional & Conductor \\
Coil  & Strands & Coat & Cable & Waste & Sheath & Encapsulation
                                                  & material  & Sub. \\
\hline\\
PF1, UL  & \Z4.9 & 0.3 & \Z0.7 & \Z1.5 & 0.2 & 0.2 & 0.0 & \Z7.7 \\
PF2, UL  & \Z3.6 & 0.5 & \Z1.1 & \Z1.3 & 0.2 & 0.3 & 0.1 & \Z7.0 \\
PF3, UL  & \Z1.3 & 0.7 & \Z1.5 & \Z0.9 & 0.7 & 0.4 & 0.1 & \Z5.7 \\
PF4, UL  & \Z1.3 & 0.7 & \Z1.6 & \Z0.9 & 0.7 & 0.4 & 0.1 & \Z5.7 \\
PF5, UL  & \Z1.1 & 0.6 & \Z1.2 & \Z0.7 & 0.6 & 0.4 & 0.1 & \Z4.6 \\
PF6, UL  & \Z0.5 & 0.3 & \Z0.6 & \Z0.4 & 0.3 & 0.2 & 0.1 & \Z2.4 \\
{\it Total PF} &  25.4 & 6.0 &  13.6 &  11.3 & 5.3 & 3.7 & 0.9 &  66.3 \\
\\ \hline\\
\end{tabular}
\label{pf_cost_conductor}
\end{sidewaystable}

\begin{sidewaystable}
\caption{}
\centering{\bf ARIES-ST System Winding Pack Costs (M\$)}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c c }
\hline
 & & & & & & & & Total  \\
Coil & Conductor & Insulator & Tooling & Winding & Dummies & Heat & Leads
               & winding pack \\
\hline\\
PF1, UL        & \Z7.7 & 0.4 & 0.5 & \Z3.3 & 0.2 & 0.2 & 0.1 &  12.3 \\
PF2, UL        & \Z7.0 & 0.3 & 0.5 & \Z4.3 & 0.2 & 0.2 & 0.1 &  12.6 \\
PF3, UL        & \Z5.7 & 0.1 & 0.3 & \Z5.5 & 0.9 & 0.0 & 0.1 &  12.5 \\
PF4, UL        & \Z5.7 & 0.1 & 0.3 & \Z5.4 & 0.8 & 0.0 & 0.1 &  12.5 \\
PF5, UL        & \Z4.6 & 0.1 & 0.3 & \Z4.4 & 0.8 & 0.0 & 0.1 &  10.3 \\
PF6, UL        & \Z2.4 & 0.0 & 0.2 & \Z2.6 & 0.6 & 0.0 & 0.1 & \Z6.0 \\
{\it Total PF} &  66.3 & 2.2 & 4.2 &  50.9 & 7.1 & 0.7 & 1.2 & 132.6\Z \\
\\ \hline
\end{tabular}
\label{pf_cost_winding}
\end{sidewaystable}

\begin{sidewaystable}
\caption{}
\centering{\bf ARIES-ST total PF System Costs (\$M)}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c c c c }
\hline
        & Winding &         &             & Hardwre $\&$  &             & PACE \\
Coil    & Pack    & Support & Engineering & Engineering & Contingency & Direct
                                                           & OPEX & G$\&$A& Total \\
\hline\\
PF1, UL &  12.3 & \Z0.6 & \Z3.7 &  \Z16.6 & \Z4.9 & \Z21.4 & \Z1.9 & 0.7 & \Z24.1 \\
PF2, UL &  12.6 & \Z0.9 & \Z3.8 &  \Z17.3 & \Z5.1 & \Z22.4 & \Z2.0 & 0.8 & \Z25.1 \\
PF3, UL &  12.5 & \Z2.6 & \Z4.4 &  \Z19.4 & \Z5.8 & \Z25.2 & \Z2.3 & 0.9 & \Z28.4 \\
PF4, UL &  12.5 & \Z2.6 & \Z4.4 &  \Z19.4 & \Z5.8 & \Z25.2 & \Z2.3 & 0.9 & \Z28.3 \\
PF5, UL &  10.3 & \Z2.1 & \Z3.6 &  \Z16.0 & \Z4.8 & \Z20.7 & \Z1.9 & 0.7 & \Z23.3 \\
PF6, UL & \Z6.0 & \Z1.1 & \Z2.0 & \Z\Z9.1 & \Z2.7 & \Z11.8 & \Z1.1 & 0.4 & \Z13.3 \\
{\it Total PF}
      & 132.6\Z &  19.4 &  43.6 &   195.6 &  58.0 &  253.6 &  22.6 & 8.7 &  285.0 \\
\\ \hline
\end{tabular}
\label{pf_cost_total}
\end{sidewaystable}

\begin{table}
\caption{}
\centering{\bf Total Cost Related Parameters}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c c c c }
\hline
 & \multicolumn{2}{c}{Coil Current} & Mass of Winding & \multicolumn{3}{c}{Unit
Cost} \\ \cline{2-3} \cline{5-7}
Coil &(MA-m)    & (MA-m-T) & Pack (tonnes) & (\$/kA-m) & (\$/kA-m-T) & \$/kg  \\
\hline \\
PF1, U,L       & \D185.2 & \Z2,818 & \Z27 &  127.8 & \Z8.3 & 857 \\
PF2, U,L       & \D298.2 & \Z3,208 & \Z35 & \Z83.0 & \Z7.7 & 697 \\
PF3, U,L       & \D553.5 & \Z4,338 & \Z91 & \Z51.0 & \Z6.5 & 309 \\
PF4, U,L       & \D546.2 & \Z3,948 & \Z90 & \Z51.6 & \Z7.1 & 311 \\
PF5, U,L       & \D447.3 & \Z2,956 & \Z73 & \Z51.8 & \Z7.8 & 313 \\
PF6, U,L       & \D231.5 & \Z1,295 & \Z42 & \Z57.2 &  10.2 & 311 \\
{\it Total PF} & 4,524.1 &  37,133 &  782 & \Z65.4 & \Z7.9 & 378 \\
\\ \hline
\end{tabular}
\label{pf_cost_scaling}
\end{table}

\begin{table}
\vspace{-1.cm}
\caption{}
\centering{\bf Impact of Experience on PF system costs (1998\$M)}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{l c c c}
\hline
Operation/material  & First-of-a-kind & Scaling &   10th-of-a-kind  \\
\hline \\
Conductor: \\
\quad\quad Strands             &     \Z25.4 & IM   &  12.7 \\
\quad\quad Coat                &    \Z\Z6.0 & LCE  & \Z2.3 \\
\quad\quad Cabling             &     \Z13.6 & LCE  & \Z5.2 \\
\quad\quad Waste               &     \Z11.3 &      & \Z0.0 \\
\quad\quad Sheath              &    \Z\Z5.3 & LCE  & \Z2.0 \\
\quad\quad Encapsulation       &    \Z\Z3.7 & LCE  & \Z1.4 \\
\quad\quad Additional matieral &    \Z\Z0.9 &      & \Z0.0 \\
{\it Conductor subtotal}       &     \Z66.3 &      &  23.8 \\
Winding pack: \\
\quad\quad Insulation          &    \Z\Z2.2 & LCE  & \Z0.8 \\
\quad\quad Tooling             &    \Z\Z4.2 &      & \Z0.0 \\
\quad\quad Winding             &     \Z50.9 & LCE  &  19.6 \\
\quad\quad Dummies             &    \Z\Z7.1 &      & \Z0.0 \\
\quad\quad Heat treatment      &    \Z\Z0.7 & LCE  & \Z0.3 \\
\quad\quad Leads               &    \Z\Z1.2 & LCE  & \Z0.4 \\
{\it Winding pack subtotal}    &      132.6 &      &  44.9 \\
Support                        &     \Z19.4 & LCE  & \Z7.5 \\
Engineering                    &     \Z43.6 &      & \Z0.0 \\
Hardware $\&$ enginering       &      195.6 &      &  52.4 \\
Contingency                    &     \Z58.0 & 20\% &  10.5 \\
PACE direct                    &      253.6 &      &  62.9 \\
PACE G$\&$A                    &     \Z22.6 & 10\% & \Z6.3 \\
OPEX                           &    \Z\Z8.7 &      & \Z0.0 \\
\hspace{1cm} {\it TOTAL}       &      285.0 &      &  69.2 \\
\\ \hline
\end{tabular}
\label{improvedcost}
\end{table}

\clearpage

\begin{table}
\caption{}
\centering{\bf PF coil Currents for Conventional and High Squareness Parameter ($\zeta$)}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{c c c c c }
\hline
Coil No. & $R^{(a)}$ (m) & $Z^{(a)}$ (m) & $\zeta= -0.15$ & $\zeta= 0.1$ \\
\hline
\hspace{2.5cm} & \hspace{2.5cm} & \hspace{2.5cm} & \hspace{2.5cm} & \hspace{2.5cm} \\
\Z1      & \Z2\D         &  10.5         &   10.01\N\Z    &  \N48.26  \\
\Z2      & \Z3\D         &  10.5         &   12.00\N     &  \N15.74  \\
\Z3      & \Z4\D         &  10.5         &    9.05\N      &   -26.82\Z \\
\Z4      & \Z7\D         &  10.5         & \Z-0.99       &   -13.72  \\
\Z5      & \Z8\D         &  10.5         & \Z-2.12       &  \Z-3.92\Z \\
\Z6      & \Z9\D         &  10.5         & \Z-2.57       & \N\Z0.89  \\
\Z7      &  10.5         &  10.5         & \Z-2.59       & \N\Z2.94  \\
\Z8      &  10.5         & \Z9.5         & \Z-3.45\Z      & \N\Z5.79  \\
\Z9      &  10.5         & \Z8.5         & \Z-4.27       & \N\Z8.26  \\
 10      &  10.5         & \Z7.5         & \Z-4.84       & \N\Z8.12  \\
 11      &  10.5         & \Z6.5         & \Z-4.9\Z\Z     & \N\Z2.91  \\
 12      &  10.5         & \Z5.5         & \Z-4.23       &  \Z-7.17  \\
 13      &  10.5         & \Z4.5         & \Z-2.76       &   -16.14  \\
 14      &  10.5         & \Z3.5         & \Z-0.65       &   -13.35  \\
 15      &  10.5         & \Z2.5         &  \Z1.73\N     & \N\Z7.96  \\
\\ \hline
\multicolumn{5}{l}{$^{(a)}$ Coil location is around the loci of a rectangle, as
described in the text.}
\end{tabular}
\label{pf_squareness}
\end{table}

\begin{table}
\caption{}
\centering{\bf PF Coil Currents for High Squareness, Internal Coils}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{c c c c c }
\hline
Coil No. & $R$ (m) & $Z$ (m) & Coil         & Optimum Coil \\
         &         &         & Current (MA) & Current (MA) \\
\hline \\
 1       & 2\D\Z   &  10     & \N10.55      &  \N12.7 \\
 2       & 3\D\Z   &  10     &  \N9.35\Z    &  \N10.1 \\
 3       & 5.5\Z   & \Z8     &   -6.115     &   -7.71 \\
 4       & 5.6\Z   & \Z7     &   -4.922     &   -3.32 \\
 5       & 6.15    & \Z6     &  \N3.508     &  \N3.88 \\
 6       & 6.6\Z   & \Z5     &  \N0.458     & eliminated \\
 7       & 8.15    & \Z4     &   -6.089     &   -9.08 \\
 8       & 8.4\Z   & \Z3     &   -5.467     &   -3.99 \\
 9       & 8.55    & \Z2     &  \N0.75\Z    & eliminated \\
\\ \hline
\end{tabular}
\label{current_hig_square}
\end{table}

\begin{table}
\caption{}
\centering{\bf Superconducting Performance of Internal Poloidal Field \\
for High Squareness Plasma}
\vspace{1.cm}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{lcccccccc  }
\hline
Coil & $f_{c}$ & $Q"_{max}$ & $f_{tr}$
                                    & $\Delta T_{head}$
                                            & $E_{mar,min}$
                                                    & $f_{Jprot}$
                                                            & $B_{max}$ \\
     &         & (W/cm$^2$) &       & (K)   & (J/cm$^3$) &  & (T) \\
\hline \\
PF1  & 0.618   & 0.1674     & 0.762 & 5.554 & 2.304 & 0.645  & 11.9\Z \\
PF2  & 0.625   & 0.1005     & 0.526 & 7.686 & 3.723 & 0.795  &  8.2   \\
PF3  & 0.603   & 0.0310     & 0.697 & 1.795 & 5.505 & 0.557  &  6.5   \\
PF4  & 0.629   & 0.0277     & 0.671 & 2.083 & 8.469 & 0.615  &  5.8   \\
PF5  & 0.617   & 0.0243     & 0.618 & 2.679 & 3.339 & 0.334  &  4.4   \\
PF6  & 0.629   & 0.0179     & 0.500 & 3.544 & 5.330 & 0.208  &  2.5   \\
PF7  & 0.632   & 0.0287     & 0.641 & 1.969 & 6.209 & 0.786  &  6.0   \\
PF8  & 0.623   & 0.0271     & 0.623 & 2.184 & 7.998 & 0.839  &  5.5   \\
PF9  & 0.644   & 0.0184     & 0.513 & 3.462 & 4.992 & 0.386  &  2.7   \\
\\ \hline
\end{tabular}
\label{performance_high_square}
\end{table}
\newpage

\begin{figure}[p]
\vskip1.in
\centerline{\epsfig{file=ast-8-01.eps,height=6.5in}}
\caption
{Equilibrium field parameters for steady state plasma with low ``squareness'' and
non-divertor PF coils external to the TF coil.}
\label{ast-8-01}
\end{figure}

\begin{figure}[p]
\vskip1.in
\centerline{\epsfig{file=ast-8-02.eps,height=6.5in}}
\caption
{Equilibrium field parameters for steady state plasma with high ``squareness'' and
PF coils internal to the TF coil.}
\label{ast-8-02}
\end{figure}



\end{document}