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\begin{document}

\title{\bf 5. OPTIONS FOR PLASMA REGIMES OF OPERATION}
\author{
\autlist{Stephen ~C.~Jardin}{Tak-Kuen~Mau}{David~A.~Ehst}
\autlist{Charles~E.~Kessel,~Jr.}{BongJu Lee}{Charles~G.~Bathke}
}
\date{ }
\maketitle

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

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

\chapter{OPTIONS FOR PLASMA REGIMES OF OPERATION}

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

The Starlite project aims at developing the most attractive and credible
conceptual design for a fusion power plant, based on the physics understanding
and experimental data established to date.  This design will utilize the
tokamak magnetic confinement concept, which has emerged as the clear
concept-of-choice in the worldwide fusion program.  However, there are at least
five distinctly different tokamak operating modes that have been proposed for
utilization in a \DT-fueled tokamak power plant.  These five operating modes
differ from one another in one or more of the following areas: (i)~choice of
stability regime ({\it i.e.,} first regime, second regime, or mixed),
(ii)~choice of pulsed or steady state operation, and (iii)~choice of
conventional or low aspect ratio.  While each of the five operating modes leads
to a self-consistent design that is optimized within its unique set of design
constraints, the five modes optimize to very different plasma performance and
engineering requirements, and hence, a choice must be made among them.

The five tokamak operating modes that have been evaluated by the Starlite
project are: (1)~a steady state, first stability regime (FS) similar to
\AI~\cite{Naj91}; (2)~a pulsed, first stability regime (PU) similar to
PULSAR~\cite{Najpu}; (3)~a steady state, second stability (SS) regime similar
to \AiiIV~\cite{Najss}; (4)~a steady state, reversed shear (RS)
mode~\cite{Kes94}; and (5)~a steady state, low aspect ratio
configuration~\cite{Pen95}.  Each of the five operating modes has a substantial
theoretical basis involving the computation of self-consistent ideal MHD
equilibrium and stability, bootstrap current, and current-drive efficiency.
However, not all of the five modes have been experimentally prototyped to the
same degree.

We have identified a set of critical tokamak physics parameters called physics
Figures of Merit (FOM).  Comparing the FOM parameters for each of the five
operating modes with what have actually been obtained experimentally
provides a way of assessing how credible the different tokamak operating modes
are~\cite{Mau95}.  For example, if there are two operating modes that lead to
approximately the same cost of electricity (COE) projections, but one is
significantly closer to having been experimentally prototyped in each of the
key tokamak physics areas, then that one operating mode would clearly be
preferred as a design choice.

\begin{figure}[b]
\vspace*{1.5in}
\centerline{\psfig{file=sti-5-1-01.ps,height=4.truein,clip=}}
\caption[sti-5-1-01]
{Flowchart showing strategy for Starlite fusion power plant evaluation.}
\label{sti-5-1-01}
\end{figure}

In the remainder of this chapter, we define and motivate the FOM parameters in
each of the critical tokamak physics areas (Sec.~\ref{s-5-2}), summarize each
of the five tokamak operating mode concepts(Sec.~\ref{s-5-3}), present figures
comparing the five concepts with the tokamak data base that has been assembled
for ITER(Sec.~\ref{s-5-4}), and present arguments for why the reversed shear
(RS) operating mode appears to be the most attractive one at this time.  A
chart illustrating the relationship between the physics, technology, and
economic assessments of the concepts and the project mission and requirements
statements is shown in Fig.~\ref{sti-5-1-01}.

\section{PHYSICS FIGURES OF MERIT}
\label{s-5-2}

The performance properties and hence the economics of the power plant will be
largely determined by the baseline tokamak physics parameters.  These are
significantly different for each of the five candidate designs.  For the power
plant to be both economically attractive and physically credible, several of
these parameters must be at or near their allowable limits, but none may exceed
them.  In an attempt to quantify this and to aid in concept selection, five
critical areas of tokamak physics have been identified.  In each of these
areas, we have further identified one or more critical parameters, or figures
of merit (FOM), which are dimensionless (wherever possible) measures of how
close to the theoretical limits a tokamak can be operated.  Before the detailed
engineering design can proceed, there must be sufficient experimental data in
place to demonstrate that a tokamak can operate reliably with the design values
of the FOMs in the five critical areas.  Thus, by comparing the FOMs of the
five candidate designs with the existing tokamak data base we can determine the
relative credibility of the five designs.  In addition, identification of these
critical parameters should help focus present research efforts in the direction
of optimizing and improving these quantities in existing and planned
experiments in order to lead the way to a more attractive concept.  The five
critical physics areas are (A)~MHD stability, (B)~current drive, (C)~plasma
energy confinement, (D)~power exhaust, and (E)~helium ash removal.  The
relevant FOMs are discussed in the following subsections.

\subsection{MHD Stability}
\label{s-5-2-1}

There are advantages to operating a tokamak at high values of $\beta/\epsilon$
to achieve high fusion power density, $p_f$, and at high values of
$\epsilon\beta_p$ to achieve a high bootstrap current fraction, and
consequently low recirculating power.  Here plasma $\beta$ is defined as
\hbox{$2\mu_{o} \langle p \rangle / B_{T}^{2}$} and the poloidal $\beta$ given
by \hbox{$\beta_p \equiv 8 \pi^{2} a^{2}_p \langle p \rangle S / \mu_{o}
I_p^{2}$}, where \hbox{$\langle p \rangle$} denotes the volume averaged
pressure, $B_{T}$ is the toroidal field in vacuum at the plasma major radius
$R$, $I_p$ is the total plasma current, \hbox{$S \equiv(1+ \kappa^{2})/2$} is
the shape factor , \hbox{$\epsilon \equiv A^{-1}\equiv a_p/R$} is the inverse
aspect ratio, $a_p$ is the minor radius, and $\kappa$ is the elongation.
Another useful quantity that will be used in this subsection is the
circularized safety factor, \hbox{$q_{*} \equiv 2 \pi a^{2}_p B_{T} S / \mu_{o}
R I_p$}.

It should be noted that $\beta/\epsilon$, and not $\beta$, is a parameter of
fundamental importance.  It is well known that if the MHD equilibrium and
stability equations are expanded in a self-consistent inverse-aspect-ratio
ordering that allows pressure driven instabilities to be present, the so-called
high-$\beta$ ordering~\cite{Str77}, then the tokamak $\beta$ is of order
$\epsilon$ and the $\beta_p$ is of order $\epsilon^{-1}$.  Thus, to leading
order in the expansion parameter $\epsilon$, the equilibrium and stability
properties of a high-$\beta$ tokamak configuration depend only on
$\beta/\epsilon$ and on $\epsilon\beta_p$.

Furthermore, it follows that $\beta/\epsilon$ is the critical parameter if one
assumes that $p_f$ scales as $\beta^{2}B_T^4$, and that the limiting value of
$B_{T}$ scales like $\epsilon^{-1/2}$.  This scaling for the maximum field
strength at the plasma center comes from assuming that in a tokamak power
plant, the maximum toroidal field will be limited by the requirement that the
maximum field strength at the superconducting TF coil is below some critical
value, $B_{crit}$.  Assuming that the outermost part of the inside leg of the
TF coil and the inside edge of the plasma are separated by shielding, etc,
which occupies about 20\% of the major radius, leads to a dependence of field
strength on inverse aspect ratio which is very well approximated by
$\epsilon^{-1/2}$ for the range of aspect ratios: \hbox{$2.5 \leq A \leq 5$}.

It is cautioned in passing that profile effects that affect the fusion power
density have been ignored.  The true fusion power output from a \DT plasma
would be better approximated by $\langle p^{2}\rangle$ than by \hbox{${\langle
p \rangle}^{2}$} as has been done here.  The latter quantity has been chosen
for the simplifications it yields, and for its ease of measurement in existing
experiments.  However, care must be used in applying the results discussed here
to tokamak equilibria with extreme ratios of \hbox{$\langle p^{2} \rangle$} to
\hbox{${\langle p \rangle}^{2}$}.

Increasing $\epsilon\beta_p$ in a given tokamak will normally increase its
ratio of toroidal current driven by the bootstrap effect to the total current,
\hbox{$f_{BS}\equiv I_{BS}/I_p$}.  However, the bootstrap fraction actually
scales as \hbox{$f_{BS}\propto C_{BS} \epsilon \beta_p/
\sqrt{\epsilon}$}~\cite{Pom92}, where $C_{BS}$ contains dependences on current,
density, and temperature profiles.  The factor $\sqrt{\epsilon}$ reflects the
decrease in bootstrap current as the aspect ratio is reduced.

\begin{figure}[t]
%\vspace*{8.0in}
\centerline{\psfig{file=sti-5-2-01.ps,height=4.0truein,angle=-90}}
\caption[sti-5-2-01]
{The MHD stability diagram showing regimes of operation for the first-stabilty
(FS), pulsed-plasma (PU), reversed-shear (RS), and second-stabtility (SS)
Starlite power plant options.  The LAR regime is outside of this diagram, with
\hbox{$\epsilon\beta_p\sim 1$}.}
\label{sti-5-2-01}
\end{figure}

There are limits on how much $\beta/\epsilon$ and $\epsilon \beta_p$
can be increased, either separately or together.  These constraints can
be conveniently illustrated in a diagram plotting $\beta/(\epsilon S)$ vs
$\epsilon\beta_p$, as is displayed in Fig.~\ref{sti-5-2-01}.  The beta
limit, in the form $\beta \leq \beta_{N} (I_p/B_{T}a_p)$, can be
shown to be equivalent to the expression
%
\begin{eqnarray}
\left( \epsilon \beta_p \right) \left( \frac{\beta}{\epsilon} \right)
 & \leq & \left(  \frac{\beta_{N}}{20}\right)^{2} S \: ,
\label{e-5-2-1}
\end{eqnarray}
%
which is plotted in Fig.~\ref{sti-5-2-01} for two values of $\beta_{N}$.  For a
conventional first stability configuration (similar to PULSAR) with high
current (low $q_{*}$), optimally shaped current and pressure distributions, and
with sufficient triangularity in the cross-sectional shape, this equation must
be obeyed with a Troyon coefficient of $\beta_N=3.5$.  Plasma configurations
with non-optimal profiles and shapes can be unstable at values of $\beta_{N}$
lower than 3.5.  If a higher $f_{BS}$ is desired for steady state operation,
one can reduce the current or raise $q_{*}$, resulting in a lower $\beta$, as
is the case with \AI.

It may be possible to violate the Troyon limit if certain conditions are met
which allow second stability regime as in \AiiIV designs, or at very large
values of $q_{*}$~\cite{Pol94} or at very low aspect ratios~\cite{Men95}.  The
conditions which allow second stability include either elevated central safety
factor (\hbox{$q_{0} \geq 2$})~\cite{Ram91}, strong cross-sectional
indentation~\cite{Cha83}, or reversed magnetic shear~\cite{Kes94}.  In addition
to these requirements, stabilization of the external kink mode in a second
stability plasma requires a close fitting conducting wall and sufficient plasma
rotation~\cite{Bon94}.

Other constraints, also shown in Fig.~\ref{sti-5-2-01}, come from the fact that
the equilibrium equation must be obeyed, which implies $\epsilon \beta_p \leq
2$ and that the external kink mode can only be stable for $q_{*}\geq 2$.  The
expression relating these quantities for a plasma equilibrium is
%
\begin{eqnarray}
\left( \frac{\beta}{\epsilon } \right) & = & \left( \epsilon \beta_p
\right) \frac{S}{q_{*}^{2}}
\label{e-5-2-2}
\end{eqnarray}
%
which appears as straight lines in Fig.~\ref{sti-5-2-01}.

It is natural to choose as the MHD figures of merit the parameter pair
($\beta / \epsilon, \epsilon \beta_p$).
Note that a systems analysis is required to choose where in this
space the fusion power plant should operate.  There will always be a
tradeoff between high $\epsilon \beta_p$ and high $\beta / \epsilon$
as described by Eq.~(\ref{e-5-2-1}), and the preferred design will
most likely optimize at intermediate values of each as is in all ARIES designs.
An explicit illustration of the tradeoff between high $\beta$ and high
$\beta_p$ is given in Ref.~\cite{Ehs95}, in which an economic
analysis determines the values of these parameters that minimize the COE
of a first stability equilibrium with an \AI type of
current drive performance.

\begin{figure}[b]
\centerline{\psfig{file=sti-5-2-02.ps,height=4.0truein,clip=}}
\caption[sti-5-2-02]
{MHD figures of merit for long-pulse ELMy, H-mode discharges in several
existing devices and the five Starlite fusion power plant options (FS, PU, RS,
SS, and LAR).}
\label{sti-5-2-02}
\end{figure}

Existing long-pulse, ELMy H-mode discharges with high $\beta$ and high
bootstrap fraction are plotted in the two-dimensional parameter space of
Fig.~\ref{sti-5-2-02}, together with the design values for the five Starlite
power plant options.  This figure allows one to assess how close a proposed
tokamak power plant is to the existing MHD database.  In this respect, both the
FS and PU concepts are close to the database.  Several caveats must be kept in
mind, however.  One is that the PBX-M data are based on highly indented plasmas
($i\simeq 0.25$), which do not extrapolate well to power plant regimes.  The
second is that the nature of MHD changes at very high temperatures,
transitioning from a resistive to a collisionless regime.  This fact makes the
lower temperature results in smaller, colder, present day experiments not
completely relevant for prototyping the MHD regimes in a burning plasma.
Another caveat is that the MHD time-scales needed for plasma profiles to fully
relax and for weakly unstable dissipative MHD instabilities to grow can be very
long by today's standards, so that few if any of the discharges displayed in
Fig.~\ref{sti-5-2-02} are truly in steady state.

\subsection{Current Drive}
\label{s-5-2-2}

The theory for non-inductive current drive~\cite{Fis87,Ehs87,Ehs91}
demonstrates that the driven current density, $j_{cd}$, is proportional to the
product of the local absorbed power density, $p_{cd}$, and the local electron
temperature, $T_e$, divided by the electron density,
%
\begin{eqnarray}
j_{cd} & = & A_{0} \, p_{cd} \, \frac{T_e}{n_e} \left(\frac{\tilde{j}}
           {\tilde{p}}\right) \: .
\label{e-5-2-3}
\end{eqnarray}
%
Here $A_{0}$ is a constant.  The normalized local current drive efficiency
$(\tilde{j}/\tilde{p})$ (defined in \cite{Fis87}) is a dimensionless function
of the location in electron velocity space where momentum and energy are
absorbed.  In a steady state plasma with no applied loop voltage, the
total non-inductively driven current, $I_{CD}$, is found by integrating the
local driven current density, $j_{cd}$, over the plasma cross section.
Including the Pfirsch-Schl\"{u}ter and diamagnetic equilibrium contributions,
the total driven current is of the form
%
\begin{eqnarray}
I_{CD} & = & \gamma_{CD} \, \left ( \frac{P_{CD}}{\overline{n}_e R} \right ) \:
,
\label{e-5-2-4}
\end{eqnarray}
%
%\vspace*{8.0in}
which may also be obtained by dimensional analysis~\cite{Ehs86}).  Reference to
Eq.~(\ref{e-5-2-3}) shows roughly that $\gamma_{CD}\sim
T_e(\tilde{j}/\tilde{p})$.  Detailed calculations of self-consistent steady
state tokamaks~\cite{Ehs87} have refined the temperature dependence for a power
plant (\hbox{$T_{e0}\geq 15$~keV}) to \hbox{$\gamma_{CD}\propto T_{e0}^{n}$},
where \hbox{$0.6\leq n\leq 0.8$}, depending on details of the plasma and
current density profiles.

Because the current-drive efficiency for most of the established current-drive
techniques is low, steady-state tokamak power plants have to rely heavily on
the bootstrap current.  For a high $\beta_p$ tokamak plasma, the toroidal
plasma current, $I_p$, consists of two components, one generated by one or more
non-inductive current-drive sources with power $P_{CD}$, and the other due to
the toroidal bootstrap effect, {\it i.e.,} \hbox{$I_p=I_{BS}+I_{CD}$}. To
account for these two factors, a more appropriate, bootstrap-enhanced
current-drive figure of merit, $\gamma_B$, is proposed, which is the same as
the conventional measure of current-drive efficiency ($\gamma_{CD}$) but with
$I_{CD}$ replaced by $I_p$, and is given by
%
\begin{eqnarray}
\gamma_{B} & = & (\overline{n}_e/10^{20})I_pR/P_{CD} \: .
\label{e-5-2-5}
\end{eqnarray}
%
The expression $\gamma_B$ can be viewed as a global integral of the
current-drive efficiency over the plasma minor cross section, including the
bootstrap contribution.  Thus, to lowest order, $\gamma_B$ depends on the
plasma equilibrium and on the electron temperature, $T_e$; to next order, it
depends on details such as current drive techniques, plasma $Z_{eff}$, and
equilibrium $T_e$ and $n_e$ profiles.  It is clear from Eq.~(\ref{e-5-2-5})
that $\gamma_{B}$ can be made large if a large part of $I_p$ is due to the
bootstrap effect, {\it i.e.,} if \hbox{$f_{BS}\equiv I_{BS}/I_p$} is close to
unity.  In recent years, significant advances have been made in achieving high
bootstrap current fraction in high-$\beta_p$ experimental discharges, and
Fig.~\ref{sti-5-2-03} illustrates some of the results.  As shown in this
figure, $f_{BS}$ values close to 0.8 have been obtained.

\begin{figure}[b]
\centerline{\psfig{file=sti-5-2-03.ps,height=3.6in,clip=}}
\caption[sti-5-2-03]
{Large tokamak experiments which display substantial bootstrap
fraction at high poloidal beta.  Note that poloidal beta definitions
vary somewhat; and plasma conditions (collisionality, density
gradient, impurity content, {\it etc.}) also vary.}
\label{sti-5-2-03}
\end{figure}

For steady-state tokamak power plants, various non-inductive techniques need to
be considered for sustaining the plasma current ({\it i.e.,} the supply the
difference between the bootstrap and equilibrium plasma currents).  Depending on
the reference equilibrium, a combination of these techniques may be required to
drive currents in different locations within the plasma.  The bulk of the
present experimental database on current drive has been obtained using lower
hybrid waves and neutral beams.  In these discharges, typically
\hbox{$f_{BS}\leq 0.1$}, so that $\gamma_{B}\simeq\gamma_{CD}$.
Figure~\ref{sti-5-2-04} shows the experimental values of the current-drive
efficiency as a function of central electron temperature, $T_{e0}$ for lower
hybrid current drive (LHCD) ~\cite{Tib87}, the measured values lying within the
expected range of $\tilde{j}/\tilde{p}$.  With lower hybrid power alone, the
highest value of $\gamma_{CD}=0.34$, measured on JT-60~\cite{Ima90}, is
displayed in the figure.

\begin{figure}[b]
\vspace*{0.6in}
\centerline{\psfig{file=sti-5-2-04.ps,height=3.8in,clip=}}
\caption[sti-5-2-04]
{Experimental values of the lower-hybrid current-drive efficiency as a function
of central electron temperature, $T_{e0}$; for most of these experiments the
bootstrap current contribution is small so $\gamma_{B}\simeq\gamma_{CD}$.}
\label{sti-5-2-04}
\end{figure}

\begin{figure}[b]
\centerline{\psfig{file=sti-5-2-05.ps,height=3.7in,clip=}}
\caption[sti-5-2-05]
{Fast-wave current-drive experimental database on DIII-D~\cite{Deg95}, Tore
Supra~\cite{Lit95}, and TFTR~\cite{Rog95}; best data point for lower-hybrid
current-drive on JT-60~\cite{Ima90} and for lower-hybrid and FWCD synergy on
JET~\cite{Gor92}. Reference $\gamma_{B}$ values for Starlite power plant
options (FS, PU, RS, SS, and LAR) are also shown.}
\label{sti-5-2-05}
\end{figure}

There are two other current-drive techniques, namely, fast magnetosonic waves
in the ion cyclotron range of frequencies (ICRF) and electron cyclotron waves,
that exhibit potentials for power plant applications.  The fast wave technique
shows significant promise for on-axis current drive, particularly in view of
the fact that a typical fusion plasma core is inaccessible to the lower-hybrid
waves.  In Fig.~\ref{sti-5-2-05} the most recent experimental data on ICRF
fast-wave current drive (FWCD) are plotted.  Most of these data points come
from DIII-D~\cite{Deg95}, where the plasma was preheated either by
electron-cyclotron waves or by neutral beam injection, and where a four-strap
directional antenna is used.  Preliminary FWCD data taken at
Tore-Supra~\cite{Lit95} and TFTR~\cite{Rog95} are displayed alongside the
DIII-D data, and were obtained with two-strap 90$^\circ$ phased antennas in
preheated plasmas.  Also shown in this figure is the record value of
$\gamma_{CD}=0.45$ achieved to date on JET~\cite{Gor92}, when a synergistic
combination of lower-hybrid and ICRF power was used.  For reference and
comparison, the highest $\gamma_{B}$ value of 0.34, achieved on JT-60 using
lower-hybrid power alone~\cite{Ima90}, is also displayed.

In Fig.~\ref{sti-5-2-05}, the design values of $\gamma_B$ (using a combination
of RF techniques) for the FS, SS, RS, and LAR power plant options are also
shown.  These design points are at much higher values of $T_{e0}$ than in
present experiments.  It is clear that considerable advances in the
current-drive database with FWCD are required in order to reach the
power plant regime.  However, as the target plasma temperature improves with
higher input power, and as the bootstrap fraction is raised in future devices,
the value of the measured $\gamma_{B}$ is expected to increase accordingly.

It should be noted that the current-drive data quoted so far have all been
taken in transient discharges, with the driven current deduced either from
loop-voltage measurements or from comparison between co- and counter-current
drive discharges.  The only truly steady state discharge to date was achieved
on TRIAM-1M~\cite{Ito90}, where lower-hybrid current-drive was used to maintain
the discharge at \hbox{$I_p\sim 22$~kA} for over one hour, which well exceeds
the current profile relaxation time.  However, the plasma parameters were
modest, with \hbox{$\langle n_e\rangle < 0.2\times 10^{19}$~m$^{-3}$}, and an
input lower-hybrid power of 50~kW.

More recently, a completely non-inductively-driven quasi-stationary state of
0.1~s duration was achieved during a transient DIII-D discharge when 1.5MW of
FWCD and 1.0~MW of electron-cyclotron current-drive (ECCD) were
injected~\cite{Deg95}.  During this period, the plasma current was held
constant at 170~kA by a standard feedback control of the loop voltage that
stayed approximately near zero.  Detailed calculations showed that the FWCD,
ECCD and bootstrap effect account for 100, 10, and 60~kA, respectively.  In
spite of these advances, it remains clear that database need to be developed
for long pulse and steady state discharges with the use of non-inductive
current drive.

\subsection{Energy Confinement}
\label{s-5-2-3}

Plasma energy confinement is one of the most important issues for a fusion
power plant design, but is not yet well understood.  It is measured by the
global energy confinement time, $\tau_E$, which is defined as the time for the
transport of plasma energy across the confining magnetic field, from the core
to the edge region.  From a single particle orbit perspective, the value of
$\tau_E$ depends intrinsically on the size of the toroidal plasma, and on the
magnitude of the confining magnetic field.  However, the actual level of energy
confinement is governed by the detailed transport processes induced by drift
wave turbulence and microinstabilities due to various plasma gradients and the
presence of magnetically trapped particles.  As a result, the tokamak plasma
can exhibit a variety of confinement modes.

There are two classes of plasma confinement regimes in tokamak discharges that
involve auxiliary heating power.  The first class includes L-mode discharges
where the energy confinement is low and where no attempt is made to improve the
confinement by external means.  The second class includes regimes with enhanced
confinement (quiet H-mode, ELMy H-mode, Supershot, PEP H-mode, high-$\beta_p$
H-mode, VH-mode, enhanced reversed shear mode, {\it etc.}).  In general, better
energy confinement, together with higher normalized $\beta$ lead to a more
compact, and potentially more economical fusion power core, limited only by the
allowable magnetic field at the toroidal-field coils, neutron wall loading,
{\it etc.}and MHD stability limits.  In a fusion power plant, the plasma will
have to operate in one of these enhanced confinement regimes to be viable.

Among the various energy confinement regimes, L-mode discharges have been
studied most extensively.  As part of the ITER Conceptual Design Activities, an
empirical $\tau_E$ scaling~\cite{Yus90} was obtained from a large number of
tokamak L-mode discharges with different heating methods (neutral beam and RF)
and different exhaust configurations (divertor and limiter), using an ordinary
least squares regression technique.  This confinement time scaling is given by
%
\begin{eqnarray}
\tau_{ITER89-P} & = & 0.048 \, I_p^{0.85} \, R^{1.2} \, a^{0.3}_p \,
  \kappa^{0.5} \, \bar{n}_{20}^{0.1} \, B^{0.2} \, A_i^{0.5} \, P^{-0.5} \: ,
\label{e-5-2-6}
\end{eqnarray}
%
where $A_i$ is the ion mass number, and SI units are used except for plasma
current $I_p$ (MA), total heating power, $P$ (MW), and the line-averaged
electron density $\bar{n}_{20}$ ($10^{20} /m^{3}$).

On the other hand, except for the quiet and ELMy H-modes, confinement scalings
for the enhanced confinement regimes of operation have yet to be
established. This is partly because of an insufficient database and partly
because many of these discharges rely on detailed control of the plasma
profiles that may require a new methodology to parameterize.  The reference ITER
plasma operational regimes~\cite{Per94} will be based on the ELMy H-mode
confinement regime in order to ensure ignition with a modest heating power
requirement and moderate ash buildup in the plasma.  However, unlike ITER which
has a relatively conservative near-term goal, selection of the power plant
operation scenario will require the consideration of a much broader range of
enhanced confinement modes in order to maximize its economic potential.

An important consideration for ignition devices (such as ITER) and fusion power
plants is the plasma pressure $\langle p\rangle\equiv\langle nT\rangle$ at
which these enhanced confinement modes are achieved.  For ion temperatures in
the range of 5--25~keV, typical of a \DT-burning plasma, the fusion power is
proportional to \hbox{$\langle nT\rangle^2$}.  Using simple power balance, the
ratio of fusion power to the rate at which energy is conducted away is
proportional to $\langle nT\rangle\tau_E$, which more appropriately
characterizes the confinement capacity for a fusion plasma than $\tau_E$ alone.
As an example, the ITER-CDA device will require a confinement capacity of
\hbox{$T_{i0}n_{DT0}\tau_E\sim 4-8\times 10^{21}$~keV$\cdot$s/m$^{3}$} for a
fusion \hbox{$Q\sim 5-\infty$}.  Using $\langle nT\rangle\sim\beta B_{T}^{2}$
and \hbox{$\chi_E\sim a^{2}_p/\tau_E$}, where $\chi_E$ is a volume averaged
heat diffusivity, one can obtain:
%
\begin{eqnarray}
\frac{\beta}{\chi_E} & \sim & \frac{\beta \, \tau_E}{a^2_p} \: \sim \:
     \frac{\langle nT\rangle\tau_E}{(a_p B_{T})^{2}} \: .
\label{e-5-2-7}
\end{eqnarray}
%
Note that in Eq.~\ref{e-5-2-7}, the quantity $\beta\tau_E/a^{2}_p$ provides a
normalized measure of the confinement capacity, by factoring out the dominant
dependences of the device size and magnetic field.  This parameter is also
proportional to $\beta/\chi_E$, which was previously proposed as a power-plant
figure of merit~\cite{She85}.

Another commonly used figure of merit for confinement capacity can be derived
from the quantity \hbox{$\langle nT\rangle\tau_E$}, irrespective of machine
size and easily measurable in present experiments.  By invoking a ``generic''
L/H-mode scaling~\cite{Gol94} of \hbox{$\tau_E\propto
HI_pR^{3/2}\kappa^{1/2}P^{-1/2}$}, and noting that \hbox{$P\propto (\langle
nT\rangle/\tau_E)Ra^{2}_p\kappa$}, one can derive the relation \hbox{$\langle
nT\rangle\tau_E \propto (HI_p/\epsilon)^{2}$}, where $H$ is the H-mode
confinement enhancement factor.  Neglecting shape factors ($\delta$, $\kappa$)
and substituting \hbox{$q_{*}\propto \epsilon a_p B_{T}/I_p$} into the above
expression yields the relationship
%
\begin{eqnarray}
\frac{\langle nT\rangle\tau_E}{(a_p B_{T})^{2}} & \propto & \left(
    \frac{H}{q_*} \right)^2 \: ,
\label{e-5-2-8}
\end{eqnarray}
%
denoting that $H/q_{*}$ as a figure of merit.  However, the derivation of this
figure of merit depends on the ``generic'' L/H-mode scaling.  Recently, the
ITER H-mode Database Working Group derived global confinement scalings from
various subsets of the H-mode confinement database and found that the parameter
exponents can differ substantially from those of the ITER-89P L-mode scaling.
For example, for ELMy H-modes, the thermal energy confinement scaling is found
to be~\cite{Kay94}:
%
\begin{eqnarray}
\tau_{H-mode} & = & 0.045 \, I_p^{1.06} \,  R^{1.79} \, \kappa^{0.66} \,
      \bar{n}_{20}^{0.17} \, B_{T}^{0.32} \, A_{i}^{0.41} \,
      P^{-0.67} \, \epsilon^{-0.11} \: ,
\label{e-5-2-9}
\end{eqnarray}
%
where $P$ is now the total heating power corrected for beam shine-through,
orbit loss and charge exchange losses.  Comparing Eqs.~\ref{e-5-2-6} and
\ref{e-5-2-9} illustrates that there is substantial variation from the
``generic'' L/H-mode scaling and that the use of $H/q_*$ as a figure of merit
is not universally applicable.

Since, the cost of operating a fusion power plant is strongly dependent on the
achievable fusion power density, we propose plotting the confinement figure of
merit $\beta\tau_E/a^{2}_p$ as a function of $\beta/\epsilon$.\footnote{This
combination was first proposed by R.~Goldston, PPPL(1994).} Simultaneous
attainment of high confinement capacity and high fusion power density will then
place the desirable region of operation in the upper right-hand quadrant of
such a graph. This also serves as a guide to present and near-term experiments
aimed at simulating attractive reactor confinement performance.

\begin{figure}[b]
%\vspace*{7.0in}
\centerline{\psfig{file=sti-5-2-06.ps,height=3.8truein,clip=}}
\caption[sti-5-2-06]
{Energy confinement figures of merit for ELM-free H-mode discharges
on DIII-D for various ($\delta,\kappa$) values.  Data points for JET,
JT-60U, and design values for TPX and ITER are also
displayed.~\cite{Gol94}}
\label{sti-5-2-06}
\end{figure}

In Fig.~\ref{sti-5-2-06}, taken from Ref.~\cite{Gol94}, values of
$\beta\tau_E/a^{2}_p$ is plotted against $(\beta/\epsilon)^{2}$ for ELM-free
H-modes on DIII-D, and for a number of existing and future devices, including
JET, JT-60U, TPX and ITER.  The DIII-D data are plotted for various
combinations of triangularity ($\delta$) and elongation ($\kappa$), clearly
indicating that energy confinement and energy density improve significantly
with strong plasma shaping.

Since ELMs are useful in periodically removing the $\alpha$ ash from the core,
it is useful to compare the ELMy H-mode database with power plant values.  In
Fig.~\ref{sti-5-2-07} the confinement FOMs are plotted for long pulse ELMy
H-mode discharges on a number of devices together with the reference values for
the five Starlite power plants.  Note that the very favorable results for PBX-M
are due to the highly indented plasma (\hbox{$i\sim 0.25$}) in those
discharges.  In general, the FOM values are more modest than those for ELM-free
discharges shown in Fig.~\ref{sti-5-2-06}.  As indicated, the confinement
performance of the FS option is well within those achieved on present machines,
while the LAR power plant is farthest away from the existing database.

\begin{figure}[t]
%\vspace*{8.0in}
\centerline{\psfig{file=sti-5-2-07.ps,height=4.0truein,clip=}}
\caption[sti-5-2-07]
{Energy confinement figures of merit for a number existing tokamaks and
the Starlite fusion power plants. (Data provided by Stan Kaye, PPPL.)}
\label{sti-5-2-07}
\end{figure}

It must be pointed out that experimental databases on the RS and LAR concepts
are not as developed as for the other tokamak concepts.  For the reversed shear
mode of operation, significant advances in plasma performance were reported
recently on TFTR~\cite{Lev95} and on DIII-D~\cite{Str95}.  Both experiments
reported significant enhancements in energy confinement for both electrons and
ions inside the RS region, leading to a highly peaked pressure profile near the
axis.  Of special interest are the DIII-D results which indicate transitions
from the L-mode to the ELMy or ELM-free H-mode for these discharges with
central reversed shear.  This leaves open the possibility that the H-mode data
presented in Figs.~\ref{sti-5-2-06} and \ref{sti-5-2-07} may indeed be relevant
to the RS mode.  As for the LAR concept, the most advanced results have been
from the START spherical tokamak~\cite{Syk95}, where the measured $\tau_E$ is
typically twice the neo-Alcator value, and is well represented by the
Rebut-Lallia scaling.  Data from double-null-divertor discharges on this
machine appear to indicate transition to an improved confinement regime at high
currents and densities.  However, there is no data on auxiliary heated
discharges.  Data on larger LAR experiments with higher currents, external
heating power and current drive must be developed before this mode of operation
can be used in a power plant.

\subsection{Heat Exhaust}
\label{s-5-2-4}

In a fusion power plant, the core plasma is continuously heated by several
hundred megawatts of $\alpha$ power, $P_{\alpha}$ and by the non-inductive
current power, $P_{CD}$.  The need to remove the charged-particle heat escaping
the tokamak plasma in a timely fashion is an issue of critical importance in
designing a fusion power plant.  This power crosses the separatrix into the
scrape-off layer and is deposited on the divertor plates. The average heat flux
striking the divertor plate is approximated by
%
\begin{eqnarray}
q_{PLATE} & = & \frac{1}{2\pi\lambda_{div}} \, \frac{P_{PLATE}}{R} \: ,
\label{e-5-2-10}
\end{eqnarray}
%
where $\lambda_{div}$ is the expanded power scale length measured along the
divertor plate, $R$ is the major radius, and $P_{PLATE}$ is the net power
reaching the divertor plate.  As a point of reference, the engineering design
goal for fusion power plants is to limit the peak heat flux at the plates to
$\sim$5~MW/m$^2$.

Denoting $P_{tr}$ as the power that crosses the separatrix and $f_{rad}$ as the
fraction of total plasma heating power, $P_{\alpha}+P_{CD}$, that is radiated
in the plasma core and the edge radiative mantle, then
%
\begin{eqnarray}
P_{tr}=(P_{\alpha}+P_{CD})[1-f_{rad}].
\label{e-5-2-11}
\end{eqnarray}
%
If there is no radiation in the scrape-off layer and the divertor region, then
$P_{plate} = P_{tr}$. In this case, $f_{rad}$ values of about 0.8 to 0.9 is
necessary for a tokamak power plant in order to satisfy the above engineering
design goal.  This value of $f_{rad}$ can be achieved by introducing impurities
in the plasma edge creating a radiative edge mantel.  However, the presence of
these impurities can increase the current-drive power substantially.  Another
way to reduce the peak heat flux is to introduce impurities into the divertor
region and allow for friction forces to entrain the impurities in the divertor
region without increasing the $Z_{eff}$ of the core plasma dramatically.

The atomic physics processes of potential importance in the plasma and divertor
chamber include bremsstrahlung and impurity line radiation, and charge
exchange.  Since the excitation energies of these processes are fixed
constants, the ratios between the reference plasma temperature and these values
are determined by the absolute magnitude of the former.  Lackner~\cite{Lac90}
has extended this observation to demonstrate that under the condition of
constant (or known) plasma temperature, similarity laws are obeyed in the
plasma edge with the result that the quantity $P_{tr}/R$ is in fact
equivalent to the dimensionless figure-of-merit that characterizes the regime
of divertor operation.  This figure of merit has also been independently
derived~\cite{Cat95} by using the scaling transformation properties of the
system of two dimensional fluid plasma and neutral equations together with
boundary conditions~\cite{Cat94}.

We therefore can use the quantities $P_{tr}/R$ and $f_{rad}$ as figures of
merit for comparing the divertor heat removal requirements in a given power
plant candidate to the existing experimental database.  It is essential that
reactor-level values of both of these parameters be obtained simultaneously in
order to demonstrate feasibility.  An important caveat is that this must be
achieved without a significant buildup of the injected impurity in the core.
This is characterized by the requirement that $Z_{eff}<2.6 $ for low-$Z$
impurities.  Attainment of these parameters will likely involve a splitting of
the radiating power between the plasma center, mantle, scrape-off layer, and
divertor, and will also likely require density compression of the impurity
species in the divertor region.

\begin{figure}[t]
%\vspace*{8.0in}
\centerline{\psfig{file=sti-5-2-08.ps,height=3.8truein,clip=}}
\caption[sti-5-2-08]
{Plot of heat exhaust figures of merit, $f_{rad}$ versus $P_{tr}/R$, for a
number of present experiments (TEXTOR, C-Mod, JET, JT60-U, ASDEX-U, and
DIII-D), and design values for the five Starlite fusion power plant options
(FS, PU, RS, SS, and LAR).  The dotted and chain-dotted lines represent the
trend of PU option and LAR respectively due to the variation of
$f_{rad}$. Options FS, RS, and SS follow the chained line.  Note that $f_{rad}$
of PU fusion power plant is relatively high compared to the other concepts
because no current-drive power is required.}
\label{sti-5-2-08}
\end{figure}

Data points for heat removal in several tokamak experiments are given in
Fig.~\ref{sti-5-2-08}.  In cases where there is no impurity
injection~\cite{Ite94}, values of $f_{rad}$ in the range of 0.4--0.6 is
obtained by intrinsic carbon radiation in detached plasmas, {\it e.g.,} on
TEXTOR, C-Mod, ASDEX-U, JET, JT-60U and DIII-D.  For discharges with neon
puffing, such as in TEXTOR, ASDEX-U, and DIII-D, a total radiation fraction in
the range of 0.9 is obtained.  In the case of TEXTOR~\cite{Sam93}, where a
pumped limiter was used, a radiating mantle was set up with a resultant
$f_{rad}=0.95$.  Completely detached ELM-free H-mode experiments on
ASDEX-U~\cite{Asd95} show that $f_{rad}$ can reach as high as 0.9 through a
combination of D and Ne puffing, whereas $f_{rad}$ drops to 0.55 without Ne
puffing.  In DIII-D~\cite{Leo95}, Ne puffing resulted in the simultaneous
creation of a radiative mantle and a strong radiation zone near the divertor
plates, with each region radiating approximately equal power.

In Fig.~\ref{sti-5-2-08} the range of design values of $f_{rad}$ and
$P_{tr}/R$ for the five Starlite power plant options are also plotted.  It is
clear from this figure that the experimental database has already reached the
desired value of $f_{rad}$ for power plants, either by the action of a
radiative mantle, or a combination of both scrape-off layer and core radiation.
However, these data points have been achieved at levels of $P_{tr}/R$ that
are still some distance away from those in power plants.

If the peak solid target heat flux is to be limited to values $\sim$5~MW/m$^2$,
a combination of enhanced radiation in the core, in the scrape-off layer, and
in the divertor is required.  The feasibility of obtaining this has not yet
been demonstrated, but it may be possible using techniques such as impurity
density compression in the divertor region.

\subsection{Helium Ash Removal}
\label{s-5-2-5}

Effective removal of the helium ash produced by the fusion reactions is an
important issue for fusion plasma~\cite{Rei90,Beh90,Tay90}.  It becomes
increasingly difficult to maintain an ignited plasma the greater the helium
concentration.  This is due to dilution of the fuel ions with helium which
reduces the fusion yield, the enhanced radiation losses associated with the
higher $Z$ helium.  It is well known that with helium present the energy
confinement time must increase to compensate for the above effects.  To examine
the impact of helium ash accumulation in a fusion power plant, one can use a
simple power balance for the core plasma in steady state, by neglecting
radiation and current drive power, ignoring any impurities other than helium,
and by considering all plasma species to have the same temperature and energy
confinement time.  At fixed $\beta$, the ratio of energy confinement times with
and without the presence of helium can be written as
%
\begin{eqnarray}
\frac{\tau^{wHe}_{E}}{\tau_E^{w/oHe}} & = & \left( 1 + \frac{3}{2}
\frac{n_{He}}{n_{i}} \right)^{2} \: .
\label{e-5-2-12}
\end{eqnarray}
Clearly the presence of helium in the core plasma requires an increased
energy confinement time to maintain power balance.

From steady-state helium particle balance in the core plasma (ignoring other
impurities), the ratio of helium to the fuel ion density is given by
%
\begin{eqnarray}
\frac{n_{He}}{n_{i}} & = & \frac{\tau_{He}}{(1-R_{He})} \,
 \frac{n_{i} \langle \sigma v \rangle}{4}
 \: = \: \tau_{He}^{*} \, \frac{n_{i} \langle \sigma v \rangle}{4} \: ,
\label{e-5-2-13}
\end{eqnarray}
%
where $n_{i}$ is the \DT fuel ion density, $n_{He}$ is the helium density,
\hbox{$\langle \sigma v \rangle$} is the fusion reaction rate, $R_{He}$ is the
helium recycling coefficient, and $\tau_{He}$ is the helium particle
confinement time in the core plasma.  The ratio of the core plasma helium
confinement time to $(1-R_{He})$ is referred to as the effective confinement
time $\tau_{He}^{*}$.  This time constant has physical significance in that it
reflects the mean residence time of a helium particle before finally being
pumped out of the plasma chamber.

Since many transport theories relate the particle confinement time to the
energy confinement time, the ratio of $\tau_{He}^{*}/\tau_E$ is often used to
measure the effectiveness of core ash removal.  From the simple power balance
above (ignoring bremsstrahlung radiation and current-drive power) and helium
particle balance, one can derive
%
\begin{eqnarray}
\frac{\tau_{He}^{*}}{\tau_E} & = & \frac{\frac{n_{He}}{n_{i}}}{\left(
1 + \frac{3}{2} \frac{n_{He}}{n_{i}} \right)} \left(
\frac{E_{\alpha}}{3 kT} \right) \: ,
\label{e-5-2-14}
\end{eqnarray}
%
where $E_{\alpha}$ is the alpha birth energy (3.5~MeV).
Equation~\ref{e-5-2-14} shows that as $\tau_{He}^{*}$ increases, the helium
fraction in the plasma core increases.  However, as pointed out earlier,
$\tau_E$ must then increase in order to maintain the operating point.  This
ratio is therefore the condition required on $\tau_{He}^{*}$ in order to
achieve power balance in a \DT fusion plasma with a given helium to fuel ion
density ratio.

Including both bremsstrahlung radiation and a single impurity with charge $Z$,
the ratio of helium particle confinement time to energy confinement time is
given by,
%
\begin{eqnarray}
\frac{\tau_{He}^{*}}{\tau_E} & = & \frac{\frac{n_{He}}{n_{i}}}{\left(
1 + \frac{3}{2} \frac{n_{He}}{n_{i}} + \frac{Z+1}{2} \frac{n_{Z}}{n_{i}}
\right)} \left( \frac{E_{\alpha}}{3 kT} \right)
\left[ 1 - \frac{4 C_{br} T^{0.5}}{\langle \sigma v \rangle E_{\alpha}}
Z_{eff} \left( 1 + \frac{2 n_{He}}{n_{i}}
+ \frac{Z n_{Z}}{n_{i}} \right)^{2} \right] \: , \hspace{1.cm}
\label{e-5-2-15}
\end{eqnarray}
%
where $C_{br}$ is the prefactor in the standard global expression for
bremsstrahlung power, and the plasma temperature is taken as the volume
average.  The ratio \hbox{$4 C_{br} T^{0.5} / \langle \sigma v \rangle
E_{\alpha}$} is about 0.1 for a 10-keV plasma.  Comparing Eqs.~\ref{e-5-2-14}
and \ref{e-5-2-15} shows that the introduction of impurities and radiation
leads to a lower value of $\tau_{He}^{*}/\tau_E$ to maintain a fixed ratio of
helium to fuel ions in the plasma, and is a more restrictive condition.  As an
example, a plot of $\tau_{He}^{*} /\tau_E$ is given in Fig.~\ref{sti-5-2-09}
for various helium to fuel ion ratios as a function of the volume average
plasma temperature, and assuming a 1\% oxygen impurity level.  According to
this simple calculation, for an average temperature of 10~keV, the ratio
$\tau_{He}^{*}/\tau_E$ increases from 4 to 12 as $n_{He}/n_{i}$ is varied from
0.05 to 0.3.  For the same helium concentration, it is interesting to point out
that there is an optimum temperature at which the requirement on
$\tau_{He}^{*}/\tau_E$ is most relaxed, {\it i.e.,} when the ratio is a
maximum.

\begin{figure}[b]
\centerline{\psfig{file=sti-5-2-09.ps,height=3.4truein,clip=}}
\caption[sti-5-2-09]
{Ratio of effective ash confinement to energy confinement time required
for power balance as the averaged plasma temperature and the ratio of
ash to fuel ion densities are varied.  An oxygen impurity concentration of
1\% is assumed.}
\label{sti-5-2-09}
\end{figure}

A figure of merit for helium ash removal should reflect the critical
requirements of a fusion power plant and provide a basis for experimental
tokamaks to gauge their progress toward these requirements. The primary issues
for helium ash removal are:
%
\begin{enumerate}
\item sufficiently short effective ash particle confinement time;
$\tau_{He}^{*}$
\item low non-helium impurity content; and
\item reasonable pumping speed and fueling requirements.
\end{enumerate}

The difficulty with constructing a figure of merit for helium ash removal lies
with the fact that the negative impact of helium in the core plasma is not
properly represented without an ignited plasma.  The fusion power plant
requirement for $\tau_{He}^{*}/\tau_E$ is determined by two constraints, helium
particle balance and ignited plasma power balance.  For a given amount of
helium in the plasma there is a corresponding particle confinement time and
energy confinement time.  In present day experiments, the plasma energy
confinement time is unaffected by the presence of the helium.  Therefore care
must be taken when drawing a direct correlation between the
$\tau_{He}^{*}/\tau_E$ from an experiment to a power plant.  The question
arises whether the original energy confinement time in the experiment, properly
scaled to the power plant parameters, would be sufficient to maintain ignition
with the given helium fraction in the plasma.

With this difficulty in mind, it is recommended that that ratio
$\tau_{He}^{*}/\tau_E$ be presented simultaneously with the value of
$\beta\tau_E/a^{2}_p$, which measures the energy confinement performance of the
plasma (see Sec.~\ref{s-5-2-3}).  Knowing the range of $\beta\tau_E/a^{2}_p$
values required for ignited plasma power balance would help to indicate how
well experiments are actually simulating the power plant situation.

The problem caused by non-helium impurities is the displacement of fuel ions by
the impurity ions and their associated electrons.  A reasonable measure for
this is simply $Z_{eff}$, and this should be minimized as much as possible.

The pumping and fueling figure of merit should represent the desire to remove
helium particles efficiently and not remove fuel particles.  A parameter
developed in power plant studies to reflect this is called the burn-up fraction,
and is given by
%
\begin{eqnarray}
f_{b} & = & \frac{2 \Gamma_{He}}{2 \Gamma_{He} + \Gamma_{i}}
\label{5-2-16}
\end{eqnarray}
%
and would take on the value of unity if only helium and no fuel were removed.
Here, $\Gamma_{He}$ and $\Gamma_i$ are the flux of He and \DT-fuel ions that
are removed from the plasma.

The general scheme for removing the helium ash is to use a pumped divertor,
where some fraction of the helium leaving the plasma core is pumped out of the
chamber. In this case, \hbox{$\Gamma_{He} = n_{He}^p S_{He}^{eff}$} and
\hbox{$\Gamma_{i} = n_{i}^pS_{i}^{eff}$}, where $S^{eff}$ is the effective
pumping speed (m$^3$/s), $n^p$ is the neutral particle density at the pump
aperture.

The balance for helium and fuel pumping can be approximately treated
separately, so that the burn-up fraction can be related to quantities measurable
in an experiment, as in
%
\begin{eqnarray}
f_{b} & = & \frac{ 2 \frac{n_{He}}{\tau_{He}^{\ast}}}
{2 \frac{n_{He}}{\tau_{He}^{\ast}} + \frac{n_{i}}{\tau_{i}^{\ast}} } \: .
\label{e-5-2-17}
\end{eqnarray}
%
Using Eq.~\ref{e-5-2-13} the above expression can be shown to be equivalent to
the standard definition of the burn-up fraction,
%
\begin{eqnarray}
f_{b} & = & \frac{1}{1 + \frac{2}{n_{i} \tau_{i}^{\ast} \langle \sigma
v \rangle }} \: .
\label{e-5-2-18}
\end{eqnarray}
%
Since this quantity is also known for power plant designs, comparisons
can be made directly with experiments, to ensure that the experimental
system is providing a scaled model of the reactor system.

Significant strides have been made recently in developing the database on
active particle removal experiments, notably on TEXTOR and DIII-D.  The first
substantial work on pumped discharges comes from TEXTOR~\cite{Hil90,Hil92}.
This device has eight separate limiters around the torus and each is equipped
with a turbomolecular pump.  Active pumping of the helium gas was clearly
demonstrated, and the measured $\tau_{He}^{*}/\tau_E$ values are in the range
of 10--30 in L-mode discharges.  The helium particle confinement time in the
core has been calculated, with $\tau_{He}/\tau_E$ reported to be in the range
1--2.  In ELM-free H-mode discharges, values of $\tau_{He}^{*}/\tau_E$ of about
70 were observed.  Also for these experiments, the exhaust efficiency
($1-R_{He}$) was found to increase with increasing plasma density.

A series of experiments on helium removal have been performed on DIII-D.
First, experiments with no helium pumping~\cite{Hil92} clearly showed that the
presence of ELMs enhanced the efflux of helium from the plasma edge.  More
recent data on DIII-D~\cite{Wad95}, using the argon frosted cryopump for
pumping helium that is gas puffed into the plasma chamber, indicates a
$\tau_{He}^{*}/\tau_E$ value of approximately 8, in ELMy H-modes.  It was later
shown that, with central helium fueling from a neutral beam,
$\tau_{He}^{*}/\tau_E$ of about 11 was achievable.  These experiments indicate
that control of helium in the plasma may be achieved even in H-mode discharges,
so long as ELMs are present, and represent the most power plant relevant
results to date.  In addition, helium transport studies~\cite{Wad95a} found
that the helium and electron density profiles were nearly identical, indicating
that helium accumulation is not taking place.  This was shown to be the case
for L-mode, H-mode, ELMy H-mode, and VH-mode confinement regimes.

The range of measured values for the helium-removal figure of merit on DIII-D
are shown in Fig.~\ref{sti-5-2-09}, as a function of $\beta\tau_E/a^{2}_p$.
Also shown are the contours for ignited power balance, where a power plant can
operate, at various volume-average temperatures.  These results correspond to a
reversed shear configuration with $A=4.0$, $R=5.6$~m, and $B_{T}=7$~T.  They
include profile effects, and indicate that one needs to achieve low
$\tau_{He}^{*}/\tau_E$ and high $\beta\tau_E/a^{2}_p$ simultaneously for fusion
power-plant operation.  Also displayed in Fig.~\ref{sti-5-2-09} are the five
Starlite power-plant candidates, for which $\tau_{He}^{*}/\tau_E=10$ has been
assumed, resulting in required $\beta\tau_E/a^{2}_p$ values ranging from 0.0078
for FS to 0.11 for LAR options.

\section{CONCEPT EVALUATION}
\label{s-5-3}

The five tokamak operating modes that have been evaluated by the Starlite
project are: (1)~a steady state, first stability regime (FS) similar to
\AI~\cite{Naj91}; (2)~a pulsed, first stability regime (PU) similar to
PULSAR~\cite{Najpu}; (3)~a steady state, second stability (SS) regime similar
to \AiiIV~\cite{Najss}; (4)~a steady state, reversed shear (RS)
mode~\cite{Kes94}; and (5)~a steady state, low aspect ratio
configuration~\cite{Pen95}.  Operating parameters for the five Starlite tokamak
power plant concepts under consideration are listed in Table~\ref{t-5-3-1} and
described in the following subsections.

\begin{table}
\caption{}
\centering{\bf Parameters for the Five Starlite Power Plant Candidates}
\vspace{1.0cm}
\renewcommand{\arraystretch} {1.2}
\begin{tabular}{l c c c c c } \hline
        &      FS   &    PU    &    RS    &    SS$^{(a)}$   &   LAR   \\
\hline
 & \hspace{1.2cm} & \hspace{1.2cm} & \hspace{1.2cm}
 & \hspace{1.2cm} & \hspace{1.2cm} \\
Plasma aspect ratio, $A=R/a_p$ & 4.0 & 4.0 & 4.0 & 4.0 & 1.25 \\
Major radius, $R$(m) & 7.96 & 8.68 & 5.04 & 6.40 & 5.00 \\
Plasma minor radius, $a_p$(m) & 1.99 & 2.17 & 1.26 & 1.60 & 4.00 \\
Plasma elongation, $\kappa_X$ & 1.81 & 1.80 & 1.99 & 2.03 & 3.40 \\
Plasma triangularity $\delta_X$ & 0.71 & 0.50 & 0.69 & 0.67 & 0.55 \\
Cylindrical safety factor $q_*$ & 3.77 & 2.40 & 2.37 & 4.60 & 3.54 \\
Central Safety factor,~$q_0$ &1.3&0.7&2.8&2.0&2.9 \\
Stability parameter, $\epsilon\beta_p$ & 0.54&0.32&0.56&1.22&1.14 \\
Normalized beta, $\beta_N(\%)$ & 2.88&2.70&4.76&5.28&6.42  \\
Beta parameter, $\beta/\epsilon(\%)$ &8.12&10.00&21.24&12.17&45.36 \\
Confinement ratio, $\tau_{He}^*/\tau_E$ &10.0&10.0&10.0&10.0&10.0 \\
Ignition parameter, $\beta\tau_E/a_p^2$(\%s/m$^2$)&0.78&2.18&4.17&1.35&11.05
\\
ITER-89P scaling multiplier, $H$ & 1.71&2.38 &2.40&2.47&3.02 \\
Normalized confinement multiplier, $H/q_*$ &0.45&0.99&1.01&0.54&0.85 \\
Plasma current, $I_p$(MA) &12.6&15.0&10.3&7.72&40.1 \\
Bootstrap-current fraction, $f_{BS}$ &0.57 & 0.34 & 0.89 &$>$1&0.997$^{(b)}$ \\
Current-drive efficiency, $\gamma_B(10^{20}$A/Wm$^2$) &0.56&NA&2.02&0.49&34.2 \\
Current-drive power to plasma (MW) &236.6&0&64.7&199.1&7.3 \\
On-axis toroidal field, $B_T$(T) &8.99&7.46&7.35&8.37&1.77 \\
Peak field at TF coil, $B_{TF}$(T) &16.0&13.1&15.7&15.9&14.8 \\
Normalized heat flux, $P_{tr}/R$(MW/m) &71.2&29.5&71.3&89.0&124.2 \\
Recirculating power fraction, $(1/Q_E)$ &0.29 & 0.06 &0.13&0.33&0.63 \\
COE (mill/kWh)&99.7&130.2&69.7&92.6&116.0 \\
\\
\hline
\multicolumn{6}{l}{$(a)$ This design is not optimized to the lowest COE.} \\
\multicolumn{6}{l}{$(b)$ Includes diamagnetic current.}
\end{tabular}
\label{t-5-3-1}
\end{table}

\subsection{First Stability [ARIES-I]}
\label{s-5-3-1}

The first-stability tokamak power plant concept (FS) is a modification of the
\AI~\cite{Naj91} design, but with the peak toroidal field at the coil lowered
from the \AI value of 21~T to a more practical value of 16~T.  Additionally,
the SiC-composite blanket and shield have been replaced with the same vanadium
blanket and shield as the other power plant candidates, for purposes of a
common-base comparison.  The normalized beta value is $\beta_N=2.88$, which we
calculate to be 10\% below the beta limit that is self-consistent with the
design pressure and current profiles.  The values of $q_{0}=1.3$ and
$q_{*}=3.77$ were determined by a tradeoff between high $\beta$ (and low $q$)
and high bootstrap fraction (and high $q$).  The design utilized relatively
modest shaping parameters of $\kappa_{X}=1.8$ and $\delta_{X}=0.7$ that allowed
passive stabilization of a double-null plasma with the stabilizer behind the
breeding blankets, and at the same time minimized the PF coil energy.  A
combination of ICRF fast wave and lower hybrid wave was used as the current
drive system.  The total current drive power required is high (237~MW) because
of the relatively low bootstrap fraction of 0.57.  The ignition parameter of
${\beta\tau_E}/{a_p^{2}}=0.79$ and the value of $ {H}/{q_*}=0.45$ are the most
modest of all the design concepts.

\subsection{Pulsed Operation [PULSAR]}
\label{s-5-3-2}

The pulsed-tokamak power plant concept (PU) is a modification of the
PULSAR~\cite{Najpu} design, with a reduced normalized beta value of
$\beta_N=2.70$, which we calculate to be 10\% below the beta limit.  The design
also uses the common vanadium blanket and shield design described in
Sec.~6. that represents a refinement over the original PULSAR blanket and
shield.  The current profile is calculated self-consistently from the
requirement that the plasma be in an ohmic stationary state with no external
current drive, and that the bootstrap current and plasma resistivity be
consistent with the pressure and the temperature profiles.  The design utilized
the same modest shaping of $\kappa_{X}=1.8$ and $\delta_{X}=0.5$ as did the FS
design.  The ignition parameter of $ {\beta\tau_E}/{a_p^{2}}=2.18$ and the
value of $H/q_*=0.99$ are significantly larger than those required for the
FS design.  The recirculating power fraction is very low since the design uses
only ohmic current drive which has very high efficiency.  The fact that the
tokamak is pulsed causes the design value of the peak field at the coil to be
18\% lower than for steady state designs (FS), and the fact that there is no
control over the current profile causes the $\beta_N$ to be 6\% lower.

\subsection{Second Stability [ARIES-II/IV]}
\label{s-5-3-3}

The second stability tokamak power plant concept (SS) is an updated version of
the \AII~\cite{Najss} design, where a more accurate bootstrap current
model~\cite{Kes94a} with full $\alpha$ pressure representation has been
applied.  As with the other options, the pressure is lowered to give a 10\%
margin against the MHD stability limit, and a refined vanadium blanket and
shield design has been used.  five power plant options.  The design has a
normalized beta value of $\beta_N=5.28$~(wall stabilized), but with very large
central and cylindrical safety-factor values of $q_{0}=2.0$ and $q_{*}=4.6$ in
order to obtain the high values of $\epsilon\beta_p$ needed for full second
stability access.  This design, which is not optimized with respect to the COE,
has a value of $ {\beta}/{\epsilon}=12$, only about 50\% higher than FS.  But
the bootstrap-current fraction, $f_{BS}$, exceeds unity, with the equilibrium
having a substantial bootstrap overdrive in the bulk plasma, and a plasma
current of $I_p=7.72$~MA, significantly enhancing the recirculating power over
that of \AII.  The ignition parameter of $ {\beta\tau_E}/{a_p^{2}}=1.35$ and
the value of $H/q_*=0.54$ are larger than for the FS design, but still
within the existing tokamak data base.  The design uses a combination of ICRF
fast-wave current drive to provide the seed current on axis and lower-hybrid
current drive to offset the overdriven bootstrap current in the bulk plasma
region and to tailor the current profile near the edge.

\subsection{Reversed Shear}
\label{s-5-3-4}

The reversed shear tokamak power plant concept (RS) grew out of analysis
performed for the TPX program~\cite{Kes94}.  Its combination of a current
profile peaked off axis and a peaked pressure profile leads to a
self-consistent design with a normalized beta value of $\beta_N=4.76$~(wall
stabilized), and to a value of ${\beta}/{\epsilon}=21.2$, over twice as large
as FS, but also to a value of the bootstrap-current fraction of $f_{BS}=0.89$,
leading to a very low recirculating power fraction.  The ignition parameter of
${\beta\tau_E}/{a_p^{2}}=4.17$ and the value of $H/q_*=1.01$ are larger
than for the FS design, but probably justified in light of the recent
experimental results~\cite{Lev95,Str95} showing greatly reduced transport in
the reversed shear configuration.

\subsection{Low-Aspect-Ratio}
\label{s-5-3-5}

The low-aspect-ratio tokamak~\cite{Pen95} (LAR) differs from the others in that
the TF coils are made of normal-conducting copper rather than superconducting,
and that there are no OH coils on the inboard side.  Little or no shielding is
provided on the inboard side of the tokamak in order to attain very low aspect
ratios.  Detailed MHD stability calculations show that it is possible to find
stable equilibria at very low aspect ratios with high values of the normalized
beta which simultaneously allows for high beta and high bootstrap fraction.
The reference LAR design has an aspect ratio of $A=1.25$, a normalized beta
value of $\beta_N=6.42$~(wall stabilized), and a value of
${\beta}/{\epsilon}=45.4$, significantly larger than the other designs.  The
bootstrap current density profile is well aligned with the equilibrium current
profile over most of the plasma cross section, so that the pressure-driven
current (bootstrap+diamagnetic) is calculated to be 99.7\% of the plasma
current, the seed current being located near the magnetic axis.  As a result,
the current-drive power requirement of 7.3~MW (low-frequency fast wave) is the
lowest among the steady state candidates.  One caveat of this result could be
that the current-drive power is extremely sensitive to variations in the plasma
profiles.  The ignition parameter of ${\beta\tau_E}/{a_p^{2}}=11.1$ and the
value of $\gamma_{B}=34.2$ are largest of the five concepts but since there is
so little data available for the Low-A configuration, it is impossible to
determine how credible this is.  The large amount of power dissipated by the
copper coils leads to a very large recirculating power fraction.

\section{Starlite Reference Design}
\label{s-5-3-6}

Five Starlite power plant designs based on five distinct operating modes have
been analyzed by the systems code, using a common basis of economics and
engineering assumptions.  The results of these analyses in terms of the design
physics FOM and COE values for the five candidates have been presented in
Table~\ref{t-5-3-1} for comparison.  The ARIES systems code is used to estimate
the cost of electricity (COE) values for these options using the same economic
assumptions~\cite{Bat95}.  The blanket and shield design used for all five
power plant candidates is a refinement of the \AII vanadium blanket and
shield, and is described in Sec.~6.

Except for the second stability (SS) option, each of the concepts corresponds
to a self-consistent power plant design (at the level of systems code)
optimized to its unique set of design choices. While the absolute values for
the COE reflect a high degree of uncertainty in material costs and the fact
that each design is not completely optimized through a rigorous design study,
we believe that the relative rankings of the five concepts are accurate given
present understanding and data base.

The first-stability options, steady0state (FS) and pulsed-plasma (PU) require
relatively modest extrapolations in physics parameters from the present
database.  The pulsed-plasma tokamak is the most expensive and appear to be
unattractive as a power plant.  The COE for the FS design is higher than the
requirements established for the Starlite designs (Sec.~2). Most probably this
design requires the use of high-field magnets and advanced SiC-composite
blankets (to achieve a high level of safety) to become attractive.

The low-aspect ratio tokamak is furthest from the experimental data base,
practically in all the critical physics areas.  (However, this is somewhat
mitigated by the recent theoretical analysis that shows that its operating
point may in fact be achievable.)  It is also the second least economical
(after PU) of the five concepts with a COE value of 116~mills/kWh.  These
findings, together with the rather modest parameter ranges for present and
planned LAR experiments~\cite{Syk95}, and a number of high-leverage but yet
unresolved engineering issues (see Sec.~8), precludes the LAR concept from our
present consideration for the reference Starlite power plant.  Nevertheless,
this design is the least developed of Starlite candidates and the power plant
potential of the LAR concept is sufficiently high as to warrant further
investigation and, perhaps, a future full-scale evaluation.

Of the remaining candidates, the reversed-shear concept is the most attractive
in terms of economics, having a COE of $\sim$70~mills/kWh, that is
significantly lower than those of the rest.  The second-stability option is
second in terms of economics.  There is reason to believe that the
second-stability equilibrium could be better optimized to better align the
bootstrap current with the equilibrium current, and thus further minimize the
required external current drive.  However, even so, it is believed that the
projected COE values for the SS power plant will not fall below
80--90~mills/kWh.  Also there is theoretical concern that the second-stability
configuration may be difficult to maintain in practice, since a lowering of the
pressure gradient locally would cause an instability region to develop and
propagate, thus making it configurationally unstable. Lastly, the is not
experimental data for this concept.

Overall, the Starlite team concluded that the reversed-shear plasma offer the
combination of sound economic potential and a growing experimental data base as
many key aspects of the reversed-shear concept have already been demonstrated
in several devices ({\it e.g.,} TFTR, DIII-D, JET, and Tore Supra).

\section{SUMMARY AND CONCLUSIONS}
\label{s-5-4}

Physics performance assessments have been carried out, in conjunction with
systems analyses, in order to select the best realizable and economically
attractive fusion power plant design among five different options.  These
candidates include tokamak operating modes similar to \AI, \AiiIV, PULSAR, the
reversed shear mode, and the low-aspect-ratio magnetic configuration, and are
labeled FS, SS, PU, RS and LAR, respectively.

To facilitate the physics analysis, plasma performance parameters, or figures
of merit (FOM), in five critical physics areas have been identified with the
intent to keep track of progress in achieving the required performance levels
for the power plant.  The five physics areas of interest are MHD stability,
current drive, heat exhaust, energy confinement and helium ash removal.  To be
inclusive of the five operating mode candidates, attempt has been made to
select the FOMs based on fundamental performance quantities that are measurable
in experiments and that are independent of plasma size and machine parameters.
The identified figures of merit are given as follows:
\begin{itemize}
\item {\bf MHD Stability:}
\begin{itemize}
\item Power density parameter: $\beta/\epsilon$
\item Stability parameter: $\epsilon\beta_p$
\end{itemize}
\item {\bf Current Drive:}
\begin{itemize}
\item Normalized current-drive efficiency: $\gamma_{B}\equiv
 \overline{n}_{e}I_pR/P_{CD}$
\end{itemize}
\item {\bf Energy Confinement:}
\begin{itemize}
\item Ignition parameter: $\beta\tau_E/a^{2}_p$
\item Power density parameter: $\beta/\epsilon$
\end{itemize}
\item {\bf Heat Exhaust:}
\begin{itemize}
\item Normalized heat flux: $P_{tr}/R$
\item Total radiation fraction: $f_{rad}$
\end{itemize}
\item {\bf Helium ash removal:}
\begin{itemize}
\item Particle confinement parameter: $\tau_{He}^{*}/\tau_E$
\item Ignition parameter: $\beta\tau_E/a^{2}_p$
\item Effective charge: $Z_{eff}$
\item Helium burn-up fraction: $f_{b}$
\end{itemize}
\end{itemize}

In Sec.~\ref{s-5-2} values for these figures of merit in the five critical
physics areas that were measured in experiments are plotted along with the
design values for the five Starlite power plant options.  Based on the results
displayed in these figures, it is clear that the FS and PU power plant options
have physics performance parameters that are closest to the existing database.
On the other hand, the LAR concept demands the largest physics performance
extrapolations from the most recent data obtained in machines operating in this
mode.  Taking into account the projected COEs for the five power plant options
as given in Table~\ref{t-5-3-1}, we conclude that the RS and SS modes of
operation are the most attractive among the candidates, because they have the
lowest COEs.  Among these two options, the reversed shear concept presently
emerges as the best choice for the reference power plant design.  This is
because it is economically superior, is significantly closer to having been
experimentally prototyped in each of the key tokamak physics areas than the
second stability concept, and therefore has the least uncertainty in achieving
the required values of all of the physics parameters at a reasonable
cost.

Having chosen the reversed-shear concept as the basis for the Starlite
reference power plant design, it is useful to identify physics areas in which
to focus present and future research efforts towards realizing this goal.  We
first note that the experimental data that are used in this study are taken
entirely from L-mode and H-mode discharges, without the use of any profile
tailoring.  Thus, a systematic development and collection of database for
reversed shear discharges on large high-power devices are in order, including
all five aforementioned critical physics areas.  From a broader perspective, it
is also clear that the existing tokamak database does not contain discharges
that simultaneously achieve values of all the physics FOM parameters
needed to make an attractive fusion power plant.  This highlights the need for
continued physics research aimed at concept improvement, in particular in
developing modes of tokamak operation that prototype power plant values of each
of the FOMs identified.  Finally, we emphasize the need to develop experimental
database in long pulse or steady state discharges with the use of current drive
and profile control in fusion relevant regimes.

\clearpage

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\end{thebibliography}

\end{document}






Here the total plasma density is defined by $n_{o}=n_e + n_{i} +
n_{He}$ and impurities are ignored until later.  In addition,
quasineutrality
requires that $n_e=n_{i} + 2 n_{He}$, and we assume a 50-50 mixture
of deuterium and tritium for the present discussion.
Profile effects are not included in this discussion.

The general scheme for removing the helium ash is to use a pumped divertor,
where some fraction of the helium leaving the plasma core is pumped
out of the chamber.  The amount of helium that must be pumped with
the divertor is given by
\begin{eqnarray}
\Gamma_{He} = \left( \frac{V_{c} n_{He}}{\tau_{He}} \right)
\left( 1 - R_{He} \right)
\label{eq-5b}
\end{eqnarray}
where $V_{c}$ is the core plasma volume, and the first term in
parentheses is the helium flow from the core plasma into the SOL
and divertor.  The second term is the fraction of the helium that
is actually pumped out of the chamber.
In steady state, the product of these two terms is equal
to the helium production rate from fusion reactions in the core plasma.

The divertor pumping requirement is given by
\begin{eqnarray}
n_{He}^p S_{He}^{eff}+n_{i}^pS_{i}^{eff} = \Gamma_{He} + \Gamma_{i}
\label{eq-5c}
\end{eqnarray}
where $S^{eff}$ is the effective pumping speed (m$^{3}$/sec), $n^p$
is the neutral particle density at the pump aperture, and $\Gamma_{i}$
is the amount of fuel ions that are pumped and is defined the same
way as Eq.~\ref{eq-5b}.
Note that the divertor
pumps both helium and fuel particles simultaneously, the
amount of each being determined by their densities at the pump aperture.
Directly related to this particle removal is particle fueling, in order
to maintain a fixed fuel ion density in the plasma core,
\begin{eqnarray}
\Gamma_{fuel} = 2 \Gamma_{He} + \Gamma_{i}
\label{eq-5d}
\end{eqnarray}
Recycling large amounts of DT fuel compounds the requirements on the fueling system.
In addition, if the ratio of the helium to the fuel particle densities
at the pump aperture could be made larger than the ratio of helium to
fuel ion densities in the core plasma, then helium removal would be
more efficient.