ENERGY
CONFINEMENT
IN
ALCATOR
A.Gondhalekar, D.Overskei, R.Parker and J.West
PFC/RR-78-15
December 1978
Francis Bitter National Magnet Laboratory and
Plasma Fusion Center,
Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139
ENERGY CONFINEMENT IN ALCATOR
A.Gondhalekar, D.Overskei, R.Parker and J.West
Francis Bitter National Magnet Laboratory and Plasma Fusion Center
Massachusetts Institute of Technology, Cambridge, MA.02139.
ABSTRACT
Stable discharges
obtained
in
with
deuterium
at
peak
fe =1.5xlQ 1 5am- 3 have
density
BT =8.7T
in the Alcator tokamak.
been
Complete
thermal equilibration between electrons and ions is observed, with
temperatures of 900eV.
Nearly
confinement,
classical
is
The maximum value of fiTE
behaviour,
observed.
At
from
the
densities
is
suppressed,
the
viewpoint
highest
densities,
and
the
dominant
confinement can be attributed to neoclassical
.
is 3x1013cm-3.s.
attained where the anomalous electron thermal conductivity
lower
peak
ion
of
a
energy
regime is
observed
role
thermal
in
at
energy
conduction.
The anomalous electron thermal conduction varies inversely with density.
The observed ion thermal conductivity is neoclassical at high density,
but seems to be somewhat greater at density less than 2x10 cm 3
Dependence of energy confinement on B
constant
observed.
fi and
IP,
is also investigated.
With
no significant effect of increasing BT on tE
However, the highest achievable density and TE
is
increase with
B T.
Stable operation
achieved.
Energy
improvement in TE
of
high
confinement
current,
low
qL discharges
has
been
for such discharges is described.
Some
is observed at high current.
PAGE 2
I
INTRODUCTION
An essential advance in
experimental
years has been in the ability
moderate temperatures. The plasma
tokamak
physics
in
recent
to obtain high density plasmas with
density now attainable is 10-100
times larger than that
higher densities has been
possible only a few years ago. Operation at
accompanied by substantial improvement in
energy confinement. The high density regime first observed in Alcator
has since been attained in many other tokamaks. Although it is not yet
clear
what factors favour the ability to obtain high d4nsity, available
heating power would seem to be one of the more important'ones. Tokamaks
with low impurity content and high toroidal magnetic field and hence
high ohmic heating power density have, therefore, yielded the highest
density
and relatively high values for energy confinement. In Alcator,
the maximum peak density, ', so far achieved is 1.5xl0 15cm
ith an
energy confinement time TE = 20ms., giving ATE = 3x10 1 3 cm- 3 .s at peak
electron and ion temperatures of 900eV.
A description of the Alcator tokamak has been given elsewhere[l].
It is a device with major radius R=54cm and limiter radius aL=10cm. The
unique capability of Alcator to operate over a wide range of parameters,
with toroidal field 3T .<BT ,9T, plasma current 80kA (I (300kA, and line
averaged density 5x10 1 2cm- 3 <f, <7.5x10 1 4 cm- 3 , has enabled study of the
dependence of energy confinement on these parameters. The advantages of
high density operation have been discussed previously[2,3].
In this
paper, further elucidation of this behaviour is given. We show that the
higher density discharges can be
understood
as determined
by
neoclassical ion thermal conduction in the central core, whereas at
lower densities anomalous electron thermal conduction dominates. A
preliminary account of these observations has been given earlier[4,5,61.
High density discharges are obtained by neutral gas injection into
the plasma.
Equilibrium is first established in a low density plasma
with fi~ 3x10 1 3cm- 3 . Neutral gas is then injected at the edge of the
plasma through a programmable fast valve, bringing the density to the
desired value[3].
Energy confinement studies discussed here were
PAGE 3
under
performed
entails
roughly
This
the
and
fields
equilibrium
various
the
adjusting
performance.
optimum
give
to
invested in 'tuning' the machine
was
effort
Much
conditions.
discharge
stationary
temporal behaviour of density and plasma current until the lowest plasma
resistance is observed for the required values of BT, I, and fie. Thus
due
radiative power loss
reported
data
toroidal
A brief description of the influence of
density is described.
field
the
for
minimised
In section III the dependence of energy confinement on
here.
magnetic
is
impurities
to
and
on energy confinement is given in
current
plasma
high
sections IV and V. Other aspects of
qL discharges
low
current,
have been discussed elsewbere[7d.
II
PLASMA REGIMES
7.2x10 1 4
fe =
with
m-
3 .
6~e =
density
Peak
obtained
discharges
density
Fig.1 illustrates one of the highest
1.5x10 1 5cm- 3 ,
and
Loop voltage VR, plasma current
temperatures Te
= 900eV were observed.
Ip and
ffe were maintained constant within 10% for 100ms.
density
peak
Peak
density of greater than 1015cm-3 was maintained for about 150ms.
The experiments described in
out
carried
5x10
1 3 cm-3
electron
in
4 ,6xl0
deuterium
14
temperature,
the
with
m-3. Fig.2
of
BT = 6T,
l30kA.,Ip <160kA
shows
typical
were
paper
this
remainder
and
profiles
radial
of
and electron density, ne(r), measured by
Te(r),
Thomson scattering of ruby laser radiation.
The
temperature
electron
profile is best described by
T (r) = Te exp(-r2/a4)
factor,
The radial profiles of current density, j(r), and safety
are determined in the usual way by assuming j (r)
and wall conditions in Alcator
permit
plasmas
cc3/2
Te (r).
to
be
q(r),
Clean vacuum
produced
resistivity is nearly equal to the calculated classical value.
whose
Thus the
effective ion charge in the plasma, Zeff , is close to unity.
For discharges studied here, we find
axis,
o ,
always
assumes
a
that
the
safety
minimum value, 0.85 <q 0,l.
factor
on
This is in
U
PAGE 4
agreement with deductions made from sawtooth X-ray emission
With
the
profile
3 2
2
a qL
r qO.
smaller
above and Zeff(r)~ 1, it is easily shown that
rC is the radius of the current
than
9.5cm<r
given
aL due
<aL=10cm.
signals[8].
to
displacement
qL is
the
of
safety
channel
which
can
the plasma column;
factor
at
be
usually
the
limiter.
Empirically, a qL ~ 120 cm 2.is measured in Alcator.
Furthermore, assuming that the induced toroidal electric
constant
across
the
field
is
plasma cross-section, E(r)=constant=VR/27rR, it is
easily shown, with Spitzer-Hgrm resistivity, that for a deuterium plasma
22/3
Te ~ 4 x 10 (BT - zeff/vR
BT
eV
q )
is in tesla and the the loop-voltage VR
is in Volts.
Measurements
of electron temperature under a large variety of plasma conditions bear
out these relationships with Zeffl and 0.85 <,qo l.
This confirms,
albeit
only
for
clean plasmas, an early intuition[9] that to know the
temperature and its distribution in an ohmically heated tokamak plasma,
one
need
measure
only
the
loop voltage, plasma current and toroidal
magnetic field.
The density profile is best described by
ne(r)
The value of a
here,
with
=
e 11-r2/a2
depends on
the
density.
For
BT =6T, Ip ~ 150kA, the value of a
linearly from 0.75 at f~ 1014 c
relationship
C
between
q (or IP/BT) and a
a
above.
and
3
experiments
considered
increases approximately
to 2.0 at fe =6x10 1 4cm-
3.
No
simple
ffe could be established as in the case of
The value of a
will depend in a complicated
way
on the mechanism of gas ingestion at the plasma edge, and transport
of plasma to the center of the discharge, processes which are not
understood at present.
During gas injection, the electron density
evolves
without
profile [2].
significant
inversion,
(dn/dr>,0),
in
the
radial
This would seem to exclude certain models of plasma density
build-up in which transport of plasma to the center of the column is
sustained by instability induced by unfavourable gradients of plasma
PAGE 5
density.
It has been postulated that the neoclassical pinch might operate in
Alcator to transport plasma formed at the edge of the column to the
center against the density gradient[10I.
is
strong only when Vse <8.
The neoclassical pinch
Near the edge,
effect is correspondingly weak.
effect
v *, is large and the pinch
However, the
small
density
inversion
observed at the edge[2] may cause rapid transport across the edge region
7cm 4r <,10cm.
plasma
to
At r<7cm,
the
the
interior.
pinch
effect
will
efficiently
convect
Fig.3 shows the radial variation of v*e
low and high density discharges.
As density increases
and
the
for
plasma
becomes more collisional, the pinch effect weakens and eventually stops.
This could be the origin of the 'density limit' observed experimentally.
In Alcator, at given B
and I, , density can be increased until
Attempts to increase the density further by
of additional neutral gas at the edge cause disruption. The
V*e (minimum).c 8-10.
injection
density can be increased by raising ET and I,
increasing
the
temperature
and
This has the effect of
.
reducing v*
Density can then be
.
increased until again v *
(minimum) = 8-10. In discharges where Y'e is
maintained at a constant value, the ratio A
n e/ Ife, and hence the value of
a,
are observed to increase continuously, indicating steady convection
of plasma to the center.
All these observations can be accounted for in
a semi-cruantitative way by model
computations
using
the
neoclassical
pinch [10].
Measurements of peak
charge-exchanged
discharges
yield[3,11].
in
neutral
ion
temperature
deuterium,
particles
also
are
emitted
by
using
made
from
the
by
analysis
of
the plasma, and for
thermonuclear
neutron
Ion temperatures so determined are consistent with
J
0H = E
2
3
i(Te
-
Wei
fe
is the electron-ion equilibration time at plasma center, POH is the
peak ohmic power input.
This relation gives the maximum temperature
difference that
can
be
sustained
by
the
available
heating
power.
PAGE 6
Measurements
indicate
peak ion temperatures typically only about 100eV
less than the corresponding electron temperature at high
density.
The
variation of peak electron and ion temperatures with density is shown in
Fig.4[l1.In the following, the ion temperature profile is assumed to be
of the same shape as the electron temperature profile.
A rough characterization of the plasma regimes realized in
under
these
conditions
can
dimensionless parameters:
be
the
obtained
from
collisionality
the values of various
parameter
particles, v* =21/ Z(gVth) (R/r)' , the
collisionality
transit
the
particles, v*
<E >=<vdrift vtherma>,
v(gR/Vth),
=
and
Alcator
for
trapped
parameter
streaming
for
parameter,
the ratio of the applied electric field to
the critical run-away field, <E/E
of V
,
v
>.
Fig.3 shows the radial variation
CR
, and the safety factor q. The plasma can be characterized
as being predominantly in the plateau
regime
of
neoclassical
theory,
verging on the Pfirsch-Schlter regime.
III
DENSITY DEPENDENCE OF ENERGY CONFINEMENT
A study of the variation of energy confinement
with
density,
at
constant
toroidal magnetic field B
current, 130kA<Ip,<160kA, has been
closely
and
made
in
order
to
power
=6T, and plasma
ascertain
energy
confinement approaches neoclassical values.
energy confinement time is defined as
aL
=
TE(EX)
VR
VR
(niTi + neTe)2nrdr/
27TR
balance
how
The global
IPVR
is the resistive part of the loop-voltage induced around the torus.
is determined from the measured total loop-voltage VL, corrected for
the time variation of poloidal flux between the plasma and the voltage
loops, where the mutual inductance involved has been measured directly.
Fig.5
density,
falling
illustrates
showing
electron
understood
as
due
a
the
gradual
temperature
to
variation
of
the
induced
voltage
with
increase in VR, corresponding to steadily
as
increased
density
increases.
This
may
be
power transfer to the ions and their
steadily growing role in energy loss.
The variation with density of the
PAGE 7
experimentally
Fig.6.
determined
energy
confinement time TE (EX) is shown in
We observe that T E (EX) increases
approximately
linearly with
- e at constant B
TPEand I . The curve labelled TE (NC) in Fig.6 gives
the value of the energy confinement time if neoclassical ion thermal
conduction
were
the
dominant
conditions identical to
those
energy
in
the
loss
experiment.
NC
energy confinement time at each point, TE
for
The
plasma
neoclassical
(r), is calculated from
(n T
27r
f
NC~r)
mechanism,
+ neTe )dr'
2 7rrQNC
N (r)
Q
r) is the heat flux
due
to
neoclassical
ion
thermal
conduction.
NC
'rE (NC) is then the value of TE (r),
0 4r <0.7aL.
Neoclassical coefficients
Hinton[12]
are
used
in
these
line averaged over a region
given
by
Hazeltine
and
computations.
within a factor of 1.4 of the neoclassical
highest
density.
Comparison
between
Energy confinement time
value
the
two
is
observed
at
the
curves shows that the
plasma is afflicted with anomalous energy loss at low density, and that
this loss is reduced as density increases in Alcator. This excess
energy loss is attributed to anomalous radial electron heat
We
show
later
that
the
anomalous
electron
heat
conduction.
conductivity
is
suppressed as density increases.
$p
Fig.7 shows the variation of poloidal-beta,
is defined as
density
fe-
is the ratio of the plasma kinetic pressure and the pressure of
the
p = 8w < n
p
p , with
poloidal
magnetic field Bp.
+ n T
T
>/B2
The maximum value of $P is also in accord
with neoclassical estimates.
The linear dependence of the energy confinement tine on ne
a
unique
way
of
dependence of TE
between
the
two
representing
the
variation of T E
on the streaming parameter < E>.
may
be
deduced.
Wobig [13]
not
Fig.8 shows the
Strong
has
is
shown
correlation
that
this
PAGE 8
representation may be more generally applicable when comparing different
tokamaks
with
each
other,
or
with stellarators.
Energy confinement
properties of stellarators have thus been attributed to
relatively
low
Fig.9 shows the same data, indicating the dependence of TE on
the
current density in these devices[13].
collisionality
parameter
for
trapped electrons, <v
04r O0.6 aL. Again, strong correlation
between
>, averaged over
and
TE
<v*e>
may
be
deduced.
Each of these dependences implies a different mechanism for
energy
loss.
It should be emphasised that it is not possible to vary Re, < >
or <V*e > independently of the other two, and therefore it is not
possible
to
theories
that
However,
the
choose
between
purport
data
to
is
the many possiblities.
be
not
able
accurate
to
explain
or
There are several
these
observations.
complete enough, nor are the
theories definite enough in their forecasts to be falsifiable
with 'the
aid of available data.
Radial electron heat conduction has long
been
identified
major anomalous energy loss mechanism in tokamaks[14].
as
the
It has also been
known that small perturbations of the confining magnetic field cause the
rapid electron heat conduction along such a field to thermally connect
the
interior
of
the
limiter [15,16,17].
plasma
Such
astrophysical plasmas[18].
a
tokamak
has
column
situations
to
an
exterior
wall
are familiar in the literature on
The subject of anomalous heat conduction
recently
received
or
renewed
and
more
in
sophisticated
treatment[19,30].Experimental verification of magnetic field fluctuations
as
the
cause
of
anomalous radial heat conduction in Alcator has also
been claimed[20].
Power balance in the central core of the plasma is next examined.
Energy confinement time at the plasma center, TEo , is defined as
TE
=
-
(n Ti
2'1
+ neTe)/E-jo
Here, the peak densities ne,i, peak electron and ion temperatures 'i'e and
Ti, are directly determined. The peak current density, jo, is deduced
I
PAGE 9
from 'i'e by
toroidal
assuming
electric
The value of
the
jo
electron
Spitzer-Harm
and
the
induced
E is uniform across the plasma cross-section.
is consistent with the current distribution deduced from
profile.
It
is
also
Fig.10 shows the variation of T
at constant B
that
field
temperature
0.85 <qo <I.
resistivity
and IP.
in
agreement
with the peak
with
density,
TEo
does not increase linearly with density but
seems to saturate. This variation of T
at high density, akin to the
neoclassical, indicates that the core of the plasma column may be
dominated by neoclassical losses.
Since, at high density, most of the energy
core
seems
to
be
transport
out
of
the
attributable to ion heat conduction, the ohmic heat
input may be put equal to the neoclassical ion conduction loss and the
ion temperature and its distribution computed and compared to the
experimental value. We thus have
QOH W
r
OH/2,r = f2Tr'E-j(r')dr'/2?r
=
0
We then put, for r <5cm
6 QNC (r) = QOH(r)
Two model
ion temperature profiles were
NC
expression for Q1 (r).
They were of the form
substituted
into
the
T (r) = Za r2n, n=0,1,2,3
and
T (r) = a1 exp(-a 2 r )
Both models give the same peak temperature, which is in agreement with
the measured value[3,11].
Fig.ll shows the result of the calculation
using the gaussian model. The effects of possible departures of the ion
thermal
conductivity
from
neoclassical
are also included.
The upper
dotted curve in Fig.l1 shows the result with an anomaly factor, 6 , of
unity(ion thermal conduction equal to the neoclassical). The error-bar
PAGE 10
at the peak indicates the uncertainity in the calculation. We see
within
the
accuracy
of
the
calculation,
the
that
experimental peak ion
temperature can be accounted for by an ion thermal conductivity equal to
the
neoclassical.
In
the
factor of 1.5 is employed;
multiplied
by
a
factor
lower
i.e.
of
dotted
the
1.5
curve in Fig.l1, an anomaly
neoclassical
everywhere.
ion
The
heat
deduced
flux
is
peak ion
temperature is then well short of the measured, implying that for
these
plasma conditions an anomaly, if any, in the ion thermal conductivity is
less than 1.5 of neoclassical.
This agreement confirms the
of
role in energy loss, at high density, to
attributing
the
dominant
neoclassical ion thermal conduction.
with
As
expected,
gross
correctness
disagreement
measurement is obtained when the above procedure is applied to low
density discharges, as shown in Fig.12, demonstrating the existence,
low
density,
at
of a dominant energy loss process other than neoclassical
ion thermal conduction.
Radial fluxes for r
4(0.5aL may
be
deduced
from
the
experimental
values of ne(r), Te(r) and Ti(r), neglecting losses due to radiation and
At plasma densities nie>/ 2x1 4 cm
charge-exchange.
of
3
, the
central
core
the
plasma is opaque to neutral particles of energy less than lkeV.
Charge-exchange losses for such plasmas are important only for the
region r>5cm.
Spatially and temporally resolved bolometric measurements
of radiative and charge-exchange losses[21] show
machine
conditions
involved
in
that
for
plasma
and
the studies reported here, neglecting
these losses does not significantly affect calculation of power
balance
in the central core of the plasma, defined as the region 0 ,r <5cm.
The equilibration power transferred from the electrons to the ions,
Pei(r), is set equal to the power transported by the ions, P (r),
r
P.(r)
=
P ,(r)
=
f2r'[
n.(T
- T.)/T
]dr'
0.
Tj is the electron-ion equilibration time[22].
then
EX
Q.
r
P (r) /2rr
The ion
heat
flux
is
PAGE 11
EX
The ion thermal diffusivity X.
EX
(r), is determined from
EX
(r) = -x
Q1
(r)- n (r)-VT (r)
The power transported by the electrons, Pe(r), is then given by
r
e(r) = POH(r) - P .(r) =f27rr'E-J(r')
- P
dr'
(r)
EX
The electron heat flux, Qe (r), and
X Er)
are
determined
the
electron
thermal
Re>3x
as
for
the
experimental determination of
Pei
is
difference
and ion temperatures.
between
electron
ions.
At
uncertain
uncertainties in the calculated heat fluxes
at
owing
diffusivity
1 4cm-3
to
the
the
small
This gives rise to
high
density.
Fig.13
shows the ratios of the experimentally determined electron heat flux and
the
neoclassical
electron
heat
flux
at
'He=1.4x10 4cm- 3 and
4
he =5.5x10O c-3.
We observe that at low density, the
electron
heat
flux
is
200
times larger than the neoclassical, as seen in other tokamaks[23]. When
radiative and charge-exchange losses are properly included, this factor
of 200 might be reduced to 100-150. As density increases in Alcator,
this
anomaly
ne>5x10 14
in
m- 3 it
the
electron
heat
flux
diminishes,
until
at
is at most ten times larger than the neoclassical loss
by the electrons.
Lastly, knowing the ion
and
electron
heat
fluxes,
EX
QEX
Q X(r) and QE (r) respectively, the ion and electron heat diffusivities
may be computed and compared to the neoclassical values.
Fig.14 shows
EX
EX
the variation of X
and Xe , averaged over 3cm 4r <5cm, with density
ne- The corresponding neoclassical heat diffusivities, XiIC
and Xe
EX
are
also
shown.
We
see
that Xe
c l1/f and again that at
NC
14
-3
e =5.5xlO cm
the ions, XE
at fie
2 xlO 14
EX
-3
cm-
)EX
were x.
1
TFR
e
NC
EX
, Xe 4lOXe whereas at He =10 cm , Xe > XNC. For
X
for nfe>/ 3xl014m3, but shows an unfavourable trend
tokamak[24].
We
_
1-2xNC , as previously
conclude
i
from
this
study
suspected
that
in
the
as density is
increased in Alcator, a gradual transition from the anomalous electron
thermal conduction regime to the neoclassical ion thermal conduction
regime takes place in the central core of the plasma.
PAGE 12
IV
TOROIDAL MAGNETIC FIELD DEPENDENCE OF ENERGY CONFINEMENT
The dependence of
n
B
and
e
I
=3 .5T
P
constant
and B
obvious
=7 .7T
differences
TE
on
BT
and
varying B
has
in deuterium at n
with
small
Measured profiles of electron
shown
Fig.15.
the
peak
The
density
with
Te
(B/VR)
temperature
keeping
cm- 3 and I =115kA.
electron
and
density
temperature,
2
discharges
sawtooth
profiles
temperature profile narrows when B
2/3
~ 2x10
Both
emission.
However,
by
No
were observed in the macroscopic properties of the
characteristics,
in
investigated
Experiments were conducted with
T'
plasma, such as Zef f or MHD activity.
temporal
been
in
Te,
is increased.
aT aIP/BT as
discussed
showed
similar
fluctuations on X-ray
and
temperature
are
both cases are similar.
increases
and
the
This is in accordance
earlier.
also shows similar dependence on BT [11].
The
ion
The total energy
content is nearly the same for the two discharges, and since the power
input is also nearly equal, the energy confinement time, TE ~ 9ms,
remains unchanged when BT is increased.
Fig.16 shows more data along these lines.
The plasma conditions
were not as uniform as in the example just given. The data reenforces
the observation that at fixed density the energy confinement is not
affected
by
the toroidal magnetic field, as shown by the dotted lines.
However, the highest density, and therefore the maximum attainable
energy
confinement,
Fig.16.
increase
with
B , as shown by the solid line in
This seems to be the chief merit of an ohmically heated high
field tokamak.
The physical understanding of this result is as follows:
At constant density and plasma current,
increasing
B
has
an
T
insiqnificant effect on T
because although the peak energy density
increases with B , the temperature profile narrows so that the average
energy density remains the same as that at lower B . With larger B ,
the facility for higher plasma current density and consequently ohmic
input power density increases.
obtained.
This permits higher plasma density to be
Since energy confinement improves with density, the maximum
achievable energy confinement time also increases with B .
PAGE 13
V
PLASMA CURRENT DEPENDENCE OF ENERGY CONFINEMENT
For the successful operation of a self-sustaining controlled fusion
device, it is essential to efficiently confine and equilibrate the high
energy charged particle products of a fusion reaction.
of "boot-strap" heating
of
the plasma.
This requirement for efficient
confinement of high energy charged particles applies
auxiliary
plasma
This is a means
also
heating methods in use at present.
to
all
the
In a tokamak, the
confinement of high energy charged particles is achieved with the aid of
the poloidal magnetic field.
Thus, it is important to be able to
operate a tokamak with the largest possible plasma current compatible
with
MHD
stability
and
favourable
energy confinement.
these requirements have been thought to be incompatible.
made
the
plasma
In the past,
Large currents
more susceptible to severe MHD activity which in turn
degraded energy confinemrent[25,26).
In
keeping
with
this
thinking,
1/2
energy confinement was belived to depend on (B IP)
in Alcator[2].
We
have sought to reexamine this dependence with more accurate and complete
diagnostics,
and
technical
improvements
which
permit
us
a
larger
latitude in available density, plasma current and of course the toroidal
field.
The
section.
plasma
dependence
of
T.
Eon
Here, we present studies
current.
PT was
discussed
T
of
the
behaviour
in the previous
of
T
E
at
high
Stable discharges with qL=1.9 have been obtained, but
not enough to study systematically.
The high current, low q
investigated were in deuterium, with BT =6T, 2x104
215kA 4I, <235kA and 2 . 4 .<qL2. 6 .
At constant
discharges
-3
fie5xlO 4m-3I
BT the temperature
profile is much wider for the high current discharges than for the lower
2
current
ones,
temperature
again
rises
by
similar increase[ll].
densities
are
according
about
P
15%.
aT aI/B .
The
peak
The
peak
electron
ion temperature shows a
The measured energy confinement times at
shown
confinement times for the
l30kA ,I 4160kA,
to
in
same
Fig.17(solid
n
and
points).
BTbut
are shown (dotted line
lower
T (EX) ).
E
For
various
comparison,
plasma
current,
We observe that in
all cases the confinement time is at least as good as, if not somewhat
greater than, that at lower current. It must be remarked that it is
PAGE 14
more difficult to obtain stable high current discharges than low current
ones with
L>/ 3. At present, the probability of producing a stable high
current discharge is smaller than that for a low current one.
But it
seems to be only a matter of gaining more understanding of the necessary
machine 'tuning' in order for reliable high current operation to become
routine.
High current discharges that do survive show no degradation of
energy confinement; indeed some improvement seems possible.
In Fig.17 the corresponding neoclassical energy confinement times,
T E(NC),
are also shown.
It is tempting to infer from the observed
improvement in
the
dominant
TE (EX) with higher current that all is
role
of
neoclassical ion loss.
seems susceptible to fundamental criticism.
between
TE
E
EX
With high current
in
the
the gap
The electron
high
over the corresponding value for low current discharges.
dependence
of
anomalous
conductivity on the temperature profile, i.e.
flat profiles appears to be greater than
profiles[2'i].
on
Furthermore,
the
X
that
absence
with
However, such inference
also shows an increase
correspond to the reported
B
accord
(NC) and the measured confinement time widens.
thermal diffusivity Xe
case
in
This may
electron
thermal
for discharges with
for
of
current
a
cases
with
peaked
significant effect of
(EX) should also caution us about the role of high current
energy confinement.
T
T
E
in
Lastly, the important point about high current in a tokamak is that
is beneficial to confinement of high energy charged particles.
it
Observations
from
RF
heating
experiments
on
Alcator[28]
allow
a
tentative conclusion that this expectation is fulfilled.
VI A
flTE
In conclusion, since
nT E,
increases
TE
increases with
E
dependence of fiTE
on 5
facilitates conception
e
high
-ne, the
quality
-2e
in proportion to n , as shown in Fig.18.
power-density
fusion
reactors.
of
factor,
The strong
relatively
compact
Detailed tokamak reactor design
calculations reveal that the high field, high density tokamak approach
offers great promise for rapid progress in the development of fusion
PAGE 15
power production[29].
Compact tokamak
ignition
experiments
based
on
these notions are also under consideration.
ACKNOWLEDGEMENTS
It is a pleasure
operating
team:
acknowledge
contributions
of tthe
Alcator
S.Cologgero, J.Gerolamo, J.Maher, C.Pa k and F.Silva,
and the Alcator group.
acknowledged.
to
This
Many valuable contributions by S.Wolfe are
also
work is supported by the U.S. Department of Energy
under contract No. ET-78-C-01-3019.
PAGE 16
REFERENCES
[1]
U.Ascoli-Bartoli, G.Bosia, G.Boxman, P.Brossier, B.Coppi, L.De Kock,
B.Meddens, B.Montgomery, A.Oomens, L.Ornstein, R.Parker, L.Pieroni,
S.Segre, R.Taylor, P.Van Der Laan and R.Van Heyningen. Proceedings
of the Fifth International Conference on Plasma Physics and
Controlled Nuclear Fusion Research, Tokyo, Japan, 1974.
[2]
E.Apgar, B.Coppi, A.Gondhalekar, H.Helava, D.Komm, F.Martin,
B.Montgomery, D.Pappas, R.Parker and D.Overskei. Proceedings of the
Sixth International Conference on Plasma Physics and Controlled
Nuclear Fusion Research, Berchtesdaden, W.Germany, 1976.
[3]
M.Gaudreau, A.Gondhalekar, M.H.Hughes, D.Overskei, D.Pappas,
R.R.Parker, S.M.Wolfe, E.Apgar, H.Helava, I.H.Hutchinson,
E.S.Marmar and K.Molvig. Phys. Rev. Letters 39 (1977)1299.
[4]
A.Gondhalekar, D.Overskei, R.R.Parker and J.West. Bull.Am.Phys.Soc.,
22 (1977)1092.
[5]
A.Gondhalekar, R.Granetz, D.Gwinn, I.Hutchinson, B.Kusse, E.Marmar,
D.Overskei, D.Pappas, R.R.Parker, M.Pickrell, J.Rice, L.Scaturro,
J.Schuss, J..West, S.Wolfe, R.Petrasso, R.E.Slusher and C.M.Surko.
Proceedings of the Seventh International Conference on Plasma
Physics and Controlled Nuclear Fusion Research, Innsbruck,
Austria, August 1978.
[6]
A.Gondhalekar, D.Overskei, R.R.Parker and J.West. International
Conference on Solids and Plasmas in High Magnetic Fields,
Cambridge, U.S.A., September 1978.
[7]
D.O.Overskei, A.C-ondhalekar, I.Hutchinson, D.Pappas, R.Parker,
J.Rice, L.Scaturro, and S.Wolfe. International Conference on
Solids and Plasmas in High Magnetic Fields, Cambridge, U.S.A., 1978.
[8]
D.Gwinn and R.Granetz. MIT Plasma Fusion Center Report
PFC/RR-78-8 (1978).
[9]
R.Taylor. 1975 Quotation.
[10] M.H.Hughes. Princeton University Plasma Physics Laboratory Report
PPPL-1411 (1978).
PAGE 17
[11] D.S.Pappas and R.R.Parker. MIT Plasma Fusion Center Report
PFC/RR-78-5 (1978).
[12] R.D.Hazeltine and F.L.Hinton. Physics of Fluids 16(1973)1883.
[13] H.Wobig, Max-Planck-Institut fur Plasmaphysik, Garching, W.Germany.
Private communication, August 1978.
[14] L.A.Artsimovich. Nuclear Fusion 12(1972)215.
[15] M.G.Rusbridge and P.A.H.Saunders. Report of the Culham Laboratory
Study Group on Plasma Instibilities, CLM-M21, March 1963.
[16] M.C.Rusbridge. Plasma Physics 11(1969)35.
[17] D.H.Birdsall, S.A.Colgate, H.P.Furth, C.W.Hartman and
R.L.Spoerlein. Nuclear Fusion Suppl. Pt.3(1962)955.
[18] J.R.Jokipii. Reviews of Geophysics and Space Physics 9(1971)27.
[19] J.D.Callen. Phys. Rev. Lett. 39(1977)1540.
[20] K.Molvig, J.E.Rice and M.S.Tekula. Phys. Rev. Lett. 41(1978)1240.
[21] L.Scaturro and M.Pickrell. Bull. American Physical Society
23(1978)873.
[22] S.I.Braginskii. In: Reviews of Plasma Physics, M.A.Leontovich, ed.
(Consultants Bureau, New York),
1(1965)205.
[23] EQUIPE TFR. Proceedings of the Sixth International Conference on
Plasma Physics and Controlled Nuclear Fusion Research, Berchtesgaden,
W.Germany, 1976.
[241 EQUIPE TFR. Proceedings of the Seventh International Conference on
Plasma Physics and Controlled Nuclear Fusion Research, Innsbruck,
Austria, August 1978.
[25] S.V.Mirnov and I.B.Semenov. Proceedings of the Fourth International
Conference on Plasma Physics and Controlled Nuclear Fusion Research,
Madison, U.S.A., 1971.
[26] S.V.Mirnov. Paper presented at the IAEA Advisory Group meeting on
Transport Processes in Tokamaks, Kiev, U.S.S.R., November 1977.
[273 B.B.Kadomtsev. Nuclear Fusion 18(1978)553.
[28] J.Schuss and R.R.Parker,
Alcator Group. December 1978,
Private Communication.
[29] D.R.Cohn, R.R.Parker and D.L.Jassby. Nuclear Fusion 16(1976)31 and
16 (1976)1045.
30] W.Horton and R.D.Estes. University of Texas Fusion Research Center
Report FRCR 170,
May 1978.
PAGE 18
FIGURE CAPTIONS
FIG.1
Oscillograph of an
ultra-high
Maximum value of ie is
with BT =8.7T and IP =235kA.
Fig.2
Radial profiles of electron
value of
Fig.3
Radial
3
discharge
in
Alcator.
. Discharge is in deuterium,
Time: 50ms/div.
temperature
and
density
for
two
e , in deuterium with BT =6T, 130kA <Ip, \160kA.
variation
for
x',
density
7.2xlO 1 4c
of
electrons
the
and
collisionality
ions
at
parameters
v*
two
values
of lie
profile of the safety factor, g(r), and
values
for
<E/E CR> are also shown.
Radial
< E > and
D 2 plasma, BT =6T, 130kA ,<I,,<160kA.
Fig.4
Variation of
Fig.5
showing nearly complete equilibration at high density.
Variation of the resistive loop-voltage, V , with
peak
and
electron
and
ion
temperatures
with
n- ,
density.
R
D2 plasma, BT =6T, 130kA <IP.<l60kA.
Fig.6
Variation of the measured energy confinement time
density
H, .
T
(EX) with
E
Also shown is the neoclassical energy confinement
time
TE(NC) for identical plasma conditions.
that
if
neoclassical
The figure
means
ion thermal conduction were the dominant
energy loss irechanism, the power needed to sustain these plasmas
would be lot less than what is measured.
Fig.7
Variation of poloidal-beta,
p , with density.
Fig.8
Variation of
the
T E(EX)
with
average
streaming
parameter,
K >=<V/V>
drift
Fig.9
Variation of
thermal
TE (EX) with the average
collisionality
parameter
for trapped electrons, < v*e >
Fig.10
Energy confinement time TEo
the
T
Eo
at plasma
center
plotted
against
peak electron density ne. At high density the variation of
is akin to the neoclassical, indicating that the core of the
plasma may be dominated by neoclassical losses.
PAGE 19
Fig.11
The peak ion temperature and profile deduced by attributing
entire
heat
5 e =5. 5x10
measured
flux
to
4cm-3.
neoclassical
ion
conduction
loss,
The deduced peak ion temperature agrees
T. =605eV.
An anomaly factor 6 is included.
Fig.12
Ion
temperature
deduced,
plasma
much
is
with
less
D 2 plasma, BT =6T, I P =130kA.
higher
than
electron
temperature
is
in contradiction with experiment, when the loss of all
energy is attributed to neoclassical. ion
thermal
conduction at low density, fie =1.4x10 1 4cm 3 . D2 plasma, B
Ip =143kA.
Fig.13
at
At this
density, an anomaly in ion thermal conduction, if any,
than 1.5 of neoclassical.
the
Ratio of the measured electron heat flux
neoclassical
electron
heat
flux
for
=6T,
to
the
corresponding
low
and
high
density
discharges.
Fig.14
Variation with density of the experimental
for
EX
electrons, X
EX
thermal
EX
(solid circles)and ions x.
e
diffusivity
(open circles).
1
For comparison, the corresponding neoclassical
Xe a 1/ne.
thermal diffusivities, x
and xNC , for ions and electrons
e
1
respectively, are also shown.
Fig.15
Radial
profiles
deuterium
of
plasmas
electron
at R
temperature
~ 2x10
14
-3,
cm , I
and
density
115kA, with B
for
35
3.5T
and 7.7T.
Fig.16
Variation of
Fig.17
Energy
T
E
(EX) with B
confinement
points),
compared
time
to
the
TE (NC), and to the energy
D
Fig.18
T
in
.
high
current
corresponding
confinement
discharges(solid
neoclassical values,
time
at
with
density,
low
current.
plasmas, BT =6T, 215kA <IP <235kA.
Variation of the quality factor, nTE
-CE a
en'
,
showing
-1
VL(.6 V/div)
IP(5 0 kA /div
)
Fe (1014 crr3/fr)
POSITION
BT= 8 -7 T
Fig. 1
keV
1.5 Te (r)
1.0
0.5
0 -
ne (r) (10
14
cm- 3 )
--
5- 10
OO
10
10
0
RADIAL POSITION (cm)
- - =e1.4x 1014 cm
3
- e =5.5x 10' 4Cm-3
Fig. 2
I.4xI0 14 cm
Fe
3
<9> = 0.019
< E/ECR > = 0.027
ne = 5.5 xIO 4Cm-3
<> = 0.005
<E/EcR > =0.005
4
40
*
30
20/
2
-
10
0.-0
--
2
8
6
RADIAL POSITION (cm)
4
Fig.
3
0
10
A
T (keV)
1.5 1
0
8
A
1.0 k
Te
0
U
-I-
U
Ii
0.5
*
0
A
SCATTERING
THOMSON
Te
A
o
CHARGE
T
EXCHANGE
A
NEUTRONS
I
0
I
I
I
4
2
fie ( 1014 CM-3)
Fig. 4
I
I
6
VR (Volts)
3
2 -
0
*
2
4
nie (10
14 cm- 3
Fig. 5
6
T (ms)
60
40
TE(NC)
TE(N C)
20
0
=
r27rr'
4
(ni Tj + neTe)
2rr QC (r)
2R
fl
dr'
21
-j
niTi+neTe)rdr
7E (EX)
TE
0
2
4
Fe ( 1014 Cm-3)
Fig. 6
(EX)
6
1P
2-
,
niTi +feTe>
87r <
I~p~ B2
P
~ie
(I014 CM 3 )
Fig. 7
0
ZE (iS)
0
0
20 10
S
0
0
0
0
10
0
I
0
*
0
KVdrift/Vthermal ~
0
I0
<(> x 10-3
Fig. 8
20
ZE (inS)
I
0
20
0
S
S
10
~
-.
\Vthe
0
-
-
-
R
r
20
10
(7/*
Fig. 9
e)
ZEO (Ms)
20
( i T+ne~e)
10 -E0
5
0
e
(1014cm~)
Fig. 10
E-
10
T (keV)
-
T(r) MEASURED
0.8
--
T (r) DEDUCED
0.6-
0.4
02
neA= 5.5 x
MEASURED
04Crr=.
=1.5
Te = 671 eV
A
T = 605 eV
-5
0
RADIAL POSITION (cm)
Fig. 11
5
T (keV)
Te(r) MEASURED
3.0 k
---
/
2.0
/
/
/
/
/
/
/
/
T (r) DEDUCED
N
/
/
8 = 1.0
1.0
ne=
-3cm-
l.4x,1
Te
A
MEASURED Te = 1340 eV
A
Ti
730 eV
1
L
5
0
RADIAL POSITION
Fig. 12
(cm)
EX
QNC
e (r)
100
10
I' ,, , .
0
j
ne = 5.5 x 10 4 cm-3
2
.
I
. .. .I
I
I I I I
Ii I I
I
I I I I I I I I I I
I I I
I
4
6
8
RADIAL POSITION (cm)
Fig. 13
I I I
I I I I
I
10
x (10 3 cm2's
3
EX
xEX
e
oX
=
e
oXEX
0
2
0
0
0
0
o
0
0
000
0*
00
0
O
0
NC
XNC
e
0
4
2
C -3))
-i (1
(i0F14 cm
Fig. 14
6
1.2
02
6
1.01
2
Y291
14
--
-cr3
8
cm
Ts
Br'77 T
.-- 115
0.8
135 T
-~I1k
0.6-
.-
+
0.4,0.21-10
0
5
4 -
f
E
u302
ci
00
-10
0
RADIAL POSITION r(cm)
Fig. 15
0
TE (Ms)
20
* D2
5.0
O H2
3 .5 5qL
S
nl14 : 7.0
6.2
0
3.15 14 <43.3
10
1 8
80
I
0
5
TOROIDAL FIELD BT (Tesla)
Fig. 16
t0
7E (Ms)
80r-
ZE (NC)
215 kA < Ip
s 235kA
60-
40-
0E
(Ex) (215 kA 5 Ips 235 kA)
0
0
20 F
0
.
-
"E (Ex) (130 kA <IpI5 6OkA)
000
0
. I
I
2
4
e (10 14 cm-3 )
Fig. 17
6
3I
13-r
AlE
3
8
0
0
0{/
n
--2
A
E
1.
E6
0
0
0
0.,0
0
I
2
I
I
4
6
n (10 14 cm~ 3
Fig.
18
I