~.
ENERGY CONFINEMENT IN ALCATOR
A. Gondhalekar, D. Overskei, R. Parker, J. West
and S. Wolfe
Francis Bitter National Magnet Laboratory and
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA. 02139
PFC/RR-79-6
(supersedes 78-15)
June 1979
This work was supported by the U.S. Department of Energy Contract
No. DE-AC02-78ET51013. Reproduction, translation, publication, use
and disposal, in whole or in part by or for the United States government
is permitted.
LL~.1~
ENERGY CONFINEMENT IN ALCATOR
A.Gondhalekar, D.Overskei, R.Parker, J.West and S.Wolfe
Francis Bitter National Magnet Laboratory and Plasma Fusion Center
Massachusetts Institute of Technology, Cambridge, MA.02139.
ABSTRACT
Nearly classical behaviour, from the viewpoint of energy confinement,
is observed in the central core of the plasma column in Alcator. At the
highest densities, a regime is attained where the anomalous electron
thermal conductivity observed at lower densities is suppressed, and the
dominant role in energy confinement can be attributed to neoclassical
ion thermal conduction. The anomalous electron thermal conduction varies
inversly with density. The observed ion thermal conductivity is neoclassical.
Dependence of energy confinement on B
constant n
and IPe,
T
is also investigated. With
no significant effect of increasing BT on
observed. However, the highest achievable density and TE
TE
is
increase with BT.
Stable operation of high current, low qL discharges has been
achieved. Energy confinement for such discharges is described. Some
improvement in
T
E is observed at high current.-
Stable discharges with peak density up to 1,5x10
15
-3
cm
have been
obtained in deuterium at BT = 8.7 T. Complete thermal equilibration between
electrons and ions is observed, with peak temperatures of 900 eV. The
-3
13
maximum value of nTE is 3x10
cm .S.
PAGE 2
I
INTRODUCTION
An essential advance in
has
years
been
in
the
moderate temperatures.
times
larger
than
ability
The plasma
that
to
physics
tokamak
now
attainable
only a few years ago.
accompanied
in
by
substantial
is
10-100
Operation at
improvement
in
This behaviour had been seen in many tokamaks[1,2),
but most widely studied first in Alcator because of the large
available density.
recent
obtain high density plasmas with
density
possible
higher densities has been
energy confinement.
experimental
range
in
Although it is not yet clear what factors favour the
ability to obtain high density, 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
have,
therefore, yielded the highest density and relatively high values
for energy confinement.
far
density
achieved is
In Alcator, the maximum peak
1
1.5xlO
3 with
cnf
giving nTTE = 3x1 I"cm- .s at
density,
ns
an energy confinement time T E = 20ms.,
peak
electron
and
ion
temperatures
of
900eV.
A description of the Alcator tokamak has been
given
elsewhere[3].
It is a device with major radius R=54cm and limiter radius a =10cm.
The
unique capability of Alcator to operate over a wide range of parameters,
with toroidal field 3T. BT.<9T, plasma current 80kA(<Ip<300kA,
averaged density 5xlO"cmf <rie<7.5xl0"cm
,
and line
has enabled study of
the
The advantages of
dependence of energy confinement on these parameters.
high density operation have been discussed previously[4,5,6,7]. In this
paper, further elucidation of high density operation is given. We show
that the higher density discharges can be understood
neoclassical
ion
thermal
in
conduction
as
discussed
in
section
III.
A
preliminary
observations has been given earlier[8,9,10].
influence
dominates.
account
of
This
these
A brief description of the
of toroidal field and plasma current on energy confinement is
given in sections
q
by
the central core, whereas at
lower densities anomalous electron thermal conduction
is
determined
IV
and
V.
Other
aspects
discharges have been discussed elsewhere[ll].
of
high
current,
low
PAGE 3
High density discharges are obtained by neutral gas injection
the
plasma.
Equilibrium
with ri
=3x10 1 3 cm-
plasma
through
desired
.
a
Neutral gas is then injected at the
Energy
under
confinement
studies
stationary discharge
invested in 'tuning'
roughly
is first established in a low density plasma
entails
edge
of
the
programmable fast valve, bringing the density to the
value[7].
performed
into
the machine
adjusting
to
the
discussed
conditions.
give
various
here
Much
optimum
were
effort
performance.
equilibrium
fields
was
This
and
the
temporal behaviour of density and plasma current until the lowest plasma
resistance
is observed for the required values of BT, I
radiative power loss
reported
here.
due
to
impurities
and ri e.
is minimized
for
Thus
the
data
Low impurity content may also help restrict disruptive
MHD activity to tolerable low levels.
II
PLASMA REGIMES
Fig.1 illustrates one of the highest
=
with
7.2xl 10"cm-3
Peak
.
density
temperatures TeJi= 900eV were observed.
Tp and
density
density
discharges
i, = 1.5xl0-1cm~,
obtained
and
peak
Loop voltage VR, plasma current
Peak
fe were maintained constant within 10% for 100ms.
density of greater than 101 5cm-3 was maintained for about 150ms.
The experiments described in
carried
5x10
1 3c- 3
electron
out
in
deuterium
gi e<6x104cmtemperature,
3.
with
Fig.2
Te (r),
the
remainder
of
BT = 6T,
l30kA,(Ip<l6OkA
shows
typical
this
radial
paper
were
and
profiles
of
and electron density, ne(r), measured by
Thomson scattering of ruby laser radiation.
The
electron
temperature
profile is best described by
Ted
- Te exp(-r2/a )
The radial profiles of current density, j(r),
and safety
factor,
are determined in the usual way by assuming j(r) I T3 (r).
and wall conditions in Alcator
permit
plasmas
to
be
Clean vacuum
produced
resistivity is nearly equal to the calculated classical value.
effective ioii charge in the plasma, Zeff, is close to unity.
q(r),
whose
Thus the
PAGE 4
For discharges studied here, we find
axis,
gO,
always
a
assumes
that
the
safety
value, 0.85 4%,<l.
minimum
factor
on
This is in
agreement with deductions made from sawtooth X-ray emission signals[1 2 1.
With the
a2
a Tq --,
smaller
profile given above and Zeffgr)~ 1, it is easily shown that
r3 iscren2a
qo. rc is the radius of the current channel which can be
than
aL due
9.5cmrC (a=10cm.
to
displacement
qLis
the
of
safety
the plasma column;
factor
at
the
limiter.
120 cm2 is measured in Alcator.
Empirically, a2 qL
Furthermore, assuming that the induced toroidal electric
constant
across
the
usually
field
is
plasma cross-section, E(r)=constant=VR/2r R ,it
is
easily shown, with Spitzer-Hirm resistivity, that for a deuterium plasma
'4x
102
e=
2/3
0(BT
Zeff/VR
q
eV.
BT
is in tesla and the the loop-voltage VR
of
electron
temperature
is in Volts.
under a large variety of plasma conditions at
high density bear out these relationships for
These
relationships
confirm,
intuition that to know
Measurements
the
albeit
ZeffIl
and
0.85,<q
\l.
only for clean plasmas, an early
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) = nel1 - r 2 /a2 Ia
The value of a depends on
here,
with
the
density.
For
experiments
BT =6T, I = 150kA, the value of .a increases approximately
linearly from 0.75 at He ~10 '4cm~3 to 2.0 at 'ie =6x10 1 4cm
relationship between a
and
qL (or Ip/BT) and aL above.
way
considered
3
. No
simple
ne could be established as in the case of
The value of a will depend in a complicated
on the mechanism of gas ingestion at the plasma edge, and transport
of plasma to the center
understood
evolves
at
without
profile[6].
present.
of
the
During
significant
discharge,
gas
inversion
processes
injection,
which
are
not
the electron density
(dne/dr> 0)
in
the
radial
PAGE 5
Other observations concerning density
that
at
B T and
given
IP,
density
build-up
can
worth
be
noting
increased
are
until
v*e(minium) =10. V*e is the collisionality parameter for trapped
electrons, v*e = 2' Ve(Rth)t (P/r)3/2.
Fig.3 shows the radial variation
of v*e for high and low density discharges.
Attempts to increase the
density further by injection of additional gas at the edge cause
disruption.
has
The density can be increased by raising BT and 1P .
This
the effect of increasing the temperature and reducing V*e. Density
can then be increased until again v*e(minimum) _10.
In discharges where
fe is maintained at a constant value, the ratio i4/ ie, and hence the
value of a , are observed to increase continuously, indicating steady
convection of plasma to the center. No satisfactory explanation exists
for the observed rapid increase of
neutral
plasma
density
upon
injection
of
gas
at the plasma boundary. The neoclassical trapped particle
pinch model has been proposed to account for the above observations, and
does so in a semi-quantitative way[131.
Measurements of peak
charge-exchanged
discharges
in
yield[7,15].
ion
temperature
are
made
by
analysis
neutral particles emitted from the plasma[141
deuterium,
also
by
using
the
of
and,for
thermonuclear
neutron
Ion temperatures so determined are consistent with
OH = E
e=
n(e
-Tgei
Tei is the electron-ion equilibration time[16] at plasma center, POH is
the peak ohmic power input. This relation gives the maximum temperature
difference that
Measurements
less than
be
indicate
the
Measurements
can
sustained
the
the
available
heating
power.
peak ion temperatures typically only about 100eV
corresponding
of
by
ion
electron
temperature
temperature
profile
at
using
high
density.
charge-exchange
neutral particle analysis show that this may be represented in the central
region by the same gaussian shape as the electron temperature profile[33].
No firm data about the ion temperature toward the outside exists.
Measurements of this are in progress, and preliminary data from spectroscopy
of impurity ions shows that Ti > Te for r>, 6.5cm [34]. Thus in the central
region
2 2
Ti(r)
=T
exp(-r /a
)
PAGE 6
of
variation
The
and ion temperatures with density is
electron
peak
profile.
temperature
electron
the
determined for
aTi is equal to aT
shown in Fig.4.
temperature
The shaded region in Fig.4 indicates the peak electron
calculated
using
shown in Fig.5.
is
somewhat
and the measured loop-voltage
Zeff=,
0.85 <q,,<1.0,
The measured peak electron temperature at
higher
than
which
1.1 Zef<,l.2,
measurements [17].
indicating that at Fe< 2 xlO 14cm-3,
expected,
agreement
rough
in
is
low density
previous
with
A rough characterization of the plasma regimes realized in Alcator
conditions
these
under
the
dimensionless parameters:
v* =21/2vRV
Sv(qR/Vth)(R/r
particles,
particles, v*-
transit
< E>=<vdri ft
thermal>,
,
the
and the safety factor q.
v* , v,,
collisionality
parameter
for
parameter,
streaming
the
trapped
the ratio of the applied electric field to
the critical run-away field, <E/ECR>.
of
for
collisionality parameter
3/2
=v (qR/Vth),
and
the values of various
from
obtained
be
can
as being predominantly in the plateau
Fig.3 shows the radial
variation
The plasma can be characterized
regime
of
neoclassical
theory,
power
balance
verging on the Pfirsch-Schluter regime.
DENSITY DEPENDENCE OF ENERGY CONFINEENT
III
A study of the variation of energy confinement
with
density,
at
constant
and
toroidal magnetic field BT =6T, and plasma
current, l30kA ,I, 160kA, has been made in order to ascertain how
closely energy confinement approaches neoclassical values. The global
energy confinement time is defined as
' aL
VR
2(nT
+ n T )27rrdr/I
E(EX) = 2'R
0
torus.
VR
is the resistive part of the loop-voltage induced around the
VR
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
illustrates
the
variation
of
the
induced
voltage
with
F
density,
showing
falling
a gradual
electron
understood
as
increase in VR, corresponding to steadily
temperature
due
to
as
density
increased
Fig.6.
may
be
The variation with density of the
confinement time
energy
determined
This
power transfer to the ions and their
steadily growing role in energy loss.
experimentally
increases.
We observe that t E(EX) increases
T
E(EX) is shown in
approximately
linearly with
and I V The curve labelled T E(NC) in Fig.6 gives
at constant B
fi
the value of the energy confinement time if neoclassical ion thermal
conduction
were
the
dominant
conditions identical to
those
energy
the
point,
energy confinement time at each point,
TE
21TrQ
Q N r) is the heat flux
due
TE
value
0 .r
then
<0. 7 aL.
Hinton[18]
the
used
in
of
density.
ion
(r) ,
NE
coefficients
Comparison
computations.
between
the
thermal
conduction.
averaged over a region
given
within a factor of 1.4 of the neoclassical
highest
plasma
experiment.
The neoclassical
NC (r), is calculated from
T
neoclassical
these
for
(r)
to
Neoclassical
are
NC
mechanism,
+ n T )I dr'
1(n T
NC27rr'
(NC) is
in
loss
value
two
by
Hazeltine
Energy confinement time
is
observed
at
loss
is
reduced
as
increases in Alcator.
density
energy loss is attributed to anomalous radial electron heat
We
show
later' that
the
anomalous
electron
the
curves shows that the
plasma is afflicted with anomalous energy loss at low density, and
this
and
heat
that
This excess
conduction.
conductivity
is
suppressed as density increases.
Fig.7 shows the variation of poloidal-beta, ap , with
8
is defined as
a
aP
density fie.
= 8r<niTi + neTe>/B
2
p
p
is the ratio of the plasma kinetic pressure and the pressure of
poloidal
magnetic field B P.
with neoclassical estimates.
the
The maximum value of $P is also in accord
PAGE 8
Radial electron heat conduction has long been
major
in
support
mechanisms
of
giving
rise
be
evidence
and experimental
anomalous
to
the
This subject has
anomalous energy loss mechanism in tokamaks[1).
recently received renewed examination[19,20],
to
beli:red
electron
heat
conduction in Alcator has been claimed[20,21J.
Power balance in the central core of the plasma is
next
examined.
Energy confinement time at the plasma center, T EO , is defined as
T EO
2 (T
+ neTe)/Ej0
Here, the peak densities n^el, peak electron and ion temperatures 'e
'Ti, are
directly determined.
from Te by
assuming
electric
toroidal
The value of
the
j0
Spitzer-Harm
resistivity
and
at constant BT and IP.
profile.
It
T EQ
induced
is
also
that
indicates
in
agreement
with the
with
density,
peak
does not increase linearly with density but
This variation of T EQ
seens to saturate.
neoclassical,
the
is consistent with the current distribution deduced from
Fig.8 shows the variation of T EQ
0.85. 4q, <l.
that
is deduced
E is uniform across the plasma cross-section.
field
temperature
electron
j0 ,
The peak current density,
and
the
core
at high density, akin to
of
the
the
plasma column may be
dominated by neoclassical losses.
Since, at high density, most of the energy
core
seems
to
transport
out
of
attributable to ion heat conduction, the ohmic heat
be
and
input may be put equal to the neoclassical ion conduction loss
ion
temperature
its
and
experimental value.
distribution
computed
and
the
compared to the
We thus have
r
Q
the
(r) = POH/2nr
OH
af
f 2wr'E'J(r')
0
dr'/27Tr
We then put, for r ,5cm
NC
QC (r) = QOH(r)
Two model
ion
NC
temperature
expression for Q3 (r).
profiles
were
They were of the form
substituted
into
the
PAGE 9
3
Ti(r) =Qa r2n
n=0
and
T (r) = a
exp(-a 2 r2
Both models give the same peak temperature, which is in
the
measured
value[7,15].
Fig.9
using the gaussian model.
thermal
conductivity
agreement with
shows the result of the calculation
The effects of possible departures of the ion
from
neoclassical
are also included.
dotted curve in Fig.9 shows the result with an anomaly
unity(ion
at
the
temperature.
indicates
We
see
the
uncertainity
in
the
,
factor, 6
thermal conduction equal to the neoclassical).
peak
The upper
of
The error-bar
peak
deduced
ion
that within the accuracy of the calculation, the
experimental peak ion temperature can be accounted for by an ion thermal
conductivity equal to the neoclassical. In the lower dotted curve in
Fig.9, an anomaly factor of 1.5 is employed; i.e. the neoclassical ion
heat flux is multiplied by a factor of 1.5 everywhere.
ion temperature is then well short of the measured,
these
plasma
conditions
an
anomaly,
if
any,
conductivity is less than 1.5 of neoclassical.
The deduced peak
implying
in
the
that
ion
This agreement
for
thermal
confirms
the correctness of attributing the dominant role in energy loss, at high
density, to neoclassical ion thermal conduction.
Radial fluxes for r .0.5aL
may be
deduced
from
the
experimental
values of ne (r), Te(r) and Ti (r), neglecting losses due to radiation and
charge-exchange. At plasma densities h >e2x10 1 4 cm 3 , the central core
of
the
plasma is opaque to neutral particles of energy less than lkeV.
Charge-exchange losses for such
region r>5cm.
plasmas
are
important
only
the
Spatially and temporally resolved bolometric measurements
of radiative and charge-exchange losses have been made[22].
that
for
They
show
for plasma and machine conditions involved in the studies reported
here, these processes contribute to the loss of at
heating
power
0 <r <5cm.
most
20% of
ohmic
in the central core of the plasma, defined as the region
Therefore neglecting these
losses
does
not
significantly
affect calculation of power balance in the central core of the plasma.
The equilibration power transferred from the electrons to the ions,
PAGE 10
P
(r),
is set equal to the power transported by the ions, Pi(r),
r
P.(r) = Pei(r)
f 27Tr' I
0
=
n(Te- T±)/'etldr'
The ion
Tei is the electron-ion equilibration time.
flux
heat
is
then
Qi (r) = Pi(r)/21r
x
The ion thermal diffusivit
L
(r),
is determined from
(r) = -XX(r)-ni(r)- VT1 (r)
The power transported by the electrons, Pe(r), is then given by
r
Pe(r) = POH(r)
Pei(r) = f 2wr'E*j(ri)dr'- Pei(r)
0
EX
The electron heat flux, Qe (r), and the electron thermal diffusivity
At fie>3x10 1 4 cm 3 , the
as for the ions.
are
determined
x-r)
-
experimental determination of
difference
between
electron
is
Pei
owing
uncertain
high
at
small
This gives rise to
and ion temperatures.
uncertainties in the calculated heat fluxes
the
to
Fig.10
density.
the ratio of the experimentally determined electron heat flux and
ne =1.4x10 14 cm~5 and
at
flux
heat
electron
neoclassical
shows
the
~ne =5.5x10 1 4 cm- 3 .
electron
We observe that at low density, the
heat
200
is
flux
When
times larger than the neoclassical, as seen in other tokamaks[23].
radiative and charge-exchange losses are properly included,
this
factor
As density increases in Alcator, this
14
anomaly in the electron heat flux diminishes, until at Re>5 x10 cm-3 it
of 200 might be reduced somewhat.
is at most ten times larger than the neoclassical loss by the electrons.
Lastly, knowing the ion and electron
respectively,
and x
,
over
averaged
3cm <r,<5cm,
with
NC
.
Xe
corresponding neoclassical heat diffusivities, xi
shown.
EX
Xe
We
EX
<loxe
that XE
see
e
whereas
and
Q
(r)
Fig.ll shows the variation
and compared to the neoclassical values.
EX
QX(r)
and electron heat diffusivities may be computed
ion
the
fluxes,
heat
:
t014-3
at
l/Ee and
ne =10 1 an
again
EX
, xe
density
NC
and xe
of
ne.
The
are
also
that at he =5.5x1014cm- 3
N.
>> X .
For
the
ions,
PAGE 11
Hi e
ie> 3xl04 cm- 3 , but shows an unfavourable trend at
where
~ 1-2 xipeiul
as previously suspected in the TFR
XNC for
xE
1 acn
<2xlO
3
tokamak[24).
We
should
caution
that
the
unfavourable
trend
in
observed at low density may only be a result of not having given
i
proper consideration to impurity and charge-exchange losses which are
xEX
not negligible at ie<2x10 14 cm-3.
loss
may come
from
ripple
Additional contributions to ion energy
trapped
particles.
Thus, when all these
effects are properly included in the ion energy balance, the apparent
ananaly in ion thermal conduction at low density may be eliminated.
We conclude from
Alcator,
a gradual
this
study
transition
conduction regime to the
that
as
density
from
the
anomalous
neoclassical
ion
thermal
takes place in the central core of the plasma.
is
increased
in
electron thermal
conduction regime
Suppression of electron
thermal conduction, together with increased power transfer to
the
ions
as density increases cause the energy confinement time to increase with
density, until the dominant role in energy transport is taken over by
ion
thermal
conduction.
confinement time in
this
Since
regime
this loss increases with density, the
saturates- or
decreases
as
density
increases, as has recently also been observed in ISX-A[25] and similarly
interpreted[26].
PAGE 12
'IOROIDAL MAGNETIC FIELD DEPENDENCE OF ENERGY CONFINEMENT
IV
The dependence of
on
E
BT
keeping
by
investigated
been
has
Experiments were conducted with
varying BT.
and
constant
I
and
i
T
3
14
BT =3.5T and BT =7.7T in deuterium at he = 2xl0 crf and IP =ll5kA.
differences
obvious
were observed in the macroscopic properties of the
fluctuations on X-ray
sawtooth
small
with
characteristics,
similar
showed
plasma, such as Zeff or MHD activity. Both discharges
temporal
No
emission. Measured profiles of electron density and temperature are
The density profiles in both cases are similar.
shown in Fig.12.
peak
the
However,
electron
temperature profile narrows when BT is increased.
te
with
a)
and
R) /I/B2
(BT
This is in accordance
The total energy
also shows similar dependence on BT [151.
temperature
the
power
energy confinement time, TE
9ms
content is nearly the same for the two discharges, and since
is
input
equal,
nearly
also
remains unchanged when BT
the
ion
The
earlier.
discussed
as
the
and
'i't, increases
temperature,
is increased.
Similar observations have been
made in TFR[27].
Fig.13 shows more data along these lines.
were
not
The
as uniform as in the example just given.
conditions
plasma
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
confinement,
increase
with
energy
Br,
attainable
maximum
high
ohmically heated
The physical understanding of -this result is as follows:
field tokamak.
constant
the
as shown by the solid line in
This seems to be the chief merit of an
Fig.13.
At
therefore
density
and
plasma
current,
increasing
BT
has
an
because although the peak energy density
increases with BT, the temperature profile narrows so that the average
insignificant
energy
density
effect
on TE
remains
the facility for higher plasma current density
input power density increases.
obtained.
With larger BT ,
the same as that at lower B .
and
ohmic
consequently
This permits higher plasma density to be
Since energy confinement improves with density,
achievable energy confinement time also increases with Br
the
maximum
,
PAGE 13
PLASMA CURRENT DEPENDENCE OF ENERGY CONFINEMENT
V
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. This is a means
of
boot-strap
heating
of
the plasma.
This requirement for efficient
confinement of high energy charged particles applies
auxiliary
plasma
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
operate a tokamak with the largest possible
with
and
stability
MHD
favourable
important to be able to
plasma
current
made
the
Large currents
more susceptible to severe MHD activity which in turn
plasma
degraded energy confinement[28,29].
energy
In the past,
energy confinement.
these requirements have been thought to be incompatible.
compatible
confinement
was
In
with
this
believed to depend on (BT/Ip)
dependence
We have sought to reexamine
this
complete
technical
diagnostics,
keeping
and
in Alcator [6].
with more
improvements
thinking,
accurate
which
permit us a
larger latitude in available density, plasma current and of course
field.
toroidal
The
previous section.
high
but
enough
qL discharges
2x1014CM-3 iie
constant
to
study
for
ion temperature shows
confinement
9
times
plasma
T E (EX) ).
as
of
TE
at
have been obtained,
current,
low
in
deuterium,
with
B
2 .4 <qL <2 .6 .
4235kA and
=6T,
At
The
systematically.
high
the
lower
ones,
current
according
again
at
a
similar
increase[15].
The
are
shown
densities
various
measured
in
For comparison, confinement times for the same
points).
least
discussed in the
The peak electron temperature rises by about 15%.
a , I /BT.
lower
BT was
the
temperature profile is much wider for the high current
than
2
T E on
Stable discharges with qL=1.
were
investigated
5x101 4cm-3 , 215kA <I
BT the
discharges
of
Here, we present studies of the behaviour
plasma current.
not
dependence
and
current,
l30kA
<Ill60kA,
We observe that in all cases
the
are
shown
confinement
to
The peak
energy
Fig.14(solid
n and
B T but
(dotted line
time
is
at
good as, if not somewhat greater than, that at lower current.
PAGE 14
difficult
It must be remarked that it is more
low current ones with q L> 3. At present, the
than
discharges
current
high
stable
obtain
to
probability of producing a stable high current discharge is smaller than
But it seems to be only a matter of gaining
that for a low current one.
more understanding of
reliable
the
current
high
necessary
machine
'tuning'
become
routine.
to
operation
for
current
High
confinement;
energy
of
discharges that do survive show no degradation
order
in
indeed some improvement seems possible.
In Fig.14 the corresponding neoclassical energy confinement
TE(NC),
are
also
shown.
It
is
tempting to infer from the observed
improvement in TE(EX) with higher current that all is
the
dominant
role
of
ion
neoclassical
in
accord
Such inference seems
loss.
The electron thermal
(NC) and the measured confinement time widens.
also shows an increase in the high current
diffusivity X
with
With high current the gap between
susceptible to fundamental criticism.
T
times,
over
case
This may correspond
the corresponding value for low current discharges.
to the reported dependence of anomalous electron thermal conductivity on
the
appears to be greater than that
Furthermore,
for discharges with flat profiles
profile, i.e. xEX
e
temperature
absence
the
should also caution
us
of
about
for
a
role
of
profiles[30].
effect of B
significant
the
peaked
with
cases
high
current
on
T E (EX)
in
energy
confinement.
Lastly, the important point about high current in a tokamak is that
it
is
beneficial
to
confinement
from
RF
heating
Observations
of
high
experiments
energy charged particles.
on
Alcator[31]
allow
a
tentative conclusion that this expectation is fulfilled.
VI
SUMMARY AND CONCLUSIONS
We have
density
shown
tokamak
seems to exercise
electron
thermal
the
possibility of
discharges.
the
obtaining
stable
ultra-high
We have demonstrated that plasma density
strongest
influence
conduction in Alcator.
in
suppressing
anomalous
We have also demonstrated the
possibility of obtaining high current, low qL discharges, and shown that
II
PAGE 15
this
need
not
have
deleterious effects on confinement;
in fact some
improvement in global energy confinement time seems possible
plasma current.
We have also observed
permits higher density to be achieved,
confinement.
that higher toroidal field
and thus
longer
energy
The measurements suggest an empirical relation for energy
confinement in Alcator,
Since TE
higher
at
T
[s-1 3.8xlO9 %[cm~3]a 2 [CM2
e
L
increases with he, the quality factor, frrE , increases in
to fi2
e , as shown in Fig.15. These results have been used to
develop detailed concepts for a high field high density tokamak
proportion
reactor[32].
Compact
tokamak
ignition
experiments
based
on
these
notions are also under consideration.
ACKNOWLEDGEMENTS
It is a
operating
pleasure
team:
to
acknowledge
contributions
of
the
Alcator
S.Caloggero, J.Gerolamo, J.Maher, C.Park, and F.Silva,
and the Alcator group.
This work is supported by the U.S. Department of
Energy under contract No. ET-78-C-01-3019.
PAGE 16
REFERENCES
[1]
Artsimovich, L.A., Nuclear Fusion 12(1972)215.
[2]
Berry, L.A., Callen, J.D., Clarke, J.F., Colchin, R.J., Crume, E.C., Dunlap, J.I
Ednnds, P.H., Haste, G.R., Hogan, J.T., Isler, R.C., Jahns, G.L., Lazar, N.H.,
Lyon, J.F., Murakami, M., Neidigh, R.V., and Wing, W.R., Proceedings of the
[3]
Fifth International Conference on Plasma Physics and Controlled Nuclear
Fusion Research, Tokyo, Japan, 1974.
Ascoli-Bartoli, U., Bosia, G., Boxman, G., Brossier, P., Coppi, B., De Kock, L.,
Meddens, B., Montgomery, B., Oomens, A., Ornstein, L., Parker, R., Pieroni, L.,
Segre, S., Taylor, R., Van Der Laan, P., Van Heyningen, R., Proceedings
[4]
of the Fifth International Conference on Plasma Physics and
Controlled Nuclear Fusion Research, Tokyo, Japan, 1974.
Parker, R.R., Bull. American Physical Society 20(1975)1372.
[5]
Pappas, D.S., de Villiers, J., Helava, H., Parker, R.R., and Taylor, R.J.,
[6]
Bull. American Physical Society 20(1975)1360.
Apgar, E., Coppi, B., Gondhalekar, A., Helava, H., Komm, D., Martin, F.,
Montgomery, B., Pappas, D., Parker, R.,Overskei, D., Proceedings of the
Sixth International Conference on Plasma Physics and Controlled
Nuclear Fusion Research, Berchtesgaden, W.Germany, 1976.
[7]
[8]
[9]
Gaudreau, M., Gondhalekar, A., Hughes, M.H., Overskei, D., Pappas, D.,
Parker, R.R., Wolfe, S.M., Apgar, E., Helava, H., Hutchinson, I.H.,
Marmar, E.S.,Molvig, K., Phys. Rev. Letters 39(1977)1299.
Gondhalekar, A., Overskei, D., Parker, R.R. West, J., Bull. American
Physical Society 22(1977)1092.
Gondhalekar, A., Granetz, R., Gwinn, D., Hutchinson, I., Kusse, B., Marmar, E.,
Overskei, D., Pappas, D., Parker, R.R., Pickrell, M., Rice, J., Scaturro, L.,
Schuss, J., West, J., Wolfe, S., Petrasso, R., Slusher, R.E., Surko, C.M.,
Proceedings of the Seventh International Conference on Plasma
Physics and Controlled Nuclear Fusion Research, Innsbruck, Austria, 1978.
PAGE 17
[10] Gondhalekar, A., Overskei, D., Parker, R.R., West, J., International
Conference on Solids and Plasmas in High Magnetic Fields,
Cambridge, U.S.A., September 1978.
[11] Overskei, D.O., Gondhalekar, A., Hutchinson, I., Pappas, D., Parker, R.,
Rice, J., Scaturro, L., Wolfe, S., International Conference on
Solids and Plasmas in High Magnetic Fields, Cambridge, U.S.A., 1978.
[12] Gwinn, D., Granetz, R., MIT Plasma Fusion Center Report PFC/RR-78-8(1978).
[13] Hughes, M.H., Princeton University Plasma Physics Laboratory Report
PPPL-1411(1978).
[14] Gaudreau, M.P.J., Kislyakov, A.I., Sokolov, Yu.A., Nuclear Fusion 18(1978)1725.
[15] Pappas, D.S., Parker, R.R., MIT Plasma Fusion Center Report PFC/RR-78-5(1978).
[16] Braginskii,S.I., In: Reviews of Plasma Physics, M.A.Leontovich, ed.
(Consultants Bureau, New York), 1(1965)205.
[17] Terry, J.L., Chen, K.I., Moos, H.W., Marmar, E.S., Nuclear Fusion 18(1978)485.
[18] Hazeltine, R.D., Hinton, F.L., Physics of Fluids 16(1973)1883.
[19] Callen, J.D., Phys. Rev. Lett. 39(1977)1540.
[20] Horton,W., Estes,R.D., Nuclear Fusion 19(1979)203.
[21] Molvig, K., Rice, J.E., Tekula, M.S., Phys. Rev. Lett. 41(1978)1240.
[22] Scaturro, L., Pickrell, M., Bull. American Physical Society 23(1978)873.
[23] EQUIPE TFR, Proceedings of the Sixth International Conference on Plasma Physics
and Controlled Nuclear Fusion Research, Berchtesgaden, W.Germany, 1976.
[24] EQUIPE TFR, Proceedings of the Seventh International Conference on Plasma Physic
and Controlled Nuclear Fusion Research, Innsbruck, Austria, 1978.
[25] Murakami,M., Neilson,G.H., Howe,H.C., Jernigan,T.C., Bates, S.C.,
Bush,S.C., Colchin,R.J., Dunlap,J.L., Edmonds,P.H., Hill,K.W.,
Isler,R.C., Ketterer,H.E., King,P.W., McNeill,D.W., Mihalczo,J.T.,
Neidigh,R.V., Pare,V.K., Saltmarsh,M.J., Wilgen,J.B., Zurro,B.,
Phys. Rev. Letters 42(1979)655.
[26] Waltz,R.E., Guest,G.E., Phys. Rev. Letters 42(1979)651.
[27] EQUIPE TFR, Proceedings of the Seventh European Conference on
Controlled Fusion and Plasma Physics, Lausanne, Switzerland, 1975.
[28] Mirnov,.S.V., Semenov, I.B., Proceedings of the Fourth International Conference
on Plasma Physics and Controlled Nuclear Fusion Research, Madison, U.S.A., 1971.
ME ~
PAGE 18
[29] Mirnov, S.V., Paper presented at the IAFA Advisory Group meeting on
Transport Processes in Tokamaks, Kiev, U.S.S.R., November 1977.
[30] Kadantsev, B.B., Nuclear Fusion 18(1978)553.
[31] Schuss, J., Parker, R.R.,
Alcator Group. December 1978, Private communication.
[32] Cohn, D.R., Parker, R.R., Jassby, D.L., Nuclear Fusion 16(1976)31 and Nuclear
Fusion 16(1976)1045.
[33] Dnestrovskij,Yu.N., Lysenko, S.E., Kislyakov, A.I., Nuclear Fusion 19(1979)293,
Alexeev, Yu.A., Gaudreau, M., Kislyakov, A.I.,
Memorandum,
Alcator Group Internal
March 1978.
[34] Terry, J.L., Alcator Group. June 1979, Private Communication.
I I II
- -
.-- I------
-----
PAGE 19
FIGURE CAP'IONS
Fig.1
Maximum value of He is 7.2xl 1
Radial profiles of electron
Discharge is in deuterium,
cm-.
with BT =8.7T and I, =235kA.
Fig.2
in Alcator.
ultra-high density discharge
Oscillograph of an
Time: 50ms/div.
temperature
and
density
for
two
valuesof fe , in deuterium with BT =6T, l30kA-(II,160kA.
Fig.3
Radial
V**
variation
for
of
electrons
the
and
ions
at
v
and
two
values
of Ri
profile of the safety factor, q(r), and
values
for. < C >
<E/ECR> are also shown.
Fig.4
collisionality parameters
Variation of
showing
peak
nearly
and
ion
temperatures
complete equilibration
Radial
at
with
the measured loop-voltage and assuming Zeff=1.
Variation of the resistive loop-voltage, VR,
D2 plasma, B
Fig.6
fe ,
high density. The
shaded region shows the peak electron temperature expected
Fig.5
and
l30kA \<I 4l60kA.
D2 plasma, BT =6T,
electron
.
with
from
density.
=6T, l30kA\(I \<160kA.
Variation of the measured energy confinement time
T E(EX)
with
Also shown is the neoclassical energy confinement
time T E(NC) for identical plasma conditions. The figure shows
that if neoclassical ion thermal conduction were the dominant
density
fie .
energy loss mechanism, the power needed to sustain these plasmas
would be much less than what is measured.
Fig.7
Variation of poloidal-beta, $P , with density.
Fig.8
Energy confinement time 'r E
the
at plasma' center
peak electron density Ae.
plotted
against
At high density the variation of
-rEO is akin to the neoclassical, indicating that the core of the
plasma may be dominated by neoclassical losses.
Fig.9
The peak ion temperature and profile deduced by attributing
entire
heat
flux
to
neoclassical
ion
conduction
loss,
the
at
Rl
PAGE 20
fie =5.5x10 1 4cn- 3 . The deduced peak ion temperature agrees with
At this
measured T1 =605eV. An anomaly factor 6 is included.
density, an anomaly in ion thermal conduction, if any,
than 1.5 of neoclassical.
Fig.10
electron
less
D2 plasma, BT =6T, I =l30kA.
to
the
corresponding
low
and
high
Ratio of the measured electron heat flux
neoclassical
is
flux
heat
for
density
discharges.
Fig.ll
thermal
Variation with density of the experimental
(solid circles), and ions xV (open circles).
for electrons, X
XX
and
diffusivities, XF
thermal
corresponding
the
comparison,
For
l/TIe.
diffusivity
,
C
neoclassical
for ions and electrons
respectively, are also shown.
Fig.12
Radial
profiles
deuterium
plasmas
at he
density
and
temperature
electron
of
for
2x10 1 4 cm-3 , IP= 115kA, with BT =3.5T
and 7.7T.
Fig.13
Fig.14
Variation of TE (EX) with BT
Energy confinement time in
compared
points),
to
the
TE (NC), and to the energy
D
Fig.15
2
plasmas, B
=6T,
corresponding
confinement
e
discharges(solid
neoclassical values,
low
time
at
with
density,
current.
215kA (I P235kA.
Variation of the quality factor,
E
current
high
E
,
showing
II
VL(I.6 V/div)
,vtesmanejse
,ra
omra
1'7mma
Ip( 5 0 kA /div)
Fe (101 4 c m-3/fr)
POSITION
D2
Fig. 1
BT=.8 -7 T
1.5
Te (r)
keV
1.0
0.5 -
0
ne (r) (10
10
14
cm-3 )
--
5-
0-
-10
0
RADIAL POSITION (cm)
Fe = 1.4 x 10' 4 cm-3
ne = 5.5 x IO'4cm-3
Fi-g.
2,
10
Fe = .4xl0
4
cm
3
<9 > = 0.019
<E/ECR> =0.027
4
5i=5.5xIO1 Cm-3
Kg> = 0.005
(E/ECR>=0.005
4
40-
.
I
Z*
30 -
IVI
20 -
0
0
2
--
2
6
4
RADIAL POSITION (cm)
Fig. 3.
!0
8
12
A
T (keV)
1.5-
0
A
1.0
T0
0.5
* Te
0
THOMSON
A
o
T
*
T
CHARGE
A
SCATTERING
EXCHANGE
NEUTRONS
4
2
fe (1014 cm- 3 )
Fig. 4.
6
VR (Volts)
3
21S
0
Ii
I
Ii
i
2
Fe (10
Fig. 5.
14
4
cm- 3 )
Ii
I
6
CE (ms)
60
ZE (NC)
40
/
TE (NC)
=
4o
(ni Ti +neTe)}dr
27rr'
2-irr Q C (r)
20-
4i
2
R fOL
3(niTi+neTe)-rdr
E(EX) =VR'IP
*
. 0
0
0
"E (EX)
*0
0
I
4
2
Fe ( 10 14 c m-3 )
Fig. 6.
6
I
I3P
2-
000
010
0
.46
2
Fe(io' 4 cm- 3)
Fig. 7.
lEO(ms)
20
3e
n
10-
T
ii~ +^iete
0
ZEO
=
5
0
A
n (1014 cm- 3 )
Fig. 8.
E-jo
10
T(keV)
-
T(r) MEASURED
0.8
--
T.(r) DEDUCED
0.6
0 -- -
0.4
ne
0.2 -
5.5 x 1014 crrn3
MEASURED
A
Te = 671 eV
1.5
A
T= 605eV
0
-5
RADIAL POSITION (cm)
Fig. 9.
5
QEX
Q NC( r)
Se =1.4 X 10'
4
cm- 3
100
ne=
5.5 X 1I014 cm-3
10
A
'A
I I
0
U I i liI III III III 111111 j 1 l
2
ib111111111i
H III I I III IlIll
8
6
4
RADIAL POSITION (cm)
Fig. 10.
1
10
I
1-3 cm 2 -s )
3
xEX a
IlHe
e
e
XEX
O XEX
K
4I
2
0
*0-
0
*
0
o
0
0
00
-
O
00
00
I F-
0
X! o
XNC
Xe
0
2
4
ii (1014 cmfig. 11.
3
)
6
It
1.2 -
1.0
L
D
-
14
-BT=3.5 T
-3
0.8
0.6
H
---
-7--
0.4
-
0.2
L
I
-10
5
0
I0
.4
3F
0
2
0
-\I 0
0I
RADIAL POSITION r (cm)
f 'g~12.
)
TE (Ms)
20
5.0
s
14 5 7.0
O H2
3 .5 s
qL
6.2
3.1.
51
n4:5 3.3
10
8
0
5
0
TOROIDAL FIELD BT (Tesla)
Fig. 13.
IJ
10
EE
(Ms)
80
TE (NC)
215 kA
s
Ip
s
235kA
60
40
Z E: (Ex) (2I5kA 5 Ip5 235 kA)
0
0
20
--
0
.--
''
"E (Ex) (130
I
I
2
4
e (10 14 c m-3 )
Fig. 14.
k A5 Ip < 160kA)
6
13
A
3-
-
-3
flTE (10 cm *S)
a
0
4n
A
-c
1.
0
0
0
00000 0~
0
dmp
2
4
n (10
Fig. 15.
4 cm~ 3 )
6