PFC/JA-88-24
The Production and Maintenance of High
cp Tokamak
Plasmas by Means of RF Current Drive
S.C. Luckhardt, K.I.-Chen, S. Coda, J. Kesner,
R. Kirkwood, B. Lane, M. Porkolab, J. Squire
June 1988
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA
This work was supported by DOE Contract No. DE-AC02-78ET-51013.
Submitted for publication in Physical Review Letters
The Production and Maintenance of High ei
Tokamak Plasmas by
Means of RF Current Drive
S.C. Luckhardt, K.-I. Chen, S. Coda, J. Kesner,
R.
Kirkwood,
B.
Lane, M. Porkolab, J. Squire
Plasma Fusion Center and Research Laboratory of Electronics
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
ABSTRACT
It
is
shown that in tokamak plasmas sustained by RF current
drive, the contribution of the
population
to
the
poloidal
suprathermal
RF
driven
electron
beta (Pp ) can be substantial if the
total current is comparable to the Alfven critical
current,
I
4Tmc
v
4vm v . Equilibria with values of eP up to approximately 1.2
p 0e
c
p
were obtained, and no equilibrium or gross stability
observed.
-1-
limits
were
Instability
limit
of
ideal
MHD
the maximum achievable
P
achievable
would
3
remove
ballooning
in
a
modes is believed
tokamaks.
significant
Increases
the
investigate
confinement
the
P
high
required
regime
for
of
reaching
tokamak
(P1 >P11 )
energetic
operation
poloidal
component
In these experiments
by
means
the
.
anisotropic
energetic
pressure
electron
bulk
(P 11>P,)
component
electron
values
of
the inverse aspect
In the present paper we report results in
plasma
various
the
of
maximum
beta ranged up to 1P=0.8/a where e is
ratio, a/R
of
To
the plasma2-6 or by forming an anisotropic
electron
cyclotron heating.
in
feasible,
ignition.
experiments have been carried out either by heating
Maxwellian component of
the
design constraint
tokamak D-T fusion reactors, make advanced fuel reactors
and ease
in
to
which
the
is produced primarily by an
generated
and
sustained
by
lower-hybrid RF current drive.
The poloidal beta of a plasma with anisotropic pressure, such
as
those produced by RF current drive, may be written as8
/(B 2 /2p )+Pi
p=
2
p2
Ba
=
1i
I/(2Ta),
/(B2a /2p ) where
where P 9pp = m e f e v 2p ,
and the overbar indicates both integration over
velocity space and volume average.
produced
model of
electron
P Ii. = m e f e V21'
tail
to
the
The
contribution
the
RF
pressure can be evaluated for a
the RF driven electron tail consisting of a
-2-
of
flat
plateau
with
a
perpendicular
function is f (v
=
0
temperature
2
v1
otherwise.
T0.9
fexp(-mv /2T
The
upper
The
) for v
velocity
distribution
< v1
< v2
f
and
limit, v 2 , is equal
to
the
the RF spectrum,9 and
highest parallel phase velocity component of
typically v 1
tail
= 4(Te/m) 1/2. With fftd 3 v = nt(r),
the tail
density,
the poloidal beta as defined above can be evaluated as
=T(+3[
2
0
A
RF
me v 2
with
the approximations v 1 /V 2
defined IA as
usual
that
<
<< 1. We have also
1, and v 2 2/c2
the Alfven current,10
A=17kAiv 2/c where
i
is
the
relativistic factor evaluated at v=v 2 * Equation 1 indicates
the
poloidal
proportional
IRF =A
beta
IRF
to
of
the
RF
thus the high
driven
tail
is
inversely
PP regime may be reached when
1
for an RF current driven plasma. 1
In the Versator II tokamak R0 = 0.405m, aL = 0.13m, and
=
= 0.32, and the plasma is sustained by lower-hybrid current
a L/R
drive at a
current
frequency of 800 MHz. In the
drive
was
initiated
following the opening of
The
e
current
than the L/R
was
time
then
of
during
the ohmic
present
the
heating
experiments,
current
decay
transformer
RF
phase
circuit.
maintained by RF drive for a time greater
the
plasma
-3-
(5-10
msec
typically)
with
vanishing
inductive loop voltage. For
where
(=)3-+1
p i /2,
P*
p
)_If2f rdrd6 B ), as obtained from
11=(a2B
i
0 0
equilibrium measurements,8, 1 2 ,1 3
decay
5.1.
phase
P3
from
the example shown in Fig. 1,
an
initial
rose
linearly during the
value of 1.6 to a maximum value of
13
was initially maintained at a steady level of
p
then
after
a
4
msec
electrons occured, as
t=27msec.
at
At
quiescent
period,
a
loss
=
time p3
p
of energetic
emission
abruptly decreased by 12%,
4.4. This electron loss burst occured irregularly and is
to
be
caused
by
the
Parail-Pogutse 4
for
the
duration
relaxations or decreases
energetic
in Fig.
with
a
in
of
the
13
p
=
believed
RF
discharge
p
limiter (see
1) was generally observed during the
was
pulse without further
p . Interestingly, an increase in
electron flux to the
rise
to
microinstability of the
anisotropic electron population. Subsequently, the
maintained
5.1.
p
indicated by a burst of hard x-ray
this
current
the
the hard x-ray signal
rise
of
P ,
along
in the loop voltage. The flux then decreased during
the current flattop. This behavior was a repeatable characteristic
of
these experiments. In the following we will be
the
concerned
with
equilibrium properties of the steady-state RF driven phase of
these plasmas.
An independent indication that high poloidal beta
were
indeed
obtained comes
the magnetic axis at
outward
shift
of
high
equilibria
from the outward equilibrium shift of
eap
p
15
which
produces
the density profile. The total
the centroid of the density profile, AN9
-4-
relative
an
observable
outward shift of
to
its
initial
position
at
1
low
(*
p
< 1.0) is plotted in Fig. 2 against 13
p
p
Also plotted in Fig. 2 is
the
of
high
the magnetic axis
equilibrium
code
density
equilibrium
ap p ,
simulations.
the theory of Ref.
the
at
theoretical prediction for
15,
profile
shift
and
the
results
of
(In order to obtain P* from
p
1 1/2 = 1.0 was
taken.)
peak
to
of
the shift
appears
MHD
1
p
in
The outward shift of
agree
well
with
the
the magnetic axis, within the experimental
uncertainty.
A further confirmation of
hard
the outward shift was found in
x-ray emission profile of
measured
with
a
the energetic electron population.
the x-ray bremsstrahlung emission
The major radial profile of
collimated
NaI(Tl)
crystal
a
into a recessed vacuum port viewing dump so that
walls
and
limiter
vertical
of
was
from
were eliminated. The pulse height system
Fig.
1).
The
x-ray counts detected in the energy range of 15-100keV
is plotted in Fig.3 against
profile
chord
stray x-rays
collected counts during the RF driven flattop (see
number
was
detector and pulse
height spectrometer. The detector viewed along
the
the
found
to
the major radius. The centroid of
be
shifted
outward
the
to R=0.43m from the
geometric center R =0.405m. The width of the profile
at
the
one
e-fold decay point was W HXR=0.10m +0.015m.
To
width of
obtain
1
p
from
13
p
a value for
1 /2
1
is needed. Using the
the x-ray profile as an approximation to
RF current profile 1i
can be
calculated.
-5-
the width of the
Modelling
the
current
profile
as
J=J exp(-r /N
coordinate, and X
)
where
r
is
the
minor
is the Gaussian width, the internal
radius
inductance
can be written as 1 120.55+21n(aL X). Taking X =WHXR/2 =0.05m, the
value
1 /2
of
is 1.2. With 13 =4.4 during the x-ray gate period,
i
p
the value of ep
is 21.0, and at the highest 13
(= 5.1) e13 2 1.2.
p
p
p
Owing to the large values of 13
obtained here, the value of 13
is
p
p
relatively insensitive to errors in 1 /2, for example, even a 30%
error in X
would only produce an 8% error in the value of 13
The
.
central value of q (=B r/B R) can also be calculated from the
?
P~
Gaussian current profile model, q
2T B X2/(p R
IF). For a
0
0 J
0 0 RF)
width X =0.05 m, IRF= 5kA, and B =O.7T, q is 4.4. Hence for
the
case
shown
in Fig. 1 the current profile modeling indicates q
1, and in this case the value of qcyl
>
(=eB /B ) =29.
A test of the validity of Eq. 1 is provided by the scaling of
13
with the RF current and
toroidal
field. The values
of 13*
p
attained during
the RF driven flattop are shown in Fig. 4 as a
function of IRF. The data indicates that
an
3p
approximately
follows
I RF-1 scaling, and increases with increasing B . Evaluating Eq.
1 with v 2 =1 .9x108 m/sec, for B =0.7 T, and v 2=2.13x108
B =0.9T
(where
criterion
16
solid
we
plotted
in
Fig.
4.
11/2
Here
we
=
2
2
0.1.
Although
there
may
be
gives
in
Ref.
some variation of l
current, taking the prediction of Eq. 1 for
-6-
1.0
13
the
have also used the
prediction for the tail perpendicular temperature T
2T /mv
for
have used the lower-hybrid wave accessibility
to calculate v 2 ), and taking
curves
m/sec
and
1 /2=1
9.
with
yields
generally good quantitative agreement with the data for
Ideal
MHD
theory
predicts
stable
access
to
stability regime of high toroidal mode number (n)
can be raised sufficiently. 1 7
if q
experiment,
assess
this may be
the
18
achievable
predictions
of
formula
Troyon
for
pressure profiles and q 0 1,
RF
ballooning modes
current
Princeton
PEST
kink/ballooning
cannot validly be used here since
second
drive.
To
MHD equilibrium and stability
theory, modeling was done using the
simple
the
As suggested by the present
with
ideal
Pp .
mode
it was obtained
conditions
code. 1
The
instability
with
optimized
that are not well
satisfied
in this experiment. Equilibria which best modelled the experiments
had
approximately circular plasma boundaries, elongation 0.9-1.0,
and were found to be stable to high
highest
region
e13
( 2
17,18
was
sufficiently
define
of
of
613
the
ef3
found
narrow
exists
seen
q 0 >8
and
realistic)
0.3
epp1
the
for
in
<
ef3
p
unstable
region.
<
0.4,
for
least
stable
value
n modes, but at higher e3
that
the
enhanced
losses
these modes
of
energetic
this experiment during the ramp up of app are
present
profile,
the
pressure profiles. Here we
the most unstable or
high
experiment)
0.8. However, if
x-ray
at
the second stability
due to such instability activity. For q 0 4.4 (as
for
modes
or wider pressure profiles, an unstable range
restabilize. It may be
electrons
when
(but
lower q0
ballooning
stable transition to
transition as
For
.
1.2). A
n
then
these
the current
q0
could
Stability
of
-7-
modes
profile
be
is
estimated
above
restabilized
above
narrower
than
lower, which would expand
anisotropic
pressure
the
the
(P 11>P 1 )
equilibria
was
also calculated,21 and these equilibria were also
found to be stable.
from
the
x-ray
If indeed q 0 4.4 in Versator
profiles,
then the
II,
as
inferred
theoretical modeling suggests
p
that Versator is beyond the critical
needed for
transition
to
the second stability region.
In
conclusion,
can be used
these experiments show that RF current drive
to produce high poloidal beta plasmas (e3pl)
with the
pressure and current supplied by the RF driven energetic
component.
Magnetic
measurements
limit was not encountered as
value
in
the
Pp
indicate
was
increased
ohmic inductive phase to
produced,
0.4 and q 0
e1p
=
= 4.
1.1
in
with
the
beam
stability was shifted to higher
current
driven
61p
(p1)
low current and high q 0
that
obtained
second
experiment
that it may be
to reach stable equilibria at
could
raise
is reached,
one
the plasma pressure and current keeping the pressure
to 1 , thus
deep within the
and q cyl
1.2
the second stable regime
P and current. Specifically, once high eap
q
22
transition to
higher
plasmas
to
plasmas. Owing to
placing
possible to use the technique of entering
proportional
initial
up
Ref.
the transition region. It should be pointed out
initially at
its
ranging
reported in
differences in the profiles and geometry, the
in
from
transition to second stability at e3p G
Recent experiments
neutral
an equilibrium
its maximum during the RF
driven flattop phase, and equilibria with eap
were
that
electron
raising P
at
fixed
13 .
Further,
for
second stability regime, one could reduce
while maintaining stability.
-8-
The authors would like
with
able
B.
Coppi,
to
acknowlege
useful
S. Migliuolo, J.J. Ramos, and D.
conversations
Sigmar, and the
technical assistance of Edward Fitzgerald and John Nickerson.
This work was supported by US
DE-AC02-78ET-51013.
One
Department
of
of the authors (R.K.)
TRW graduate fellowship.
-9-
Energy
contract
#
was supported by a
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Coppi, A.
Ferreira,
J. W-K. Mark, and J.J. Ramos, Nucl.
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Nucl. Fusion 21,
3.
M. Keilhacker, et al.,
4.
R.D. Stambaugh, et al.,
1409 (1981).
Nucl. Fusion Supplement 1, 71
Nucl. Fusion
Supplement
(1985).
1, 217
(1985).
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(1987).
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et al.,
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Morris, Proceedings of the third joint Varenna-Grenoble
International Symposium on Heating in Toroidal Plasmas, ed.s C.
Cormezano, G.G. Leotta, and E. Sindoni, EUR 7979 EN, 2, 647
(1982).
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-10-
9. V. Fuchs, R.A. Cairns, M.M Shoucri, K. Hizanidis, and A. Bers,
Phys. Fluids 28, 3619 (1985).
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11.
S. von Goeler (private communication).
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(1971).
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-11-
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-12-
to be published, also General
FIGURE CAPTIONS
Fig. 1
Time history of plasma current,
13 (= P p +11 /2),
p
loop voltage, density,
hard x-ray emission, equilibrium field
current, and toroidal field for a
driven plasma with high
typical RF current
Pp .
Fig. 2 Comparison between the outward shift of the density
profile peak, A N' with the MHD theory prediction of
magnetic axis shift at high
the
Pp .
Fig. 3 Radial profile of hard x-ray emission in the energy range
15-100keV for
the equilibrium in Fig. 1. The limiters were
at R0 = 0.27m and 0.53m, and R
Fig. 4
=0.405m.
Comparison of RF driven equilibrium values of
with
w
the
p
prediction of Eq. 1. B =0.9T for the upper curve and
B =0.7T for the
lower curve.
-13-
10.
IP (kA)
X-RAY GATE
0.
0.
VL (volts)
C
5e(xIO12C
-3
LC
0.0
5.0
0 p*
0.0
HXR
0
IEF (kA)
1.0 -
I
I
0.0
8.0
B4 , (k G)
/-I-
nn.
10.0
20.0
RF
RF
30.0
TIME (MILLISECONDS)
14
-
I
40.0
CD
LO
LO
w0
Z
z
0
-F 0
o F-
.12
I
CD
10
I
14
0;
0
D/Nv
15
0
0
S
4
It
I-
LO
44
'-4
'-4--i
/
S0
-4-i
~V)
0O
1-4-1
i
0
0
U")
I
0
(A!900 L
0
16
L)
0
C*
0
SiNflOo
LO
N~~
0
C*-4
--
F-
4-4
c;
U'O
I-
Li..
Up)
I
I
a
I
0
'-
dj
17
0