PFC/JA-83-33
MARFES:
AN EDGE PLASMA PHENOMENON
B. Lipschultz, B. LaBombard, E. S. Marmar,
M. M. Pickrell J. L. Terry, R. Watterson, S. M. Wolfe
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA
02139
October 1983
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.
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1
MARFES: AN EDGE PLASMA PHENOMENON
B. Lipschultz, B. LaBombard, E. S. Marmar, M.
J. L. Terry, R. Watterson, S. M. Wolfe
M.
Pickrell*
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA
Abstract
A tokamak
phenomenon,
edge phenomenon,
dubbed the
'marfe',
is described.
This
observed in medium to high density Alcator C discharges,
is
characterized by greatly increased radiation, density, and density fluctuations, and decreased
temperature
in a
inner major radius edge of the plasma.
relatively
small volume at
the
The marfe appears to be confined
to minor radii greater than or on the order of that of the limiter.
The
affected region is typically above the midplane, extending poloidally for
about 30 degrees
and
for
360 degrees
toroidally.
The
temperature and
density of the core plasma are unaffected by the marfe.
port model
is
used
thermal instability,
mechanism out of
onset is observed.
current and
to
show that
with impurity
the marfe
volume.
the marfe
is
the manifestation
of a
radiation being the main energy loss
A density
threshold,
nm is found to be an increasing
a decreasing
A simple trans-
function of intrinsic
Detailed observations from spectroscopy,
function of plasma
plasma
bolometry,
nm for marfe
impurity levels.
Langmuir probe meas-
urements, interferometry and CO2 scattering are described.
*Present address:
Mexico.
Los
Alamos
Scientific
Laboratory,
Los
Alamos,
New
2
I. Introduction
In Alcator C tokamak discharges a phenomenon is frequently observed
which dominates the physics of the edge plasma [1,2,3].
[4] has been coined to describe this occurre,. ze.
The marfe is charac-
terized by a region of cold dense plasma localized
radius edge
of the plasma.
The name 'marfe'
to the smaller major
Similar observations have been reported
on
other devices [5,6,7].
It is apparent
that the marfe
thermal instability
[8,9,10],
is the manifestation
in which radiation supplants conduction to
the limiters as the principal heat loss mechanism
The conditions for its
of a saturated
for the edge
region.
occurrence and location are not as well understood.
There is evidence from tokamaks
with poloidal divertors that heat flows
from the
main
[11,12].
This, we feel, is linked to the marfe occurrence on the opposite
plasma
predominantly
to
the
The precise location
side of the plasma.
well as the conditions
for marfe onset,
larger
major
radius
at the plasma inner
are determined
edge
edge,
as
by the geometry
and magnitude of conduction flows and radiation losses [2].
The marfe
is
a phenomenon
of the main and edge plasmas.
involving
transport
We observe,
and atomic
physics
using Langmuir probes
[131,
that electron density and temperature are not constant on a flux surface
during a marfe.
Large amounts of poloidally asymmetric radiation emission
are measured. Since the input and radiated powers for the main plasma are
not affected by the marfe we can conclude that the total power incident
on the limiters
involved in
has
these
been
reduced.
inhomogeneities
An understanding
could
be
used
to
of
the
control
mechanisms
the
power
flowing into the scrape-off layer. If that power could be dissipated over
3
a large
area at
and radiation
the plasma
edge through charge-exchange
neutral losses
then the remaining sputtering and heat loads on the
[14.],
limiter/divertor plate surfaces would be greatly reduced. Similar effects
are obtained when the high-recycling conditioi
analogous to a marfe,
is
created in a divertor chamber.
A general
The effect
of
characterization
the marfe
of
the marfe
is
given
on the density interferometer
in
Section
II.
is discussed
in
Section III.
Specific observations regarding Langmuir probe measurements
at the marfe
location
data related
to the power radiated by different
The relationship
of
are presented
a marfe
to
a
in
Section
thermal
IV.
Section
regions
instability
of the plasma.
is discussed
Section VI and a discussion on the marfe location is related
VII.
V reviews
in
in section
Sections VIII and IX summarize this paper and detail current inves-
tigations respectively.
II. General characterization
Alcator C has major and minor radii of 64 and 16.5 cm respectively.
Typical operating
parameters
2.5 x 101 4 cm- 3 with
central
are
ion
Signals from various diagnostics,
rence at
120 ms,
are
shown
t
B tor ' 8T$
and
electron
displaying
in Figure
1.
pm)
chord (1a)
tered out
view
of
its
appearence of
the
field
of
noise on the phase
shift display.
effect on the central vertical chord (1b)
litude,
high frequency,
fluctuations.
=
keV.
occur-
the vertical
is refracted
detector,
ne
j 1
of a marfe
At marfe onset,
(119
kA,
temperatures
evidence
inside density interferometer
of
plasma > 400
resulting
In contrast,
or scatin
the
the only
is the appearance of low amp-
Significant effects are also to be
4
found in such traces
detector,
along
a
(ld); and C III
as:
chord
power
at
emission
the
same
(4651A ) horizontal
(1c),
major
chordal
measured
radius
as
by a bolometer
la;
emission (le).
Ha emission
Line emis-
sion from higher ionization states of carbon and other impurities show no
This leads us to conclude that the marfe is an edge pheno-
such effect.
menon.
Confirmation is supplied by two simultaneous perpendicular
views
of the marfe in addition to measurements ,of parameters from plasma within
the limiter radius.
Characterization of the marfe onset involves several factors:
plasma density (F ),
plasma current,
fixed plasma current,
the marfe occurs for He above a critical density,
nm.
and discharge
As the plasma current is increased,
dependence is shown
in Figure
low-z gaseous impurities.
into a non-marfing
2.
to a value
discharge.
integrated
comparable
plasma (out to r = a).
on the signal
to
nm has been lowered
A plot of this
by injection of
The
over
N VI emission
(3a)
and total power
open circles) both rise by a factor = 2.
the marfe
the integral of
volume
(3b,
triangles)
rises
radiated power over the bulk
This observation, combined with effects observed
from the -12
indicate that a marfe
nm also increases.
For a
Figure 3 shows the effect of nitrogen injection
radiated from the bulk plasma (3b,
Radiated power
cleanliness.
cm chord of the density interferometer(3c),
has occurred.
The
total
ohmic input power
rose
from 1.0 to 1.5 MW during the N 2 injection.
The location in major and minor radii of full poloidal limiters has
been varied for confinement studies in Alcator C [15].
plasmas have been produced at three major radii:
Marfes occurred
at the inside
edge
of
the plasma,
10 cm minor radius
57.5,
64 and 70.5 cm.
similar to 16.5
cm
5
plasmas,
for the first
second.
One
first
and third major radial positions,
obvious difference
between
and third were located close to,
surface of the vessel (tangent
still
in place)
while
three
repectively,
to the
the second
these
16.5 cm.
case was
but not for the
cases
is
that the
the inner and outer
radius limiter which was
centrally
located,
with the
vessel walls
far
these data:
the marfe location is not a result of the flux surface geom-
from the plasma.
etry specific to
16.5 cm
One
can draw two
radius plasmas;
conclusions
from
the wall proximity may affect
edge plasma parameters such as electron densi.ty and temperature, although
there is
no direct
experimental
evidence
to
support
this
conjecture.
Impurity levels for the three cases, as monitored through Zeff, showed no
significant differences.
We can further
characterize
the profile information
measurements from
the location of the marfe by examining
supplied by various diagnostics.
several
ports,
and
correlation
of
Multichord Ha
separate
diagnos-
tics, indicate that the marfe location is toroidally symmetric, that is,
not following field lines. Figure 4 shows two such profiles derived from
a
vertically
viewing
bolometer
visible continuum array (4b).
array
above.
Horizontal
widths of
the marfe
In Alcator C,
fluctuations as
center varies
brightness
profiles
we have observed,
changes in both the magnitude
measured
by
a horizontally
viewing
slightly above the midplane.
profile measurements
the marfe
and
These measurements indicate that the marfe
occurred at the plasma's inside edge,
precise position of
(4a)
from the midplane to 8 cm
indicate typical
to
be
in the
vertical halfrange
with the onset of a marfe,
and spatial distribution of
the
CO2
laser
The
scattering
5-8
cm.
dramatic
edge density
technique
[16].
6
The scattered
laser
frequencies between
power,
which
is
20 and 1000 khz,
proportional
to
-n2 and
is shown in Figure 5a.
include
Concurrent
with the onset of a marfe at 150 ms, a large increase in scattered signal
is recorded.
A
similar
effect
visible continuum detector array
is
found
horizontal
on
(Figure
5b).
The
scattering
ments are averages along a vertical chord through the plasma.
of over
two orders
of magnitude in scattered
of
chords
the
measureIncreases
power are often
observed
when the scattering volume intersects the marfe region.
The spatial distribution of the edge density fluctuations was studied
correlation method
using the crossed-beam
derived by performing
[16].
a cross-correlation
of
Spatial information is
two
C0
2
laser
scattering
signals which have chordal views through the plasma crossing at an angle
of 2.9 degrees.
The cross-correlation of these scattered signals provides
of the relative
a measure
amplitude
of the density
fluctuations
in the
The shared volume of these
shared volume of the two observation chords.
two chords is approximately 6 cm in vertical extent and 3 mm wide in both
Vertical
transverse directions.
the common
scattering
scans
volume vertically
of
ff2
are
performed
from shot to shot.
by
moving
Moving the
entire arrangement in major radius permits comparison of density fluctuations at different major radius locations.
A vertical
shown in
Figure
scan of
6a.
the crossed
The major
inside the magnetic axis.
points in time before (open
beams
radius
of
through the marfe
this vertical
region
scan was
is
4 cm
Correlation coefficient scans corresponding to
circles)
and during (closed circles)
a marfe
are nearly identical, even though the scattered laser power has increased
over two orders of magnitude in the interval between the two measurements.
7
A single narrow region (less than the instrumental width) of fluctuations
was found
at
the
limiter
radius
above
the
midplane.
A
similar
scan
through a vertical chord 4 cm in major radius outside the magnetic axis
appears in
Figure
6b.
In this
symmetric profile with
case,
before the marfe
the marfe,
the
circles)
a peak at both upper and lower limiter
Such a profile is typical of a non-marfe
seen.
(open
scattered
signal
rises
by a
discharge
factor
of
a
radii is
[17].
During
15 in a region
localized to a narrow band at the upper limiter radius.
We conclude that
density fluctuations
the
marfe,
exist at
the marfe
region
before
onset
of
a
then increase dramatically in magnitude and spread across the top
of the poloidal
cross-section after marfe onset.
density fluctuations
The amplitude of these
was reduced as the poloidal distance from the marfe
along the edge plasma was increased.
III.
Interferometer effects
As noted above, one of the signatures of the marfe is the "break-up"
of the signal from the innermost chord of the far infrared interferometer.
The normal output of this diagnostic is a display of the phase lag between
a probe and reference
beam.
the plasma along the -12
During the marfe,
the beam passing through
cm chord no longer reaches the detector; as a
result, the phase comparator circuit receives only wide-band preamplifier
noise at one input, producing the "hash" shown in Fig. la.
The most
straightforward
explanation
of
the interferometer
signal
loss is that the density in the marfe region exceeds the cut-off density
for the laser frequency.
However,
the cut-off density
corresponding
to
X = 0.119 mm is 7.9 x 1016 cm- 3 , more than two orders of magnitude larger
8
We therefore regard this explanation as
that a typical central density.
extremely improbable.
A second, more likely mechanism, is refraction of the probe beam by
a strong density gradient
Deflection of
in the vicinity of the marfe.
the beam by an angle of ~ 20 mrad would be sufficient to cause the observed
loss of
signal.
The refraction due to a uniform (or
smoothly varying)
density gradient, is approximately given by
all
Ym
S
-
---
.(1)
The refraction index
where Xm is the path length in the marfe.
=
(1 - 5 /W2) 1/2
1
-
/22,
to the path results in refraction.
and
Taking
6 > 2
perpendicular
gradient
the
only
x
10-2, and the thickness
of the marfe Xm - 2 cm we find
6n
-
1.5 x 101 5 cm~ 4
(2)
.
6x
3
4
Since the density in the marfe is typically a few 101 cm- , this gradient
corresponds to a (perpendicular)
scale length of the order of millimeters,
which is not unreasonable.
IV. Edge probe measurements
A Langmuir
probe
[13]
marfe location as determined
ments (Figure 4).
with larger
same time,
and vertically inserted
into the
from the above brightness profile measure-
The ion density and electron temperature in that region
are shown in Figure 7.
marfe,
was built
The edge density (Figure 7a)
increases
occurring
the electron temperature
at
(Figure
increases during a
larger minor
radii.
7b) decreases.
At the
However,
in
9
contrast to the density change, the temperature decrease is greatest just
If these data are extrapolated to slightly
outside the limiter radius.
slightly increased (~
find the plasma
we
radius,
within the limiter
findings
These
2).
cooled
observations
similar to
are
the density
and
on the FT tokamak [7].
poloidal
other
at
measurements
Edge probe
angles
also
have
At 45 degrees away from the marfe center,
obtained from Alcator C.
been
the
density was observed to drop slightly, and the electron temperature stayed
relatively constant
degrees),
as
the marfe
away poloidally
Further
began.
(135
These data agree with
there was normally no measurable effect.
spectroscopic measurements of the marfe's poloidal extent.
probe
The Langmuir
was
amplitudes for frequencies
also
up to
to
used
kHz.
10
measure
(Figure
7c).
cm prior to a marfe.
amplitude was found to peak at 17.5
fluctuation
density
fluctuation
The
There was no
radial dependence after marfe onset.
V.
Radiated Power
During a marfe,
the
radiated
power
at
the plasma
undergoes
edge
This is illustrated by bolometer array meas-
considerable changes [2,3].
urements shown in Figure 8 for discharges bounded by a molybdenum limiter.
At low
ne,
ions in the
most
of
central
the
plasma.
radiated power decreases
scrapeoff layer,
of the plasma,
measured
although
As
rapidly.
radiation
ne
is
raised,
Meanwhile,
concentrated
is
emitted
by
molybdenum
the magnitude
the power
of
radiated by the
at the smaller major radius edge
is only a small fraction of the total ohmic input.
the marfe threshold is passed,
this
When
radiated power in the rather small marfe
10
region increases to a value on the order of that which is radiated by all
As ;e is in-
range of 20% to 30% of the total ohmic input power (POH).
creased still
further,
the power
the
This value is typically in
of the plasma inside the limiter radius.
radiated
by both the marfe
region and
the bulk of the plasma also increase.
Because such
from the
large
amounts
small
relatively
of
volume,
marfe
20 watts/cm3 .
there are typically
radiated
We
power
local
have
are
being
radiation
identified
emitted
emissivities
four
groups
of
processes which might contribute to this large value of local emissivity.
They are atomic and molecular hydrogen radiation, charge-exchange neutral
emission, and low-z impurity radiation.
Measurements of molecular
been obtained.
line
radiation
have
Although the intensity of these lines increases dramati-
cally during a marfe,
ments indicate
and atomic hydrogen
based on absolute brightness measure-
calculations
~ 10% of
that a maximum of
from
the power radiated
the
marfe region can be accounted for by molecular and atomic hydrogen processes.
that
The hypothesis
neutrals
charge-exchange
greatly
contribute
to marfe power losses was nullified by examining data obtained from two
thermistor detectors
detector was placed
mounted
flush with
so as to have a direct
only a short expanse of edge plasma.
the main plasma,
"view"
chamber
wall:
of the marfe
One
through
The second "viewed" the marfe through
which should reionize virtually all neutrals which have
trajectories passing through it.
plus edge
the vacuum
plasmas
during
The total power radiated by the central
a marfe,
as measured
by
these
271 steradian
11
viewing bolometers,
well as
to
each
was
compared
other.
measurements were
The
equal
to
from the bolometer
to that
magnitudes
within
of
all
three
experimental
array,
as
radiated
power
uncertainties.
This
indicates that charge-exchange neutrals are not a significant energy loss
channel from the marfe.
The remaining process
local radiated
power
in
which
could
a marfe
is
Profile
impurities located there.
account
for the large
thru line emission
cm < r < rwall)
of
from the low-z
of this emission in the
measurements
visible and ultraviolet wavelength ranges have been made.
from the plasma periphery (14
value
Low-z radiation
was found to be primarily
emitted from the smaller major radius edge of the plasma, which is consistent with the bolometer array measurements discussed above.
emission lines of
C III,
asymmetry increased with
emission increases
not the
case
though the
for
edge
C IV,
and
the higher
is
the magnitude of this in-out
C V,
When a marfe occurs, the asymmetry in C III
e..
with bolometer
in accordance
plasma
ionization
expected
not
derived
from
that
calculate the approximate local
measurements.
to
in
coronal
Even
equilibrium
we have utilized steady state
equilibrium
emissivity.
be
This is
above.
states discussed
(because of particle transport processes),
cooling rates
For measured
condition
assumption
to
Utilizing the edge density
and temperatures probe measurements described in Section III, and taking
carbon as a representative
low-z impurity,
we find local edge Zeff's of
>1.5 are required to explain the observed radiation emissivities from the
marfe region.
This includes some extrapolation to radii smaller than the
limiter radius.
The marfe typically has little or no direct effect on the parameters
12
of the central plasma.
that the marfe
density.
Circumstantial
effect
an indirect
may have
evidence,
however,
does indicate
central
on the
molybdenum
Returning to Figure 8, one finds that the regimes of molybdenum-
and marfe-dominated
discharges
are
observation could be coincidental,
mutually
exclusive.
Although
this
no discharge has been recorded with a
simultaneous occurence of large amounts of both central and edge derived
of both types of radiation occur
signals
detectors
Individual
shown:
two chords viewing vertically
chiefly through the marfe
from
in the same discharge but at different
times.
by edge
where large amounts
This is further illustrated by Figure 9,
radiation.
region.
the
bolometer
array
This
edge
are
center and two
through the plasma
This discharge is initially dominated
at approximately 200 ms from the start
radiation which,
discharge, disappears.
in
is
radiation
replaced
by
of the
molybdenum
radiation from the central plasma.
The response time of the detectors is
approximately 20 ms.
concluded
It
may
be
control the
source,
influx and/or retention
main plasma
somehow
inhibit
Studies of
the
transport
impurities indicate
that
unaffected by the marfe.
the marfe
suppresses
the
of
the
the
occurence
artificially
impurity
edge
that
of molybdenum ions
of
a
marfe
or
in the
vice-versa.
trace
non-recycling
injected
transport
which
conditions
confinement
and
are
We are thus led to conclude that the onset of
source
of
molybdenum.
Presumably,
decreased
edge temperatures lead to a suppresion of the mechanism responsible for
molybdenum evolution from the limiters.
VI. Thermal instability and parallel transport
The thermal
stability
of
the
edge
plasma
with
tokamak density limit has been discussed elsewhere [8].
respect
to the
We consider,
in a
13
similar fashion, the electron energy equation:
aE
3
-
=
DnT
5
-
3T
=
2
V -
-
(-KVT
+
-nTV)
Qei + SEe
-
(3)
2
at
For this simple discussion we reduce the above equation to one dimension
along a field line and neglect
in energy sources (SEe),
duction, will
and Qei.
or increase in the divergence
3E/3T
cause
convective terms
<
0.
Following
use the continuity equation to rewrite Eq.
Any decrease
of the heat con-
Braginskii
[18],
we
can
1 in terms of T rather than
nT:
3
-n-
3T
-3
2
at
2
5
nv - VT - nTV - v -
-
=
V - (-KVT + -nTv)
2
Qei
Again, we discard the velocity terms.
as that of Eq. 3,
(4)
+
SEe
The right hand side is now the same
but the time derivative is operating on Te.
Thus, the
imbalance of right hand side terms causes an explicit change in Te. If we
require pressure to be
ne,
constant along a field line,
of terms,
of such an imbalance
then the effect
would be opposite to that on Te.
on
The
energy loss term for electrons includes radiation:
SEe
=
-
-nenofo(Te)
I
ni is the impurity density
the constituent neutral
rate (watts-m3 ).
instability to
for the Ith impurity species.
no refers
to
gas density and fi(Te) is the radiation cooling
dfi(Te)/dTe < 0 is a necessary condition for a thermal
occur in
coronal equilibrium,
edge plasma.
(5)
Z nenifi(Te)
the edge
this
Any decrease
plasma.
For
impurities of
condition can be satisfied
in
Te for a fixed density
Z < 8
over areas
in
of the
or pressure will
14
cause the radiation
Te, causing
to increase.
This heat loss will
to the perturbed
conducted
unless power
even more losses,
further decrease
region correspondingly increases.
The thermal stability of this 1-D system can be judged by depressing
the local temperature an amount 6T and by examining the new power balance.
Should the radiation term increase faster than the conduction term, aT/at
x
would be negative and a thermal instability would occur.
=
L is far away
to the location of the temperature perturbation while x
is fixed.
along the field line where the temperature
power
equilibrium
scribing the
-
nInefi(Te)
V
balance
(CK>
prior
5
--
VT
to
0 corresponds
The
equation deis
perturbation
the
(K/T>( VT) 2
(6)
2
where one impurity is assumed to dominate and <K> is the averaged value
conductivity
of the thermal
For a perturbation -6Te
over L.
at x
-
0,
an instability occurs if:
5
neni[fi(Te - 6Te)
-
>
fi(Te)]
(K/T>[(VTfinal)
-
2
-
VTinitial) 2 ]
2
VT
>
(7)
6Te
+ 5<(/T>L
Rearranging equations, the instability criterion becomes:
-5
dfj
-
< K/T >
(
neniL
dTe
Using carbon
[13], we have
(8)
VT
cooling
rates
[19]
and
edge
Langmuir probe
calculated values for the left-(LHS)
measurements
and right-(RHS)
hand
15
sides of
VQT is
Eq.
8
evaluated
as a
using
the
equilibrium
the instability condition is first
this radius,
of
condition
a local edge carbon density, nc = .02 x ne,
Eq.
met at r=16.9 cm.
This difference
can be
found
to
attributed
6.
of
Assuming
this calculation predicts that
In Figure 10, for
we plot both sides of equation 8 versus Fse.
density nm is higher than that
The value
and Re.
radius
of minor
function
The threshold
= 2.5 x 10 14).
experimentally
("e
the crudeness
of the model.
The
actual carbon abundance and cooling rate in the marfe region are unknown.
In addition,
no field line outside the limiter radius is continuous from
the outside to the inside edge of the plasma.
heat flow should be included;
poloidal Pfirsch-Schlflter
Some sort of perpendicular
either diffusion out of the main plasma or
bulk
convective
in the edge
flows
[201
would
circumvent the limiters.
Eq.
8
was
also
replacing
evaluated
carbon
with
oxygen
as
the
dominant impurity. No unstable cases were found in the plasma edge simply
because the slope of the cooling function fI is positive for most values
of edge temperature. The implication is that an 'oxygen' marfe must start
at a
radius
slightly less
than rlim.
At these
radii,
field lines
can
transport heat more readily; implying that this type of marfe will be more
difficult to initiate.
analyzes this situation
The work of Ohyabu [8,91
and shows that it can lead to a major disruption.
As the plasma He increases,
initiating a marfe.
This
behavior
experimental data reviewed above.
raised,
the edge ne(Te) increases (decreases),
is evidenced
Furthermore,
by both Figure
as the plasma
10 and
current is
one finds that the edge temperature rises due to increased heat
flow into the edge (Figure 11).
A rise in edge temperature would raise the
16
marfe threshold
nm
according
to
Eq.
8
and
experiment
(Figure
2).
Perpendicular heat transport is inherently the mechanism that
allows the marfe to saturate or reach steady state.
the perpendicular
Perhaps
VT, increase.
nificant.
and parallel heat transport,
more
Eventually,
an
importantly,
equilibrium
As Te (x = 0) drops,
which are proportional to
convective
is
reached
terms
similar
become
to
that
sigof
plasmas near limiter/divertor surfaces.
The poloidal and toroidal extent
of the marfe have been discussed above.
In addition,
the marfe
not restricted to radii greater than that of the limiter.
from two observations:
region is
This is inferred
the marfe appears at all toroidal angles
First,
even though the edge plasma is divided toroidally into several separate
Second,
regions by full poloidal limiters.
Figure la is derived
the density signal shown in
chord which passes between
from an interferometer
poloidal limiter rings separated by only 2 cm.
VII. Discussion
Both PDX
heat flow is
plasma.
[11]
and
[121
ASDEX
the smaller major
a minimum near
[211
Analytic modelling
reported
have
of
perpendicular
that
radius periphery of the
Pfirsch-Schlilter
flows
plasma suggest that this in-out asymmetry in perpendicular
due to bulk flow convection.
the previous
section
assumed
heat flow to the edge plasma
The point
where a marfe
inside edge of the plasma.
in the main
flux is
heat
The thermal instability model described in
some
poloidal
in the equilibrium
occurs
(x
= 0)
of
asymmetry
would
perpendicular
state before
then
be
a marfe.
located
at the
ASDEX [6] and FT [7] report marfe-like phenom-
ena on the midplane at this location.
In Alcator C the marfe is normally
17
located above the midplane at the inside edge of the plasma.
bute this positional
difference
experiments to up-down
asymmetries
large to smaller major radius.
asymmetry in flows:
between marfes
in heat
There
on Alcator
We attriC and other
flowing along the edge from
could be
several
causes
of
this
heat flows out of the main plasma may not be up-down
symmetric; the edge plasma may rotate poloidally due to a radial electric
field; and/or there
may be radiation losses
in the edge which lead to
asymmetric poloidal temperature gradiepts and therefore, asymmetric
poloidal heat flows.
There exists little
the first
experimental
evidence
two possible causes stated above.
to support
or disqualify
Fluctuations propagating in
the ion diamagnetic drift direction have been detected, for Tie > 1.5 x 1014
using CO 2 laser
scattering
related to a poloidal
Plasma
convection
experimental
asymmetric heat flows
These propagating fluctuations may be
bulk flow.
Pfirsch-Schlilter plasma
There is more
[171.
suggested
rotation as a modification
flows is
discussed
evidence to
low-Z impurity
radiation
spectroscopic measurements
edge impurity
that a
C III
shell
from the edge
we know that there
increases
with
vertical
asymmetry
exists
intensities
(bottom/top)
as
cause
20.
of
profiles uti-
This emission is typ-
12.
which
emission
simultaneous
support the third
C III brightness
above.
lizing a horizontal view are shown in Figure
ical of
in reference
of
plasma.
is
a in-out
ie.
as
Figure
well.
a function
From vertical
asymmetry in
12
The
of ne is
indicates
ratio
of
given in
Figure 13.
Several points should be noted about these C III brightness profile
data.
First,
the marfe does not occur at the lower inside edge of the
18
plasma (region 1), where the pre-marfe local radiation losses are highest.
In addition,
the radiation losses
implication is
that
accordingly.
the
heat
from
region 1 increase with R e.
conduction
to
that
region has
The
increased
In particular, at the marfe onset, region 1 is not affected,
implying a very 'stiff' source of heat conduction.
The second point to be noted is that the radiation losses from the
edge
of
the
Examining
Eq.
8,
upper inside
changed.
plasma
the
(region
marfe
2)
are
at
appears
constant
region
as
2 not
is
Re
because
radiation losses have increased, but rather because the heat conducted to
that region (RHS of Eq. 8) must have decreased.
We might
losses are
have
the
expected
marfe
greatest before the marfe.
ae
where increasing
no
has
Re is
as
explanation follows:
effect
on
occur
there.
fixed
flow increases
to
It
there.
follows
region
1
statement in terms
of Eq.
8,
the
right
hand
constant while
and
that
decreases
as
region
The
C III
to
He
2,
One possible
in
region 2 is relatively constant as a function of R e
is relatively
radiation
occurs in region
losses.
radiation
Te
the
where
Instead it
increased,
C III emission
resulting in increased
to
1
decreases,
emission from
indicating that Te
the heat
increases,
2.
region
Putting
this
we see that the left hand side is staying
side
drops
in magnitude
for
region
2.
Eventually, the instability condition is met there.
VIII.
Summary
The marfe
major radius
is
a
cool high-density
periphery
of
the
plasma.
region
It
located
appears
for
at
ne
the
smaller
above
some
19
The
threshold density, nm..
value
of
nm
is
increased
by
raising
the
plasma current and decreases by increasing the impurity density.
Experimentally, the edge region is characterized both before and during a
marfe by poloidal variations
radiation is
marfe.
both
in-out
The magnitude
Before a marfe
occurs,
in a
and
number
up-down
of these
of parameters.
asymmetric,
relative
inside edge of the plasma.
and during
increases
with Eie.
increase in magnitude and
af.ter the onset of a marfe,
Also,
a
are localized to the upper-
These fluctuations
expand poloidally during a marfe.
before
asymmetries
density fluctuations
Edge impurity
the
local (marfe region) electron density increases and temperature decreases.
Power radiated
~ .2-.3
from
this
edge
region
typically
to
increases
levels
The power radiated from this small fraction of the edge
x POH.
plasma is often equal
(central) plasma.
to,
or greater
that
than,
from the bulk
emitted
The marfe thus supplants the limiter as an edge energy
sink.
A simple
thermal
instability
model
is
model,
This
discussed.
combined with the hypothesis that perpendicular heat flow out of the main
plasma is not poloidally uniform, correctly predicts the marfe characteristics: threshold
density,
nm;
location
in
minor
radius
poloidal
and
Alcator C, exhibits verti-
angle; and scaling of nm with plasma current.
cal asymmeties in impurity radiation emission. This asymmetry in radiated
power causes
asymmetries
vertical asymmetries
one
in edge power
might
inside midplane of the plasma.
expect
flows.
the
In the absence
marfe
to
be
of these
located
at
the
If vertical asymmetries in emitted power
are present, the marfe location could shift off the midplane, as observed
in Alcator C.
20
Further work
is
needed
to
from onset through saturation.
understand
the
dynamics
of
the marfe
The physics involved in this phenomenon is
quite complicated, similar to that of the plasma located at limiter/divertor surfaces.
IX. Continuing investigations
Currently work
on
understanding
the
marfe
is
being
pursued
both
experimentally and theoretically
at M.I.T..
built to measure edge parameters,
at one toroidal location, simultaneously
A multiprobe array is being
at a number of poloidal angles and minor radii.
A one-dimensional
numerical model for transport along a field line [22] is being utilized
to understand the marfe. This model includes convective as well as conductive transport in a time-independent,
ular source terms
be implemented.
single fluid treatment.
Perpendic-
of both uniform and nonuniform spatial dependence can
The
earlier
analytic work mentioned
[20]
is being ex-
tended to a more rigorous two-dimensional numerical model.
Acknowledgements
The authors
would like to thank the rest
outside collaborators
U.S.D.0.E.
for their assistance.
contract # DE-ACO2-78ET51013.
of the Alcator group and
This work was supported by
21
References
[11
J.
L.
Terry,
et al.,
Hydrogen Line
Phys. Soc.,
[2]
B.
"Strongly
Emission
in
Some
Enhanced
Alcator
Low-Energy
Continuum
C Discharges"
Bull.
and
Amer.
26, 886(1981).
Lipschultz,
B.
LaBombard,
M.M.
Pickrell,
J.L.
Terry
"Marfes:
Poloidally Asymmetric Edge Conditions in Alcator C" Bull. Amer.
Phys.
Soc., 27, 937(1982).
[3]
M. M.
Pickrell,
"The Role of Radiation on the Power Balance of the
Alcator C Tokamak" M.I.T. Plasma Fusion Center Report, PFC/RR-82-30.
[4]
The name
"marfe"
is a concatenation
Marmar and Wolfe.
of the last names
of authors
Indications of a marfe occurence were first noted
on signals from diagnostics operated by those persons.
[5]
D.
R.
[6]
H.
Niedermeyer,
Baker,
R.T.
Snider,
et al.,
M.
Nagami,
presented
Nuclear Fusion 22,
807(1982).
at the European Physics
Society
conference in Aachen, September, 1983.
[7]
F. Alladio et al., Physics Letters, 90A, 405(1982)
[8]
N. Ohyabu, Nuclear Fusion, 9, 1491(1979)
[91
N. Ohyabu, Kakuyugo-Kenkyu, 43, 9(1981).
[101 J. Neuhauser, "Characteristics of a Radiating Layer Near the Boundary
of a Contaminated Plasma", Max-Planck-Institut ffr Plasmaphysik, IPP
1/182(1980).
[11] D.
K.
Owens,
et.
al.,
Journal
of
Nuclear
Materials,
93-94,
213
(1980).
[12] H.
Keilhacker,
et al., Max-Planck-Institut
IPP 111/72, (1982).
fur Plasmaphysik,
Report
22
LaBombard,
[13] B.
Lipschultz,
B.
of
Probe Measurements
the
Pickrell,
M.
Edge
Y.
in Alcator
Plasma
"Langmuir
Takase,
C"
Bull.
Amer.
Phys. Soc., 27, 1036(1982).
[14] B. Lenhert, Nuclear Fusion, 19, 1319(1978)
[15] B.
Blackwell,
et.
al.,
9th
(IAEA
International
Conf.
1982) 1983,
Baltimore,
Physics and Controlled Nuclear Fusion,
on Plasma
IAEA-
CN-41/C-4.
[16] C.M. Surko and R.E. Slusher Phys. Fluids 23, 2425(1980).
[17] R.L.
C.M.
Watterson,
Surko
and
R.E..
Slusher,
"Spectra,
Spatial
Distribution and Propagation Velocity of Low Frequency Fluctuations
in Alcator C" Bull.
[18] S.I.
[19] D.
E.
Braginskii,
Post,
Amer.
Reviews
et al.,
Phys.
Soc.,
27,
937(1982).
of Plasma Physics,
Vol.
1,
Atomic Data and Nuclear Tables,
205-311(1965).
20,
397(1977).
[20] B. LaBombard, M.I.T., Plasma Fusion Center Report.
[21] M. D. Rosen and J. M. Greene, Princeton Report PPPL-1315.
[221 B.
Lipschultz,
M.I.T.,
Plasma Fusion Center Report
# PFC/RR-83-25.
23
Figure Captions
Figure 1:
Diagnostic traces vs. time.
The marfe occurs at 120 ms.
a) The inside (-12 cm) vertical density interferometer chord;
b) The central vertical density interferometer chord;
c) The inside (-12 cm) bolometer channel; d) H-alpha emission
which saturates after marfe onset; and e) C III line emission
(4651A).
Figure 2:
Threshold density, nm, for marfe to occur vs. plasma current.
Figure 3:
The effects of N 2 injected into a non-marfing discharge:
a)
N VI emission (1897A); b) Power radiated from the marfe area
at the plasma edge (closed triangles) and from the main plasma
(open circles); c) Line-averaged electron density from inside (-12
cm) vertical interferometer chord.
Figure 4:
Brightness profiles before and during a marfe:
a) Bolometer
profiles as viewed vertically, and b) Visible continuum profiles
viewed from the horizontal direction.
Figure 5:
Evidence of high-frequency edge density fluctuatons during
a marfe: a) n~ 2 signal from CO 2 scattering; and b)
Horizontal chord of the visible continuum array.
The marfe
begins at 150 ms.
Figure 6:
Two-beam CO2 laser correlation measurements before (open circles)
and during (closed circles) a marfe.
The two traces shown in
a) and b) correspond to vertical profile measurements through
the plasma for R-Ro
=
+4 cm. and R-Ro = -4cm. respectively.
I
24
Figure 7:
Langmuir probe measurements, before and during a marfe, versus
minor radius outside the limiter radius: a) Ion density; b)
Electron temperature; and c) Fluctuation amplitude.
Figure 8:
Fraction of the ohmic input power radiated from the
marfe region (x-x-x) and from the remaining bulk of the
plasma (closed circles) vs. -ne
Figure 9:
Brightness of four vertical bolometer chords vs. time:
traces
a) and b) principally view the inside edge of the plasma and
are a measure of power radiated from the marfe region; traces
c) and d) are central chords and thus are good measures of
molybdenum radiation.
Figure 10:
The left-(LHS) and right-(RHS) hand sides of Eq. 6 plotted
as a function of ne.
Figure 11:
Te, at r - 17.3 cm, versus plasma current for a fixed
Figure 12:
C III brightness profiles (horizontal view):
e.
before the marfe,
the intensity of emission from the bottom inside edge of the
plasma increase with ne (open circles); when the marfe
occurs the intensity at the upper inside edge of the plasma
increases (closed circles).
Figure 13:
Pre-marfe ratio of C III brightness from lower inside over
upper inside edge of the plasma vs. ne.
I
I
i
a
bl
C
d
I
0
100
I
200
msec
Figure 1
300
400
nm vs. PLASMA CURRENT
3.3
X
x
E
X
x
x
X X
X
E
C
2.71X
X
C
x
2. 1
X
(D
X
1.5 L
25 0
x
I
.
350
450
.
550
Plasma Current (kA)
Figure 2
sv/~f1
Injection Time
a
Cn
z-
800
-A-
Power from
Marfe
6001
-o-- Power from
Bulk
4001
0
-J
2001
C,)
C
zd
0
100
200
300
400
500
Figure 3
MILLISECONDS
8447
BOLOMETER
IC
a]
W
111r411~
0
wr
C
MARFE
0d
C
-12.0
'I
-8.0 -4.0
0
HORIZONTAL
4.0 8.0
12.0
POSITION (cm)
VISIBLE CONTINUUM
16.0
b]
MARFE
+
+1I 4
top
-16
VERTICAL
POSITION
bottom
PFC-&99
Figure 4
I
I
I
i
I
I
I
300
400
a
0
100
200
500
Time (msec)
Figure 5
0.80
0-
I
0.60
-I
S0
0.40
/
E-0
0.20
C
CR/
Ol
-20
-10
0
+10
+20
+
+30
0
0.8010.600.40-
0.20
0
0
.Oo
'
ZI
-20
0-Oi
-10
0
+10
+20
+30
Vertical Distance
(cm)
Figure 6
1 015_
/
A o o/
14
10
-
/
4.1 mm
0
0
8/
0
0
E
0
0
0
Am
.0/I
/
10
0
0
.0
/
0
Y 2.5 mm
0
z
0
0
0
10
0
/
0
0 - AVERAGE DENSITY
BEFORE MARFE
I
/
10
-J
18.5
* -AVERAGE
DENSITY
DURING MARFE
0
0
n
18.0
m
17.5
17.0
165
16.0
RADIAL POSITION (cm)
Figure 7 a
20-1
00
0
15-
0
D:
LU
0
10-
03
z
0
0
C")
LU
0
0
BEFORE MARFE:
0
0-PEAK Te
5-
DURING MARFE:
7.
*-AVERAGE
Figure 7b
0
-I.
18.5
In
~m
18.0
I
17.5
17.0
RADIAL POSITION (cm)
16.5
1
16.0
Te
0.5-
0
0,4-
0.3.
cr
0
S
S
0
S
0
0
0
.
0
0.2-
0
0
8:
.
0
0
8
0
0.1-
0
0
0
0
0
0
18.5
,~
00-
I
I
18.0
17.5
RADIAL
v
I-.
BEFORE MARFE
DURING MARFE
17.0
POSITION
16.5
16.0
(cm)
Figure 7 c
0.8 K-
0.6
I
0
a-
4x
0
*0
0
a-
x
0.4
0.2
x
0
0
x
xxxx-X
I
2
I
4
6
ne (1014 c m3)
Figure 8
marfe
a) -12.6cm
04
b) -Il I m
-
-c
c) -2.5 cm
d) Center
I
I
I
Time (100
I
I
I
I
ms/div)
Figure 9
6f7Z
o -R.H.S
0~x - L. H.S
0
-6
C
a
10
100
10
10
14
>(10 c
-3-
6.0 -
5.01-
0
4.0
I-
3.0
2.0
I
200
I
300
Plasma Current
400
(kA)
Figure 11
9471
C II BRIGHTNESS PROFILE:
MARFE AND
PRE-MAREE
987
-
6
0 5
U
z
1-
4 -
CC
3 00
Top
-
-0
Midplane
Bottom
Figure 12
PFC - 820/
4
I
I
C'T
.5101.J.
-F (014i3i3
LU-80
Fiur 13