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Impure tokamak PEDESTALS with strong radial electric field
Silvia ESPINOSA, and Peter J. CATTO
{espinosa, catto}@psfc.mit.edu
epsi.pppl.gov
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA.
Theoretical modelling
Tz [eV]
From radial impurity
force balance
principles understanding
of ETBs has not yet been obtained.
Numerical
and analytical studies areTcomplicated
by the short
pol
T
pol
1 @pzradial
scale lengths in the pedestal [11, 12] and experimental
Ttor
Er =
+ Vz,tor
Bpol andVusually
Btor
measurements
are challenging
limited
to a single
z,pol
Zenz @r poloidal location, such that information
Ttor about variations of
600
400
400
200
200
HFS
LFS
H-Mode parameters:
Ip=0.62 MA, PRF=2.6 MW
B0=5.5 T, BφHFS=8.1 T, BφLFS=4.1 T
BθHFS=0.72 T, BθLFS=0.56 T
neped=1.3 1020 m-3, Tped=350 eV
Vpol > 0
a) Strong radial electric field (Kagan et al [3–5])
0 on a flux surface is often missing. As
plasma parameters
40
Vpol > 0 I-Mode parameters:
poloidal asymmetries are expected to scale with the ratio
Eofr Vtor
20
20 radius and radial scale length
poloidal Larmor
[13], they
Ip=-1.3 MA, PRF=4 MW
Er Vtor
could be important E
inrthe
pedestal region. Recent neoclassical
B0=-5.6 T, BφHFS=-8.4 T, BφLFS=-4.2 T
dia
V
>
0
0
0
tor
E
r Vpol
calculations
have indeed revealed strong poloidal asymmetries
BθHFS=-1.62 T, BθLFS=-1.07 T
(b)
ped
associated with−20
steep pedestal gradients [12, 14].
neped=1020 m-3, T =800 eV
−20
Er dia
Bφ, Ip >0
In this paper, we present new experimental insights on
−40
−40
the poloidal structure
ofE the
pedestal. In particular, our
r Vpol
Figure 1. Left: typical magnetic equilibrium of a lower single null
measurements
indicate
that
in
the
pedestal,
plasma
potential
discharge on C-Mod. Arrows indicate the positive direction of HFS
−60
−60
Er
H-mode,
and temperature are not necessarily constant on a flux and LFS poloidal flows as well as toroidal flow, magnetic field, and
Er
low field side
−80
−80
surface. The measurements,
performed on the Alcator C-Mod plasma current. Right: some key parameters of the discharges
[15–17],
are 0.9
enabled
a recently
developed
gas- discussed in this paper.
0.9
0.92
0.94
0.96 tokamak
0.98
1
0.92using
0.94
0.96
0.98
1
Nucl. Fusion 53 (2013) 122002
Letter
ρ
puff charge exchange recombinationρ spectroscopy technique
18
18
x 10
x 10
(GP-CXRS)
[18],
allowing
for measurements at both the high collisionality, while I-mode is a low collisionality regime,
5+
gure 3. (a) GP-CXRS
6 measurements (B ) at the LFS midplane in H-mode. The
3 top panel shows boron temperatures measured with
LFS
orradial
high-field
sideobtained
(HFS) using
and the
outboard
or ,low-field
oidal and toroidal viewing optics. The bottom panelinboard
shows the
electric field
equation
(1). Er,dia
ELFS
usually obtained with the ion ∇B drift away from the active
r,Vpol , and Er,Vtor
HFS
ow, respectively, the4 contributions from the individual
terms
on
themidplane.
right of equation
(1).technique
(b) The same
in (a) for measurements
at the
HFS
2 This
side
(LFS)
hasas previously
allowed
X-point. The decoupling between energy and particle transport
S midplane.
insights about poloidal1 variations of toroidal flow and impurity
in I-mode, as well as other properties [6, 25, 29], make it
Nucl. Fusion
Letter
2 53 (2013) 122002
(a) I-Mode, LFS
(b) I-Mode, HFS
density on Alcator C-Mod
a promising regime for future fusion reactors. Some key
18
18 [19, 20] and ASDEX-U [21, 22].
x
10
x
10
0
0
6
3
As shown
here,
GP-CXRS
reveals clear Er wells and impurity scalar parameters of the EDA H-mode and I-mode discharge
1500
1500
600
800
LFS
LFS
T
temperature
pedestals
at
both
measurement
locations
in
I-mode investigated here are given in figure 1. Both discharges are
tor
HFS
4
600
HFS
2
1000
1000
400
and TEDA
plasmas. When HFS measurements are run in a lower single null configuration. The I-mode discharge
tor H-mode 400
Tpol
2
1
500
mapped
along
magnetic
flux
surfaces
to
the
LFS,
there is an is performed in reversed field, with toroidal field and plasma
500
200
Tpol
200
uncertainty in the radial alignment of HFS and LFS profiles current in the counter-clockwise direction if viewed from
00
0
0
0.92
0.94
0.96
0.98
1
0.9 magnetic
0.92
0.94
0.96
0.98
1
600
800
due to uncertainties
in the
reconstruction.
Aligning
above. Figure 2 displays radial profiles at the LFS midplane of
ρ
60
60
ρ
B
θ
600the impurity temperature profiles align
the
profiles
such
that
and
ρ
=
ρ , the radial temperature
the
ion
Larmor
radius
ρ
i
400
i
Bθ i
Er Vtor(TB ) from an EDA Figure
Figure 40
1. Boron density (nB ) and temperature
E
Vtor
2. Boron density(nB ) and
temperature
(T
)
from
an
40
B
400shift
well and
with
respect
results
ofHFS
thenB HFS
Er rsquares,
and electron density scale lengths LT = |Tz /(dTz /dr)| and
H-mode, with the HFS nB in green squares, and
the LFS in
nB an
in outward
L-mode,
with the
in green
the LFS
nB in to
200
red circles.
present.
20
20 A clear in–out density asymmetry isthe
circles.
asymmetry is
LFS one by ared
substantial
ofnotitspresent.
width. On the other Lne = |ne /(dne /dr)|, and the collisionality [30] ν ⋆ =
200 In–outfraction
1.5
00
hand,
aligning
the
0 location
18 of the Er wells results in LFS to
0
qR/(ϵ
vth,i ) in these plasmas. Electron density ne is
ν
ˆ
ii
E
dia
x
10
0.94 density
0.96
0.98
1
Large 0.92
boron impurity
asymmetries
are observed
in
0.9
0.92
0.94
0.96
0.98
1
r
E
dia
ρ
HFS
impurity
ratios up to ≈1.7.
ρ r
measured at the top of the machine with the Thomson scattering
all types
ELM-free,
and temperature
−20
−20of H-mode plasmas on C-Mod: EDA,
LFS
2
zfluxzsurfaces
z to the z
ELMy
[22].
These
H-modes
encompass
range
of section
pedestal
2,
we
discuss
the
experimental
setup
and
diagnostic
[31]
and
mapped
along
magnetic
Figure 1.
Boron
density
(nB ) and
temperaturea (T
)In
from
an EDA Figure
2.
Boron
density(n
)
and
temperature
(T
)
from
an
HFS
B
B
B
−40
main −40
ionwith
collisionalities
high collisionality
regime
H-mode,
the HFS nB covering
in green the
squares,
and
the
LFS
n
in
L-mode,
with
the
HFS
n
in
green
squares,
and
the
LFS nB in
B
Belectric field measurements
Er Vpol
diagnostic
technique.
Radial
LFS midplane. In figure 2, we also show the radial profile of
red
circles.
A
clear
in–out
density
asymmetry
is
present.
(Pfirsch–Schl¨
u
ter),
intermediate
(plateau),
and
collisionless
1 In–out asymmetry is not present.
red circles.
Er Vpol
−60
−60
term
(banana). The density asymmetry is alwaysare
with apresented
larger boron in section 3, followed by inboard-outboard
a clear pedestal.
the impurity (B 5+ ) temperature, Tz , revealingInertial
r
ucl. Fusion 54 (2014) 083017
C. Theiler et al
18
rfrominin−80section
−80
density
on boron
the HFS.
Note that
this asymmetries
asymmetry
isare
opposite
x
10
Large
impurity
density
observed
comparisons
4.
In
the
latter,
we
also
discuss
Here and throughout this paper, the radial coordinate ρ = r/a0
0
that
expected
due
to
centrifugal
effects
[23].
all types
of H-mode plasmas on C-Mod: EDA,
ELM-free,related
and −100with
questions
the
measurement
technique and
(b)
H-Mode,
E aligned
LFSgive
−100
1000
(a)
H-Mode,
T
aligned
is used. It is a flux surface label, where r is the radial distance
0.92
0.92
0.94 r 0.96
0.98
1
0.94
0.96 a range
0.98 of pedestal
1
ELMy [22].0.9
These 0.92
H-modes
encompass
HFS
further details
in appendix. Sectionρ 5 describes simplified
of a flux surface at the LFS midplane from the magnetic axis
ρ high collisionality
main600
ion collisionalities
covering the
regime 600
3.2.
L-mode
measurements
500
(Pfirsch–Schl¨uter), intermediate (plateau),
and collisionless
1 which species are
to determine
expected to have and a0 is the value of r for the last closed flux surface (LCFS).
Tpol,LFS
Testimates
pol,LFS
In
general,
accurate
boron
density
measurements
are
difficult
(banana).
is always4.with
larger boronto
Thea equivalent
figure 3temperature,
for I-mode.
400 The density asymmetry Figure
400
poloidally
varying
what poloidal potential Typically, a0 ≈ 22 cm on C-Mod. Figure 2 shows that for
in
ohmic
L-mode
plasmas
due
to
a
reduced
level
of
boron
density on the HFS. Note that this asymmetry is opposite from
T
in
plasma due
(leading
to lower
signal).[23].
In
L-mode plasmasimply for00the
pol,HFS
asymmetries
electron
density,
T0.96
the H-mode case, the main ions are in the plateau regime, 2
0.94
0.98 and 1what insights
1.02
thatthe
expected
to
centrifugal
effects
200
200
pol,HFS
1000 mainly by the poloidal
with sufficientdrift
signal,
there is no
discernible
boron
densitydetermined
ρ
e electron diamagnetic
direction.
It shows
onlyget
a weak
and
the toroidal velocity ⋆
we
from
total
parallel
force
balance.
Section
6
summarizes
1 < ν < ϵ −1.5 ≈ 6, and, from the center of the Tz pedestal z
asymmetry
(these
plasmas
are
generally
RF-heated,
with
the
p around the3.2.
mid-pedestal,
where a strong dip is observed in terms
equation
(1).from
As an
inI-mode,
H-mode,
is also
0
0 in 3.
L-mode
measurements
Boron density
with toroidal
the HFS nBvelocity
in
the drift
results.
active40X-point in the unfavourable ion ∇B
direction 40Figure500
at ρ ≈ 0.985 outwards (towards larger minor radii), in the
mode. At somewhat larger minor radii, however,
there
is
a
green squares,
and the LFS
nB and
in red
circles. sheared near the LCFS
co-current
in
I-mode
[38]
strongly
E
HFS
to general,
ensure the
plasma
doesn’t
transition
to anr H-mode.
In
Er HFS
e
In
accurate
boron
density
measurements
are difficult
Pfirsch–Schl¨uter regime. In I-mode, main ions are in the
ong shear in
poloidal
velocity
and
the
velocity
is
oriented
at
the
HFS.
theohmic
rare
the plasmas
plasma transitions
to an H-mode
this 20
20 cases
in
L-mode
due to a reduced
level of inboron
⋆
matches
well between
the LFS and HFS, similar to the
< 1, almost all the way to the LCFS. In
banana
regime,
ν
0very and
ong the ion-diamagnetic
drift
direction
near
the
LCFS.
While
2.
Experimental
setup
diagnostics
magnetic
geometry,
an
impurity
density
asymmetry
forms).
in the plasma (leading to lower signal). In L-mode plasmas
0.94
0.96
0.98
1
1.02
L-mode plasmas. An example is shown in figure 3 for an
Figure
boron
forboron
an to
RF-heated
amagnetic and
toroidal
terms
also
contribute
the
agreement with previous studies [3, 6], we find that in the
02 showsvelocity
with
sufficient
signal,density
there
ismeasurements
no
discernible
density 0
ρ
ped
ped
I-mode
plasma
with
parameters
I
=
1.2
(MA),
T
=
800
e
p
θ
variations
ofAlcator
temperature
and
potential
L-mode
plasma
with
Ip =
(MA),
Te
= 400
(these
plasmas
are1.1
generally
RF-heated,
with
the4. Poloidal
, this shear
in poloidal
velocity
is responsible
for(eV),
ucture of Erasymmetry
and
L
can
be
comparable
to
ρ
pedestal
region
both
L
The
experiments
are
performed
on
the
C-Mod
tokamak
ped
T
ne
20
−3
i.
ped
Figure
3.
Boron
density
from
an
I-mode,
with
the
HFS
n
in
20
−3
(eV),
n
=
0.8
×
10
(m
),
P
=
3.0
(MW)
and
B
e
RF
X-point
in (m
the unfavourable
ion ∇B
drift
direction
neEr−20
=well
0.95 in
× 10
),with
PRF =
(MW)
and
B0 =
5.8 (T). −20
I-mode,
a 1.5
stronger
shear
layer
asymmetricactive
green
nB in reddevice
circles. operating at
These are conditions not covered by any current analytical
at
MIT,
a compact,
walled
B0 = squares,
5.6all-metal
(T).and the LFS
to
ensure
theofplasma
doesn’t
transition
to
an
H-mode.
In
The
position
the
slight
break
in
slope
of
T
,
at
ρ
≈
0.96,
is
B
the outer edge of the Er well. This asymmetric structure is In figures 3 and 4, we have shown HFS and LFS radial
treatment
of neoclassical theory (see e.g. [12]). We note that
the rare
cases
the plasma
transitions
to In
an
H-mode
infields,
magnetic
used
as the
pedestal
top location
(‘ped’).
this
plasma,
Tthis
−40
B −40 densities, neutral opacity, and parallel heat
LFS
E
profiles
of
T
and
E
as
a
function
of
the
coordinate
ρ.
For
tually observed
in
all
I-modes
investigated
with
GP-CXRS.
z
r
r
matches
very
well
between
the
LFS
and
HFS,
similar
to
the
magnetic
geometry,
an inimpurity
density
asymmetry
forms).
is
at the same
level as
the H-mode
plasma
(see similar
figure
1), to4.those
Comparison
of E
boron
densityHere,
pedestal
parameters
r LFS
depending
on the application, a more accurate expression for
fluxes
expected
in
ITER.
we
focus
on
L-mode
plasmas.
An
example
is
shown
in
figure
3
for
an
the
mapping
of
the
discrete
radial
measurement
locations
of
well.
It
is
FS measurements
in
I-mode
also
reveal
an
E
r
Figure
2
shows
boron
density
measurements
for
an
RF-heated
but the
−60gradient in TB and ne (not shown) are much reduced −60
⋆
ped
ped
than the one above could be used [32, 33]. Replacing q by
ν
measurements
in
enhanced
D-alpha
(EDA)
H-mode
[7]
and
I-mode
plasma
with
parameters
I
=
1.2
(MA),
T
=
800
e
p
The
boron
density
profiles
at
the
LFS
and
HFS
are
fit
using
(i.e.
at
L-mode
levels).
Additionally,
the
density
fluctuations
L-mode plasma with Ip = 1.1 (MA), Te
= 400 (eV),
ped
ped
tanh fits
between
location
4 −80(eV),
ne[25],=and
0.8the
×difference
1020
(m−3
), PRF the
= pedestal
3.0 (MW)
and
L∥ /(πR) for instance, with L∥ the distance along the magnetic
measured
reflectometry
are1.5characteristic
L-mode
23–26].
These
are
both
high-confinement
regimes
ne −80
= 0.95from
× 1020
(m−3 ), PRF =
(MW)I-mode
and B0of=[6,
5.8 (T).
at0the
LFS(T).
and HFS, "ρped = ρped,HFS − ρped,LFS , is shown in
B
= 5.6
plasmas.
The position of the slight break in slope of Twith
≈ ETB
0.96, isthat
B , at ρ
field between LFS and HFS midplane when going around the
an
typically
does
not 0.96
feature
ELMs.
Different
0.9
0.92
0.94
0.96
0.98
1
0.9 4 for
0.92
0.94
0.98
1
figure
several
H-mode,
I-mode,
and
L-mode
shots.
For
used as the pedestal top location (‘ped’). In this plasma, TB
⋆
near the
direction
opposite
to
the
X-point,
would
reduce
ν
ρ
ρ
edge
instabilities,
the
quasi-coherent
mode
in
EDA
H-mode
[7]
the
H-modes,
an
upward
trend
in
"ρ
with
q
is
seen.
ped
95
is at I-mode
the same
level as in the H-mode plasma (see figure 1), 4. Comparison of boron density pedestal parameters
3.3.
measurements
It is important
to realize
that for H-mode
plasmas
the
separatrix, by a factor 0.65–0.75 for ρ = 0.99–0.999.
the
weakly
coherent
mode
in
I-mode
[6,
27,
28],
are
but the gradient in TB and ne (not shown)and
are much
reduced
igure 5. Effects
of
different
radial
alignments
of
the
HFS
and
LFS
measurements
for
the
H-mode
of
figure
3.
In
(a),
profiles
are
aligned
I-mode
plasmaslevels).
are characterized
generally
by an
H-mode- The
growing
difference
in nB pedestal
location
between
theusing
LFS
boron
density profiles
at the and
LFS
and
HFS
are
fit
at L-mode
Additionally,
the aligned
density
fluctuations
The main diagnostic used in this work is GP-CXRS [18].
believed
to
regulate
particle
transport
avoid
impurity
uch that the T(i.e.
profiles
align.
In
(b),
the
E
wells
are
instead.
Also
shown
in
(b)
as
a
red
curve
is
the
HFS
E
well
calculated
from
z
r L-mode-like electron density
r the pedestal width
like
temperature
pedestal,
but an
and HFS
is notand
justthe
a simple
shift,between
but rather
tanh
fits [25],
difference
the
pedestal location
measured
from
reflectometry
are
characteristic
of
L-mode
quation (2). Itprofile
is the[24].
HFS The
Er profile
expected
fromshow
theaccumulation
LFS
measurement
the LFS
assumption
that
plasma
potential
is a flux
function.
these
regimes.
EDA
obtained
at A localized source of neutrals leads to charge exchange
B5+ density
profiles
a steeper
gradientinand
on
the
is also
increasing
with
q95 , whereas
the HFS
boron
at
the
LFS
and
HFS,
"ρped =H-modes
ρped,HFS
− ρare
plasmas.
ped,LFS , is shown in
Shot: 1120803014 Time:0.922s −0.999s
) Models need to allow
strong impurity diamagnetic flow e↵ects.
5+
(m−3)
5+
B
n
B
T 5+ (eV)
B
n 5+ (m−3)
Larger impurity density in the
high field side ) Need to allow
strong in-out asymmetry.
(eV)
5+
Shot: 1120803011 Time:0.93459s
Shot: 1120803011
−1.1202sTime:0.93459s −1.1202s
Shot: 1120921026 Time:0.966s −1.145s
(eV)
n
B
5+
B
5+
(m−3)
TTz [eV]
(eV)
n
B
5+
(m−3)
2-In-out impurity density asymmetry [2] X
5+
1110309024
Shot: 1120907026 Time:1.2334s
Shot: 1120907026
−1.3614s Time:1.2334s −1.3614s
Er [kV/m]
Shot: 1120803014 Time:0.922s −0.999s
0
40
5+
5+
5+
Shot: 1120921026 Time:0.966s −1.145s
B
5+
T
B
T
Er [kV/m]
5+
5+
3-Potential and impurity temperature pol. variation [1]
5+
5+
n
B
5+
5+
B
5+
B
(eV)
T
Tz [eV]
5+
5+
5+
5+
Shot: 1120803014 Time:0.922s −0.999s
r
5+
Shot: 1120803014 Time:0.922s −0.999s
E [kV/m]
T
B
5+
5+
5+
5+
Shot: 1120824011 Time:1.1308s
Shot: 1120824011
−1.2137s Time:1.1308s −1.2137s
5+
(m−3)
5+
(eV)
5+
5+
5+
5+
n
5+
(m−3)
Due to magnetic equilibrium reconstruction uncertainties in
E is undetermined.
the pedestal, the proper
profile alignment
E
) Potential
and impurity
temperature
are NOT flux
functions
simultaneously.
5+
Main hypothesis:
- E ⇥ B drift comparable to the poloidal
projection of vk .
v
v
Physical insight:
- Also electric trapping of ions.
c) Novel features
Hypothesis: Strong E (sonic impurities allowed) &
Magnetic trapping
1 @pz
pz @
Electric and magnetic trapping
0
Trapped
u
vi
i
Passing
Trapped
Energy
scatter
- Bootstrap current enhanced.
Pitch
angle
scatter
0
v
vi
- Inwards E in subsonic pedestal.
b) Impurities (Helander et al [6–8])
Pot.grad.
Inertial term
2
nz
1 @pi
pi @
Main hypothesis: Weak electric field &
⇠
Parallel momentum conservation for impurities:
(
(
⇠
(
⇠
(
⇠
(
m
n
V
·
rV
·
b
+
r
p
+
n
zer
+
b
·
(r
·
⇡
)
=
R
(
⇠
z
z
z
zi
k
k
(
⇠
(
|
{z
}
|{z}
{z
}
| {z }
| {z } |
Press.grad.
mz nz Vz · rVz · b +
{z
}
|
Viscosity
rk p z
| {z }
Press.grad.
Frict.
By quasineutrality, assuming Ti and Te are flux functions:

z nz T e T i
@nz
+ T i b · r✓
= Rzi
|{z}
hn i (Ti + zi Te )
@✓
|
{z
} Friction
Press. + pot. grad.
Energy conservation for impurities: Equilib. Tz ⇡ Ti ( )
) Impurities rearrange on each flux surface, reducing
their parallel friction with the bulk ions.
5+
1
2
Tz
|
3
2
Vz · r
{z
Tz
nz
!
References
[1] C. Theiler et al., Nucl.Fusion 54,083017
[2] R.M. Churchill et al., Nucl.Fusion 53,122002
r
[3] G. Kagan et al., PPCF 52,055004
nd "ρ = 0.03 (I-mode) with respect to the position indicated
y EFIT. We now discuss different approaches to align HFS
3
!
dρ
"
!
dr
"
[4] G. Kagan et al., Phys.Rev.Lett. 105,045002
[5] P.J. Catto et al., PPCF 53,054004
[6] P. Helander, Phys.Plasmas 5,3999
Viscosity
Pot.grad.
}
+
⇠
⇠
r
·
q
z
⇠
| {z }
Compressional heating
|
{z
Viscous
}
Results:
• Strong impurity diamagnetic flow e↵ects X
4570
Frict.
2
nz
B
=
hnz i
hnz i
Dn E
z
B2
d
d
d
d
nz (Tz Ti )
⌧zi
|
{z
}
Equilibration
Poloidal impurity density
are observed on many tok
Plasma Phys. Control. Fusion 54 (2012) 045004
Chen et al.
Phys. Plasmas, Vol. 7, No. 11, November 2000
• Strong poloidal imp. density variation: X
Tz d ln pz
zz e d
+
D
E
Tz d ln pz
+ zz e d
) nz higher in the HFS
FIG. 7. The hollowness of the carbon profiles against the toroidal rotation in
a number of discharges.
Asymmetry of light
impurities on JET
n! z
nz
free and ELMy phases. The evolution of hollowness in the
discharge follows the increase and decrease of the toroidal
rotation.
Plotting the hollowness against ! for a number of discharges in Fig. 7, there appears to be an interdependence of
these two parameters: The faster the plasma rotates, the hollower the carbon becomes. If the ion distribution were
strongly affected by the toroidal plasma rotation, the asymmetric distribution of the density profile in the midplane
would have a hollow profile. In JET the in–out asymmetry
has been observed in a high confinement discharge.15 In Fig.
8 the tomographic image is of the soft x-ray emission that
comes mainly from carbon and other light impurities judging
by the spectroscopic measurements. The emission, which is
proportional to the impurity density, becomes progressively
peaked off-axis following the increase of the toroidal rotation velocity. Note that the Mach numbers of carbon, neon,
and chlorine all exceed one. This indicates that toroidal rotation could be one of the driving mechanisms for the hollow
carbon profiles.
B
Figure 8. Comparison of measurements (solid) with modeling (black dashed
6
centrifugal force and cyclotron heating. For a HFS-heated plasma (a), includ
LFS-heated plasma (b), the extended theory (8) is shown to agree well with m
5
4
3
0
0.9
FIG. 8. The poloidally asymmetric emission from mostly light impurities.
preciably in the time period of residence of nickel ions in the
Figure 9. Demonstration of the sensitivity of the ICRH-driven
plasma, and thus a constant
background
wasfraction,
subtracted.
in/out asymmetry
to the minority
fm . NearThe
r/a ∼ 0.5
whereradiation
the largest inboard
impurity accumulation
observed, the
background-subtracted
measured
by soft isx-ray
asymmetry is shown to have a weak dependence on fm , presumed to
cameras is identifiedbefrom
spectra
the soft x-ray pulsedriventhe
by the
drop in Tof
⊥ /T∥ as the minority fraction is increased.
height analyzer as line radiation from helium-like nickel. An
At r/a ∼ 0.5 the modeling shown
in figure 9(b)
for the LFSasymmetry in the background-subtracted
reconstructed
soft
heated plasma that matches experiment, this results in drift
x-ray emission is shown
in Fig. 9 for 6.440 s. It is believed
velocity that varies over the flux surface ∼v sin θ with the
Figur
e[φ(θ
(right
figure
modi
the o
and i
abov
in fig
neces
that h
tool f
field.
of wh
inclu
R
on an
accum
rever
[12, 1
asym
d
radial drive velocity, vd , approximately 3.5 m s−1 , as shown in
figure 10. No significant flux-surface averaged, radial particle
flux will occur unless the density also has a non-zero up/down
asymmetry. In this work, the main focus has been in/out
asymmetry driven by minority heating and the centrifugal
force, and future work will focus on ion-impurity friction
effects which are responsible for the up/down asymmetry.
Neoclassical theories have shown that a poloidal potential
˜ e ∼ ε,
variation of order of the inverse aspect ratio, eφ/T
can impact transport by causing electrostatic trapping which
complements the magnetic trapping inherent to the tokamak.
It was shown that radial electron transport can, in some
˜ e rises to ∼4ε
cases, be enhanced by a factor of 2 as eφ/T
[11]. The bootstrap current can also be influenced by this
8
IV. ASYMMETRIC DISTRIBUTION OF IMPURITY IN
RADIO FREQUENCY HEATING ONLY PLASMAS
An in–out poloidal asymmetry of the impurity distribution has been observed in a plasma "pulse 40051# with rf
heating only in an optimized shear experiment. The rf heating power was 3 MW. The asymmetry is reversed in comparison with the asymmetry due to the unbalanced neutral
beam heating.
An asymmetry of tomographic reconstructed nickel soft
x-ray emission was observed during nickel injection experiments. Nickel was injected at 6.405 s. The electron temperature and density profiles in this discharge do not change ap-
2
1
) Allowing the impurity pressure to vary strongly
radially allows not only strong impurity diamagnetic
flow e↵ects, but also the strong poloidal impurity
density variation observed experimentally.
Acknowledgements
[7] T. Fu
¨ lo
¨p et al. Phys.Plasmas 8:3305
[8] M. Landreman et al. Phys.Plasmas 18:092507
=
(
(
(
⇡z : rVz
(
Div.heat flux
5+
than that of the electron density in I-mode, due in part to density
width
remainsI-mode,
fairly constant.
It is noteworthy
figure 4pedestal
for several
H-mode,
and L-mode
shots. For
4+
ionization
physics
(the
ionization
energy
of
B
is
∼330
eV,
so
that
through
all
the
changes
between
the
different
regimes,
the
H-modes,
an upward trend
in "ρped between
with q95 isHFS
seen.
he CXRS diagnostics
to
ρ-space,
we
have
used
magnetic
now
results
in
substantial
differences
and LFS
2
3.3.
I-mode
measurements
the B5+ profile will tend to follow the background temperature the HFS
boron
density
pedestal
remains
relatively
fixed
in
It
is
important
to
realize
that
for
H-mode
plasmas
the
quilibrium reconstruction from normal EFIT [39]. Due to impurity temperatures in the pedestal region, with LFS values
anddifference
position, while
the
LFS boron density
pedestal width
profile). plasmas
In the I-mode
plasmas, the
boron impurity
density width
5+
are characterized
an H-modegrowing
in nBby
pedestal
between
ncertaintiesI-mode
in the reconstructed
locationgenerally
of the by
LCFS
of exceeding
the HFS ones
a factorlocation
of up to
≈1.7.the LFS
like temperature pedestal, but an L-mode-like electron density and HFS is not just a simple shift, but rather the pedestal width
≈5 mm [20, profile
40], there
is some freedom in the radial alignment
Wethenote
that
used an
alignment
ofthe
theHFS
Erboron
wells in
[24]. The B5+ density profiles show a steeper gradient 3 on
LFS is
alsowe
increasing
with
q95 , whereas
f HFS and than
LFSthat
profiles.
Throughout
paper, due
for LFS
figures
5(b)pedestal
and 6(b)
a proxy
to constant.
minimize
HFS - LFS
of the electron
densitythis
in I-mode,
in part to
density
widthasremains
fairly
It isthe
noteworthy
ata, the location
of the
LCFS,
ρ = 1, isenergy
adjusted
thateV, so
asymmetry
in plasma
potentialbetween
#. Indeed,
assuming
plasma
ionization
physics
(the ionization
of B4+such
is ∼330
that through
all the changes
the different
regimes,
5+
the Bcoincides
profile will
tendthe
to follow
the background
temperature
the HFS
density pedestal
relatively
fixed inHFS
approximately
with
temperature
pedestal
foot potential
is aboron
flux function,
we can remains
determine
the expected
width and
position,
whileone
the as
LFS
boron density pedestal width
profile).
In the
I-mode
plasmas,
density
ocation. This
requires
radial
shifts
of "ρthe
= boron
0.01 impurity
(H-mode)
E profile
from
the LFS
follows
⇠
⇠
⇠· ⇡z ) = Rzi
+ nz zerk + ⇠
b ·⇠
(r
|{z}
{z
}
| {z } |
Energy conservation for impurities:
Text
1 @pz
pz @
zz 1 @pi
zi p i @
⇠
Momentum conservation for impurities:
Pitch
Energy
angle
scatter
scatter
Passing
k
•
−3
Despite
substantial
(a) H-Mode, LFSE × B flow [9, 10]. (b)
H-Mode,
HFSprogress, a first
600
C. Theiler et al
C. Theiler et al
Novel features
•
•
•
m ]
Nucl. Fusion 54 (2014) 083017
cl. Fusion 54 (2014) 083017
Helander et al [6–8]
18
1-Impurity diamagnetic flow e↵ects [1] X
Kagan et al [3–5]
•
z
Interesting Alcator C-Mod H-Mode observations:
Physics in theoretical model
Strong radial electric field
Impurities
Poloidal density variation
Poloidal variation of Tz /
Strong ion temp. gradient
n [10
Challenge: Understanding the edge to control confinement.
Chen et al. POP 2000
Motivation and Experimental evidence
Work supported by the U.S. Department of Energy Office of
Science under Award Number DE-FG02-91ER- 54109 and by
”La Caixa” Fellowship.
FIG. 9. Tomographic reconstruction "background subtracted# for the nickel
injection in the rf heated plasma at 35 ms after the nickel injection.
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