**P3-29**

**On MARFE stability and movement in an ELMy H-mode Discharge in NSTX**

F. Kelly^a^, R. Maqueda^b^, R. Maingi^c^, J. Menard^a^, B. LeBlanc^a^,
R. Bell^a^, S. Paul^a^

*^a^Princeton Plasma Physics Laboratory, Princeton, NJ USA*

*^b^Nova Photonics, Princeton, NJ USA*

^c^Oak Ridge National Laboratory, Oak Ridge, TN USA

**Abstract**

The results of a comparison of MARFE theory with experiment in the
National Spherical Torus Experiment are presented. Using a fast-framing
camera, MARFEs are observed to move and to interact with ELMs during the
ELM cycle. A basic MARFE theory was applied to NSTX Thomson scattering
and CHERS data. MARFE theory generally correlated with experiment, but
timing restrictions, uncertainty in the location of the separatrix
location and lack of spatial resolution constrained the analysis. The
movements of MARFEs are interpreted to result from the combined effects
of the E × B and diamagnetic drifts.

**1. Introduction**

The maximum plasma density attainable before the occurrence of a change
in the discharge performance is a fundamental operational boundary for
fusion devices \[1\]. Multifaceted Asymmetric Radiation From the Edge
(MARFE) is a poloidally and radially localized but toroidal symmetric
region of high density, low temperature, strongly radiating plasma that
is frequently observed at the high field side (HFS) of toroidal
confinement devices when the edge density increases beyond a certain
limit. Edge Localized Modes (ELMs) are periodic bursts of particles and
power released by filaments aligned with the magnetic field from the low
field side (LFS) of toroidal confinement devices during the high
confinement mode (H-mode) of operation which characteristically form
large density pedestals with steep gradients inside the low field edge.
The National Spherical Torus Experiment (NSTX) is unique among toroidal
confinement devices in that MARFEs and ELMs can coexist within the same
H-mode discharge \[2\]. In this paper we present the results of an
analysis of MARFE stability and movement in NSTX.

NSTX operates using up to 7 MW of neutral beam injection at low aspect
ratio with R = 0.85 m and a = 0.65 m (R/a ≈ 1.3), elongations up to 2.8,
plasma currents up to 1.5 MA, B~T~ = 0.3 to 0.55 T and triangularities
up to 0.8 \[3-6\]. Plasma facing components are protected from the
plasma by a combination of graphite and carbon fiber composite tiles.
The dominant impurity is carbon. This experiment was NSTX shot 117125
conducted with plasma current I~p~ = 0.9 MA and on-axis toroidal field
B~t~ = 0.45 T, in a double null discharge shape with elongation κ \~
2.4, triangularity δ \~ 0.7, and the ion grad-B drift toward the lower
X-point.

Observations of MARFE and ELMs with a fast-framing digital camera and
discussion of measurements of the plasma parameters is presented in
Section 2. Basic MARFE stability theory is reviewed and applied to NSTX
measurements in Section 3. A model for MARFE movement is presented in
Section 4. Conclusions are presented in Section 5.

**2. Experimental observations and measurements**

The rapidly evolving MARFE and ELM structures were observed in NSTX
using a Phantom 7.1 fast-framing digital camera \[2\]. A wide-angle,
fish eye elevation view of the center column together with upper and
lower divertor regions were obtained for NSTX shot 117125 with a
D~α~-line bandpass filter. A highly-radiating, poloidally and toroidally
localized region of cold, dense plasma (plasmoid) is seen to spiral
helically upward around the center column, approximately following the
magnetic field pitch (see Fig. 4a of Ref. 2). This plasmoid is the
result of Type III ELM activity in which heat is transported along the
field lines from the ELM filament on the LFS to a ring MARFE that
encompasses the center stack. The parallel heat flux partially burns
through the ring MARFE and the remnant plasmoid moves away from the
lower divertor following the local magnetic field line at a speed of \~
15 km/s. The motion of the plasmoid stagnates, typically above the
midplane, as the ELM filament has released its excess pressure. The ring
MARFE reforms as it moves downward towards the lower divertor. Several
cycles of this MARFE/ELM interaction are shown in Fig. 2. The downward
velocity of the ring MARFE is seen to be slowing from 1.77 km/s at 658
ms, to 1.54 km/s at 660 ms, to 1.49 km/s at 661.5 ms, to 1.46 km/s at
663 ms. By 665 ms, the downward velocity has slowed to 0.94 km/s and
MARFE has thickened substantially and then begins to move upward just
before a Type I ELM occurs. The variation in MARFE velocity and size is
due to changing edge parameters.

The kinetic profile diagnostics used to measure the edge parameters
include Thomson scattering (TS) and charge exchange recombination
spectroscopy (CHERS). The Thomson scattering diagnostic provides
measurements of the electron density and temperature profiles along the
major radius, n~e~(R,t) and T~e~(R,t), using two lasers with a time
resolution of 16.6667 ms (2 × 30 Hz) and utilizes 30 spatial channels.
CHERS provides measurements of the C^6+^ ion density and temperature,
and toroidal velocity profiles, n~i~(R,t), T~i~(R,t) and v~Φ~(R,t) of
the intrinsic carbon impurity with a time resolution of 10 ms and
utilizes 51 spatial channels. The TS measurement is essentially
instantaneous while the CHERS measurement is integrated over \~8.2 ms,
buffered in \~1.8 ms and centered in the 10 ms time interval. Since the
plasma profiles are dynamically evolving, the MARFE stability analysis
is restricted to times where the difference between the TS and CHERS
sample time is a minimum, that is where \| t~TS~ --t~CHERS~ \| \< 1.5
ms. This gives the best chance of obtaining consistent data to use in
our comparison with theory.

The spatial resolution of the TS measurement is not sufficient to
resolve the electron temperature and density in the NSTX plasma edge
where steep gradient exist in H-mode. Thus, we depend on interpolation
algorithms to obtain estimates from the TS data. An additional problem
is that equilibrium codes EFIT and LRDFIT do not accurately determine
the location of the separatrix. It is believed, however, that the HFS
separatrix is more accurately determined since the magnetic field
sensors are located closer to the plasma edge on the HFS. Therefore, we
adjust the TS and CHERS profiles using the following procedure developed
by one of the authors (RM). We assume the electron temperature is
constant on the poloidal flux surface and the HFS separatrix is
accurately located. In ψ~N~-space, the LFS T~e~ data points are shifted
visually until the data points appear to form a smooth profile with a
couple of T~e~ data points from the HFS. This ψ~N~-space shift is then
used to adjust the TS and CHERS data that satisfy the timing requirement
stated above. The carbon impurity fraction, f~C~ = n~C~/n~e~ , was
estimated from the CHERS C6+ density and TS electron density. The carbon
fraction was observed to generally decrease from the pedestal to the
separatrix due recombination into lower charge states. It was assumed
that carbon fraction was usually constant in the edge, therefore the
maximum f~C~ value in the edge was used.

The observations and measurements using the procedures described above
with LRDFIT04 are summarized in Table 1. Occasionally, e.g. at 527 ms,
the assumption that the HFS separatrix is accurately determined by the
equilibrium code seemed to be invalid.

**3. Basic MARFE stability theory**

MARFEs were first observed in Alcator-C and attributed to a radiative
thermal instability in the parallel energy balance by Lipschultz, et al.
\[7\]. Stringer \[8\] and Neuhauser \[9\] concluded that parallel
conduction controls the onset of thermal instability. Drake \[10\]
identified the MARFE as a radiative condensation instability with
astrophysical counterparts. Wesson and Hender \[11\] observed that the
most unstable mode varies as cos θ with wave number k = 1/qR, where θ is
the poloidal angle, q is the safety factor and R is the major radius.
The Wesson and Hender model used the coronal radiation model L~z~(T) of
Post, et al. \[12\]. This was modified by Mahdavi, et al. \[13\] and
Maingi and Mahdavi \[14\] who incorporated the non-equilibrium radiation
effect of neutrals in a uniform edge distribution to obtain an equation
that is equivalent to

$n_{\text{marfe}} = \sqrt{\frac{\left( \frac{\kappa_{0}}{Z_{\text{eff}}} \right)T^{\frac{1}{2}}/(qR)^{2}}{- \sum_{}^{}\underset{z}{}f_{z}\frac{\partial}{\partial T}\left( \frac{L_{z}\left( T,f_{0} \right)}{T^{2}} \right)}}$
(1)

the MARFE density limit, where
$\kappa_{||} = \left( \kappa_{0}/Z_{\text{eff}} \right)T^{\frac{5}{2}}$
is the Spitzer parallel conductivity, f~z~ = n~z~/n~e~ is the impurity
fraction and f~0~ = n~0~/n~e~ is the neutral fraction. Defining the
MARFE Index, MI = n~exp~/n~marfe~, the calculation of MARFE stability
for NSTX discharge 117125 using Eq. (1) is shown in Fig. 3 assuming f~0~
= 10^-3^ and the Thomson and CHERS data in Table 1. Figure 3 shows the
trend of MI to tend toward 1 when a MARFE is born or already exists. The
uncertainty in the measured parameters is rather large.

**4. MARFE movement**

Chankin \[15\] found that the growth rate of the MARFE instability is
unaffected by the poloidal E × B drift. Chankin's analysis found that
the only consequence of poloidal E × B rotation was that the poloidal
rotation of the MARFE was at the same velocity as the background plasma.
In H-mode plasmas, the radial electric field just inside the separatrix
is negative. Thus, in NSTX shot 117125 the movement of the MARFE should
be directed downward, however, at 377 ms the MARFE was observed moving
upward. Another possible explanation is offered by Tokar \[16\]. The
MARFE moves because one of the MARFE borders is cooled and the other
heated by drift diamagnetic heat flows, due to their pressure
dependence. Here, we make the additional observation that the motion of
the MARFE due to diamagnetic heat flows will be relative to the velocity
of the background plasma.

We use non-stationary equations for heat transport taking into account
heat flows both across and along magnetic surfaces. Due to the Shafranov
shift of magnetic flux surfaces, the temperature and density gradients
are largest at the LFS of the discharge. These gradients drive
instabilities which cause the heat loss though the edge boundary, q~b~,
to be poloidally asymmetric. We assume the θ dependence of q~b~ to be of
the form $q_{b} = {\overline{q}}_{b}(1 - \beta\text{cos}\theta)$ where
${\overline{q}}_{b} = \frac{Q_{b}}{A_{p}}$, *Q~b~* is the net power
transported to the periphery, A~p~ is the area of the peripheral
magnetic surface, *β* is the asymmetry factor for power transport and
*θ* = 0 at the HFS midplane. In NSTX between 70% and 80% of the power is
transported through the LFS. We assume
${\overline{q}}_{\text{LFS}}/{\overline{q}}_{b} = 0\text{.}\text{75}$and
thus$\beta = \frac{\pi}{4}$ and
${\overline{q}}_{\text{HFS}} = 0\text{.}\text{25}\ {\overline{q}}_{b}$
*.*
Defining$\alpha_{\nabla T} = \nabla_{r}\frac{T_{i}}{\nabla_{r}}T_{e}$ ,
$\alpha_{T} = \frac{T_{i}}{T_{e}}$ and taking
$\frac{\partial T}{\partial r} = - \frac{q_{b}}{\kappa_{r}}$, we may
write
$q_{d,\bot = \frac{5}{2}\frac{P}{eB}\frac{q_{b}}{\kappa_{}}\left( 1 - \alpha_{\nabla T}\alpha_{T} \right)}$.
Taking the terms describing the dependencies of the pressure on t and θ,
and assuming the other terms constant, we write the heat equation as:

$\frac{3}{2}\frac{\partial P}{\partial t} + \frac{5}{2}\left( 1 - \alpha_{\nabla T}\alpha_{T} \right)\frac{q_{b}}{{eB\kappa}_{r}a}\frac{\partial P}{\partial\vartheta} = C$
(2)

where P = n(T~i~ + T~e~) and *a* is the minor radius. We take
perturbations of P of the
form$\overset{\sim}{P} \propto \text{exp}\left( V_{\vartheta d}t - a\vartheta \right)$
and estimate the poloidal diamagnetic drift velocity to be

$V_{\theta d} = \frac{5}{3}\frac{q_{b}}{{eB\kappa}_{r}}\left( 1 - \alpha_{\nabla T}\alpha_{T} \right)$
(3)

Using Thomson measurements of n~e~ and T~e~ and CHERS measurements of
T~i~ on the low field side (LFS), we estimate for shot 117125 at 377 ms
$\alpha_{\nabla T}$= 3.9 , $\alpha_{T}$=9.4 and V~θd~ = 1.0 km/s upward.
At 660 ms, we estimate $\alpha_{\nabla T}$= 0.85 , $\alpha_{T}$=8.2 and
V~θd~ = 3.6 km/s upward. We estimate from the fast-framing camera images
the experimental poloidal velocity of the MARFE to be 1.88 km/s upward
at 377 ms and 1.54 km/s downward at 660 ms. If the total poloidal MARFE
velocity is the poloidal diamagnetic drift velocity relative to the
background plasma velocity, then the E × B drift is 1.7 km/s downward
and E~r~ = -3.3 kV/m at 377 ms and 2.6 km/s downward and E~r~ = -4.6
kV/m at 660 ms. Similar values of the radial electric field during
H-mode were measured by Biewer \[17\] in NSTX shot 110077, which was
double-null, D fueled, B~T~(0) = -0.45 T, I~p~ = 1 MA and P~NBI~ up to
5.1 MW. Due to the uncertainties in measurements and many assumptions
made in calculation, these estimates are themselves uncertain. However,
the calculation illustrates that reasonable assumptions lead to values
that are the correct order of magnitude.

**5. Conclusions**

The MARFE density limit predicted by basic MARFE theory, roughly agrees
with NSTX experimental measurement, but uncertainties in the data limit
the comparison. The theory of Chankin \[15\] that the E × B drift
controls MARFE movement is not consistent with observation in NSTX.
Tokar \[16\] proposed a theory that the MARFE moves because one of the
MARFE borders is cooled and the other heated by drift diamagnetic heat
flows, which is also not consistent with observations in NSTX. However,
if the poloidal movement of the MARFE is the sum of the E × B drift and
diamagnetic heat flow driven motion, then MARFE movement in NSTX may be
explained with an E~r~ of the right order of magnitude. In another
paper, we will examine whether diamagnetic drift can describe the
movement of Type V ELMs or the shearing of convective cells responsible
for anomalous transport.

**Acknowledgements**

Research sponsored in part by U.S. D.o.E. contracts DE-FG02-04ER54767,
DE-AC02-76CH03073 and DE-AC05-00OR22725.

**References**

\[1\] M. Greenwald, Plasma Phys. Controlled Fusion 44 (2002) R27.

\[2\] R.J. Maqueda, R. Maingi, K. Tritz, et al., J. Nucl. Mater. 363-365
(2007) 1000.

\[3\] B.P. LeBlanc, R.E. Bell, S.M. Kaye, et al., Nucl. Fusion 44 (2004)
513.

\[4\] S.M. Kaye, M.G. Bell, R.E. Bell, et al., Nucl. Fusion 45 (2005)
S168.

\[5\] M.G. Bell, R.E. Bell, D.A. Gates, et al., Nucl. Fusion 46 (2006)
S565.

\[6\] J.E. Menard, M.G. Bell, R.E. Bell, et al., Nucl. Fusion 47 (2007)
S645.

\[7\] B. Lipschultz, B. LaBombard, E.S. Marmar, et al., Nucl. Fusion 24
(1984) 977.

\[8\] T.E. Stringer, in *Proc. 12 European Conf. on Controlled Fusion
and Plasma Physics,* Budapest, Hungary, 1985 (European Physical Society,
Budapest, 1985), part I, p. 86.

\[9\] J. Neuhauser, W. Schneider and R.O. Wunderlich, Nucl. Fusion 26
(1986) 1679.

\[10\] J.F. Drake, Phys. Fluids 30 (1987) 2429.

\[11\] J.A. Wesson and T.C. Hender, Nucl. Fusion 33 (1993) 1019.

\[12\] D.E. Post, et al., At. Data Nucl. Data Tables 20 (1977) 397.

\[13\] M.A. Mahdavi, et al., in *Proc. 24^th^ European Conf. Controlled
Fusion and Plasma Physics*, Berchtesgaden, Germany, 1997, Vol. 21A, p.
1113, (European Physical Society,1997).

\[14\] R. Maingi and M.A. Mahdavi, Fusion Sci. and Technol. 48 (2005)
1117.

\[15\] A.V. Chankin, Phys. Plasma 11 (2004) 1484.

\[16\] M. Z. Tokar, Contrib. Plasma Phys. 32 (1992) 341.

\[17\] Biewer, et al., Rev. Sci. Inst. 75 (2004) 650.

**Figure captions**

Table 1: MARFE observations for NSTX discharge 117125 at the Thomson
Scattering times and the data used in the MARFE stability calculation if
\| t~TS~ -- t~CHERS~ \| \< 1.5 ms.

Fig. 1: MARFE/ELM cycles in NSTX discharge 117125: (a) "streak" image
showing the plasmoid spiral upward, stagnate, reform a MARFE which moves
downward until an ELM partially burns though the MARFE leaving a
plasmoid as a remnant to begin a new cycle and (b) the D~α~ light signal
from the lower divertor.

Fig. 2: Cases observed in NSTX discharge 117125 with case numbers
assigned. The center image is nearest the TS time given, the left image
-72.5 μs earlier and the right image +72.5 μs later.

Fig. 3: Case numbers and MARFE Index at the sample times where \| t~TS~
--t~CHERS~ \| \< 1.5 ms.

Table 1:

TS time \[s\] Condition CHERS time T~e~ \[eV\] n~e~ \[m-3\] f~C~ \[%\]

0.326662 no marfe 0.32525 59 2.0E19 7.2

0.343345 no marfe 0.33525

0.359992 no marfe 0.35525

0.376685 upward move 0.37525 35 2.2E19 6.4

0.393332 no marfe 0.38525

0.410015 no marfe 0.40525

0.426662 no marfe 0.42525 35 1.6E19 5.2

0.443345 no marfe 0.43525

0.459992 no marfe 0.45525

0.476685 birth 0.47525 34 2.9E19 6.2

0.493322 stagnation 0.48525

0.510025 stagnation 0.50525

0.526662 no marfe 0.52525 134 3.2E19 4.8

0.543345 birth 0.53525

0.559992 no marfe 0.55525

0.576685 no marfe 0.57525 39 2.1E19 6.7

0.593332 birth 0.58525

0.610025 no marfe 0.60525

0.626662 burn 0.62525 35 1.8E19 10.7

0.643355 stagnation 0.63525

0.660002 move down 0.65525

0.676685 stable at top 0.67525 37 2.1E19 4.4

0.693332 no marfe 0.68525

0.710015 birth 0.70525

0.726662 birth 0.72525 36 2.1E19 4.8

0.743355 no marfe 0.73525

0.759992 no marfe 0.75525

0.776685 no marfe 0.77525 74 2.9E19 5.9

0.793332 no marfe 0.78525

0.810015 stagnation 0.80525

![](media/image1.png){width="2.75in" height="1.375in"}

**Fig. 1**

**Case 0: no MARFE; t = 0.326662 s Case 6: stable at top; t = 0.676685
s**

![](media/image2.png){width="2.640972222222222in"
height="1.0798611111111112in"}![](media/image3.png){width="2.640277777777778in"
height="1.0798611111111112in"}

**Case 1: MARFE birth; t = 0.726662 s**

![](media/image4.png){width="2.640972222222222in"
height="1.0798611111111112in"}

**Case 2: move up; t = 0.376685 s**

![](media/image5.png){width="2.640972222222222in"
height="1.0798611111111112in"}

**Case 3: stagnation; t = 0.493322 s**

![](media/image6.png){width="2.640972222222222in"
height="1.0798611111111112in"}

**Case 4: move down; t = 0.660002 s**

![](media/image7.png){width="2.640972222222222in"
height="1.0798611111111112in"}

**Case 5: burn; t = 0.626662 s**

![](media/image8.png){width="2.640972222222222in"
height="1.0798611111111112in"}

**Fig. 2**

![](media/image9.wmf){width="2.875in" height="2.095138888888889in"}

**Fig. 3**