Impact of Lithium-coated PFCs on the Edge Neutral Density on NSTX
Evan T.R. Rosenman, Harvard University
Devon J. Battaglia, Oak Ridge National Laboratory
ABSTRACT
Wall recycling of deuterium is reduced on NSTX by applying solid
lithium coatings to the carbon composite plasma-facing components. The
impact of the reduced recycling on the neutral density profile in the
scrape-off layer (SOL) is inferred using a high-speed camera (268 Hz)
with an H-beta filter and a chordal view of the SOL (0.2 cm resolution).
The recorded intensity profile is converted to a radial profile of plasma
emissivity using an absolute calibration of the camera and an Abel
Inversion. The neutral density is computed by dividing the plasma
emissivity by a function of the electron density and temperature, which are
estimated using data from the Thomson scattering diagnostic. Initial
calculations indicate that the neutral deuterium density decreases as the
total amount of pre-shot lithium deposited in NSTX increases. The error in
the profile measurement is quantified via Monte Carlo techniques. This
work is supported by US DOE contracts DE-AC02-09CH11466 and DEAC05-00OR22725.
Introduction
In thermonuclear fusion devices, plasma – extremely hot, ionized gas – ultimately
escapes a confinement region and interacts with a material surface. In a device known as
a tokamak, the plasma confinement is provided by specially designed magnetic fields
inside a metal vessel. As the field of plasma physics and fusion energy science progresses
toward the creation of a sustainable energy source, the power delivered to the material
wall by the plasma becomes large and the issue of plasma-material interaction (PMI)
becomes increasingly important.
One of the many PMI effects is wall recycling, in which energetic ionized
particles in the plasma knock neutral particles off the tokamak wall. These cold, neutral
particles can then become ionized and enter the plasma. If this source of neutral particles
1 is too large, the plasma fueling cannot be adequately managed because there is no way to
control when or where the plasma is fueled and with what types of neutrals.
In 2007, the evaporation of lithium onto the carbon composite plasma-facing
components of NSTX was shown to reduce wall recycling [1]. The reduced fueling of
neutral particles provided access to plasma discharges with improved plasma
confinement and elimination of unstable bursts from the plasma edge known as edgelocalized modes [2]. Lithium application is believed to reduce wall recycling because it
has an affinity for chemically reacting with hydrogen, leading to the formation of
compounds that are more difficult to liberate from the Tokamak wall. It has been
theorized that this reduced recycling affects the density of neutral particles in the plasma
and thus the plasma fueling; if so, the reduced fueling may alter the edge conditions of
the plasma and explain the improved confinement. Yet without a diagnostic to measure
the density of neutral particles within the plasma, it is difficult to gauge whether this is a
plausible explanation for the confinement effects achieved by lithium deposition within
the Tokamak.
In order to help answer this question, a radial profile of the density of neutral
particles was produced using data from two different diagnostics: the Edge Neutral
Density Diagnostic (ENDD) [3], and the Thomson Scattering Diagnostic [4]. This
methodology of measuring neutral density is novel in that it exploits existent diagnostics
on NSTX to produce new information – doing so without any additional cost.
2 Theory
D
E
T
E
C
T
O
R
Top-­down view of a detector viewing a cylindrically symmetric volume. Reprinted from [6].
A tokamak, to first order, can be treated as a cylindrically symmetric volume.
Thus, the recorded intensity on the detector will be proportional to the chordal brightness
[5,6],
Equation 1
This equation relates the brightness B, a function of the tangency radius Rt that is
measured in photons/area/second, to the emissivity ε, a function of the cylinder radius
that is measured in photons/volume/second.
The recorded light intensity from a detector can be converted into an emissivity
estimate using a mathematical manipulation known as an Abel Inversion. The integral
equations can be treated as a series of linear equations if the plasma is divided into
3 concentric layers where the emissivity is unchanging. In the above diagram, five such
layers are shown, and are labeled as “emission zones.”
For any chord through the plasma, the path length of the chord within each zone
can be calculated using simple geometry. The measured brightness along the chordal path
is given by the sum of the products of the emissivity within each shell times the path
length through that shell. The path lengths are then be compiled into a length matrix, Dij,
which relates the emissivity vector Ej to the brightness vector Bi by the following
relationship:
Bi = Dij * Ej
By simply taking the inverse of the D matrix, the emissivity profile can thus be calculated
using the brightness vector:
Ej = Dij-1 * Bi
The calculated Ej vector will give the emissivity of the plasma at each of the radii
corresponding to the middle of the shells of constant emissivity.
Once the emissivity vector is obtained, this data can be used to solve for the
neutral density. This equation is derived from the fact that neutral atoms with electrons
that have been excited above the ground-state shells will emit a photon when the
electrons decay toward the ground state. The number of photons per second emitted by
bound electrons in a volume of plasma for a shell transition from shell m to shell n is
given by [7]:
Equation 2 4 Assuming that the electron temperature exceeds 3 eV, meaning that the rate of ion
recombination will be negligible in comparison to the rate of ionization, the reaction rate
will be essentially equal to the ionization rate [8]:
where A is a constant known as the Einstein coefficient and N is the number of atoms.
Thus, the emissivity is equal to:
where the neutral density is approximately equal to N1 since the number of excited atoms
is a very small percentage of all neutral atoms. Using this equation, a neutral density (nd)
profile can be calculated from the previously described emissivity profile as below:
nd (r) = ε(r) / (Nm/N1 (r))
Materials and Methods
The ENDD, a high-speed (268 frames per second) camera positioned at a window
to the Tokamak, was fitted with a special filter in order to measure only the H-Beta
wavelength of light (this is the 486 nanometer wavelength emitted by a hydrogen atom
when one of its electrons falls from the fourth quantized energy level to the second). Due
to the presence of the filter, the intensity at each pixel of the ENDD data was proportional
to the total number of H-beta photons emitted from a single mid-plane chord through the
plasma over a 3.73 millisecond interval.
A program was written in the IDL [9] coding language to produce such emissivity
data for several different shots on NSTX. A median filter was applied over every fourpixel square within the ENDD data in order to remove the effects of high-energy x-rays,
5 which were able to penetrate the camera filter and cause intermittent bright spots on the
ENDD images. The recorded intensity on the final frame in the ENDD data (taken after
the plasma had extinguished) was then subtracted from the data in order to remove the
dark noise signal of the detector. A 106-entry array – a “brightness vector,” Bi – was thus
produced for every single ENDD frame, with each entry representing the brightness
measured from a particular chord through the plasma.
A program was written in IDL to produce the D matrix corresponding to the
geometry of the NSTX Tokamak. Using previous spatial calibration measurements [3] to
find the tangency radius corresponding to every pixel in the ENDD data, the program was
then used to produce an array containing the emissivity values at 106 different radii
between 1.40 meters and 1.65 from the center of the plasma. These radii span from the
tokamak wall to a few centimeters inside the plasma edge.
A program was also written in IDL to produce the radial N4/N1 profiles. All the
data to produce such a profile was obtained from the Thomson Scattering Diagnostic
data, which gives measurements of both electron density (ne) and electron temperature
(Te). The value of N4/N1 at any specific radius – which is a function of both ne and Te –
can also be calculated using the diagnostic.
Because the N4/N1 values were often relatively small and served as the
denominator in the neutral density-calculating equation, the neutral density values were
extremely sensitive to error within the Thomson data. Furthermore, the spatial resolution
from the Thomson Scattering diagnostic was relatively poor, offering data for only a few
radii within the range of interest.
6 The sensitivity to small errors in the TS data was reduced by imposing a
hyperbolic tangent fit to the ne and Te profiles. The profiles are described using four
coefficients C0, C1, C2, and C3 that define a hyperbolic tangent curve for radial values, R,
by the following equation:
ne(R) = C0 – C1 * tanh((R – C2)/C3)
Hyperbolic tangent fits were imposed on both the ne and temperature data provided by
the Thomson diagnostic. The minimum values for both the electron temperature and the
electron density were defined in both equations by the quantity C0 – C1.
Electron density and electron temperature values were calculated at each of the
radii where inversion data had been obtained. Using both of these inputs, a linear
interpolation was performed on a table of N4/N1 values that had been calculated
experimentally [8]. The resulting values were then compiled into a 106-member array of
N4/N1 values at each of the desired radii.
Results
The code was applied to data from NSTX shot 138574 to see if the produced
neutral density profile matched theoretical predictions. Four plots are given in Figure 1,
showing the intensity profile, the average emissivity profile, the photon emission rate,
and the neutral density profile of the shot. Brightness data in Fig. 1(a) is time-integrated
over 3.7 ms intervals from 0.4 to 0.7 seconds from the beginning of the shot. All data is
averaged over the 0.4 to 0.7 second time interval. Units in plots a, b, and are arbitrary.
The red line in Fig. 1(d) is the average neutral density profile over the timeframe of
7 interest. The dotted line is the approximate location of the separatrix, the boundary
between confined and unconfined plasma.
Figure 1: (a) the Hβ intensity (brightness) profile, (b) the corresponding average emissivity profile, (c) the
photon emission rate, and (d) the neutral density profile for discharge 138574. 8 Figure 1(d) shows that neutral density falls rapidly within a thin layer outside the
plasma seperatrix. This behavior matches the prediction that neutral particles ionize very
rapidly once they encounter the plasma with sufficient energy to ionize the neutrals, thus
causing a rapid decrease in neutral density just within this region. The neutral density
outside the seperatrix appears to remain relatively constant, varying only within a single
order of magnitude. This also matches theoretical predictions.
For the purposes of gauging the effect of lithium deposition on wall recycling and
neutral density, two separate shot groups were identified. The shots were chosen to have
nearly identical levels of input heating power and gas injection and to have similar outer
separatrix locations and similar occurrences of edge localized modes, in order to
minimize the likelihood that variations among the neutral density profiles would be
caused by non-lithium parameters. The two shot groups and their corresponding lithium
depositions are listed below:
Shot Number
GROUP 1
Lithium Deposition (mg)
129060
129061
129075
0
188
943
Shot Number
GROUP 2
Lithium Deposition (mg)
138574
138576
138577
138578
138592
138593
138594
71.92
87.46
88.05
90.92
283.11
281.94
243.94
Group 1 Plot
The first group of shots was run through the program to produce the following
plot, which gives the average neutral density over the interval from 0.4 to 0.55 seconds.
9 The black (solid) line corresponds to 943 mg pre-shot lithium (129060), while green
(dash-dot) line corresponds to 188 mg pre-shot lithium (129061), and blue (dotted) line
corresponds to no pre-shot lithium (129076). Neutral density units are arbitrary.
Figure 2 Group 2 Plot
The second group of shots was run the program to produce the following plot.
Average neutral density is now given over the interval from 0.4 to 0.65 seconds. All the
shots with roughly 100 mg Li deposition are colored in blue while those with roughly 300
mg Li deposition are colored in green:
10 Figure 3
Observations and Conclusions
The qualitative plots from both shot groups seemed to indicate that the effect of
lithium on neutral density confinement is relatively minor. The group one shots
demonstrate that there is a small effect when comparing the neutral density of lithiumcoated shots to lithium-free shots; it appears that the addition of the initial 188 mg of
lithium does reduce neutral density beyond roughly 150 cm from the plasma center. The
addition of a far greater quantity of lithium in the 950 mg lithium shot seems to have an
extremely minor impact.
The data from the shots in the second group also support that the neutral density
does not have a strong dependence on the amount of lithium deposited. The neutral
density profiles are within a similar range for discharges with 100 mg and 300 mg of
lithium deposition. Thus, taken together, both sets of shots seem to indicate that the
11 deposition of a small quantity of lithium has some effect on the confinement of neutral
particles, but beyond a low threshold, additional lithium deposition has no real impact.
The data from this experiment supports that lithium coatings on NSTX walls
reduce the wall recycling, but the reduction does not vary significantly with the amount
of lithium evaporated. While this data has provided meaningful evidence to support the
idea that lithium deposition has an effect on wall recycling, it is by no means conclusive,
and more data and improved measurements will be needed to confirm this theory.
The IDL code that was written to produce the qualitative neutral density plots for
this experiment can be used as a diagnostic on any subsequent group of shots in order to
confirm the observed effects. When several subsequent shot groups are isolated and the
effects of lithium deposition are further studied, more concrete statements can be made
about the effects of lithium deposition on neutral density. Because of the large possibility
for error in the Edge Neutral Density Diagnostic and the Thomson Scattering Diagnostic
data, a relatively large dataset will need to be analyzed in order to find statistical trends.
Furthermore, this diagnostic can be used for a number of other purposes in the
future. The current incarnation can be utilized to create qualitative neutral density plots in
the separatrix region for any shot in which the ENDD and Thomson Scattering
Diagnostic are operational. If a calibration of the camera is obtained – so that the
measured brightness of each pixel can be converted into an estimate of the number of
emitted photons – then the a quantitative calculation of the neutral density is possible. A
quantitative measurement would support a number of calculations on NSTX that
currently rely on educated estimates of the neutral density, such as neutral beam and
radio-frequency heating efficiencies and impurity transport.
12 1 H. W. Kugel, M. G. Bell, et al., Phys. Plasmas, 15, 056118 (2008) 2 R. Maingi, et al., Phys. Rev. Lett., 103, 075001, (2009) 3 P. W. Ross, Ion Power Balance in Neutral Beam Heated Discharges on the National Spherical Torus Experiment (NSTX), Ph.D. Thesis, Princeton University. June, 2010. 4 B. P. LeBlanc, R. E. Bell, D. W. Johnson, D. E. Hoffman, D. C. Long, R. W. Palladio, Rev. Sci. Instr., 74, 1659 (2003) 5 K. Tritz, Current Profile Reconstruction Using X-­ray Imaging on the Pegasus Toroidal Experiment, University of Wisconsin-­‐Madison. (2002) 6 R.E. Bell, Rev. Sci. Instr. 66, 558 (1995) 7 I.H. Hutchinson, Principles of Plasma Diagnostics, Sec. Edition. Cambridge University Press, New York. 2002 8 D. Stotler, C. Karney, R. Kanzleiter, S. Jaishankar, User’s Guide for DEGAS 2, Release V.4.3, Princeton Plasma Physics Laboratory, (2009) 9 Visual Information Solutions, www.ittvis.com 13