Tomographic reconstruction of
H
␣
emissivity profiles in HANBIT magnetic
mirror device
Jung-Sik Yoon,
a)
Dong-Cheol Seo, and Hoon-Kyun Na
Korea Basic Science Institute, National Fusion R&D Center, 52, Yeoeun-Dong, Yusung-Ku,
305-806 Daejeon, South Korea
(Received 13 June 2004; accepted 27 September 2004; published online 20 December 2004)
Hydrogen is the main constitute of plasmas in HANBIT magnetic mirror device, therefore,
measurement of the emission from excited levels of hydrogen atoms is an important diagnostic tool.
From the emissivity of H
␣
radiation one can derive quantities such as the neutral hydrogen density
and the source rate, i.e., the rate at which the plasma protons are replenished by ionization of neutral
atoms diffusing into the plasma. The reconstruction of emissivity profiles from H
␣
radiation
measurement is a highly undetermined and ill-posed inversion problem, due to the restricted
viewing access, number of chords and the increased noise level. An unbiased and consistent
probability theory based approach within the framework of Bayesian inference is provided by the
maximum entropy method which is independent of model assumptions, but allows any prior
knowledge available to be incorporated. The formalism is applied to the reconstruction of H
␣
emissivity profiles in HANBIT magnetic mirror device. © 2005 American Institute of
Physics. [DOI: 10.1063/1.1831671]
I. INTRODUCTION
The HANBIT magnetic mirror device (HANBIT),
1,2
which is operated as a joint plasma research facility, has been
constructed at Korea Basic Science Institute (KBSI) for basic
study and technology development of high temperature
plasma confinement, plasma heating and diagnostics, and
plasma applications, such as high temperature material test-
ing for tokamak divertors. It is normally operated with the
ion cyclotron resonance frequency (ICRF) for plasma pro-
duction at 3.5 MHz with a slot antenna with gas puffing and
the line-integrated densities are in the range between 2
ϫ10
12
and 1 ϫ10
14
cm
−2
. Hydrogen is the main constitute of
plasmas in HANBIT, therefore, measurement of the emission
from excited levels of hydrogen atoms is an important diag-
nostic tool. Thus, H
␣
monitor system
3
has been installed in
order to measure the temporal and spatial evolution of the
plasma and neutral particle density qualitatively. From the
emissivity of H
␣
line one can derive quantities such as the
neutral hydrogen density and the source rate, i.e., the rate at
which the plasma protons are replenished by ionization of
neutral atoms diffusing into the plasma. But in general, only
line-integrated H
␣
radiation measurements can be taken of
the emission of a plasma, thus tomographic inversion of
these measurements is needed to prove the internal structure
of a plasma.
Tomography is a method to study the internal structure
of object in a nondestructive way. The first application of
tomography techniques to resolve internal structures was by
x-ray imaging in medicine in the 1960s and now it became
an important and widely-used diagnostic in many science
and industry.
4,5
In plasma diagnostics, tomography technique
is also receiving much attention since it is a way to resolve
the internal structure of plasmas from line-integrated
measurements.
6–13
Various techniques have been used to solve the tomog-
raphy problem. The well known method of two-dimensional
reconstruction of the local emissivity from line-integrated
measurements, originally developed by Cormack.
14,15
A
modified Abel inversion
16
is used for the 1D inversion at a
normal (major radial, constant toroidal angle) plasma cross
section. More general methods for profiles with noncircular
cross sections are based on the fast Fourier transformation
7
and linear least-squares techniques.
17
However most of these techniques assume smooth spa-
tial variation of the emissivity profile and their solutions are
not stable to small changes in the initial data. Because, in
common experimental situations, we have a only finite num-
ber of measurements and noise is always included in experi-
mental data. Thus, it is highly underdetermined and ill-posed
inversion problem. A promising approach to the tomography
problem is the maximum entropy method (MaxEnt),
18–21
and
ideal tool for recovering information from incomplete and
noisy data and it offers several important advantages over
other reconstruction techniques without any assumptions or
restrictions which are tacitly made in the other approaches.
The MaxEnt concept is based on Bayesian statistics and pro-
vides a consistent description of probabilistic inference,
yielding the most probable and least biased solution consis-
tent with available noisy data and additional prior knowl-
edge. It allows reconstruction of arbitrary asymmetric emis-
sivity profiles without any assumption or restrictions implied
in other approaches. The MaxEnt formalism based on Shan-
non’s entropy was introduced by Jaynes
22–24
and it was ap-
plied to H
␣
tomography,
8,9
soft x-ray tomography in a toka-
mak device,
10
stellarator.
6,11,21
a)
Electronic mail: jsyoon@kbsi.re.kr
REVIEW OF SCIENTIFIC INSTRUMENTS 76, 013502 (2005)
0034-6748/2005/76(1)/013502/7/$22.50 © 2005 American Institute of Physics76, 013502-1