Royal Swedish Academy of Sciences Physica Scripta
Phys. Scr. T161 (2014) 014007 (6pp) doi:10.1088/0031-8949/2014/T161/014007
Atomic data and collisional–radiative model
for beryllium and its ions
Dmitry Kondratyev
1
, Leonid Vainshtein
2
, Igor Bray
3
, Dmitry Fursa
3
and
Yuri Ralchenko
4
1
Forschungszentrum Jülich GmbH, Institute of Energy and Climate Research—Plasma Physics,
EURATOM Association, D-52425 Jülich, Germany
2
P N Lebedev Physical Institute RAS, Leninsky Prospect 53, Moscow 119991, Russia
3
ARC Centre of Excellence for Antimatter–Matter Studies, Curtin University, Perth, Western Australia,
Australia
4
National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
E-mail: d.kondratyev@fz-juelich.de
Received 20 September 2013
Accepted for publication 9 December 2013
Published 2 May 2014
Abstract
In this work we present a collisional–radiative model constructed for all ionization stages of
beryllium. Convergent close-coupling, K-matrix and Coulomb–Born-exchange methods were
applied to calculate the necessary atomic data. For the neutral beryllium atom a comparison of
all methods is given. Fractional ion abundances, radiative power losses and electron cooling
rates were calculated as functions of electron temperature. The comparison with other
available data shows a rather good agreement.
Keywords: elementary processes, beryllium, collisional–radiative model
(Some figures may appear in color only in the online journal)
1. Introduction
Beryllium is used in the ITER-like wall at JET and is
foreseen as a plasma-facing material in the main chamber of
ITER [1]. For interpretation of spectroscopic measurements
and for modelling of the beryllium impurity behaviour in
plasma, collisional atomic data (cross sections of elementary
processes) are required. The ‘effective’ rate coefficients
given in existing atomic databases (e.g. ADAS [2]) are
sometimes insufficient for applications. The formation of
beryllium hydrides (BeH, BeH
2
) and their ions in the edge
plasma, and the subsequent fragmentation directly populating
excited atomic states and affecting the measured light
emission can be mentioned as an example. Unfortunately
due to the high toxicity of beryllium the experimental
cross sections are practically unavailable in the literature.
The most accurate theoretical methods, such as convergent
close-coupling (CCC) [3] or the R-matrix with pseudostates
(RMPS) [4] demand very large computation time (especially
at intermediate energies when continuum coupling effects are
important) and the corresponding cross sections (first of all,
for transitions between excited states) are still fragmentary.
To overcome the lack of data relatively simple, fast and
sufficiently accurate methods such as the K-matrix [5] or Born
(Coulomb–Born for ions) with exchange and normalization
(BEN) can be applied.
In this paper, we present a collisional–radiative model
(CRM) constructed for all ionization stages of beryllium. For
neutral Be and selected transitions in Be
+
the sophisticated
CCC method was used. The cross sections for ions Be
2+
,
Be
3+
were computed by the ATOM code [6] using the
K-matrix (for excitation) and the normalized Born (for
ionization) methods. Also at the example of beryllium atom
we present a comparison between the K-matrix and CCC
results. Supplementary data associated with this paper (cross
sections σ , rate coefficients 〈υσ 〉 as well as the adjusted
parameters for fitting formulas) are partially presented on the
website [7] and are available in electronic form upon request.
In the following, we use atomic units with the Rydberg
unit for energy and temperature (Ry = 13.6 eV). Cross
sections are given in the units π a
2
0
= 0.8797 × 10
−16
cm
2
where a
0
is the Bohr radius. We also use the dimensionless
collision strength = g
0
σ E (here g
0
is the statistical weight
of the initial state) and the designation
[ j
1
j
2
j
3
...] = (2 j
1
+1)
1/2
(2 j
2
+1)
1/2
(2 j
3
+1)
1/2
....
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