NATIONAL INSTITUTE FOR FUSION SCIENCE㼀㼔㼑㻌㻣㼠㼔㻌㻶㼍㼜㼍㼚㻙㻯㼔㼕㼚㼍㻙㻷㼛㼞㼑㼍㻌㻶㼛㼕㼚㼠㻌㻿㼑㼙㼕㼚㼍㼞㼛㼚㻌㻭㼠㼛㼙㼕㼏㻌㼍㼚㼐㻌㻹㼛㼘㼑㼏㼡㼘㼍㼞㻌㻼㼞㼛㼏㼑㼟㼟㼑㼟㻌㼕㼚㻌㻼㼘㼍㼟㼙㼍㻔㻭㻹㻼㻼㻞㻜㻝㻤㻕
Edited by Daiji Kato, Ling Zhang, and Xiaobin Ding

( Received - Apr. 08, 2019 )NIFS-PROC-114

May 10, 2019

This report was prepared as a preprint of work performed as a collaboration research of the
National Institute for Fusion Science (NIFS) of Japan. The views presented here are solely thoseof the authors. This document is intended for information only and may be published in a journal
after some rearrangement of its contents in the future.
Inquiries about copyright should be addressed to the NIFS Library, National Institute for Fusion
Science, 322-6 Oroshi-cho, Toki-shi, Gifu-ken 509-5292 JAPAN.
E-mail: tosho@nifs.ac.jp<Notice about copyright>
NIFS authorized Japan Academic Association For Copyright Clearance (JAC) to license our
reproduction rights and reuse rights of copyrighted works. If you wish to obtain permissions ofthese rights, please refer to the homepage of JAC (http://jaacc.org/eng/) and confirm appropriateorganizations to request permission.

The 7th Japan-China-Korea Joint Seminar on Atomic
and Molecular Processes in Plasma (AMPP2018)
Jul. 24 – 26, 2018, Hefei, China
Edited by Daiji Kato, Ling Zhang, and Xiaobin Ding
Abstract
The 7th Japan-China-Korea Joint Seminar on Atomic and Molecular
Processes in Plasma (AMPP2018) was held on July 24 – 26, 2018 at Instituteof Plasma Physics in Hefei, China, as one of the activities of Post Japan-China
Core University Program, JSPS-NSFC-NRF A3 Foresight Program in thefield of Plasma Physics “Study on Critical Physics Issues Specific to SteadyState Sustainment of High-Performance Plasmas”, and the NINS program of
Promoting Research by Networking among Institutions (Grant Number
01411702).
Topics of AMPP2018 cover spectroscopic properties of impurity ions infusion plasmas, plasma-wall interactions, diagnostics of laser induced
plasmas, highly charged ion physics, atomic and molecular collision dynamics,
plasma simulation and diagnostics, and application of statistical methods toatomic data evaluation. In the seminar, there were 34 oral talks (including 5
talks by phD students). The total number of registered participants was 100(89 from China, 10 from Japan, and 1 from Korea). The present issue of theproceedings has collected 12 papers from the delegates of the seminar. The
present issue includes abstracts of all presentations in the seminar, thescientific program, and the list of participants.
Keywords:
charge transfer, Auger process, recombination, three-body fragmentation,
atomic structure, oscillator strength, cross section, tungsten, lanthanide,highly charged ion, X-ray scattering, EUV spectroscopy, visible forbiddenlines, hydrogen recycling, LHD, EAST tokamak, statistical analysis

Preface“If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one
sentence passed on to the next generations of creatures, what statement would contain the mostinformation in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or
whatever you wish to call it) that all things are made of atoms …” (quotes from 1. Atoms in
Motion, Feynman Lecture on Physics). Many characteristics of plasmas can also be understoodin terms of atomic and molecular processes taking place in the plasmas. More specifically,
electronic, atomic, and photonic collision processes and radiative transitions play a decisiverole for atomic and molecular abundance, photon emission and absorption properties, andenergy balance of plasmas. Emission and absorption line spectra of atoms and molecules givea precise measure of temperature, densities, constituent species, etc, of fusion and astronomical
plasmas. It is, therefore, obvious that constant communications of researchers of atomic andmolecular processes and plasma research are important for further development in applicationsof atomic and molecular data to plasma researches. New knowledge in atomic physics offers
novel ideas to understand plasma behaviors. Collaboration with plasma researchers creates new
applications and researches of atomic and molecular processes in plasmas. The seminar seriesof Atomic and Molecular Processes in Plasma (AMPP) has been offering a uniqueinterdisciplinary meeting for researchers of atomic and molecular processes and plasma
research in Japan, China, and Korea to discuss about these issues.
The 7th Japan-China-Korea Joint Seminar on Atomic and Molecular Processes in Plasma(AMPP2018) was held on July 24 – 26, 2018 at Institute of Plasma Physics in Hefei, China, as
one of the activities of Post Japan-China Core University Program, JSPS-NSFC-NRF A3
Foresight Program in the field of Plasma Physics “Study on Critical Physics Issues Specific to
Steady State Sustainment of High-Performance Plasmas”, and the NINS program of Promoting
Research by Networking among Institutions (Grant Number 01411702). This seminar is theextension of the last six seminars that were held in 2004 in Lanzhou, China, in 2007 in
Dunhuang, China, in 2009 in Xi’an, China, in 2012 in Lanzhou, China, in 2014 in Lanzhou,
China, and in 2016 in Chengdu, China. Topics of AMPP2018 cover spectroscopic properties of
impurity ions in fusion plasmas, plasma-wall interactions, diagnostics of laser induced plasmas,
highly charged ion physics, atomic and molecular collision dynamics, plasma simulation anddiagnostics, and application of statistical methods to atomic data evaluation. In the seminar,
there were 34 oral talks (including 5 talks by phD students). A poster session was also organized.
The total number of registered participants was 100 (89 from China, 10 from Japan, and 1 from

Korea). The present issue of the proceedings has collected 12 papers from the delegates of theseminar. The present issue includes abstracts of all presentations in the seminar, thescientificprogram, and the list of participants.
On behalf of the organizing committee, we would like to express our sincerest thanks to
all the participants who made active contributions not only in the formal presentations butalso
in the fruitful discussions. We would like to acknowledge everybody who devoted very hard
work for preparing the seminar. Finally, we would like to acknowledge the administrative as
well as the financialsupports from Institute of Plasma Physics, CAS and National Institute for
Fusion Science.

Ling Zhang
Institute of Plasma Physics, CAS, Hefei, China
Xiaobin Ding
Northwest Normal University, Lanzhou, China
Daiji Kato
National Institute for Fusion Science, Toki, Japan

Contents

Preface
Contents
Photo of Participants
PapersHajime Tanuma
Soft X-ray emissions from inner-shell excited Li-like ions in charge transfer collisions of metastable He-like ions with neutral gases

1

Yulong Ma
Theoretical investigation of resonant multiple Auger processes of core-excited Ar 2p3/2-14s

5

Daiji Kato
Statistical properties of atomic structures of r-process elements

11

Shigeru Morita
Estimation of photon emission coefficients in tungsten UTA transitions using LHD plasmas

17

Takehiko Esaka
Application of matrix decomposition technique to tungsten spectra measurement data

21

Ling Zhang
Estimation of density profiles of W43+-W45+ in EAST H-mode plasma

27

Fumihiro Koike
A consideration on the accuracy of GRASP calculations

32

Nobuyuki Nakamura
Visible spectra of multiply charged heavy ions obtained with a compact electron beam ion trap 36
Ya-Wei Liu
Oscillator strengths and integral cross sections of the valence-shell excitations of oxygen 40
molecule studied by fast electron and X-ray scattering
Shu-Xing Wang
Electron-ion recombination of Be-like Ca

46

Takuya Osugi
Statistical Analysis of Hydrogen Recycling in the Peripheral Region of LHD

50

Lei Chen
Three-body fragmentation dynamics of CF42+ induced by 1 keV electron collision

56

Seminar Program

61

Collection of Abstracts

65

Participants List

110



Soft X-ray emissions from inner-shell excited Li-like ions in charge transfer
collisions of meta-stable He-like ions with neutral gases
Hajime Tanuma* and Naoki Numadate
Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
Abstract
We show soft X-ray emission spectra in collisions of He-like C, N, and O ions with neutral gases.
Emissions are identified as transitions from doubly excited (inner-shell excited) Li-like ions produced incollisions of meta-stable He-like. Comparison with previous works and some discussion is given.
1. Introduction
In Tokyo Metropolitan University, we have performed ion-beam collision experiments using a 14.25 GHz
ECR (electron cyclotron resonance) ion source which produces a plasma of temperature about 106 K. When
we measured soft x-ray emissions in the collisions of helium-like O ions, O6+, with helium gas, we observedhigh energy photons of 560 and 630 eV by using of a silicon drift detector (SDD) accidentally. Since theionization potential energy of O5+, which is produced in charge transfer reaction in the O6+ - He collisions, is
138 eV, we can say that these high energy emission is not due to singly excited O5+ (1s2nl) ions.
Therefore, we consider that the emissions from 1s2snl states produced in charge transfer collisions ofhelium-like ions in the meta-stable triplet states, 1s2s 3S1, were observed in our experiments. As it is wellknown that the helium-like ion beam produced with an ECR ion source is a mixture of the ground state andthe long-lived excited state and has few percent of the meta-stable state, the formation of 1s2snl states might
be possible. However, the most probable decay process of the inner-shell excited state is usually Auger
electron emission, and the radiative emission is not strongly expectable.
We have looked for the previous similar studies in the literature, and we found a series of experiments
in Grenoble, France, using C4+, N5+, and O6+ ions [1, 2, 3]. In these experiments, the results with He and H2target gases were reported. Then we have performed the experiments with same three kinds of helium-likeions and various gas targets in this work.
2. Experiments
Multiply charged ions produced with this ion source were extracted with an electric potential of 15 kV
and the charge-state of the ions was selected by using a double-focusing dipole magnet. The ion beam witha single charge state was introduced into a collision cell filled with a target gas, and photon emissions fromthe collision cell in an EUV (extreme ultra-violet) region were observed with a compact grazing-incident
spectrometer equipped with a gold-plated cylindrical mirror for light condensing and a variable-line-spacing(ca. 1200~lines/mm) grating. A CCD (charge coupled device) camera with a Peltier cooling system was* Corresponding author’s email: tanuma-hajime@tmu.ac.jp-1-1Intensity / arb. units
Intensity / arb. units
Intensity / arb. units
Intensity / arb. units
Intensity / arb. units

installed in the spectrometer. Target gas pressures in a gas
C4+ + He

cell was around 1x10-2 Pa, and not only single collisions
but also double collisions might happen. Typical ion beam
current which had been monitored at the end section of a

2

3

4

Wavelength / nm

56

C4+ + Ar

beam line was 1 µA.
3. Results and Discussion
Figure 1 show soft X-ray emission spectra incollisions of 60 keV C4+ ion beam with He, Ar, N2, Xe,and O2 target gases. The spectrum in the C4+ - He system

2

3

4

Wavelength / nm

5

6

is quite similar to the previous measurement [1]. The weak
peak around 3.7 nm correspond to the 1s-3p transition

C4+ + N2

between 1s22s 2S and 1s2s3p 2P states, and the strong peakaround 4.5 nm might be due to the 1s-2p transition
between 1s22s 2S and 1s2s2p 2P states. The identification

2

3

4

Wavelength / nm

5

6of these transition is confirmed by the comparison withthe theoretical calculations [4, 5].

C4+ + XeIn the spectra of Ar and N2 targets, the 1s-3p peak isprominent, and the 1s-2p peak splits to the emissions fromthe 1s2s3p 2P and 1s2s3p 4P states. Ar and N2 have very

2

3

4

Wavelength / nm

5

6

similar ionization potentials of 15.76 and 15.60 eV,
respectively. It is well known that the cross sections and

C

4+

+ O2

excited state distribution after the collisions of multiply
charged ions with neutral atoms/molecules depend on theionization potential of targets. Therefore it is quite

2

3

4

Wavelength / nm

5

6reasonable that spectra of Ar and N2 targets are very
similar each other.

Figure 1. Soft X-ray spectra observed in
4+collisions of C

ions with five kinds oftarget gases.

Since Xe and O2 have very similar ionization
potentials of 12.13 and 12.30 eV, respectively, we expectedthat the spectra with both targets might be similar.
However, as shown in figure 1, two spectra aresignificantly different. The reason of this finding is not understood yet. But, Xe is a very heavy atom andstrong spin-orbit interaction might be expected. Therefor this fact might be related to the charge transfer
mechanism involving spin-orbit interaction.
The soft X-ray spectra measured in the collisions of N5+ ions with five different target gases are shownin figure 2. In these spectra, not only the 1st diffraction by a grating but also the 2nd order diffraction whichappear at the position of two-times longer wavelengths are observed at the same time. As can be seen in these
spectra, the 2nd order diffraction provides us better energy resolution, and it is much useful in our
measurements. In the He target case, the 1s-3p transition has about half intensity of the 1s-2p transitions. But-2-2

Intensity / arb. units
Intensity / arb. units
Intensity / arb. units
Intensity / arb. units
Intensity / arb. units

in other targets, the intensity of 1s-3p transitions are

N5+ + He

much smaller than the 1s-2p ones. In the 1s-2p transitions,the 1s22s 2S- 1s2s3p 4P is always stronger than the 1s22s
2

2

3

4

5

6

Wavelength / nm

7

S- 1s2s3p 2P. Concerning to the target dependence of theemission spectra, Ar and N2 targets show almost same
spectra, and Xe and O2 targets have significant difference

N

5+

+ Ar

in the relative intensity of 1s-3p transitions, namely avery weak 1s-3p line observed only in collisions of N5+
with Xe. According to the classical over the barrier model,

2

3

4

5

6

Wavelength / nm7

the dominant principal quantum number of captured
electron orbital must be four in the cases of Xe and O2

N

5+targets. Therefore the missing of 1s-3p transition means+ N2

the dominant state produced in the single electron capture
is 4p or 4f states, and the population of 3p state createdby the cascade processes might be very small. The reason
2

3

4

5

Wavelength / nm

67

why only Xe target shows different behavior might bedue to the strong spin-orbit interaction in the heavy

N5+ + Xeelement atom.
Figure 3 shows the soft X-ray emission spectra in thecollisions of O6+ ions with five different target gases.

2

3

4

5

Wavelength / nm

67Here also the 2nd order diffraction has observed with the
1st order ones. The 1s-3p transition was observed only in

N5+ + O2

the case of He target. And the spectra with Ar, N2, and O2
targets are almost same, but that with Xe show a peakcorresponding to the 1s22s 2S- 1s2s3p 2P transition. This

2

3

4

5

Wavelength / nm

67

Figure 2. Soft X-ray spectra observed incollisions of N5+ ions with five kinds of target
gases.

target dependence also might be related to the strong
spin-orbit interaction in the heavy element atom Xe.
4. Possible Application
In the dense target gas, double and more multiple

collisions of projectile ions with gas atoms/molecules will occur very frequently. Bare and hydrogen-likeions will become metastable helium-like ions and also inner-shell excited lithium-like ions. Since a few
fraction of bare and hydrogen-like ions are contained in the solar wind, the soft X-ray emissions which are
discussed in this work might be observed in the atmosphere of planets. Therefore the soft X-ray emissions
from the inner-shell excited lithium-like ions will be a new tool for the spectroscopic analysis of the planet
atmosphere by a X-ray observatory satellite.
5. Outlook
In this work, the resolution of the EUV spectrometer was about 0.1 nm. But, when we optimize the-3-3Intensity / arb. units

Intensity / arb. units
Intensity / arb. units

Intensity / arb. units
Intensity / arb. units

O6+ + Healignment and a slit width, the resolution of 0.02 nm might
be achieved. In the preliminary high resolution
measurement with long exposure time give much morenarrow and weak lines. In these measurements, not only

2

3

4

Wavelength / nm

5

6single electron capture but also transfer excitation, which
produce 1s2p3l states, and two-electron one-photon

O

6+

+ Ar

processes, for example the transition of 1s23s 2S 1s2s(3S)4p, were observed. These new results will be
submitted to a journal soon [6].

2

3

4

Wavelength / nm

5

6

Acknowledgements
O

6+

We thank Kento Shimada, Yoshiyuki Uchikura,+ N2

Takuto Akutsu, Yohei Yamada, and Takumi Ohna for
their support of the experiments. We also thanks post
Japan-China-Korea A3 Foresight Program and post Core
2

3

4

Wavelength / nm

56

O6+ + Xe

University Program (Post CUP) for giving us the great
opportunity to talk on this work and discuss in theconference.

References2

3

4

Wavelength / nm

56

O6+ + O2

[1] Suraud M G et al 1988 J. Phys. B: At. Mol. Phys. 21
1219[2] Guillemot L et al 1990 J. Phys. B: At. Mol. Phys. 233353[3] Bliman S et al 1992 J. Phys. B: At. Mol. Phys. 25 2065

2

3

4

Wavelength / nm

56[4] Chen M H et al 1983 Phys. Rev, A 27 544

Figure 3. Soft X-ray spectra observed in[5] Goryaev F F et al 2017 At. Data Nucl. Data Tables 113

collisions of O6+ ions with five kinds of117

target gases.

[6] Numadate N et al 2018 to be submitted-4-

4

Theoretical investigation of resonant multiple Auger processesof core-excited Ar 2p-13/24s
Yulong Ma1, Zhenqi Liu1, Fuyang Zhou2 and Yizhi Qu1*
1School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China

2

Data Center for High Energy Density Physics, Institute of Applied Physics and Computational
Mathematics, Beijing 100088, China

Abstract
The resonant single, double, triple and quadruple Auger decays of the core-excited Ar 2p -13/2 4s areinvestigated using the multistep approaches, i.e., the cascade, knock-out and shake-off mechanisms within
the framework of many-body perturbation theory. The calculated ion yields (in percentages) of Ar+ : Ar2+ :Ar3+ : Ar4+ = 65.3 : 31.0 : 3.6 : 0.09 are in agreement with the recent experimental values of 69 : 28 : 3 : 0.03
[Y. Hikosaka et al., Phys. Rev. A 89, 023410 (2014)] and 66 : 30 : 4 : 0.2 [J. A. R. Samson et al., Phys. Rev.
A 54, 2099 (1996)]. Furthermore, the Auger electron spectra are obtained, which are consistent with theexperimental measurements. In the direct processes, the spectator processes are essential for the populationsof final states, while the participator processes become dominant as the number of emitted Auger electrons
increases. Besides, the shake processes also affect significantly the final states for the direct processes.
1. Introduction
Resonant multiple Auger (RMA) decays of a core-excited state produced by exciting an inner-shellelectron to a Rydberg orbital, may emit one, two and even more Auger electrons. The RMA decay is one of
the important relax processes for the inner-shell excited atom upon radiationless decays, which results fromthe many-electron Coulomb interaction. Therefore, investigations of such processes could give important
information on electron correlation effects and many-body problems in atomic processes [1,2]. As the highorder process, RMA decay is forbidden within the independent particle model and, hence, it is a goodcandidate for testing the theoretical modelsthat incorporate electron correlations in such process.
In the resonant Auger decay, the Rydberg electron can: (i) remain in its orbital as a spectator, (ii) takepart in the Auger process, (iii) be shaken up to a higher, or shaken down to a lower orbital, which refer to as
spectator, participator and shake processes, respectively. These processes from Ar 2p-13/24s can be represented
as follows:
2p-13/23s23p64s → 2p6(3s3p)7-q4s + qe2

6

6

8-q

2

6

6

7-q

2p 3s 3p 4s → 2p (3s3p)
-1
3/2

+ qe

-

(spectator process)(1)(participator process)(2)

2p 3s 3p 4s → 2p (3s3p) nl+ qe (nl ് 4s)-1
3/2(shake process)(3)

where q=1, 2,3 and 4 correspond the resonant single Auger (RSA), resonant double Auger (RDA), resonant
triple Auger (RTA) and resonant quadruple Auger (RQA) decays, respectively.
* Corresponding author’s email: yzqu@ucas.edu.cn-1-5

In this paper, we present the theoretical study of the RMA decays for the Ar atom with a 2p3/2 holefollowing the resonant 2p3/2 → 4s photoexcitation. In particular, the spectator, participator and shakeprocesses are explored for the populations of the final states. In order to obtain the Auger rates, the multistep
approaches, i.e., cascade, knock-out (KO) and shake-off (SO) mechanisms [3] are employed. According to
the Auger rates, we are able to present the Auger spectra and final ion yields, which are consistent with theexperimental data [4].
2. Theory
The RSA rate can be expressed as [5]
SA
if

A

where

2

N

1
\ , N ; JT M T ¦\ip  q rpq
f,

\ i represents the initial autoionizing state and \ +f , N ; J T M T(4)is the final ionic state\ +fplus a continuum Auger electron with the relativistic angular quantum number κ. JT and MT are the total
angular momentum and magnetic quantum number of the final state, respectively.
The direct RDA rate can be obtained by the KO and SO [3], which are expressed as¦ A : (H ) ,AifDDA(KO)

SA
im

mf

(5)

0

m

AifDDA (SO)¦A

\ 2f + N ; J T M T \ m+

SA
im

2

,

(6)

m

SA

respectively. Here Aim is the RSA rate for the initial state Ar 2p-13/24s to the intermediate Ar+ states. Ωβγ(ε0) is
the collision strength of the inelastic scattering by the “intermediate” Auger electron with energy ε0 from theprimary RSA process, and the matrix element \ 2f  N ; J T M T \ mrepresents the overlap integral between

the intermediate state Ar+ and final ionic state Ar2+ with the second Auger electron.
In the cascade RDA decay, the initial state Ar 2p-13/24s can undergo a RSA decay to an intermediate
autoionizing state Ar*+, and then decay further to final Ar2+ states via the emission of another electronோௌ஺௔௨௧௢௜௢௡௜௭௔௧௜௢௡

Ar 2p-13/24s ሱۛሮ Ar*+ + e- ሱۛۛۛۛۛۛۛۛۛۛሮ Ar2+ + 2e-.
Then the cascade RDA rate can be obtained from

¦A A * ,AifCDA

SA SA
im mf

1
m

(7)

(8)

m

SA

SA
where Aim and Amf are the single Auger rate for the first and second steps of the cascade RDA decay,

respectively. Ȟ௠ is the total width of the intermediate state Ar*+.
We propose a multistep approach to deal with the direct RTA decay with the KO mechanism. Additional
contribution of the SO mechanism is neglected as this mechanism could be rather weak for the Auger electronenergies below 200 eV, which was also illustrated in our previous work for C 1s-1 [6] and Ne 1s-1 [7]. In our
approach, the direct RTA decay are decomposed into a sequence of the direct RDA process and the inelastic-2-

6

scattering process within the KO mechanism:ௗ௜௥௘௖௧ோ஽஺

௄ை

Ar 2p-13/24s ሱۛۛۛۛۛۛሮ Ar2+ + 2e- ሱሮ Ar3+ + 3e-,and, hence, the corresponding direct RTA rate can be obtained from the expression,

AifDTA

¦A ³
m

DDA

where Aim

Eim
DDA
im
0

Uim (H ):mf (H ) d H ,

(9)

(10)

is the direct RDA rate from the initial state Ar 2p-13/24s to the intermediate state of Ar2+ ion,

which emits simultaneously two outgoing continuum electrons sharing the continuously distributed energyof Eim = Ei – Em, where Ei and Em are the energies of the initial state Ar 2p-13/24s and intermediate Ar2+ state,
respectively. ȳ௠௙ ሺߝሻis the collision strength of inelastic scattering off a bound electron of the intermediate
Ar2+ ion by two “intermediate” Auger electrons from the primary direct RDA process. We treat the“intermediate” Auger electrons as the incident electron for the inelastic scattering, which has kinetic energy
range from 0 to Eim with symmetrical U-shape distribution [8]. In order to simulate the energy distributionߩ௜௠ ሺߝሻ, the single energy differential cross section calculated by the binary-encounter model [9] are used.
In the cascade RTA decay, three Auger electrons are emitted in a stepwise manner through the creationand decay of intermediate autoionizing states. Based on our test calculations, the important cascade processௗ௜௥௘௖௧ோ஽஺

௔௨௧௢௜௢௡௜௭௔௧௜௢௡

(11)
Ar 2p-13/24s ሱۛۛۛۛۛۛሮ Ar*2+ + 2e- ሱۛۛۛۛۛۛۛۛۛۛሮ Ar3+ + 3eis considered, in which the final states Ar3+ are attribute to a primary direct RDA decay to an intermediate
autoionizing states Ar*2+ lying above Ar3+ threshold with a subsequent autoionization. Then the cascade RTA
rate can be obtained with

AifCTA¦A

A *m1 ,DDA SA
im
mf

(12)

m

DDA

here Aim is the direct RDA rate of the initial state Ar 2p-13/24s to the intermediate autoionizing state Ar*2+, and

AmfSA represents the rate of further autoionization from the Ar*2+ states to the final state Ar3+. *m is the total
width of the intermediate state Ar*2+.
The direct and cascade processes are also considered for the RQA decay. Similarly to the direct RTA
decay, the direct RQA decay is decomposed into a primary direct RTA decay and a subsequent KO mechanismௗ௜௥௘௖௧ோ்஺

௄ை

Ar 2p-13/24s ሱۛۛۛۛۛۛሮ Ar3+ + 3e- ሱሮ Ar4+ + 4e-.

(13)

Besides, the cascade processௗ௜௥௘௖௧ோ்஺

௔௨௧௢௜௢௡௜௭௔௧௜௢௡

(14)
Ar 2p-13/24s ሱۛۛۛۛۛۛሮ Ar*3+ + 3e- ሱۛۛۛۛۛۛۛۛۛۛሮ Ar4+ + 4e-,is considered, which results from that primary three electrons are emitted simultaneously in the primary direct
RTA decay populating into intermediate autoionizing states Ar*3+ with a further autoionization.
In this work, the rates of the RSA decay were calculated using the AUGER component of the RATIP
package [10], based on the MCDF method that is implemented in the GRASP2K program [11]. The
autoionizing rates and collision ionization strengths as well as the overlap integrals were obtained using theflexible atomic code (FAC) [5] with some modifications [6,7].
3. Results-3-

7

The calculated ion yields of Ar+, Ar2+, Ar3+ and Ar4+ ions produced by the RSA, RDA, RTA and RQA
decays, respectively, of the Ar 2p-13/24s including the cascade and direct processes are summarized in Table 1
and in agreement with the available experimental values [4,12]. Our results imply that the contributions of
the direct process become dominant with the increase of the number of emitted Auger electrons, as observedin the experiment [4].
Table 1. Ion yields (in percentages) produced by the resonant single, double, triple and quadruple Auger
decays represented by the RSA, RDA, RTA and RQA, respectively, of the Ar 2p-13/24s. The calculated ion yields
in the fifth column with the inclusions of the cascade and direct processes are compared with experimental
data [4,12].
Ions

Decays

Ar+
Ar

2+

Ar

3+

Ar4+

This work

Expt.

CascadeDirectTotal

Ref. [4]Ref. [12]

RSA

-

-

65.3

69

66

RDA

20.4

10.6

31.0

28

30

RTA

1.2

2.4

3.6

3

4

RQA

0.01

0.08

0.09

0.03

0.2

The RMA spectra including the cascade and direct processes are presented in Figs. 1-4, which wereobtained by convolving the Auger rates with Gaussian profile considering the energy resolving power E⁄∆E
= 60 of the apparatus in Ref. [4]. It is found that calculated spectra agree with the experimental spectra
obtained by multielectron coincidence spectroscopy [4]. The possible transitions with rates are indicated by
the solid vertical lines below the plots, where the colors correspond to the configurations of the final ion thatare associated with the spectator (4s orbital), participator (only 3s and 3p orbitals), shake-down (3d orbital)and shake-up (5s orbital) processes. In Fig. 1, the contributions of 3s23p44s are most important due to thespectator process for the RSA decay. The shake-down (3s23p43d) and shake-up (3s23p45s and 3s3p55s) giverise to other peaks of the RSA spectra. For the direct RDA decay in Fig. 2(a), the spectator processes are
predominant, while the contributions of the participator processes become more important for the total RDA
in Fig. 2(b) with the inclusion of the cascade and direct processes. Our results reveal that the cascade process
is dominant and the contribution is determined to be 66% of the total RDA decay, which is consistent withthe experimental estimation of ~60% [4]. The shake processes also affect significantly the populations of
final states for the RDA decay. In Fig 3(a), the participator process forming the 3s23p3 states is more favoredthan the spectator process forming the 3s23p24s states. This indicates that the participator process becomes
important for direct RTA, compared to direct RDA discussed above. For the total RTA decay in Fig. 3(b), thecalculated direct RTA decay is dominant accounting for 67% of the total RTA decay, which agrees withexperimental estimation of ~60% [4]. This is contrary to the total RDA decay, where the formations of theAr2+ states are more favored by the cascade process than direct one. In the total RTA decay, the states
belonging to the configuration 3s23p3 are most populated and, hence, the participator process forming theconfigurations 3s23p3 and 3s3p4 is dominant. Finally, the total RQA decay spectra are displayed in Fig. 4.

-4-8

According our calculations, the contribution of the direct process is far greater than that of the cascade ones.
The participator process forming the states of the configurations 3s23p2 and 3s3p3 is favored, and thecontributions of the spectator and shake processes are small.

Fig. 1

Theoretical and experimental [4] resonant single Auger electron spectra of the Ar 2p-13/24s. The

vertical solid lines below the plots indicate the possible transitions, where the colors correspond todifferent final-state configurations that are associated with the spectator (4s orbital), participator (only 3s
and 3p orbitals), shake-down (3d orbital) and shake-up (5s orbital) processes. The theoretical spectra wasshifted 1.8 eV toward low kinetic energies.

Fig. 2Same as Fig. 1, but for (a) the direct and (b) total resonant double Auger decay including thecascade and direct processes.

Fig. 3Same as Fig. 1, but for (a) the direct and (b) total resonant triple Auger decay.

-5-9Fig. 4Same as Fig. 1, but for total resonant quadruple Auger decay including the cascade and directprocesses. The theoretical spectra was shifted 1.5 eV toward low kinetic energies.
4. Conclusion
The RSA, RDA, RTA and RQA decays following the resonant 2p3/2 → 4s photoexcitation in neutral
argon are investigated theoretically. The final ion yields and Auger electron spectra are obtained according
to the Auger rates that are evaluated by using multistep approaches, namely, cascade, KO and SO mechanisms
within the framework of MBPT, which are in general agreement with the experimental measurements [4].
The spectator processes are essential for the populations of final states, while the participator processes
become dominant as the number of emitted Auger electrons increases for the direct processes. Besides, theshake processes also responsible for the final states during the RMA decays.
Acknowledgements
We would like to thank Y. Hikosaka for providing the experimental data from Ref. [4]. This work
supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300),
the National Natural Science Foundation of China (Grant Nos. 11774344 and 11474033), and the Joint
Foundation of the National Natural Science Foundation and the China Academy of Engineering Physics(Grant No. U1330117).
References[1] Pieve F D et al 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3619.
[2] Stolterfoht N et al 1986 Phys. Rev. Lett. 57 74.
[3] Amusia M Y et al 1992 Phys. Rev. A 45 4576.
[4] Hikosaka Y et al 2014 Phys. Rev. A 89 023410.
[5] Gu M F 2008 Can. J. Phys. 86 675.
[6] Zhou F et al 2016 Phys. Rev. A 93 060501(R).
[7] Ma Y et al 2017 Phys. Rev. A 96 042504.
[8] Viefhaus J et al 2004 J. Electron Spectrosc. Relat. Phenom. 141 121.
[9] Kim Y K et al 1994 Phys. Rev. A 50 3954.
[10] Fritzsche S 2012 Comput. Phys. Commun. 183 1525.
[11] Jönsson P et al 2007 Comput. Phys. Commun. 177 597.
[12] Samson J A R et al 1996 Phys. Rev. A 54 2099.

-6-

10

Statistical properties of atomic structures of r-process elements
Daiji Kato1,2*, Gediminas Gaigalas1,3, Masaomi Tanaka4,51

National Institute for Fusion Science, Toki 509-5292, Gifu, Japan2

Department of Advanced Energy Engineering Science, Kyushu University, Fukuoka 816-8580, Japan
3

Institute of Theoretical Physics and Astronomy, Vilnius University, LT-10222 Vilnius, Lithuania
4

Astronomical Institute, Tohoku University, Sendai, Miyagi 980-8578, Japan

5

National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan

Abstract
New calculations of atomic structures for r-process elements in ejecta of binary neutron star coalescencehave been conducted using HULLAC and GRASP2K codes. The results are compared and used to evaluate
impact of accuracy in the atomic calculations to opacities of electromagnetic emission from the ejecta.
Universality and physical properties in complex open f-shell energy level structures of Nd II and Er II are
investigated by coarse-graining methods. The energy level structures are well characterized in terms ofstatistics of the skewed normal distributions.
Keywords: neutron-star merger, r-process element, opacity of bound-bound transition, atomic structure
calculation, coarse-graining, Kolmogorov-Smirnov test
1. Introduction
Gravitational waves by a binary neutron-star merger (NSM) have been detected on 2017 August 17(GW170817 [1]) for the first time. Ejecta of the neutron-star merger are considered to be the cosmic originof heavy elements created by the r-process, the rapid neutron-capture process that makes half of all elements
heavier than iron. Radioactive decays of the synthesized r-process nuclei in the ejecta cause electromagnetic(EM) emission which is called as kilonova. The EM emission from the ejecta is delayed and dimmer if heavy
r-process elements such as lanthanide and actinide (open f-shell) are abundant in the ejecta. Observed light
curves of infra-red emission counterpart to GW170817 confirm the existence of some lanthanide contents inthe ejecta [2]. However, atomic data for lanthanide are far too insufficient in available databases, e.g. NIST
ASD [3], VALD [4] to make detail analysis of the EM emission. Thus, atomic structure calculations for thelanthanide elements are carried out by several research groups [5-9].
We present our atomic structure calculations for the r-process elements using two atomic codes,
HULLAC [10] and GRASP2K [11], and opacities of bound-bound transitions with the calculated data. It isalso demonstrated that potential usefulness of statistical analysis for extremely complex atomic structures ofthe lanthanide elements.

* Corresponding author’s email: kato.daiji@nifs.ac.jp

-1-

11

2. Atomic structure calculations for opacities of bound-bound transitions
In homologous expanding gas, like points on the surface of an inflating balloon, more distantions go away faster, i.e. velocity gradient. Because of this, line radiations from far distant ions are
more red-shifted. Since the radiations are absorbed in cases that the wavelengths are red-shifted into
resonance with the adjacent lines, effective opacities of bound-bound transitions in a wavelengthinterval becomes in proportion to densities of strong (optically thick) transitions. Lanthanide
elements (open f-shell) have enormous bound-bound transitions in infra-red region giving large
opacities peaking in this wavelength range. This is contrast to iron (open d-shell) which gives smaller
opacities peaking in the optical range.
For the present atomic structure calculations, two different codes, HULLAC [10] and GRASP2K[11] were used. The HULLAC code, which employs a Slater-type parametric potential, is used toprovide atomic data for many elements while the GRASP2K code, which enables more ab-initio
calculations based on the multi-configuration Dirac-Hartree-Fock (MCDHF) method [12], is used toprovide benchmark calculations for a few elements. In the HULLAC code calculations, theparametric potentials are optimized empirically such that the correct ground-state configuration andthe lowest energies of low-lying excited-state configurations in agreement with those of NIST
database are obtained. On the other hand, GRASP2K calculations are conducted by increasing thesize of active space step-by-step. The GRASP2K calculation with the largest active space includes alarger number of configuration state functions than that of corresponding HULLAC calculation.
Therefore, in the results of GRASP2K configuration interactions are more extensively taken into
account. The Breit interaction and lowest order QED effects are included in both calculations [12].
We compared calculations using two codes and available data in NIST ASD for Nd II-III and Er
II-III. Agreement between HULLAC and GRASP2K results is reasonably good. However, Er II-III
energy levels of HULLAC are higher than those of GRASP2K, which may be reflecting accuracy of
the GRASP2K results calculated with more extended configuration interactions. The discrepancy ismost significant for excited-states of Er III. For Nd II, overall agreement of our calculations with
NIST data is within 30 % which is slightly better agreement than results of Autostructure code byKasen [2]. Both HULLAC and GRASP2K give the correct ground-state and ordering of excited-stateenergies, except for odd-parity states of Er II. The lowest energy of 4f116s2 excited-state of Er II is
too high comparing with that of NIST data. It may reflect difficulty in improving electron-electron
correlation effects evenly between different parity states. Further investigation is ongoing.
The opacities of Nd II-III and Er II-III calculated with transition data of HULLAC and
GRASP2K codes are compared. The calculations assume the Boltzmann distribution of excited-state populations with ߩ = 1 × 10ଵଷ g cmିଷ , ܶ = 5,000 K or 10,000 K, and ‫ = ݐ‬1 day
after the merger. The optical depth of rapidly expanding media is in proportion to oscillator
strengths multiplied by the populations for lower levels of transitions. As expected from the good
agreement in the energy levels, both results of the opacities are very similar for Nd. However,significant differences are seen in the results for Er as does in the energy levels. GRASP2K
calculations give larger opacities than those of HULLAC because the populations for the lower levels-2-12

of GRASP2K are larger. This discrepancy is most significant for the case of Er II and reaching to afactor of about 2 at the peak of the opacity.
3. Statistical properties of atomic structures
It is practically impossible to compare the whole open f-shell energy structures level-by-level due touncertainty in identification of each level and quasi continuum spectra. Effective methods for evaluating suchcomplex structures are needed for a better understanding. Coarse-graining methods are useful forunderstanding universal natures of complex systems and parametrization of each system. The coarse-graining
methods have been applied in various fields of science including renormalization group theories [13], kinetic
models of plasma turbulence [14] and molecular dynamics of complex chemical systems [15].
Figure 1 plots differential statistical-weight distributions for two excited-state configurations of Nd II
binned with the finite energy interval of 0.1 eV. Results of HULLAC and GRASP2K calculations arecompared with available data in NIST ASD. Although the NIST data are available only at low energies,
overall profiles of the coarse-grained distributions are apparently in good agreement indicating a universal
structure behind. It is noted that GRASP2K results in the figure are presented up to the ionization thresholdof Nd II (10.783 eV). Based on the HULLAC results it is found that the universal structure is well depictedby the skewed normal distribution using the first three moments, i.e. mean ‫ܧ‬ୟ୴ , variance ߪ ଶ = ‫ ܧ(ۦ‬െ ‫ܧ‬ୟ୴ )ଶ ۧ,
and ‫ ܧ(ۦ‬െ ‫ܧ‬ୟ୴ )ଷ ۧ, of the statistical-weight distribution (see Fig. 1).

Fig. 1 Differential statistical-weight distributions of 4f35d2 (upper) and 4f35d6s (lower) configurations.
Red color stands for NIST ASD, green GRASP2K, and blue HULLAC. The results are binned with theenergy interval of 0.1 eV. Corresponding skewed normal distribution functions are plotted by purple
curves.

-3-

13

݀݃ୡ
1
‫ݔ‬ଷ
మ
= ܿ ቈ1 െ ߙଷ ቆ‫ ݔ‬െ ቇ቉ ݁ ି௫ Τଶ ,
2
݀‫ݔ‬
3
(1)
where ‫ ܧ( = ݔ‬െ ‫ܧ‬௔௩ )Τߪ and ߙଷ = ‫ ܧ(ۦ‬െ ‫ܧ‬௔௩ )ଷ ۧΤߪ ଷ (referred to as skewness). The normalization
constant c is determined such that the integral of the distribution function gives the total statistical-weightof the corresponding configuration. In the earlier works [16], the skewed normal distribution has alreadybeen suggested for statistical-weight distributions of the open f-shell configurations. Signs of the skewness
parameters ߙଷ are positive for all configurations of Nd II and Er II we have studied. This implies that large
angular momentum states that possess larger statistical-weights, preferably fall into the lower energy side,which is consistent with Hund’s rule as long as LS-coupling scheme is valid. The variances of the normal
distributions for Er II are larger than those of Nd II, which should be related to that electron-electroninteraction energies are larger for heavier elements due to orbital shrink in a stronger nuclear attraction force.
Thus, it is encouraging to parametrize complex lanthanide atomic structures in terms of the statistics of theskewed normal distribution.
In the last part of the present work, we examine statistical properties of the energy level structures for
Nd II. The coarse-graining of the energy scale is somewhat ambiguous because we can choose arbitraryenergy intervals. We may ask alternatively the null hypothesis as “Statistical distributions of energy levels
obtained by stochastic sampling are the skewed normal distribution”. This is, so to speak, coarse-graining ofour knowledge (information) on the energy level structures. In order to judge the null hypothesis,
Kolmogorov-Smirnov (KS) test [17], which is a non-parametric statistical test without binning continuous
valued samples, is applied in this study. The KS test evaluates differences between the two distributions interms of the statistic defined as,‫ܦ‬ே ‫ ؠ‬sup|ܵே (‫ )ܧ‬െ ܲ(‫|)ܧ‬,ா

(2)
where cumulative probability distributions ܵே (‫ )ܧ‬and ܲ(‫ )ܧ‬are given for our problems, respectively, as,ே

1ܵே (‫ = )ܧ‬෍ ‫[ܫ‬ாౣ౟౤ ,ா] (‫ܧ‬௞ ),
ܰ
௞ୀଵ

(3)
and
ா

1
݀݃ୡ
ܲ(‫= )ܧ‬
න
݀‫ݔ‬.
݃ୡ
݀‫ݔ‬
ாౣ౟౤

(4)
‫[ܫ‬ாౣ౟౤ ,ா] is the indicator function defined as,1, ‫ܧ‬௞ ‫ܧ[ א‬୫୧୬ , ‫]ܧ‬‫[ܫ‬ாౣ౟౤ ,ா] (‫ܧ‬௞ ) ‫ ؠ‬൜
.
0, ‫ܧ‬௞ ‫ܧ[ ב‬୫୧୬ , ‫]ܧ‬
-4-

14

(5)
The null hypothesis is accepted if the KS statistic ‫ܦ‬ே on average is smaller than a critical distance at a levelof significance. In this study, we use the significance level of 0.05, which means that deviation of normally
distributed samples over a given ܲ(‫ )ܧ‬can exceed the critical distance by chance with 5% probability. In
the Fig. 2, the average values of ‫ܦ‬ே obtained by performing 1,000 tests for Nd II 4f35d2 are plotted with thecorresponding critical distances at the significant level of 0.05. The critical distances can be fitted by thesingle curve, 1.34/ξܰ. All of the averaged ‫ܦ‬ே in the figure stay below the critical distances although it isapproaching to the critical distance at large ܰ values. Thus, the null hypothesis is accepted by the present
KS test for Nd II 4f35d2. By increasing number of sampling ܰ, we would acquire knowledge about moredetailed energy level structures which will not completely be depicted by the skewed normal distribution
resulting in the averaged ‫ܦ‬ே exceeding the critical distances.

Fig. 2 KS statistic as a function of the number of sampling for 4f35d2 configuration. Solid squares are‫ܦ‬ே values averaged over 1,000 tests for each ܰ and open circles the critical distances at the significant
level of 0.05. The dotted line is the fitted critical distance curve, 1.34Τξܰ.

4. Summary and Outlook
Available atomic data (energy levels, oscillator strengths, etc) for heavy r-process elements in NSM
ejecta are very limited. New calculations of the atomic data have been conducted using HULLAC and
GRASP2K codes. Overall agreement in the lowest energies of configurations for Nd II-III and Er II is good.
However, a significant difference remains for excited-states of Er III; GRASP2K results are in better
agreement with those of NIST ASD. The lowest energy of 4f116s2 excited-state of Er II is too high comparing
with that of NIST data. The expansion opacities of Nd II-III and Er II-III obtained with transition data
calculated using HULLAC and GRASP2K are also in good agreement. The discrepancy is most significant
for the case of Er II and a factor of about 2 at the peak of the opacity. Extended GRASP2K calculations,-5-15

uncertainty quantification of the atomic data, and more detailed analysis on opacities obtained with the data
are ongoing focusing on Nd II-IV [18].
Coarse-graining methods are applied to elucidate the universal structure in complex energy levelstructures of lanthanide elements. The differential statistical-weight distributions binned with a finite energy
interval are well depicted by the skewed normal distribution. Physical properties in the energy level structures
can be characterized in terms of the statistics. The skewness of the distributions for Nd II and Er II showsthat their energy level structures are consistent with Hund’s rule. Kolmogorov-Smirnov test is applied tojudge whether stochastic sampling of the energy levels leads to the heuristic skewed normal distribution. This
null hypothesis is accepted for Nd II 4f35d2 at the significant level of 0.05 as long as the number of sampling
is not too large.
Acknowledgements
This research was partly supported by JSPS Bilateral Joint Research Project, and the NINS
program for cross-disciplinary science study. DK is grateful to the support by NINS program of Promoting
Research by Networking among Institutions (Grant Number 01411702). GG is grateful to NIFS visiting
professorship (7 May – 7 June, 2018).
References[1] Abbott B P, Abbott R, Abbott T D et al 2017 Phys. Rev. Lett. 119 161101[2] e.g. Utsumi Y, Tanaka M, Tominaga N et al 2017 PASJ 69 101[3] Kramida A, Ralchenko Y, Reader J et al 2015 NIST Atomic Spectra Database (ver. 5.3) (Gaithersburg,
MD: National Institute of Standards and Technology) http://physics.nist.gov/asd[4] Vienna Atomic Line Database (Uppsala University, the Institute of Astronomy RAS in Moscow, and the
University of Vienna)[5] Kasen D, Badnell N R, and Barnes J 2013 ApJ 774 25[6] Fontes C J, Fryer C L, Hungerford A L et al 2017 arXiv:1702.02990[7] Wollaeger R T, Korobkin O, Fontes C J et al 2017 arXiv:1705.07084[8] Kasen D, Metzger B, Barnes J et al 2017 Nature 551 80[9] Tanaka M, Kato D, Gaigalas G et al 2018 ApJ 852 109[10] Bar-Shalom A, Klapisch M, and Oreg J 2001 J. Quant. Spectrosc. Radiat. Trans. 71 169[11@-|QVVRQ3*DLJDODV*%LHURĔ- et al 2013 Comput. Phys. Commun. 184 2197
[12] Fischer C F, Godefroid M, Brage T et al 2016 J. Phys. B: At. Mol. Opt. Phys. 49 182004[13] Wilson K G and Kogut J 1974 Phys. Reports 12C 75[14] Chen Y and Parker S E 2007 Phys. Plasmas 14 082301[15] Kmiecik S, Gront D, Kolinski M et al 2016 Chem. Rev. 116 7898
[16] Cowan R D 1981 The Theory of Atomic Structure and Spectra (Univ. California Press, Berkeley)[17] Press W H, Teukolsky S A, Vetterling W T et al 1992 Numerical Recipes in FORTRAN, 14. Statistical
Description of Data (Cambridge University Press 1986, 1992)[18] Gaigalas G, Kato D, Rynkun P et al 2019 ApJS 240 29-6-16

Estimation of photon emission coefficients in tungsten UTA transitions
using LHD plasmas
S. MORITA1,2, Y. LIU2, I. MURAKAMI1,2, T. OISHI1,2, M. GOTO1,2
1

National Institute for Fusion Science, Toki 509-5292, Gifu, Japan

2

The Graduate University for Advanced Studies (SOKENDAI), Toki 509-5292, Gifu, Japan

Abstract
EUV spectra of tungsten UTA in 15-70 Å has been studied in LHD by injecting tungsten pellet.
Radial profiles of the UTA line are measured with a space-resolved EUV spectrometer.

Density of theW24+, W25+ and W26+ ions is evaluated from the radial profile measured at specified wavelength intervals of
32.16-33.32, 30.69-31.71 and 29.47-30.47Å. In order to evaluate the ion density, a photon emission
coefficient for the W24+, W25+ and W26+ ions is calculated using a collisional-radiative (CR) model.
24+

tungsten density profile of W

,W

25+

26+

and W

The

ions is obtained from the local emissivity profile and thephoton emission coefficient in addition to the temperature and density profiles. A total tungsten ion
density, nW, near ρ = 0.7 where the W24+ ion locates is also estimated from the W24+ ion density withfractional abundance in ionization equilibrium calculated with ADAS code. The value of nW evaluatedfrom the present CR model seems to be large, when it is compared with nW estimated from the number oftungsten particles injected by the pellet. Discussions are made with the nW evaluated from the photon
emission coefficient in CL version of ADAS code.
1. Introduction
Since the edge electron temperature of ITER plasmas is estimated to range in 0.2 d Te d 4 keV,
pseudo-continuum tungsten spectra called unresolved transition array (UTA) [1] emitted at EUV
wavelength ranges of 18-33 Å and 44-64 Å are very important for studying the edge tungsten behavior in
ITER [2]. In LHD, the electron temperature of neutral-beam heated plasmas typically ranges in 1-4 keV
and has a similar temperature range to the edge plasma of ITER. A spectral structure of the UTA has beenstudied by analyzing an electron temperature dependence of the UTA line intensity at each wavelengthinterval and measuring the peak position of radial profiles of the UTA line. As a result, it has been foundthat the tungsten UTA line at wavelength intervals of 32.16-33.32 Å, 30.69-31.71 Å and 29.47-30.47 Å iscomposed of a single ionization stage of W24+, W25+ and W26+, respectively [3].
In the present study, the tungsten ion density is evaluated as the first attempt based on the previous
study on the tungsten UTA line.

A vertical intensity profile of the UTA line is measured for the W24+,

W25+ and W26+ ions at wavelength intervals mentioned above. A photon emission coefficient (PEC) is
calculated with a collisional-radiative (CR) model developed for the UTA spectrum analysis in which two
effects of inner-shell excitation and configuration interaction are newly considered [4]. The tungsten ion
density can be thus evaluated from the local emissivity profile and photon emission coefficient in addition
to the electron temperature and density profiles measured with high accuracy. A total tungsten density can-1-17be estimated from the analyzed W24+ ion density profile with PEC. The total tungsten densities analyzed
from CR-model and ADAS code are compared with that estimated from injected tungsten pellet size.
2. Tungsten UTA spectrum
The tungsten spectrum in the wavelength range of 18-36 Å is measured with EUV_Short spectrometer
after the pellet injection, as shown in Fig. 1. The ionization stage of UTA lines in each peak group isestimated by referring the previous work from CoBIT [5] and plasma device.

As shown in the figure, thetungsten UTA spectrum is composed of many ionization stages of tungsten ions, e.g. from W24+ to W33+ inthe present spectrum. These UTA lines are basically formed by four transitions of 6g-4f, 5g-4f, 5f-4d and
5g-4f. In our previous work [3], the UTA line at wavelength intervals of 27.20-27.62 Å, 28.38-28.70 Å,
29.36-30.47 Å, 30.69-31.71 Å and 32.16-33.32 Å indicated with hatched regions is found to be composedof a single ionization stage of W28+, W27+, W26+, W25+ and W24+, respectively.

In the present study, three

UTA lines at 29.36-30.47 Å, 30.69-31.71 Å and 32.16-33.32 Å are used to evaluate the tungsten density
profiles of W26+, W25+ and W24+ ions, respectively.

Fig. 1

Tungsten UTA spectrum at wavelength range of 18-36 Å.

Shaded area indicates awavelength interval in which UTA emission lines are composed of a single ionization stage.

3. Tungsten density profile of W24+ ions
Total photon emission coefficients of W24+, W25+ and W26+ at wavelength intervals of 32.16-33.32,
30.69-31.71 and 29.47-30.47 Å are calculated with CR model developed for analysis of the tungsten UTA
spectrum [4].

In the CR model, principal quantum number up to n = 7 and 11753, 13772 and 7515

J-resolved fine-structure levels are taken into account for W24+, W25+ and W26+ ions, respectively, and 19-27
electron configurations are considered for one ion. Effects of inner-shell excitation and configurationinteraction are also considered in addition to general atomic processes. The PEC at each wavelengthinterval then includes a lot of transitions. In practice, there are more than 100 thousands emission lines at
each wavelength interval.
The result of the modeling is plotted in Fig. 2(a). The PEC is approximately constant at Te t 0.8 keV,
while it is greatly sensitive to the electron temperature at Te d 0.4 keV. Since the tungsten ions always
stay at a fixed narrow temperature window, the emission intensity is not so sensitive to the central electron
temperature. In Fig. 2(b), the PEC of W24+, W25+ and W26+ at 32.16-33.32, 30.69-31.71 and 29.47-30.47
Å is calculated with ADAS code [6] (CL version). In this version, 28-29 electron configurations are-2-18

considered, while an energy level splitting among sublevels is not taken into consideration. The photon
emission coefficient of the W24+ ion obtained from ADAS code is three times larger than that from thepresent CR model. A cascade process from higher excited levels and 5g-4f inner-shell excitations may
enhance the photon emission coefficient in the ADAS code calculation.

(a)

(b)

Fig. 2 Total PEC of W24+ (32.16-33.32 Å: solid line), W25+ (30.69-31.71 Å: dashed line) and W26+
(29.47-30.47 : dotted line) calculated with (b) the present CR model and (c) ADAS code.

4. Tungsten density profile of W24+ ions
The W24+ ion density profiles analyzed with CR-model at different temperatures are shown in Fig. 3(a).
The W24+ ion density distributes in range of 3-5 u 109 cm-3. The density profile of W24+ ions is also
analyzed using PEC from ADAS code, as shown in Fig. 3(b). It is obvious that the W24+ ion density from
CR-model is roughly three times larger than that from ADAS code, reflecting the difference in the PEC.

Fig. 3. Density profiles of W24+ ions at Te0 = 2.19 (dashed line), 1.95 (solid line) and 1.82 keV(dotted line) using PEC calculated with (a) the present CR model and (b) ADAS code.
Based on the analyzed W24+ ion density profile, the total tungsten density, nw(U), is estimated from anequation of the fractional abundance of W24+. Here, the total tungsten density is estimated only from the-3-19

peak value of W24+ ion profile in the vicinity of U = 0.7. The result is shown in Fig. 4 for the PEC fromthe present CR model (solid line) and ADAS code (dashed line). It is shown in the figure that the total
tungsten density continuously decreases after the tungsten pellet injection at t = 4.3 s, while the reduction
becomes slower as a function of time.
From the profile measurement of EUV line emissions in several tungsten ionization stages, thetungsten ion slowly expands in the radial direction toward the plasma center. The result in Fig. 4 indicatessuch an expansion process. In the present case the tungsten ion almost completes the expansion at 't =0.5 s after the pellet injection, i.e., t = 4.8 s in Fig. 4. If all the tungsten ions are uniformly distributed in
the LHD plasma, we obtain nW = 4.1 × 109 cm-3 from the number of tungsten particles injected by the pellet.
The nW from PEC with the present CR model is 3.6 times larger than the nW estimated from the pellet size.
If it is compared with nW based on PEC from ADAS code, the nW from ADAS code is 1.2 times larger than
the nW from the pellet size. At present, however, it is difficult to discuss on the accuracy in the PEC
because another model in the ADAS code has entirely different values for the PEC due to different numberof electron configurations in the model. In addition, the present CR model includes possible all atomic
processes and J-resolved levels, while the inner-shell excitation of 5g-4f transitions is not accurately
considered and the dielectric recombination is not included. We need further efforts for quantitatively andaccurately understanding the UTA line intensity.

Fig. 4. Time trace of total tungsten density in the vicinity of ρ = 0.7 calculated at peak value of W24+
ion density profile (solid circles: the present CR model, solid squares: ADAS code).

References[1] S. Morita, C.F. Dong, M. Goto et al., 2-13 AIP Conf. Proc. 1545, 143.
[2] Y. Liu et al., 2018 Plasma Fusion Res. 13, 3402020.
[3] Y. Liu, S. Morita, X.L. Huang, T. Oishi, M. Goto and H.M. Zhang, 2017 J. Appl. Phys. 122, 233301.
[4] I. Murakami, H.A. Sakaue, C. Suzuki et al., 2015 Nucl. Fusion 55, 093016.
[5] H.A. Sakaue, D. Kato, N. Yamamoto, N. Nakamura and I. Murakami, 2015 Phys. Rev. A 92, 012504.
[6] H.P. Summers, 2004 The ADAS User Manual, version 2.6 http://www.adas.ac.uk.

-4-

20

Application of matrix decomposition techniqueto tungsten spectra measurement data
Takehiko Esaka1*, Izumi Murakami2, 3, Shigeru Morita2, 3,
Masahiro Hasuo1, Keisuke Fujii1
1

Graduate School of Engineering Kyoto University, Kyoto Nishikyo-ku, Kyoto, 615-8246, Japan2

Department of Helical Plasma Research, National Institute for Fusion Science, Toki, Gifu 509-5292, Japan3

Department for Fusion Science, The Graduate University for Advanced Studies SOKENDAI, Toki, Gifu
509-5292, Japan

Abstract
Because of the overlap of the fractional abundance profiles of highly charged W ions, their spectra has
been observed as a sum of the emission from W ions in many charge states. In this study, we applied one ofmatrix decomposition techniques to the W spectra observed for LHD with electron temperature of 0.5-3.0
keV. All the observed spectra were expressed with 5 spectral bases, which is much fewer than the number ofcharge states in plasmas expected from the theoretical fractional abundance data. From the comparison withthe theoretical spectral profiles, we found that this low rank characteristics of the data is caused by the highly
correlated dynamics of ions in similar charge states.
1. Introduction
Tungsten (W) was decided as the divertor material of ITER [1]. One concern of the use of W is its highradiation loss rate when W contaminates in the plasmas. Understandings of its dynamics from the divertor
region to the plasma core are essential to establish efficient plasma confinement. Almost only the method toestimate the W transport is emission spectroscopy. However, because of the temperature gradient along theline of sight and the significant overlaps of the fractional abundance profiles of the W ions [2], the observed
spectrum ‫ݕ‬ሺߣ௠ ሻ is a sum of the emission lines from W ions in many charge states,‫ݕ‬ሺߣ௠ ሻ ൌ ෍ ݂௤ ߶௤ ሺߣ௠ ሻሺͳሻ
௤where m indicates the index of the measurement wavelength, ߶௤ ሺߣ௠ ሻ is the spectrum from the W ion in
charge state q, and ݂௤ is its coefficient, which is the product of the emission rate and the ion density in eachcharge state along the line of sight. If the exact shape of ߶௤ ሺߣ௠ ሻ is known, ݂௤ can be determined byଶminimizing σ௠൫‫ݕ‬ሺߣ௠ ሻ െ σ௤ ݂௤ ߶௤ ሺߣ௠ ሻ൯ . However the exact shape of ߶௤ ሺߣ௠ ሻ is not known yet andtherefore a theoretical estimate ߶௤୲୦ୣ୭ ሺߣ௠ ሻ has been used to fit the observed spectrum. Figure 1(a) shows߶௤୲୦ୣ୭ ሺߣ௠ ሻ for q = 25, 26 in 1.2െ4.3 nm, which is calculated by a collisional-radiative (CR) model for W
ions [3, 4]. Figure 1(b) shows observed W spectrum in 1.2െ4.3 nm (black points) (the detail will be described* esaka.takehiko.86a@st.kyoto-u.ac.jp

-1-

21

later) and the reconstruction result σ௤ ݂௤ ߶௤୲୦ୣ୭ ሺߣ௠ ሻ (blue curve) by using the estimated coefficients. As
shown in this figure, thanks to the recent accuracy advances, ߶௤୲୦ୣ୭ ሺߣ௠ ሻ reconstruct the observed spectra
well in this wavelength range [3, 4, 5]. However, the observed spectra of some transitions (e.g. 4ହ Ͷ௡ାଵ െͶ଺ Ͷ௡ିଵ Ͷ transition of  ଶଵା െ  ଷହା [3]) have not been represented by the theories.
On the other hand, the estimation of the coefficient ݂௤ and the basis ߶௤୲୦ୣ୭ ሺߣ௠ ሻ from a lot of data can beviewed as a matrix decomposition problem. However, the application to the emission spectrum analysis has
not been reported yet. In this work, we applied one of the matrix decomposition technique to the W spectra
observed in LHD for the first time.

Fig. 1 (a) Theoretical calculation results of emission spectra ߶௤୲୦ୣ୭ ሺߣ௠ ሻ (q = 25, 26). (b) The observed W
spectrum (black point) and the reconstruction result by the conventional analysis (blue curve).
2. Experiments
In LHD, the emission observation of highly charged W ions has been performed with W pellet injections [6,7]. Figure 2(a) and 2(b) show the temporal development of electron temperature (ܶୣ ) and density (݊ୣ ) at
major radius R = 3.6 m (near the plasma center) measured with the Thomson scattering system [8] for atypical W pellet injection experiment. Figure 2(c) and 2(d) show the spatial distributions of ܶୣ and ݊ୣ as afunction of effective minor radius ‫ݎ‬ୣ୤୤ . After the pellet injection, ܶୣ near the plasma center dropped from 3
keV to 0.5 keV, while ݊ୣ increased from ͳͲଵଽ ିଷ to 7.0 × ͳͲଵଽ ିଷ . These changes indicate thesignificant contamination of W ions in the plasma during 4.3െ8.5 s.

Fig. 2 (a) The temporal developments of ܶୣ and ݊ୣ at plasma center (R = 3.6 m) for discharge #121517.
(b) The spatial distribution of ܶୣ and ݊ୣ in t = 4.0 s, t =4.75 s and t = 5.5 s for discharge #121517.
-2-

22

The emission was observed in 1.2–7.5 nm wavelength range with 5.0 ×ͳͲିଷ nm resolution. Figure 3 showsthe emission spectra observed at t = 4.0 s (‫ ݕ‬ሺଶ଴ሻ ) (before the W pellet injection) and t = 4.5s (‫ ݕ‬ሺଵହ଴ሻ ), 5.5 s(‫ ݕ‬ሺଷ଴଴ሻ ) (after the pellet injection), where the superscript of y indicates the index of the exposure. After thepellet injection, the quasi continuum spectra appeared. The shapes of the spectra changed depending on themeasurement timings. Since the dominant charge states of W ions are considered to be  ଶଵା െ  ଷହା inthis temperature range based on the fractional distribution [2] (later shown in Fig. 8), the spectra are also
expected from these charge state ions. We repeated the similar experiment for 5 times and the total of theobserved spectra is 4580.

Fig. 3 Observed emission spectra ‫ ݕ‬ሺଶ଴ሻ , ‫ ݕ‬ሺଵହ଴ሻ and ‫ ݕ‬ሺଷ଴଴ሻ .
3. Method
We consider multiple observed spectra,‫ ݕ‬ሺ଴ሻ ሺߣ௠ ሻ, ‫ ݕ‬ሺଵሻ ሺߣ௠ ሻ, …,‫ ݕ‬ሺ௡ሻ ሺߣ௠ ሻ, …, ‫ ݕ‬ሺସହ଼଴ሻ ሺߣ௠ ሻ. On theassumption that the spectral shape of charge state q is common in all observed spectra (i.e., their electron
temperature and density dependences are small enough), each spectrum can be rewritten as follows.
‫ ݕ‬ሺ௡ሻ ሺߣ௠ ሻ ൌ ෍ ݂௤௡ ߶௤ ሺߣ௠ ሻሺʹሻ௤where ݂௤௡depends on n. The spectral shape difference, which is seen in Fig. 3, indicates the variation of thecoefficient values. We perform a matrix factorization to the observed spectra in order to find the coefficientand the basis matrices that most represent the observed spectral matrix. Since it is yet unclear whether thecoefficients and bases estimated from the matrix decomposition exactly match ݂௤௡ and ߶௤ ሺߣ௠ ሻ. We denotethem as ܿ௜௡ and ߰௜ ሺߣ௠ ሻ, respectively, where i indicates the index of the basis. Figure 4 shows a schematic
illustration of the matrix decomposition. We use 4580 sets of experimental data for matrix. Because ܿ௜௡ and߰௜ ሺߣ௠ ሻ should be non-negative, we utilize non-negative matrix factorization (NMF) [9], which constrains
both two matrix to be non-negative. We estimate ܿ௜௡ and ߰௜ ሺߣ௠ ሻ by calculating the following optimization.
ସହ଼଴ǡ଺଴଴

 ෍௡ǡ௠ூ‫ܦ‬൫‫ ݕ‬ሺ௡ሻ ሺߣ௠ ሻห෍ ܿ௜௡ ߰௜ ሺߣ௠ ሻሻ ሺ͵ሻ௜where ‫ܦ‬ሺܽȁܾሻ is the distance measure between a and b, a typical example of which is the squared௔error‫ܦ‬୉୙ ሺܽȁܾሻ ൌ ሺܽ െ ܾሻଶ. In this study, we use KL-divergence ‫ܦ‬௄௅ ሺܽȁܾሻ ൌ ܾሺ ሻ െ ܽ ൅ ܾ. We first௕

set the random values to ܿ௜௡ and ߰௜ ሺߣ௠ ሻ, and repeat the iterative update scheme reported in
Ref.[9] for 1500 times, which is close enough to the convergence.

-3-

23

4580

4580

䞉䞉䞉

䞉 䞉䞉

䞉䞉䞉

䞉䞉䞉

×

NM F
1024

䞉䞉䞉

1024

λ

λ

Fig. 4 The schematic image of NMF.
4. Results
We performe the NMF to the observed spectra with several matrix rank I. Figure 5 shows the relation I andthe loss function defined in Eq. (3). It can be seen from this figure that the error does not greatly improvewith I ൒ 5, although at least ‫ ݍ‬ൌ ʹͳ െ ͵ͷ charge states are considered to exist in the plasma.

Fig. 5 The relation between I and the loss function ‫ܦ‬௄௅ ሺ‫ ݕ‬ሺ௡ሻ ሺߣ௠ ሻȁσ௜ ܿ௜௡ ߰௜ ሺߣ௠ ሻሻwith the optimized ܿ௜௡ and ߰௜ ሺߣ௠ ሻ.
Figure 6(a) shows all the estimated bases with NMF (blue) with I = 5. Figure 6(b) show two results of thereconstruction (green, red). The values estimated coefficients for these observations are also indicated in the
figure. Figure 6(c) shows an expanded view of the reconstruction by our method and the one by using
theoretical calculation results ߶௤୲୦ୣ୭ ሺߣ௠ ሻ. The observed spectra are well fitted with I = 5 decomposition.
3.17×

× 0.000.00×

× 0.820.05×

× 0.0017.5×

× 9.930.00×

× 15.52

D

E

F

Fig. 6 (a) The bases estimated with I = 5. (b) The reconstruction results with the estimated bases andthe coefficients. (c) Expanded view of the reconstruction by our method and the one by using thetheoretical calculation results.
-4-24

5. Discussion
Since the observed spectra are well represented by fewer bases than the expected total number of charge
states in the plasma, the following relation is expected,ିଵ෍ ‫ݓ‬௜ǡ௤ ߶௤ ሺߣ௠ ሻቑ ሺͶሻ෍ ܿ௜௡ ߰௜ ሺߣ௠ ሻ ൌ ෍ ቐ෍ ݂௤௡ ‫ݓ‬௜ǡ௤
௜

௜

௤

௤

ିଵ
where σ௤ ݂௤௡ ‫ݓ‬௜ǡ௤ൌ ܿ௜௡ and σ௤ ‫ݓ‬௜ǡ௤ ߶௤ ሺߣ௠ ሻ  ൌ ߰௜ ሺߣ௠ ሻ are satisfied, where each spectral bases is written

as a weighted sum of true emission spectra from several charge states ions. Figure 7(a) shows one of theestimated basis ߰ଷ ሺߣ௠ ሻ , and four theoretical emission spectra from  ௤ା for q = 23, 24, 25 and 26. While
the theoretical emission spectra has one peak for one charge state in 3െ4nm, the estimated basis has fourpeaks in this wavelength region. This is consistent to the above relation, where the estimated basis is thesuperposition of multiple true spectra. In order to determine the weight ‫ݓ‬௜ǡ௤ for i-th basis, we fit thesuperposition of the theoretical profiles to the estimated bases. We estimate ‫ݓ‬௜ǡ௤ by calculating the following.
ଶ୲୦ୣ୭ ቆ߰௜ ሺߣ௠ ሻ െ ෍ ‫ݓ‬௜ǡ௤ ߶௤ ሺߣ௠ ሻቇ ሺͷሻ௤where the wavelength range of 1.2െ4.3 nm is used for this fit. The results of calculated ‫ݓ‬௜ǡ௤ are shown in
Fig. 7(b). The weight estimated basis has large values in similar charge states q. It indicates that the density
dynamic of the similar charge state ions in plasma are highly correlated.
Figure 8(a) shows the fractional abundance for  ଶଵା െ  ଷହା from [2]. As shown in Fig. 8(a), the electron
temperature dependence of the fractional abundance for each charge state ion heavily overlaps each other.
This overlap is consistent to the large correlation of the density dynamics of the similar charge state ions inplasmas.
We note that although the second peak can be seen in Fig. 7(b) around q =31െ35 in ߰ଷ ሺߣ௠ ሻ െ ߰ହ ሺߣ௠ ሻ,
they may be an artifact due to the inaccurate theoretical calculation used to estimate ‫ݓ‬௜ǡ௤ .
Figure 8(b) shows the time developments of ܶୣ and the estimated coefficients ܿ௜௡ . ܿଷ௡ takes a maximum
when ܶୣ ~ 0.5 keV, and becomes smaller as ܶୣ becomes larger. Since ߰ଷ ሺߣ௠ ሻ mainly contains theemission from charge states ‫ ݍ‬ൌ ʹʹ െ ʹ͹ ions, this behavior is also consistent to the theoretical calculationof the fractional abundance, where ‫ ݍ‬ൌ ʹͳ െ ʹ͵ ions are dominant in this temperature region.

DE

Fig. 7 (a) One of the estimated bases (green), and three examples of atomic structure calculation results(blue, yellow, red). (b) Estimated values of ‫ݓ‬௜ǡ௤ for each q.
-5-

25

3

1.5

2

0.5

1
0

(b)

(a)

4

5

6

7

8

(c)

Fig. 8 (a) The fractional abundance for  ଶଵା- ଷହା [2]. (b) The time developments of ܶ௘ andthe estimated coefficients ܿ௜௡ .
In summary, we applied NMF method into the W observed spectra with the various decomposition rank.
From the loss function between observed spectra and the reconstruction, 5 spectral bases were enough toexpress the observed spectra, which was smaller than the number of charge states expected from thetheoretical fractional abundance data. We assumed each estimated basis was the sum of true emission spectrafrom W ions in several charge states. By fitting the superposition of the theoretical W ion profiles to eachestimated basis, we determined the W ions included in the basis. The basis includes W ions in similar charge
states, and it suggests the correlation between the densities of W ions in similar charge states in the plasma.
Acknowledgements
One of the authors (T. E.) wishes to thanks to post Japan-China-Korea A3 Foresight Program and post Core
University Program (Post CUP). We acknowledge the LHD experiment group for the LHD experiments.
References[1] Merola M et al 2014 Fusion Engineering and Design, 89 pp. 890-895[2] Asmussn K. et al, 1998 Nucl. Fusion, 38 967[3] Murakami I et al, 2015, Nucl. Fusion, 55 093016[4] Bar-Shalom A et al, 2001 J. Quant. Spectrose. Radiat. Transfer, 71 pp. 169-188[5] Nakano T et al 2013, J. Phys. B: At. Mol. Opt. Phys., 46 175701[6] Katai R. et al 2007, Japan. J. Appl. Phys. 46 3667
[7] Sudo S. 1993, J. Plasma Fusion Res. 69 1349
[8] Narihara K et al, 2011 J. Nucl. Mater., 415 S327-33[9] Lee D and Seung H, 2000 Neural Information Processing Systems (NIPS), pp. 556-562

-6-

26

Estimation of density profiles of W43+-W45+ in EAST H-mode plasma
L. Zhang1, S. Morita2,3, Z. W. Wu1, Z. Xu4,5, X. D. Yang1,6, Q. Zang1, H. Q. Liu1, X. Z.
Gong1, L. Q. Hu1
1

Institute of Plasma Physics Chinese Academy of Sciences, Hefei 230026, Anhui, China
National Institute for Fusion Science, Toki 509-5292, Gifu, Japan3
Department of Fusion Science, Graduate University for Advanced Studies, Toki 509-5292, Gifu, Japan
4
Advanced Energy Research Center, Shenzhen University, Shenzhen 518060, China
5
Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province,
College of Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
6
Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026,
China
2

Abstract
In order to study the behavior and radial transport of tungsten ions in long-pulse H-mode plasmas, a spaceresolved spectrometer working at 30-520Å has been newly developed to measure a radial profile of thetungsten line emission. The radial profiles of tungsten line emissions from W42+ – W45+ ions with 4p-4s and4d-4p transitions measured at 45-70Å and 120-140Å are analyzed for the ion density evaluation based on thephoton emissivity coefficient from ADAS database. The result shows that the densities of W43+ – W45+ ionsrange at 2-6×108cm-3 in steady H-mode discharges with Te(0)=3keV and ne(0)=4×1013cm-3.
1. Introduction
Impurity plays an important role in sufficiently sustaining an original performance of magneticallyconfined fusion plasmas because of the radiation power loss and ion dilution. In particular, the radiation loss inthe core plasma quickly increases with atomic number of the impurity element. In ITER, on the other hand,
tungsten is used as the divertor material instead of carbon. The use of tungsten is also planned in CFETR. In
order to examine effects of the tungsten divertor on tokamak discharges, several tokamak devices have installed
the tungsten plasma facing component (PFC), e.g. ASDEX-U [1] and WEST [2] with full tungsten environment,
JET with ITER-like wall [3]. In addition EAST tokamak has been equipped with upper tungsten divertor since2014 to improve the heat exhaust capability and to examine the ITER-like divertor configuration [4]. To study
the tungsten transport in EAST discharges, the tungsten spectra have been measured with fast-time-response
EUV spectrometers working in wavelength ranges of 10-130Å (EUV_Short) and 20-500Å (EUV_Long) [5] attime resolution of 5ms. Recently, a space-resolved EUV spectrometer working in 30-520Å (EUV_Long2) has
been developed to measure a radial profile of the tungsten line emission in long-pulse H-mode discharges withhigh heating power.
2. The space-resolved EUV spectrometerIn the space-resolved EUV spectrometer newly developed a flat-field focal plane along the wavelength
dispersion direction, which enables the use of a linear detector such as CCD, is achieved by a laminar VLS
concave holographic grating (Shimadzu 3-002) with an angle of incidence of 87°. A back-illuminated CCD

-1-

27

(Andor DO920-BN) with sensitive area of 26.6×6.6mm2 and pixel numbers of 1024×255 (26u26Pm2/pixel) isused for recording the two-dimensional image. The long axis of CCD is set perpendicular to the horizontal
wavelength dispersion for the radial profile measurement along the vertical direction, while the short axis of
CCD is set along the horizontal wavelength dispersion for the spectrum measurement. A stepping motor
installed on the spectrometer makes possible to move the CCD along the wavelength dispersion on the focal
plane for the wavelength range selection to be measured. The vertical observation range of the space-resolved
EUV spectrometer (EUV_Long2) is indicated in Figure 1. The line of sight of the fast-response EUV
spectrometers (EUV_Long and EUV_Short) is also plotted in Figure 1.

FIGURE 1. Lines of sight (LOSs) of
EUV_Long2 (blue thin lines) and LOS of
EUV_Long (purple thick line) and EUV_Short(brown thick line).

FIGURE 2. Typical EUV spectra observed with EUV_Long
from EAST H-mode discharges in wavelength ranges of (a)20-140Å, (b) 140-290Å and (c) 290-500Å.

3. Radial profiles of tungsten spectra in H-mode discharges
Figure 2 illustrates typical EUV spectra from EUV_Long observed in RF heated H-mode discharges of
EAST with heating power of PLHW=2.0-2.5, PICRH=1.2-1.8 and PECRH=0.3MW. The discharges are carried out
at line-averaged electron density of ne=3.5×1013cm-3, and Te0=3.0-3.5keV. In the spectra the pseudo-continuum
called unresolved transition array (UTA) is clearly appeared at 40-75 Å as a typical indication of the tungsten
spectrum. Line emissions from highly ionized ions in high-Z impurities are also observed in the spectra, e.g.,
Ti18+-Ti19+, Cu25+-Cu26+, Mo30+-Mo31+ and W41+-W45+. The W-UTA (5f-4d, 5p-4d, 6g-4f and 5g-4f transitions)composed of W24+-W33+ ions appeared in the wavelength range of 20-40 Å is very weak, while the W-UTA (4f4d, 4d-4p and 5d-4f transitions) composed of W24+-W45+ appeared in the wavelength range of 45-70 Å is strong.
The second order of W-UTA near 50Å is also observed near 100Å. Although isolated line emissions fromhighly ionized tungsten ions, e.g., W41+-W45+, can be identified at 120-140Å, the intensity is very weak. Then,the tungsten spectrum extended at 45-135 Å is plotted in Figures 3(a)-(c). As seen in Figure 3, there exist
many tungsten line emissions in the wavelength range. Detailed identifications are made for all the tungsten
line emissions. In order to make the accurate identification of tungsten line emissions, radial profiles of thetungsten line are extremely important as described in a previous report [6].
Tow-dimensional images of tungsten line emissions are observed in H-mode discharges as shown in
Figure 4. Identified line emissions are denoted in right hand of the CCD image. Vertical profiles of tungsten
line emissions are obtained from the CCD image, as plotted in Figures 5 (a)-(c).
Figure 5 (a) shows thevertical profile of tungsten lines from highly ionized tungsten ions existing in the W-UTA, W43+ (4s24p 2P2/1 –

-2-

28

4s4p2 2D3/2) at 61.334Å, W44+ (4s2 1S0 – 4s4p (1/2,3/2)1) at 60.93Å and W45+ (4s 2S1/2 – 4p 2P3/2) at 62.336 Å.
Based on the vertical profile of line emissions from W43+-W45+ ions, the ionization stage of other tungsten lines
can be easily estimated. Vertical profiles at the wavelength intervals indicated by shaded areas in Figure 3 (a)are plotted in Figure 5 (b). When we compare the peak position among three radial profiles, each peak locatesin different radial positions. Then, we can easily identify that three wavelength intervals of 48.81-49.02 Å,
49.24-49.57 Å and 49.79-50.01 Å arise from W26+, W27+ and W29+, respectively [6]. The ionization stage ofother tungsten line emissions at the W-UTA in Figure 3 (a) is also determined through the analysis of verticalprofiles observed from EUV_Long2.

FIGURE 3. Tungsten spectra in different wavelength
ranges of (a) 43-73 Å, (b) 77-107 Å and (c) 107-137 Å
in RF heated H-mode discharges (Te0=3.3keV).

FIGURE 4. Typical two-dimensional CCD images observed
from H-mode discharges (Te0=2.9-4.0keV and ne~3.5×1019m-3);(a) 46.6-76.9 Å, (b) 64.4-98.3 Å, (c) 95.1-134.4 Å

FIGURE 6. Vertical intensity profile of (a) W45+
(62.336Å), W44+ (60.93Å) and W43+ (61.334 Å) in WUTA, (b) W26+-W29+, (c) W45+ (126.998 Å), W43+ (126.29
Å) and W42+ (129.41 Å) and (d) Fe XXIII blended with
W44+ (132.9 Å), Cu XXVI (111.186 Å), Mo XXXII(127.868 Å) and Mo XXXI (116.0 Å) . Data are takenfrom H-mode discharges with Te0=3.3keV ((a) and (b)) and
2.9keV ((c) and (d)).

FIGURE 5. Radial profiles of (a) chord-integrated line
intensity and (b) local emissivity of W45+ (62.336Å),
W44+ (60.93Å) and W43+ (61.334Å) and (c) chordintegrated line intensity and (d) local emissivity of W45+
(126.998 Å), W43+ (126.29 Å) and W42+ (129.41 Å).
Data are taken from H-mode discharges with Te0=3.3keV((a) and (b)) and 2.9keV ((c) and (d)).

-3-

29

Vertical profiles of isolated line emissions are plotted in Figures 5 (c) and (d). Figure 5 (c) shows verticalprofiles of W42+ (4s24p2 3P0 – 4s24p2 1D2) at 129.41Å, W43+ (4s24p 2P1/2 – 4s24p 2P3/2) at 126.29 Å and W45+ (4s2
S1/2 – 4p 2P1/2) at 126.998Å. We notice that the radial profiles are more peaked compared to those in Figure 5(a) due to the relatively low electron temperature of Te0=2.9keV. Figure 5 (d) shows vertical profiles of otherheavy impurities, i.e. Cu XXVI (2s2 1S0 - 2s2p 1P1, Ei=2479eV) at 111.186 Å, Mo XXXI (3s2 1S0 - 3s3p 1P1,
Ei=1730eV) at 116.0 Å and Mo XXXII (3s 2S1/2 - 3p 2P3/2, Ei=1791eV) at 127.868 Å and Fe XXIII (2s2 1S0 2s2p 1P1, Ei=1950eV) at 132.9 Å. The line emission from Fe XXIII at 132.91 Å is totally overlapped with
W44+ (4s2 1S0 – 4s4p P1/2, Ei=2355eV) at 132.88Å. When we compare the radial profile between inner and outerregions near the plasma center, i.e. -10dZd0cm and 0dZd10cm, it may suggest an asymmetric profile. Further
experiments are necessary to confirm the truth by changing the vertical observation range.

4. Preliminary analysis of tungsten ion density profile
The chord-integrated intensity of tungsten line at vertical position of Z is calculated by integrating the local
emissivity along the line of sight of EUV_Long2, l, in the equation of
౧శ

౧శ

౧శ

౧శ

I ୛ (Z) = ‫ ׬‬ɂ୛ (Z, l)dl = ‫ ׬‬n୛ (Z, l)PEC୛ (Z, l)nୣ (Z, l)dl ,where I

୛౧శ

and ɂ

୛౧శ

(1)

mean the intensity and local emissivity of line emission from tungsten ions with౧శ౧శionization stage of q, and n୛ and PEC୛ mean the density of Wq+ ions and photon emissivity coefficient of
the line emission. Tungsten ion density profile is then analyzed from the vertical profile of tungsten spectral
intensity. Firstly, the spectral intensity measured with spectrometer has to be absolutely calibrated, and thenthe emissivity profile of tungsten line can be calculated from the vertical intensity profile based on Abelinversion technique. Finally, the density profile of tungsten ions is obtained with measured Te and ne profiles
and the PEC data.
The absolute calibration for the space-resolved EUV spectrometer has been excellently carried out at highdensity discharges with ne0=2.2×1014cm-3 in LHD [7, 8]. The EUV bremsstrahlung continuum intensity is
accurately calculated from measured visible bremsstrahlung intensity profile with considering Te profile. The
calibration factor can be then obtained by comparing the EUV bremsstrahlung intensity profile between
measurement and calculation. Since the operational density range of EAST is relatively low, e.g.
ne0=5.5×1013cm-3, the EUV bremsstrahlung intensity from EUV_Long2 is weak due to the relatively low
throughput compared to EUV_Long. In addition, the visible bremsstrahlung measurement diagnostic in EAST
has no sufficient profile data. Then, the calibration of EUV_Long2 is only carried out at short wavelength
range where the EUV bremsstrahlung emission is strong referring the data from EUV_Long from which thespectral intensity has been already calibrated [5], e.g. 4×109phs·cm-2·s-1/(counts·s-1) at 62 Å, and8.5×109phs·cm-2·s-1/(counts·s-1) at 130Å. Since the same grating and CCD as LHD are being used in EAST,
we assume the wavelength dependence of the calibration factor is identical between EAST and LHD. Thus, thevertical intensity profiles are obtained for tungsten line emissions as shown in Figures 6 (a) and (c). Figure 6(a) shows the intensity profiles of W45+ at 62.336Å, W44+ at 60.93Å and W43+ at 61.334 Å from H-mode
plasmas with Te0=3.3keV and Figure 6 (c) shows W45+ at 126.998 Å, W43+ at 126.29 Å and W42+ at 129.41 Åfrom H-mode plasmas with Te0=2.9keV.
The local emissivity profiles of tungsten line emissions reconstructed from Figures 6 (a) and (c) are plottedin Figures 6(b) and (d), respectively. The local emissivity of tungsten line emissions at the peak position
increases with the ionization stage, in particular, in the low-temperature discharge in Figure 6(d). It is not clear

-4-

30

at the moment whether the increase indicates the tungsten accumulation in the H-mode discharge. Impurity
transport simulation is necessary for further study.
In order to evaluate the tungsten ion density, PEC data from open-ADAS (arf40_ic series) is used in thepresent study. Based on Te and ne profiles measured during the H-mode phase shown in Figures 7 (a) and (b),the density profiles of W43+ and W45+ are obtained. The result is plotted in Figure 8. As a result it is found thatthe density of W43+-W45+ ions distributes in range of 2-6 ×108cm-3 in H-mode discharges of EAST which wehave analyzed in the present study.

FIGURE 8. Calculated radial profiles of W45+ and W43+
ion density in steady-state H-mode phase in (a)Te0=3.3keV and (b) Te0=2.9keV.

FIGURE 7. Radial profiles of (a) electron
temperature and (b) electron density.

5. Summary
A space-resolved spectrometer working at 30-520Å is newly developed to measure the tungsten emission
profiles. As a result, vertical profiles from several impurities are successfully observed from H-mode plasmas
in EAST tokamak. Vertical profiles of tungsten emissions from W42+ - W45+ ions are also measured at 45-70 Å
and 120-140 Å in high-temperature discharges at Tet2.5keV. The density profile of such highly ionizedtungsten ions is evaluated from the vertical profile. The preliminary analysis shows that the densities of W43+W45+ ions range in 2-6u108cm-3 in H-mode plasmas. The emission profile measurement by the space-resolve
spectrometer enables impurity transport study in H-mode discharges of EAST. In particular, the tungsten
transport study is crucially important in long pulse H-mode operations of EAST with tungsten divertor.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11575244,
11775269) and the National Magnetic Confinement Fusion Science Program of China (Grant
Nos.2014GB124006, 2015GB101000)
References[1] Neu R et al 2007 Plasma Phys. Control. Fusion 49 B59[2] Bucalossi J et al 2014 Fusion Eng. Des. 89 907-912[3] Matthews G F et al 2011 Phys. Scr. T145 014001[4] Yao D et al 2015 Fusion Eng. Des. 98-99 1692
[5] Zhang L et al 2015 Rev. Sci. Instrum. 86 123509[6] Liu Y et al 2017 J. Appl. Phys. 122 233301[7] Dong C F et al 2011 Rev. Sci. Instrum. 82 113102[8] Dong C F et al 2012 Plasma Fusion Res. 7 2402139

-5-

31

A consideration on the accuracy of GRASP calculations
Fumihiro Koike *Faculty of Science and Technology, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
Abstract
We discuss the use of Multi-Configuration (numerical) Dirac-Fock (MCDF) method that is employedin General purpose Relativistic Atomic Structure Program (GRASP) family of codes in relation to thetactics of obtaining accurate and reliable results. The proper use of spectroscopic and correlation orbitals in
the calculation is quite important. The proper choice of target states for simultaneous optimization in thecalculation is also quite important. Several examples have been illustrated for precision calculations of theatomic and ionic systems. .
1. Introduction
Accurate and reliable calculations of atomic electronic states and their transition properties areindispensable for proper understandings of fusion and other plasmas.

Accurate atomic data may enable us

to perform precision plasma modeling calculations and help us with precision plasma spectroscopy
measurements. Quite a deal of efforts has been made for this subject. For a theoretical method based on avariational principle, atomic codes such as FAC, HULLAC, Cowan’s code, GRASP family of codes[1], andothers, have been developed and they are now available. Among them, the GRASP (General purpose
Relativistic Atomic Structure Program) family of codes[1] provides us with a non-empirical relativistic
method and is believed that the code gives most reliable result if treated properly. In recent years, anelaborate large scale calculation has become feasible using a parallel processing technology to produce alarge amount of numerical values that are usable for plasma analysis.
However, we must be aware that the GRASP family of codes has its own characteristics to be treatedcarefully. The method is based on a variational principle with a positive indefinite Hamiltonian; we cannot
avoid the possibility of variational collapse in the procedure of self-consistent iteration. And, furthermore,in cases of excited state calculations, similar collapse may occur due to the possible inaccuracies ofnumerical procedure. The atomic orbitals are restricted to the L2 normalizable functions, which causes theintroduction of correlation functions in the MCDF procedure. They are sometimes quite unphysical. We
must take care of those functions carefully as to behave properly if we want to calculate the excited states.
In this report, we discuss possible tactics to minimize the errors in GRASP calculations showing several
examples that may give undesired results.
2. Characteristics of MCDF method
Based on the independent particle model, we introduce a CSF (Configuration State Function) Ȱ for the* Corresponding author’s email: koikef@sophia.ac.jp

-1-

32

ܰ-electron system in terms of the product of single electron atomic orbitals. That is
ே

Ȱ= ෑ
௜ୀଵ

߶௞೔ (‫ݎ‬௜ ) ,



  

(1)

where, ߶௞೔ is a single electron atomic orbital with quantum number ݇௜ and ‫ݎ‬௜ is the position of the i’thelectron. The CSF Ȱ may be adjusted as to satisfy the constraint such as parity or Pauli’s principle. The
MCDF method requires the introduction of an ASF (Atomic State Function) Ȳ. That is௝೘ೌೣȲ = σ௝ୀଵȰ௝ ܿ௝ ,                    (2)where, ܿ௝ are the expansion coefficients, ݆௠௔௫ is the number of CSF’s in the ASF. The set of atomic
orbitals {߶௞೔ } and the state vector ൛ܿ௝ ൟ are the target of optimization under the following variational
condition.
Ɂ‫ۦ‬Ȳ|‫ܪ‬஽஼ |Ȳۧ = 0,(3)

where, ‫ܪ‬஽஼ is the Dirac-Coulomb Hamiltonian of the atomic system. The GRASP family of codes treats
also Breit interaction and a part of QED corrections to produce better results by means of perturbation.
The MCDF method is based on a variational principle. If the problem is solved properly, an excited stateatomic state function does not contain any lower lying configuration state functions, in other words, theexcited state can be expanded in terms of only the configurations that are lying energetically higher than thetarget state. However, some care must be taken into account for configurations that contain atomic orbitals
with different parities. The parity constraint applies only for the total atomic state.
ܲȲ = ± 1Ȳ.

(4)

Individual single electron atomic orbitals are not necessarily being required to have a fixed parity. Bothconfigurations ߶ ୣ୴ୣ୬ (‫ݎ‬௜ ) ٔ ߶ ୣ୴ୣ୬ ൫‫ݎ‬௝ ൯ and ߶ ୭ୢୢ (‫ݎ‬௜ ) ٔ ߶ ୭ୢୢ ൫‫ݎ‬௝ ൯ can contribute in the same atomic statefunctions. For example, 2‫ݏ‬2‫݌‬3‫ = ݏ‬2‫(݌‬2‫ݏ‬3‫ )ݏ‬and 2‫ ݌‬ଶ 3‫ = ݌‬2‫(݌‬2‫݌‬3‫ )݌‬configurations strongly mix inthe lithium hollow atomic states [2].

This feature sometimes prevents us from assigning the atomic statesin terms of the occupation numbers for electrons in atomic orbitals.
Generally speaking, the effect of electron correlations is the strongest near the nucleus, where theelectrons have larger chance to be close each other. The correlation orbitals which are introduced in MCDF
calculations have a maximum near to the nucleus. By taking those functional shapes, we can expect that theset of orbital functions spans a complete bases space under the restriction of L2 normalizable basis.
In the followings, we illustrate two numerical examples.
3. The sub-valence inner-shell hole states of rare gas ionsSub-valence inner-shell vacancy states of rare gas atomic ions with ݊‫ ଺݌݊ݏ‬configuration decay into theground states with ݊‫ ݏ‬ଶ ݊‫݌‬ହ configuration exclusively through the optical-dipole transitions. It is worthy toinvestigate the role of electron correlations in atomic ions under such simple circumstances. In most of theatoms with moderate atomic number, there are energy differences between sub-shell atomic orbitals due tothe deviation of the effective potentials from Coulombic nature. In the case of Ar ା ions, for example, theenergy difference between 3‫ݏ‬-orbital and 3p-orbital is not very different from the energy difference
between 3‫݌‬-orbital and 3݀-orbital. Thus the 3‫ ݏ‬sub-shell single-hole configuration 3‫ݏ‬3‫ ଺ ݌‬may havestrong interaction with the 3‫ ݌‬sub-shell single-electron excited configuration 3‫ ݏ‬ଶ 3‫ ݌‬ସ 3݀ when both-2-33

configurations belong to the same symmetry. The actual system is to be represented by the linear
combination of 3‫ݏ‬3‫ ଺ ݌‬and 3‫ ݏ‬ଶ 3‫ ݌‬ସ 3݀ configurations; the 3‫ ݏ‬sub-shell hole is, in reality, partially filled
by electron. The electric dipole transitions to fill the hole with electrons inevitably suffer modification by
the configuration mixing. In spite of the simple appearance of the problems, theoretical calculations have
not yet been tackled with sufficient accuracy. The anomalous behavior of the ‫ ଺݌ݏ‬and also the ‫ ݏ‬ଶ ‫ ݌‬ସ ݀
configurations has been pointed out since a couple of decades. Cowan et al [4] discussed energy positionsof the ‫ ଺ ݌ݏ‬state in neutral chlorine and other halogens in relations to the interaction with continuum
configurations. Berrington et al [5] have made an R-matrix calculation for rare gas sub-valence hole states.
Suzuki et al [6] have measured and calculated the lifetime of Ar ା 3‫ ݏ‬sub-shell hole state.
We have calculated the ‫ ଺ ݌ݏ‬states of Ar ା , Kr ା , and Xeା , and also calculated their lifetimes against theelectric-dipole transition into ‫ ݏ‬ଶ ‫ ݌‬ହ doublet states. The calculated lifetimes are given in the last column intable 1. For each ionic species, the upper entry gives Coulomb gauge (velocity form) calculation, and thelower entry gives Babushkin gauge (length form) calculation. We have also illustrated in table 2 thelifetime values for artificial states considering only the singly occupied ݊‫ ݏ‬sub-shell configurations andonly the fully occupied ݊‫ ݏ‬ଶ sub-shell configurations. We can see that the mixing of ‫ ଺ ݌ݏ‬and ‫ ݏ‬ଶ ‫ ݌‬ସ ݀
configurations realizes the extreme lifetime elongation.
Table 1. Calculated lifetimes (in 10ିଽ seconds) of lowermostଵܵ states with different sets ofconfigurations for singly charged ions of argon, krypton, and xenon.

4. The fine structure levels of tungsten highly charged ions
Tungsten is thought as one of the good wall materials for magnetic confinement fusion reactor.
Calculations for the properties of multiply charged tungsten ions are highly desired. W ଶ଺ା ion is thesimplest system with multiple 4݂-orbital electrons in the ground state. The ground state configuration ofW ଶ଺ା is [Kr]4݂ ଶ = ‫ ڮ‬4‫ ݏ‬ଶ 4‫ ଺ ݌‬4݀ଵ଴ 4݂ ଶ , and the magnetic dipole (M1) transitions between the finestructure levels in the ground state configurations enter in the wavelength range of the visible light. Fromthe viewpoint of atomic physics, this system is interesting in the effects of correlations between the4݂-orbital electrons. The atomic ground state has less difficulty for variational calculation; a large scale
MCDF procedure is feasible for such systems. Recently, X. B. Ding et al [3] have made an extensive
MCDF calculation for this system. They pointed out that the experimentally observed line at 389.4 nm is of
the M1 transition between the firstଷ‫ܪ‬ହ and the third
-3-

34

ଷ

‫ܪ‬ସ fine structure levels with the calculatedtransition wavelength of 388.4 nm. To obtain the result, they optimized the all the possible 13 fine structurelevels simultaneously by applying the EOL option for GRASP calculation. Because the whole range of thelevel energies extends to almost 20 eV, the optimum shape of the orbitals might differ between the higher
most and lower most levels. In the present paper, we tried to improve the calculation by optimizing only thelevels that are responsible forଷ‫ܪ‬ହ െ

ଷ‫ܪ‬ସ transition, i.e., by applying the EOL option only for the first

and the third fine structure levels. The results of calculation and the convergence feature of the present
active space method are illustrated in table 2. And, the present result has been compared to the experimentin table 3.
Table 2. Convergence feature of W ଶ଺ାଷ‫ܪ‬ହ െ

ଷ‫ܪ‬ସ transition wavelength. The last column

gives the difference of the wavelength from the immediately preceding calculation.

Table 3. Comparison of the present calculation with experiments and previous calculation [3].

Acknowledgements
The present work has been partly supported by post Japan-China-Korea A3 Foresight Program and post
Core University Program (Post CUP).
References[1] Dyall K G et al 1989 Comp. Phys. Communications 55 425. Parpia F A et al 1996 Comp. Phys.
Communications 94 249. Fritzsche S 2012 Comp. Phys. Communications 183 1525. Joensson P et al2007 Comp. Phys. Communications, 177 597.
[2] Azuma Y et al 1995 Phys. Rev. Lett. 74 3768.
[3] Ding X B et al 2012 J. Phys. B: At. Mol. Opt. Phys. 45 035003[4] Cowan R D et al 1974 J. Opt. Soc. Am. 64 1474.
[5] Berrington K A et al 2001 J. Phys. B: At. Mol. Opt. Phys. 34 L149.
[6] Suzuki N et al 2016 J. Phys. B: At. Mol. Opt. Phys. 49 145002.
-4-

35

Visible spectra of multiply charged heavy ionsobtained with a compact electron beam ion trap
NAKAMURA Nobuyuki
Inst. for Laser Science, The Univ. of Electro-Communications, Tokyo 182-8585, Japan
Abstract
Visible spectra of multiply charged ions are useful not only for testing quantum mechanics theories but also for applications such as plasma diagnostics and precise atomic
clocks. We present visible spectra of tungsten and lanthanide ions obtained with a compact electron beam ion trap.
Keywords: visible spectra multiply charged ions, electron beam ion trap
1.Introduction
Visible transitions in multiply charged heavy ions are of interest for many applications. For example, transitions in multiply charged W ions are in strong demand for the
stable operation of the large scale fusion reactor ITER under construction. Since W is
the material of the plasma facing wall of ITER, sputtered W ions are considered to be themain impurity in the ITER plasma [1]. Thus it is important to diagnose and control theW inﬂux and charge evolution through spectroscopic diagnostics of W ions. Although all
the wavelength ranges, including short wavelength ranges such as EUV and x-rays, areimportant for the diagnostics, transitions in the visible range are especially important due
to the advantage that a variety of common optical components, such as mirrors, lenses,
and ﬁber optics, can be applied.
As another example, optical transitions in multiply charged ions have been proposed
for a new type of an optical clock that has a signiﬁcantly enhanced sensitivity to theﬁne-structure constant variation due to the strong relativistic eﬀects [2]. The variationof fundamental constants arises in many theories beyond the Standard Model of particle
physics and is hinted by the astrophysical observations. Recently, it was suggested thatdark matter may lead to oscillations of fundamental constants or transient eﬀects that
may be potentially detectable with such clocks [3]. It is also an advantage that the
wavefunction of the electron tightly bound in a highly charged ion is less sensitive to theperturbation such as external ﬁelds.
In this contribution, we present visible spectra of multiply charged ions relevant to suchapplications obtained with a compact electron beam ion trap, called CoBIT [4]. Recent

136results for tungsten [5] and lanthanide ions [6] are compared with theoretical calculations.
2. Experiment
The present experiments were performed using a compact EBIT, called CoBIT. Detailed
description of CoBIT is given in Ref. [4]. Brieﬂy, it consists of an electron gun, a drift
tube (DT), an electron collector, and a high-critical-temperature superconducting magnet.
The DT is composed of three successive cylindrical electrodes that act as an ion trap byapplying a positive trapping potential (typically 30 V) at both ends (DT1 and 3) withrespect to the middle electrode (DT2). The electron beam emitted from the electron gun
is accelerated towards the DT while it is compressed by the axial magnetic ﬁeld (typically
0.08 T) produced by the magnet surrounding the DT. The space charge potential of thecompressed high-density electron beam acts as a radial trap in combination with the axial
magnetic ﬁeld. Highly charged ions are produced through the successive ionization of thetrapped ions. For producing tungsten ions, a vapor of tungsten hexacarbonyl W(CO)6 wasintroduced through a gas injection system On the other hand, for producing lanthanide
ions, the element of interest was introduced with an eﬀusion cell. The temperature of thecell was 900 - 950 ◦ C.
The setup for observing visible spectra was essentially the same as that used in ourprevious studies, where the visible emission lines of tungsten ions were observed [7, 8].
Brieﬂy, the emission from the trapped lanthanide ions was focused by a convex lens on theentrance slit of a commercial Czerny-Turner type of visible spectrometer (Jobin Yvon HR320) with a focal length of 320 mm. For survey observations, a 300 gr/mm grating blazed
at 500 nm was used, whereas for wavelength determination, a high resolution 1200 gr/mm
grating blazed at 400 nm was used. The diﬀracted light was detected with either aliquid-nitrogen-cooled back-illuminated CCD (Princeton Instruments Spec-10:400B LN)
operated at -115 ◦ C or a Peltier-cooled back illuminated CCD (Andor iDus 416) operated
at -70 ◦ C. The wavelength scale was calibrated using emission lines from several standard
lamps placed outside CoBIT.
3. Results and discussion
Figure 1 shows tungsten spectra obtained with electron energies of 630 to 825 eV. As
seen in the ﬁgure, most of the observed lines revealed a distinct appearance energy, fromwhich the responsible ion for each line can be identiﬁed. For example, the lines at 389 nm
and 464 nm observed in the 825 eV spectrum can be assigned as the transitions in W26+2
37

825 eV 26+

775 eV 25+
725 eV 24+

675 eV 23+
630 eV 22+

370 380 390 400 410 420 430 440 450 460 470

wavelength (nm)Figure 1: Visible spectra of highly charged W ions observed with a compact EBIT.
because their appearance energy is just above the ionization energy of W25+ (784 eV).
Similarly, the lines marked by the arrows in the spectra of 775 eV, 725 eV, and 675 eV
can be assigned as transitions in W25+ , W24+ , and W23+ respectively. As shown in thisexample, the charge state can be assigned to observed lines by observing the dependence
on electron energy. However, it is generally diﬃcult to identify the transition. Among theobserved lines shown in Fig. 1, the W26+ lines at 389 nm and 464 nm have been identiﬁed
through the comparison with theoretical calculation as M 1 transitions between the ﬁne
structure levels in 4f 2 3HJ , J = 4 ← 5 and J = 5 ← 6, respectively [7, 9]. The other lines,
however, have not yet been identiﬁed due to the complexity increasing with the numberof 4f electrons. This is only one instance, and many lines observed so far [8] are awaiting
their identiﬁcation.
Figure 2 shows visible spectra of Ho (Z = 67), Er (68), and Tm (69). From the energy
dependence, the prominent peak in each spectrum has been assigned to the Ag-like ion ofeach element. The Ag-like isoelectronic sequence in this Z region has a simple conﬁguration with only on valence electron in 4f . The observed lines can thus be identiﬁed as theM 1 transition between the doublet in the ground term 2F . We have also observed several
lines of Cd-like ions, and identiﬁed them as M 1 transitions between the ﬁne structurelevels of the ground state conﬁguration 4f 2 through the comparison with theoretical calculations [6]. The ﬁnal goal of the present lanthanide spectroscopy is to identify visibleline in Ho14+ , which has six 4f electrons in its ground state. We have observed electronenergy dependence of Ho spectra, and assigned several lines to 14+ [10]. However, thecomplexity of the system prevent us to identify the transition. Further systematic studies

3
38

22+

Tm

21+

Er

Ho

550

600

650
700
Wavelength (nm)

20+

750

Figure 2: Visible spectra of highly charged W ions observed with a compact EBIT.
along isonuclear and isoelectronic sequences are needed.
Collaborators
Collaborators for tungsten work: Xiaobin Ding (NWNU), Chenzhong Dong (NWNU),
Daiji Kato (NIFS), Fuihiro Koike (Sophia Univ.), Izumi Murakami (NIFS), Hiroyuki A.
Sakaue (NIFS).
Collaborators for lanthanide work: Marianna S. Safronova (Univ. Delaware, Univ. Maryland), and Ulyana I. Safronova (Univ. Nevada).
References[1] C. H. Skinner, Can. J. Phys. 86, 285 (2008).
[2] J. C. Berengut et al., Phys. Rev. Lett. 105, 120801 (2010).
[3] A. Derevianko and M. Pospelov, Nature Phys. 10, 933 (2014).
[4] N. Nakamura et al., Rev. Sci. Instrum. 79, 063104 (2008).
[5] M. Mita et al., Atoms 5, 13 (2017).
[6] S. Murata et al., Phys. Rev. A 96, 062506 (2017).
[7] A. Komatsu et al., Phys. Scr. T144, 014012 (2011).
[8] A. Komatsu et al., Plasma Fusion Res. 7, 1201158 (2012).
[9] X.-B. Ding et al., J. Phys. B 44, 145004 (2011).
[10] T. Nakajima et al., Nucl. Instrum. and Methods B 408, 118 (2017).

4
39

Oscillator strengths and integral cross sections of the valence-shell
excitations of oxygen molecule studied by fast electron and X-ray scattering
Ya-Wei Liu1,2, Tao Xiong1,2, Ke Yang3, Nozomu Hiraoka4, Ku-Ding Tsuei4,and Lin-Fan Zhu1,2*
1

Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics,

University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
2

Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science andTechnology of China, Hefei, Anhui 230026, People's Republic of China
3Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, People's Republicof China
4

National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan, Republic of China

Abstract
The oscillator strengths and integral cross sections of the Schumann-Runge continuum, Longest-Band
and Second-Band of oxygen molecule have wide applications in the studies of the Earth's atmosphere andthe stellar atmospheres, but there still exist apparent discrepancies among the available data. In this work, thegeneralized oscillator strengths of the valence-shell excitations of oxygen have been determined
independently by the high-energy electron scattering and high-resolution inelastic X-ray scattering. Based on
the cross-checked generalized oscillator strengths, the optical oscillator strengths and integral cross sectionsof these excitations have been obtained, which give an independent cross-check to the previous experimental
and theoretical results.
1. Introduction
The oscillator strengths and integral cross sections of the Schumann-Runge (SR) continuum, LongestBand (LB) and Second-Band (SB) of oxygen molecule have significant applications in the studies of the
Earth's atmosphere and the stellar atmospheres. Recently, molecular oxygen was detected by the Rosetta
spacecraft in the coma of the comet 67P/CG for the first time [1]. Comets such as the comet 67P/CG, are thetheorized candidates for the building blocks of bodies like Pluto, this naturally motivates a search formolecular oxygen in the atmosphere of Pluto by making use of the data sets acquired by the New Horizons
mission during its flyby in 2015 July [2]. In the New Horizons, the Alice extreme-/far-ultraviolet imaging
spectrograph [3] has the bandpass of 52 nm to 187 nm, which covers the SR continuum, LB and SB of oxygen.
In order to explain the complex spectra observed, the OOSs and ICSs of the SR continuum, LB and SB ofmolecular oxygen are the basic and important input parameters for the theoretical modeling. However, serious
discrepancies among the available data for the dynamic parameters still exist.

* Corresponding author’s email: lfzhu@ustc.edu.cn

-1-

40

2. Experimental method
In this work, the generalized oscillator strengths (GOSs) of these excitations have been determined
independently by the electron energy loss spectroscopy (EELS) and the high-resolution inelastic X-ray
scattering (IXS). Typical energy-loss spectra of oxygen are shown in Fig. 1 along with the excited statesassigned. The different experimental techniques provide a strict cross-check for the present GOSs of oxygen,
which excludes the systematic error to a large extent. Then, the OOSs of oxygen have been obtained byextrapolating the present cross-checked GOSs to the limit of the squared momentum transfer K2Ѝ0, and the
ICSs of oxygen in a wide energy region have been determined with the aid of the newly-developed BEscaling method.

(a)Intensity(arb.units)

800

Electron scattering
E0@1500 eV

E 36u
v' 0

1

T@9°
B36u

0

(b)
100

X-ray scattering
E0@10 keV
T@38°

50

0

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

Energy loss(eV)Fig. 1 Typical energy-loss spectra of the valence-shell excitations of molecular oxygen.

3. Results and discussion
The present GOSs of the SR continuum of oxygen measured by the high-energy EELS at 1500 eV andhigh-resolution IXS are shown in Fig. 2. It is clear in Fig. 2 that, the present GOSs of the SR continuum
measured by the EELS and IXS are in excellent agreement, which indicates that the first Born approximation(FBA) is satisfied at 1500 eV in the whole squared momentum transfer region due to the fact that the IXS is
B36u

Present results:
EELS results@1500 eV
IXS results
Fitted curve of the EELS and IXS

0.1

GOS

Previous EELS results:
Xu et al.@2500 eV 2010
Lassettre et al.@611 eV 1964
Lassettre et al.@519 eV 1964
Newell et al.@500 eV 1980
Wakiya@500 eV 1978
Newell et al.@400 eV 1980
Wakiya@400 eV 1978
Wakiya@300 eV 1978
Suzuki et al.@200 eV 2011
0.01
Wakiya@150 eV 1978
0.1

1
2

K (a.u.)

Fig. 2 The present and previous GOSs of the SR continuum B 6u of oxygen.
3

-2-

41

free from the high-order Born terms [4]. As shown in Fig. 2, with the increasing of the incident electronenergies the GOSs of Wakiya at 150-500 eV [5], Suzuki et al. at 200 eV [6], Newell et al. at 400 eV and 500
eV [7] and Lassettre et al. at 519 eV and 611 eV [9] approach to the present EELS and IXS GOSs gradually,
which is in agreement with the asymptotic behaviors of the FBA.
0.015

3 

(a) E 6uPresent results:
EELS results@1500 eV
IXS results
Fitted curve(Q'=0)

0.010

GOS

0.005

0.000

Previous EELS results:
Xu et al.@2500 eV 2010
Newell et al.@500 eV 1980
Newell et al.@400 eV 1980
Newell et al.@300 eV 1980
Suzuki et al.@200 eV 2011
Newell et al.@100 eV 1980

3 

E 6u (Q'=1)

(b)

0.008

0.004

0.000

0

1

2

3

4

2

K (a.u.)Fig. 3 The present and previous GOSs for (a): LB E 6u (vc30) and (b): SB E 36u (vc 1) of oxygen.

The present GOSs of the LB and the SB of oxygen molecule by the high-energy EELS and high-resolution
IXS are shown in Fig. 3. It is clear in Fig. 3(a) that, the present GOSs of the LB measured by the EELS and
IXS are in excellent agreement, which indicates the FBA is also satisfied at 1500 eV for the LB in the wholesquared momentum transfer region. It is clear from Fig. 3(a) that, the GOSs of Newell et al. at 100-500 eV[7] and Suzuki et al. at 200 eV [6] are obviously lower than the present ones. So the FBA is not satisfied for
the GOSs of the LB of oxygen at the low incident electron energies less than 500 eV. As for the weak SB, it
is clear in Fig. 3(b) that, the present EELS GOSs of the SB at 1500 eV are in reasonable agreement with theones of Newell et al. at 400 eV and 500 eV [7] and Xu et al. at 2500 eV [8].
The accurate OOSs of oxygen are determined by extrapolating the present GOSs to the limit K2Ѝ0 andare shown in Fig. 4. As shown in Fig. 4(a), the present OOSs for the SR continuum, LB and SB of oxygen
are in excellent agreement with the EELS results of Chan et al. [10] and Lassettre & Skerbele [9], while thediscrepancies can be noticed with the ones of Huebner et al. [11] and Wakiya [5] except for the OOS of the
SB. It is clear from Fig. 4(b) that, although the strong SR continuum is thought that it should not be subject(a)-3

Optical oscillator strength (u10 )

200

1.

(c)

(b)

Present results(a): Electron impact
2.
Chan et al 1993
3.
Huebner et al 1975

160

4.
5.

Lassettre & Skerbele 1974

7.
8.
9.
10.
11.
12.
13.

Ogawa & Ogawa 1975
Ditchburn & Heddle 1953
Goldstein & Mastrup 1966
Metzger & Cook 1964
Ladenburg & Van Voorhis 1933
Watanabe et al 1953
Yoshino et al 2005

Wakiya et al 1978(b): Photoabsorption
6.
Lewis et al 1988

15
10
5
15

(c): Theory

10

5
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

14.
15.
16.

Buenker et al 1976
Yoshimine et al 1976
Li et al 1992

The list numbers

Fig. 4 The present and previous OOSs of the SR continuum, LB and SB of oxygen from top to bottom.

-3-

42

to the line-saturation effects due to its broad nature [9], the apparent discrepancies between the present OOS
and the photoabsorption results [12-17] are still observed, even for the recent photoabsorption result of
Yoshino et al. [17]. Meanwhile, the present OOS of LB and SB of oxygen are in reasonable agreement withthe photoabsorption OOSs [18-19], which may be free from the line-saturation effect due to their broader
nature of the LB and SB of oxygen. In theory (see Fig. 4(c)), Buenker et al. [20], Yoshimine et al. [21] andLi et al. [22] have calculated the OOSs of the LB and SB of oxygen by the ab initio configuration interaction
method. It is clear that, the present results of the LB and SB of oxygen are obviously different from thetheoretical OOSs [18-19].
According to the present cross-checked GOSs, the BE-scaled ICSs of the SR continuum, LB and SB ofoxygen were determined in a wide energy region by the BE-scaling method. It is clearly seen in Fig. 5 that,the present BE-scaled ICSs are slightly higher than the BE-scaled ICSs of Xu et al. [8] and the BEf-scaled
ICSs of Suzuki et al. [6], but are in excellent agreement with the experimental ICSs of Suzuki et al. at 15200 eV [6] and Wakiya at 150-500 eV [5]. Meanwhile, it is clear in Fig. 5 that, the present BE-scaled ICSs
of the SR continuum of oxygen are lower than the early experimental ICSs of Trajmar et al. [23], Wakiya [5]and Shyn et al. [24] at the low-incident electron energies (İ100 eV) except the experimental ICS of Shyn etal. [24] at 50 eV.

B6
3

Present BE-scaled ICSs
BEf-scaled ICSs of Suzuki et al. 2011
BE-scaled ICSs of Xu et al. 2010
ICSs of Suzuki et al. 2011
ICSs of Shyn et al. 1994
ICSs of Wakiya 1978
ICSs of Trajmar et al. 1972


u

120

-18

2

ICS (10 cm )

160

80

40

0

10

100

1000

Incident energy/eVFig. 5 The present BE-scaled ICSs and the previous ICSs of the SR continuum of oxygen. The presently
estimated uncertainties are shown as the shadow region.

It can be seen in Fig. 6(a) that, the present BE-scaled ICSs of the LB are obviously higher than the BE/BEf- scaled ICSs of Xu et al. [8] and Suzuki et al. [6] at the low- and moderate-incident electron energies.
Based on the obvious discrepancies [6] between their BEf-scaled ICSs and experimental ICSs [6] for the LB,
Tanaka et al. [25] thought that the well-known Rydberg-valence perturbation influences the LB [20,26], andresults in the failure of the BEf-scaling method for the determination of the ICSs of the LB of oxygen.
However, as shown in Fig. 6(a), the reasonable agreement between the present BE-scaled ICSs and theexperimental ICSs of Suzuki et al. [6] indicates that, the BE-scaling method may still be valid for thedetermination of the ICSs of the LB of oxygen based on the present cross-checked GOSs. As for the ICSs of
the SB, it can be seen clearly in Fig. 6(b) that the present BE-scaled ICSs of the SB are slightly higher that

-4-

43

8

3 

(a)

E 6u (Q'=0)(b)

E 6u (Q'=1)

Present BE-scaled ICSs
BEf-scaled ICSs of Suzuki et al. 2011
BE-scaled ICSs of Xu et al. 2010
ICSs of Suzuki et al. 2011
ICSs of Shyn et al. 1994
ICSs of Trajmar et al. 1972

-18

2

ICS (10 cm )

4

0
2

3 

1

0

10

100

1000

Incident energy/eVFig. 6 The present BE-scaled ICSs and the previous ICSs of the LB and the SB of oxygen. The
presently estimated uncertainties are shown as the shadow region.
the BE-/BEf- scaled ICSs of Xu et al. [8] and Suzuki et al. [6], but are in reasonable agreement with theexperimental ICSs of Shyn et al. [27] at 15 and 20 eV and Suzuki et al. at 15-200 eV [6] within theexperimental uncertainties except the experimental ICSs of Shyn et al. [27] at 30 and 50 eV.
4. Summary and conclusion
In this work, the GOSs of the SR continuum, LB and SB of oxygen have been determined by the highenergy EELS and high-resolution IXS. Based on the present cross-checked GOSs, the OOSs and ICSs of the
SR continuum, LB and SB of oxygen have been determined. The present OOSs and BE-scaled ICSs of the
SR continuum, LB and SB of molecular oxygen play a vital role in modeling the abundance of oxygen in theatmospheres of Earth, Venus, Saturn, Pluto, Europa, and other outer planets and satellites, and are importantfor improving these atmospherical models.
Acknowledgements
This work is supported by the National Key Research and Development Program of China (Grant Nos.
2017YFA0402300 and 2017YFA0303500) and the National Natural Science Foundation of China (Grant
Nos. 11504361, U1732133 and 11320101003). The IXS experiment was carried out in a beam time approved
by Japan Synchrotron Radiation Research Institute (Proposal No.2016A4265) and National Synchrotron
Radiation Research Center, Taiwan, Republic of China (Proposal No. 2016-2-022-1).
References[1] Bieler, A., Altwegg, K., Balsiger, H., et al. 2015, Nature, 526, 678[2] Kammer, J. A., Stern, S. A., Young, L. A., et al. 2017, Astron. J., 154, 55[3] Stern, S. A., Slater, D. C., Scherrer, J., et al. 2008, Space. Sci. Rev., 140, 155[4] Xie, B. P., Zhu, L. F., Yang, K., et al. 2010, Phys. Rev. A., 82, 032501[5] Wakiya, K. 1978, J. Ph. B: Atom. Molec. Phys., 11, 3913
[6] Suzuki, D., Kato, H., Ohkawa, M., et al. 2011, J. Chem. Phys., 134, 064311-5-44[7] Newell, W. R., Khakoo, M. A., & Smith, A. C. H. 1980, J. Ph. B: Atom. Molec. Phys., 13, 4877
[8] Xu, W. Q., Sun, J. M., Wang, Y. Y., & Zhu, L. F. 2010, Phys. Rev. A., 82, 042716[9] Lassettre, E. N., Silverman, S. M., & Krasnow, M. E. 1964, J. Chem. Phys., 40, 1261
[10] Chan, W. F., Cooper, G., & Brion, C. E. 1993, Chem. Phys., 170, 99[11] Huebner, R. H., Celotta, R. J., Mielczarek, S. R., & Kuyatt, C. E. 1975, J. Chem. Phys., 63, 241[12] Ladenburg, R., & Van Voorhis, C. C. 1933, Phys. Rev., 43, 315[13] Watanabe, K., Inn, E. C. Y., & Zelikoff, M. 1953, J. Chem. Phys., 21, 1026
[14] Ditchburn, R. W., & Heddle, D. W. O. 1953, Proc. R. Soc. London, Ser. A., 220, 61[15] Metzger, P. H., & Cook, G. R. 1964, J. Quant. Spectrosc. Radiat. Transf., 4, 107[16] Goldstein, R., & Mastrup, F. N. 1966, J. Opt. Soc. Am., 56, 765[17] Yoshino, K., Parkinson, W. H., Ito, K., & Matsui, T. 2005, J. Mol. Spectrosc., 229, 238[18] Lewis, B. R., Gibson, S. T., et al. 1988, J. Quant. Spectrosc. Radiat. Transf., 40, 469[19] Ogawa, S., & Ogawa, M. 1975, Can. J. Phys., 53, 1845
[20] Buenker, R. J., Peyerimhoff, S. D. et al. 1976, Chem. Phys. Lett., 42, 383[21] Yoshimine, M., Tanaka, K., Tatewaki, H., et al. 1976, J. Chem. Phys., 64, 2254
[22] Li, Y., Honigmann, M., Bhanuprakash, K., et al. 1992, J. Chem. Phys., 96, 8314
[23] Trajmar, S., Williams, W., & Kuppermann, A. 1972, J. Chem. Phys., 56, 3759
[24] Shyn, T. W., Sweeney, C. J., Grafe, A., & Sharp, W. E. 1994, Phys. Rev. A., 50, 4794
[25] Tanaka, H., Brunger, M. J., Campbell, L., et al. 2016, Rev. Mod. Phys., 88, 025004[26] Lewis, B. R., England, J. P., Gibson, S. T., Brunger, M. J., & Allan, M. 2001, Phys. Rev. A., 63, 022707[27] Shyn, T. W., Sweeney, C. J., & Grafe, A. 1994, Phys. Rev. A., 49, 3680

-6-

45

Electron-ion recombination of Be-like Ca
Shu-Xing Wang1, Zhong-Kui Huang2, Wei-Qiang Wen2, Simon Preval3, N. R. Badnell 4,
Stefan Schippers5, Han-Bing Wang2, Li-Jun Dou2, Xin-Wen Ma2 and Lin-Fan Zhu1*
1

Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics,
University of Science and Technology of China (USTC), Hefei, Anhui 230026, P. R. China
2

3

Institute of Modern Physics, Chinese Academy of Sciences, 730000 Lanzhou, P. R. China

Department of Physics and Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK
4
5

Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK

I. Physikalisches Institut, Justus-Liebig-Universität Gießen, D-35392 Giessen, Germany

Abstract
Electron-ion recombination rate coefficients of Be-like Ca in the center of mass energy from 0 to 51.88
eV have been measured by means of merged-beam technique at the main cooler storage ring (CSRm). The
calculation conducted with AUTOSTRUCTURE code was also presented and compared with theexperimental results. Dielectronic recombination associated with 2s2 [1S0] Ѝ 2s2p [3P0,1,2,1P1] andtrielectronic recombination associated with 2s2 [1S0] Ѝ 2p2 [3P0,1,2,1D2,1S0]transitions have beenmeasured. In addition, recombination of parent ions at the 2s2p 3P0 meta-stable state has also been identified
from the measured spectrum. Plasma recombination rate coefficients in the temperature range of 103-108 K
were derived from the measured recombination rates and compared with the results from the
AUTOSTRUCTURE code as well as previous calculations. An agreement of better than 25% iss found forthe collisionally ionized plasmas while the discrepancies are higher for photo-ionized plasmas.
1. Introduction
Astronomy is primarily an observational science by detecting photons. Various types of space-based
observatories, such as, Solar Maximum Mission (NASA), Solar and Heliospheric Observatory (NASA) and
XMN-Newton (ESA), have been launched to collect high-resolution X-ray data [1]. Electron-ion collision
processes which can result in line emissions, in particular, radiative recombination (RR) and dielectronic
recombination (DR), are consequently important sources of radiations in astrophysical plasmas. Thus, DR
rate coefficients are required to interpret the observed spectra by plasma modeling. In addition, electron-ion
recombination rate coefficients and electron impact ionization cross sections are essential for deducing thecharge state distribution in a plasma. Furthermore, determination of the man-made or astrophysical plasma
properties, such as the thermal structure and elemental abundances, requires accurate charge state distribution
data [2, 3]. Reliable recombination rate coefficients are required for understanding and modeling laboratorial
or astrophysical plasmas, while most available rate coefficients are from theory. However, the prediction of
DR resonance positions and strengths at low energy range by different theories is still a challenging task since
an infinite number of states are involved in DR process and relativistic many body effects should be taken
into account in high orders. Presently available atomic structure codes are not able to provide resonancepositions in the low energy region with sufficient precision. Therefore, accurate experimental DR rate
-1-

46

Table 1. Fitted parameters for the resonant recombination channels derived from experimental andcalculated rate coefficients. The unit of ci and Ei are 10-5cm-3s-1K3/2 and eV, respectively.
No.

Experiment

AUTOSTRUCTURE(nmax=1000)

i

ci

Ei

ci

Ei

1

5.022

0.554

3.623

0.058

2

6.169

0.038

47.5711.307

3260.089

3.252

151.7394.801

4453.8541.715

257.9222.001

51193.660

9.227

825.993

10.56262916.733

23.1881610.587

25.04876298.331

57.7205795.376

60.088coefficients are required to benchmark different theoretical methods to produce more reliable electron-ion
recombination data.
Calcium was found to be one of the most abundant element in the solar system [4, 5]. The solar atmosphere
contains plasma at all temperatures and the solar element abundances can reflect the element abundances in
the universe [6]. Line emissions caused by 2s2p 1P1 - 2s2 1S0 transition of Ca XVII at 192.8 Å were widely
observed in X-ray solar flare spectra by the Extreme-Ultraviolet Imaging Spectrometer (EIS) on Hinode [7].
Observation of the Tycho supernova remnant by XMM-Newton and Cassiopeia A by Chandra have also
shown the strong emission from the calcium ions [8, 9]. A summary of the spectral lines for Ca XVII can befound in a topical review by Doschek & Feldman [6] and the atomic data table summarized by Landi &Bhatia [10]. Laboratory study of the spectra of highly ionized calcium in the 100-250 Å range applied tosolar flare diagnostics had also been made with TEXT tokamak [11].
Our experimental results constitute a series of benchmark data for use in astrophysical and fusion plasmas.
The comparison between the measured and calculated resonances proposed that the theoretical model for
calculate the TR resonance strengths still needs some improvement.
2. Experimental result
The details of the experiment and the theoretical calculations can be found in the recent published papers[12, 13]. Fig. 1 presents the measured electron-ion merged-beam recombination rate coefficients as well as
the theoretical calculation by AUTOSTRUCTURE code. The comparison shows that the DR resonances canbe calculated with a high precision for both the resonance positions and strengths. However, the TR resonancestrengths cannot be produced very well within the present theoretical model. Most of the TR resonancestrengths were underestimated by the theoretical calculation.

-2-

47

8

Experimental result
TR contribution
DR contribution

Rate coefficient (10-9 cm3 s-1)

6
4

Sum of DR and TR

2
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2

1

0
10

20

30

40

50

60

70

Electron-ion collision energy (eV)Fig. 1 Present measured merged-beam electron-ion recombination rate coefficients compared with theseparate theoretical calculation with AUTOSTRUCTURE code.

Experimental result
Calculation DR+TR
DR of ions at 3P0 state

6e-+Ca16+(2s2[1S0])→

-9

3

-1

Rate coefficient (10 cm s )7

Ca15+(2p2[1D2]6p3/2)1/2

5e-+Ca16+(2s2p[3P0])→ e-+Ca16+(2s2p[3P ])→ e-+Ca16+(2s2p[3P0])→
0
Ca15+(2p2[3P1]8pj)J
Ca15+(2p2[3P1]8fj)J
Ca15+(2p2[3P ]8d )
1

j=3/2

j=1/2

5/2 3/2

1/2 3/2

j J

1

0
0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Electron-ion collision energy (eV)Fig. 2 Electron-ion recombination resonances at low collision energies. DR associated with parent ionsat the 2s2p 3P0 state has been identified in the measured spectrum.
Considering that the lifetime of the 2s2p 3P0 meta-stable state is rather long (~7.8×105s) compared to theexperimental time scale, the ions at other meta-stable states will decay to the ground-state since their lifetimes
are much shorter than the delay time for ion beam cooling before the measurement. A fraction of about 5%ions stored in the ring were estimated at this state. Several extremely strong resonances originating from the-3-48

parent ions at the meta-stable state have been identified from the measurement. Fig. 2 shows the results ofDR from metastable state. The present study proposed a chance to investigate the lifetime of the 2s2p 3P0
state decay to the ground-state by E1M1 two-photon transition.
In addition, for applications in astrophysics and fusion plasmas, the plasma recombination rate coefficients
have been derived from the present measured recombination rates and compared with the
AUTOSTRUCTURE calculation and previous calculated results (see [13] for discussions in detail). For
convenient use in plasma modeling codes, the plasma rate coefficients have been fitted with the formula
below:§Ei ·¸© kTe ¹

D (Te ) Te3/2 ¦ ci exp ¨ i(1.1).

The associated fitting parameters are listed in the Table. 1.
Acknowledgements
This work is partly supported by the National Key R&D Program of China under grant No.
2017YFA0402300, the National Natural Science Foundation of China through No. 11320101003, No.
U1732133, No. 11611530684, the Strategic Priority Research Program of the Chinese Academy of Sciences,
grant No. XDB21030300 and the Key Research Program of Frontier Sciences, CAS, grant No. QYZDYSSW-SLH006. The authors acknowledges the post Japan-China-Korea A3 Foresight Program and post Core
University Program (Post CUP).

References[1] Paerels F B et al 2002 Annu. Rev. Astron. Astrophys. 41 291[2] Savin D W & Laming J M 2003 Astrophys. J. 566 1166
[3] Beiersdorfer P 2003 Annu. Rev. Astron. Astrophys. 41 343[4] Asplund M et al 2013 Annu. Rev. Astron. Astrophys. 47 481[5] Feldman U & Laming J M 2000 Phys. Scr. 61 222[6] Doschek G A & Feldman U 2000 J. Phys. B: At. Mol. Opt. Phys. 43 232001[7] Ko Y K et al 2009 Astrophys. J. 697 1956
[8] Decourchelle A et al 2001 A & A 365 L218
[9] Hwang U & Laming, J. M. 2003 Astrophys. J. 597 362[10] Landi E & Bhatia A K et al 2009 At. Data Nucl. Data Tables 95 155[11] Lippmann S et al 1987 Astrophys. J. 316 819[12] Huang Z K et al 2018 Astron. Astrophys. Suppl. Ser. 235:2(8pp)[13] Wang S X et al 2018 Astrophys. J. 862:134(7pp)

-4-

49

Statistical Analysis of Hydrogen Recycling in the Peripheral Region of LHD
Takuya Osugi1*, Masahiro Hasuo1, Keisuke Fujii1
1Graduate School of Engineering, Kyoto University, Kyoto Nishikyo-ku, Kyoto 615-8246, Japan

Abstract
In order to understand the behavior of atoms and plasma particles in the peripheral region of the Large
Helical Device (LHD), the ion particle outflux to the divertor plates and the hydrogen atom influx to theplasma are statistically investigated using the ion saturation current and the Balmer-Ƚ emission intensity
measured in multiple diagnostic ports. The correlations among the AC components of the ion saturation
current are large between the pairs of port 2-4, 2-6 and 4-6. The correlations among the AC components of
the Balmer- Ƚ emission intensity are large in all the ports. The correlations between these two
measurements are large in ports 2, 4 and 6. These results suggest that the ion particle outflux is
non-axisymmetric, that the hydrogen atoms generated in some ports instantaneously spread to all the ports,
and that the hydrogen atoms are mainly generated from the direct recombination in the port 2, 4, and / or 6.
1. Introduction
In magnetic confined fusion plasmas, it is one of important studies to control particle recycling at theplasma facing components such as first wall and divertor for improvement of the confinement performance[1]. The behavior of atoms and charged particles in the peripheral region are determined by a lot ofelementally processes such as recombination, absorption and sputtering. Since there are huge uncertainties
not only in the reaction rates but also in the plasma parameters near the divertor region, it is difficult toevaluate their behaviors from the first principle quantitatively. In the Large Helical Device (LHD), therecycling flux has been estimated from the particle flux on the divertor plates by the particle balance model[2]. However, this model gives a lower estimation of the divertor recycling flux by assuming the rate of theion particle loss that does not reach the divertor plates equals to 0 than without assumption.
In this study, we fit a statistical model to experimental data of ion saturation current on the divertor
plate and Balmer-ߙ emission intensity measured for LHD plasmas, and quantified the correlations among
measurement data in multiple ports.
2. Experiment
Figure 1 (a) shows a schematic top view of LHD. LHD was designed 10-fold rotational symmetry inthe toroidal direction. The Langmuir probes were embedded in the divertor plates in the port 2, 4, 6, 7, 8, 9
and 10. Each of them measured the ion saturation current for the LHD plasma (shot number 137144). The
sampling frequency was 200 Hz. The Balmer-ߙ emissions from this plasma were measured in the port 2, 3,
5 ,6, 7, 8, 9 and 10. The sampling frequency was 200 Hz. In this paper, measurement data of the ion* Corresponding author’s email: osugi.takuya.85u@st.kyoto-u.ac.jp

-1-

50

ሺ௣ሻ

saturation current and the Balmer- Ƚ emission intensity in port ‫ ݌‬are denoted by ݅୧ୱሺଶሻrespectively. Figure 1 (b) shows temporal evolution of ݅୧ୱሺଶሻand ‫ܫ‬ୌሺ௣ሻ

and ‫ܫ‬ୌ ,measured for this plasma.

ሺଶሻFig. 1 (a) Schematic top view of LHD. (b) Measurement data of the Balmer-ߙ intensity in port 2, ‫ܫ‬ୌሺଶሻ(blue line, left axis), and the ion saturation current in port ʹ, ݅୧ୱሺଶሻof ‫ܫ‬ୌሺଶሻ
and ݅୧ୱ

(green line, right axis). The superscripts

denote the port numbers.

As can be seen in Fig. 1 (b), these two measurements have the rapidly fluctuating components inaddition to their slow trends. In this study, we focus on the fluctuation component of these data.
We extracted the AC component by subtracting the DC component of these two measurements, whichሺ௣ሻ

were obtained from a 5-point moving average. Typical AC components of ݅୧ୱሺ௣ሻand ‫ܫ‬ୌare shown in Fig.

2 (a) and Fig. 2 (b), respectively.

(a) Temporal evolution of ଓ෥నୱ ሺ଺ሻ , ଓ෥నୱ ሺ଻ሻ and ଓ෥నୱ ሺ଼ሻ at ‫ ݐ‬ൌ ͸Ǥͷ̱͸Ǥ͹, where ଓ෥నୱ ሺ௣ሻ denotes the AC

Fig. 2ሺ௣ሻ

component of ݅୧ୱ . The mean values of these measurements are properly shifted for the cleaner view. (b)Temporal evolution of ‫ܫ‬෩ୌሺ଺ሻ, ‫ܫ‬෩ୌ

ሺ଻ሻand ‫ܫ‬෩ୌሺ଼ሻat ‫ ݐ‬ൌ ͸Ǥͷ̱͸Ǥ͹, where ‫ܫ‬෩ୌሺ௣ሻ

denotes the AC componentሺ௣ሻof ‫ܫ‬ୌ .

ሺ௣ሻ

݅௜௦

ሺ௣ሻ

and ‫ܫ‬ୌare assumed to be proportional to the ion particle outflux to the divertor plate and thehydrogen atom influx to the plasma, respectively. Then the following relation is obtained,ሺ௣ሻ߁෨୧ ‫ ן‬ଓ෥నୱ ሺ௣ሻ

where ߁෨୧ሺ௣ሻis the AC component of the ion particle outflux in port ‫݌‬, ߁୧
-2-

51

(1)
ሺ௣ሻ

.

3. Statistical Modeling for particle fluxes
In order to understand plasma wall interactions, the surveys have been conducted taking various
generation paths for hydrogen into consideration [3]. The generation paths are classified into two in termsof the time scale. Some atoms are generated by the recombination (radiative, three body, charge exchange,
surface assisted recombinations) from ions and electrons and go into the plasma. We call this path as direct
recycling. On the other hand, some other atoms are absorbed into divertor plate or first walls, and released
after some conditions are met, e.g. the temperature increase of the material (indirect recycling). The direct
recycling occurs in the time scale determined by the elementary process rate (̱ͳͲ଺ Ȁ), while the timescale of the indirect one should be larger than the direct one because this time scale depends on the divertor
temperature, which doesn’t change rapidly.
ሺ௣ሻLet ߁ୌ

ሺ௣ሻbe the neutral hydrogen atom influx from the divertor plate in port ‫݌‬. ߁ୌ

be written as a sum of direct recombination effect, which equals to ߁୧ሺ௣ሻis expected to, and slow-time-scale indirect

recombination effect. We approximate this relation by the following form,ሺ௣ሻሺ௣ሻ߁෨ୌ ൌ ߁෨୧ ൅ ߝ ሺ௣ሻ

(2)

ሺ௣ሻ
where ߁෨ୌሺ௣ሻis the AC component of ߁ୌ , while ߝ ሺ௣ሻ approximates the remaining cause of the atomሺ௣ሻ
generation in port ‫݌‬. We further approximate ߁෨୧and ߝ ሺ௣ሻ follow independent zero-mean Gaussian

distribution functions,
ଶ

ሺ௣ሻ
ሺ௣ሻ
߁෨୧ ̱ࣨ ൬Ͳǡ ቀߪ୧ ቁ ൰

(3)

ሺ௣ሻ ଶ
ߝ ሺ௣ሻ ̱ࣨ ൬Ͳǡ ቀߪக ቁ ൰

(4)

ሺ௣ሻ ଶ
ሺ௣ሻ ଶ
ሺ௣ሻ
where ቀߪ୧ ቁ and ቀߪக ቁ are variance of ߁෨୧and ߝ ሺ௣ሻ , respectively. Under these assumptions,ሺ௣ሻand ߁෨ୌ follow a multivariate Gaussian distribution,
ሺ௣ሻ ଶ

ሺ௣ሻ
߁෨
Ͳ ቀߪ୧ ቁ‫ ݌‬൭൥ ୧ ሺ௣ሻ ൩൱ ൌ ࣨ ቌቂ ቃ ǡ ቎
Ͳ
ሺ௣ሻ ଶ
߁෨ୌ
ቀߪ ቁ
୧

The correlation coefficient between ߁෨୧

ሺ௣ሻ

ሺ௣ሻ

and ߁෨ୌ

ሺ௣ሻ
߁෨୧

ሺ௣ሻ ଶ

ቀߪ୧ ቁ
ሺ௣ሻ ଶ

(5)

቏ቍ
ሺ௣ሻ ଶ

ቀߪ୧ ቁ ൅ ቀߪக ቁ

is
ሺ௣ሻ ଶ

 ቂ߁෨୧

ሺ௣ሻ

ቀߪ୧ ቁ

ሺ௣ሻ

ǡ ߁෨ୌ ቃ ൌ ඩ

ሺ௣ሻ ଶ

(6)


ሺ௣ሻ ଶ

ቀߪ୧ ቁ ൅ ቀߪக ቁ

ሺ௣ሻ ଶ

ሺ௣ሻ ଶ

When this correlation coefficient is large, ቀߪக ቁ is smaller than ቀߪ୧ ቁ . Then ߁෨୧ሺ௣ሻin Eq. (1) becomesdominant compared with ߝ ሺ௣ሻ . Therefore, this suggests that hydrogen atoms are mainly generated from thedirect recombination of ions on the divertor plates and in the peripheral region.
In order to investigate hydrogen recycling based on this model, we calculate correlation coefficientsamong ଓ෥నୱ ሺ௣ሻ and ‫ܫ‬෩ୌሺ௣ሻ

in different toroidal position and those between ଓ෥నୱሺ௣ሻand ‫ܫ‬෩ୌሺ௣ሻ

in a time

window of 150 ms. These results are shown in the next section.
4. Results
The correlations among the ion particle outfluxes were evaluated from the ion saturation currents
based on Eq. (1). Figure 3 (a) and (b) show the scatter diagrams of ଓ෥నୱ ሺସሻ versus ଓ෥నୱ ሺ଺ሻ and ଓ෥నୱ ሺସሻ versus-3-52ଓ෥నୱ ሺ଼ሻ , respectively. The correlation coefficient in Figure. 3 (a) is large while that in Fig. 3 (b) is small.
Figure 3 (c) shows the correlation coefficients between all the pairs of ଓ෥నୱ ሺ௣ሻ . As can be seen in Fig. 3 (c),ൣଓ෥నୱ ሺଶሻ ǡ ଓ෥నୱ ሺସሻ ൧, ൣଓ෥నୱ ሺଶሻ ǡ ଓ෥నୱ ሺ଺ሻ ൧ and ൣଓ෥నୱ ሺସሻ ǡ ଓ෥నୱ ሺ଺ሻ ൧ were larger than the others.

Fig. 3 (a) and (b) are scatter diagrams of ଓ෥నୱሺସሻversus ଓ෥నୱ ሺ଺ሻ and ଓ෥నୱ ሺସሻ versus ଓ෥నୱ ሺ଼ሻ in a time windowof 150 ms at ‫ ݐ‬ൌ ͸Ǥ͸, respectively. Each variable is normalized to mean 0 and standard deviation 1. The
correlation coefficient ‫ ݎ‬is shown in the lower right of each figure. (c) Correlation coefficients between all
the pairs of ଓ෥నୱ ሺ௣ሻ, which is indicated by the color of the lines.
The correlations among the temporal changes of the hydrogen atom influxes were evaluated from the
AC components of the Balmer-ߙ emissions. Figure 4 (a) shows the scatter diagram of ‫ܫ‬෩ୌ
Figure 4 (b) shows the correlation coefficients between all the pairs of ‫ܫ‬෩ୌthe correlation coefficients of all the pairs of ‫ܫ‬෩ୌ

Fig. 4

ሺ௣ሻ

ሺ௣ሻ

ሺଷሻ

versus ‫ܫ‬෩ୌሺ଺ሻ.

. As can be seen in Fig. 4 (b),are more than 0.8.

ሺଷሻሺ଺ሻversus ‫ܫ‬෩ୌ
in a time window of 150 ms at ‫ ݐ‬ൌ ͸Ǥ͸. (b)(a) Scatter diagram of ‫ܫ‬෩ୌ

Correlation coefficients of all the pairs of ‫ܫ‬෩ୌሺ௣ሻ

.

The correlation coefficients between the ion particle outflux and the hydrogen atom influx wereሺ௣ሻ
evaluated by that between ଓ෥నୱ ሺ௣ሻ and ‫ܫ‬෩ୌ , where ‫ܫ‬෩ୌ is the averaged values of ‫ܫ‬෩ୌ
for all the ports.

Figure 5 shows the result of ൣଓ෥నୱ ሺ௣ሻ ǡ ‫ܫ‬෩ୌ ൧ in all the ports. As can be seen in Fig. 5, ൣଓ෥నୱ ሺଶሻ ǡ ‫ܫ‬෩ୌ ൧,

-4-

53

ൣଓ෥నୱ ሺସሻ ǡ ‫ܫ‬෩ୌ ൧ and ൣଓ෥నୱ ሺ଺ሻ ǡ ‫ܫ‬෩ୌ ൧ are larger than the others.

Fig. 5 Correlation coefficients between ‫ܫ‬෩ୌ and ଓ෥నୱ ሺ௣ሻ in a time window of 150 ms at ‫ ݐ‬ൌ ͸Ǥ͸.
5. Discussion
From the correlation analysis of the ion saturation current, it is found that the ion particle outflux fromthe plasma to the divertor plate fluctuates coherently in port 2, 4 and 6, and those to other ports behaves
independently, i.e., the ion particle outflux is non-axisymmetric. On the other hand, the Balmer-ߙ intensity
has a large correlation in all the ports. Because the Balmer-ߙ intensity is proportional to the neutral particle
influx to the plasma [4] but not the generation flux of atoms; this large correlation indicates either of thefollowing two hypotheses; hydrogen atoms are generated at all the divertor plates axisymmetrically, or thegeneration of hydrogen atoms itself is asymmetric but they instantaneously spread to all the ports resulting
in axisymmetric particle influx and Balmer- ߙ emission intensity fluctuation. However, the strong
correlation between the Balmer-ߙ intensity and the ion saturation current at the particular port suggests thelatter one, i.e. the hydrogen atoms are mainly generated in the port 2, 4, and / or 6. Note that it is notpossible in the current analysis to evaluate which ports are the dominant generation ports because theBalmer-Ƚ intensity fluctuates coherently with the hydrogen atom influx in the dominant generation ports.
In this work, we performed statistical analysis of the Balmer-Ƚ intensity and the ion saturation current.
The correlation coefficient among the AC components of the ion saturation current are larger between theports 2-4, 2-6 and 4-6 than the others. The correlation coefficients among the AC components of theBalmer-Ƚ intensity are larger than 0.8. The correlation coefficients between these two measurements arelarger in port 2, 4 and 6 than the others. As the results, we found the followings; the ion particle outflux is
non-axisymmetric, the hydrogen atoms generated in some ports instantaneously spread to all the ports, andthe hydrogen atoms are mainly generated from the direct recombination in the port 2, 4, and / or 6.
Acknowledgements
The authors would like to thank preparation of the seminar by post Japan-China-Korea A3 Foresight
Program and post Core University Program (Post CUP). This work is supported by NIFS.
References[1] U Samm and the TEXTOR-94 Team 1999 Plasma. Phys. Control. Fusion 41 B57

-5-

54

[2] Miyazawa J et al 2004 Nucl. Fusion 44 154[3] D. E. Post J. Nucl. Mater. 220-222 (1995) 143-157[4] U. Wenzel, M. Goto J. Nucl. Mater 415 (2011) S1170-S1173

-6-

55

Three-body fragmentation dynamics of CF42+ induced by 1 keV electron
collision
Lei Chen1, Zhenjie Shen1, Enliang Wang2, Xi Zhao1, Xu Shan1, Xiangjun Chen1*
1

Hefei National Laboratory of Physical Sciences at the Microscale and Department of Modern Physics,
University of Science and Technology of China, Hefei 230026, China.
2Max Plank Institute for Nuclear Physics, Heidelberg 69117, Germany.

Abstract
We report the investigation on three-body fragmentation of CF42+ induced by 1 keV electron collisionutilizing a newly built ion momentum spectrometer. With the help of coincidence measurement, more thanseven dissociation channels are observed. For the fragmentation of CF42+ into F++CF2++F, three dissociation
pathways are identified, including one sequential and two concerted pathways. Kinetic energy release
distributions for these pathways are deduced. We found that one concerted pathway is the predominated, andthe sequential breakup is likely to take place through highly-excited electronic states of CF42+.
1. Introduction
Investigations on dissociative ionization of molecules are of intensive interest in physics, chemistry as wellas biology. One of the major challenges in this area is to comprehend the molecular bond cleavage selectivity[1]. The past few decades have witnessed tremendous progresses in the development of coincidence
momentum imaging techniques [2, 3], making it feasible to reveal multi-body fragmentation dynamics forsmall molecules.
The CF4 molecule, in its ground states, has a tetrahedral structure with high symmetry. It is an important
plasma etching gas in the semiconductor industry and also a potent greenhouse gas in the earth atmosphere.
Although CF4 has been extensively studied by plenty of experimental methods [4, 5], reports on the breakup
mechanics are still scarce.
In this work, the three-body fragmentation of CF42+ into F++CF2++F is studied. The precursor ion, CF42+,
is created by electron impact at 1 keV energy. The two fragment ions are detected in coincidence by amomentum imaging system. By employing the Dalitz plot [6] and Newton diagram, two concerted and one
sequential fragmentation pathways are identified. We deduced the kinetic energy release distributions forthese three pathways and found that the sequential breakup is likely to take place through highly-excitedelectronic states of CF42+.
2. Experimental Setup
The experiment was performed using a recently built ion momentum spectrometer. As shown in Fig. 1, a
pulsed electron beam from a photoelectron emission gun collides with the gas target in the reaction zone. The
electrons are emitted from a Tantalum cathode that is illuminated by a 266 nm pulsed laser (…). The repetition
frequency and pulse duration of the laser are 20 kHz and less than 600 ps, respectively. The spot size of the-1-56

electron beam is collimated to about 1 mm diameter at the reaction zone. After the collision, the electron
beam is dumped and monitored by a Faraday cup, which comprises a 1 mm inner cup and a 6 mm diameter
outer cup. An effusive gas target is introduced into the reaction zone by a copper capillary mounted on athree-dimensional manipulator. The internal diameter and length of the capillary are 0.1 mm and 60 mm,
respectively. After the collision of electrons with the molecular target, a pulsed extraction field will be
triggered on. The fragment ions are accelerated and analyzed by a Wiley-Mclaren type time of flight (TOF)
mass spectrometer [7] towards a two-dimensional (2D) time- and position- sensitive detector (PSD), which
consists of a pair of microchannel plates (MCP) of 100 mm diameter in chevron configuration and followed
by a delay line anode. Momentum vector of each ion can be obtained by the time of flight and position on
the detector.

Fig. 1 Schematic graph of Ion Momentum SpectrometerIn the experiment, the electric field of the acceleration region is kept at 50 V/cm. M1 to M5 are
Molybdenum meshes installed to create uniform electric fields. The reaction chamber is pumped by a 700 l/s(Pfeiffer Hipace700) turbo-pump. The background pressure is better than 2×10-6 Pa and the working pressure
is about 4×10-5 Pa.
3. Results and Discussion
Fig. 2 shows the ion-ion coincidence map of the CF4 fragmentation, where more than seven fragmentation
channels can been observed. The thee-body dissociation channel CF42+ืF++CF2++F is labeled by a red oval.
The momenta of the two ionic fragments (F+ and CF2+) are obtained directly from their TOF and positions
on the detector. The momentum of neutral F atom is deduced by using the principle of momentum
conservation. It is worthwhile to mention that the fragment channels of CF4q+ (q≥3) have not been observedin present experiment.
-2-57

Fig. 2 Ion-ion coincidence map observed in the fragmentation of CF4 induced by 1 keV electron impact.
In order to identify the fragmentation mechanisms of this channel, we employ the Dalitz plot [6]. It is a
powerful analytic tool for visualization of three-body fragmentation processes. Each point in the plot
represents a specific momentum correlation in terms of the normalized energies of the fragments. The Dalitz
plot for the channel CF42+ืF++CF2++F is shown in Fig. 3(a), where the three distinct regions (labelled I, II,
and III) can be clearly observed. We adopt Newton diagrams to directly visualize the momentum correlationof the three fragments in these three regions in Fig. 3(b)-(d). In the diagrams, the normalized momentum
vectors of the fragments are plotted with one of them fixed at the x-axis and the other two plotted on theupper and lower halves of the diagram.

Fig. 3 (a) Dalitz plot of CF42+ dissociation into F++CF2++F; (b) Newton diagram for region I; (c) Newton
diagram for region II; (d) Newton diagram for region III.
-3-

58

The Newton diagram for region I is shown in Fig. 3(b), where a circular structure can be clearly observed.
This structure is due to the rotation of CF32+ before the final charge separation and the neutral F atom is lostat the first step. Therefore, the events in region I originate from sequential breakup, i.e.
CF42+ืF+CF3+ืF++CF2++F. Fig. 3(c) presents the Newton diagram for Region II. Both of the momenta of
F+ and F scatter on a localized area along the x-axis, indicating the existence of a concerted breakup. From
the Dalitz plot in Fig. 3(a), we know pathway II is the dominated one. As shown in Fig. 3(d), the Newton
diagram for Region III is a little like that of region II. The difference is, in this case, F atom obtains more
momentum than CF2+, revealing another concerted breakup pathway. However, it is not usual for the neutralfragment to obtain more energy than the charged ones, because Coulomb forces are usually stronger between
charged ions. So we propose that a charge transfer process may occur. That is, after the breakup, F+ captures
one electron and becomes a neutral F atom.

Fig. 4 KER distributions for different dissociation pathways.
Fig. 4 demonstrates the KER distributions for pathway I, II and III. The peak values are 30.5 eV, 5.5 eV
and 13.0 eV, respectively. The KER for pathway I (the sequential breakup) distributes on higher energy side.
This indicates that the sequential pathway may take place through high-lying states of CF42+.
4. Conclusion
To conclude, we built a new ion momentum spectrometer for investigating fragmentation dynamics ofpolyatomic molecules. Three-body dissociation of CF42+ into F++CF2++F is studied in present experiment.
Three breakup pathways are identified and their KER distributions are obtained. We found that concerted
breakup (pathway II) is the dominated one among the three pathways. And sequential breakup (pathway I) is
likely to happen through the high-lying states of CF42+.
-4-59

Acknowledgements
This work is supported by the National Key Research and Development Program of China(2017YFA0402300) and the National Natural Science Foundation of China (11534011).
References[1] Neumann N et al 2010 Phys. Rev. Lett. 104 103201.
[2] Dörner R et al 2000 Phys. Rep. 330 95.
[3] Ullrich J et al 2003 Rep. Prog. Phys. 66 1463.
[4] Codling K et al 1991 J. Phys. B: At. Mol. Opt. Phys. 24 951.
[5] Motohashi K et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1811.
[6] Dalitz R H 1953 Philos. Mag. 44 1068.
[7] Wiley W C and McLaren I H 1955 Rev. Sci. Instrum. 26 1150.

-5-

60

      
      !" 

# $  $ %"  &'& &( $ $       

  
23 
4$45

 
!
!
!"
! 

$  
!#
 .
.
.
#

#

 # 
44 1 + 
5, 

#".
#.
..
.#

 ( >9? 
C ,

B.
B#
D.

%"     )*  + 
+ ,   " -.   %%&'( )' '    
* %+ $ ** )  * ,-(( /&,-'&&0 1 .+   ( (%  % & + ) ' +*)* 62' + )  +%7& %*) ' * % )8 5- 
%)   
9- 1  % :) %% ;"*)+++-15 (%)%)& +% '+*)*%
<-  +++ +   %' &  +*)*5-  ) %&==4 '==4")0 1".#&< + %% %&+ %**8) ' * 1- + 
% )   %&)** % %&+ % 7** 1-95
%/  * %%-*)*% %')'   ) &>2 %* '% '% * %+ %/  *  ( % )
453-
&+%)' ) ** %?2
- ) *%' %+* * )%%&**/5 +
3 @ A   % ) *%%&%) ** % ' % 7 %&46   '*+%
?- ) 7  
3(*+&*) + )%)%)&
-15 (' )*7%(  )* + % +*)* 
.+ %%+%
&&0 1...B.
0
7   % +*  & *%%8 +& 9*   )*%+(   ' %)  '* %+ %
3A/ ) *+ %% %)%) ')** %  * '  (A,:+'*  &* %+ ?9?% *& *)  ' %& + ))*)1/ ; ! )) )

0%D#% )%



61



' $+  $  
 / &05  ..
!"
! .

"
  &
3A/A,:#.
.
 

#
  ?$
 9

#".
#.
..

9  
46
A6@ A5 (-,% 1 
A5 (.+ ,% +  &+ %% )&& ) %  %
5- %  %%  3* %+ %
,8 + *( *  && )  * 7' )'  &$" =E$"=,% +   + %% %) &$" =$ =7
+ ) *')+%  &+* *%) 7%('&+3* %+ %

2  ,% +  &'% & *&$# =$#.= ,-+'* %+ &&0 1"
3 % )%&* % ')'* %+ '   %(* 7 )1 ' %(' &&& +%%) *%3 % % & + ) '  ) %) %  * % ')' %* %+ %  -69 '0
,8 + * '  ) * (%   &  '  
'' + )% % * %')'* %+ %
5* & %F * 7 +*)' + )%  %* '
C 
'%  *+ +  )  /  *  %
453-
* & %8 *%)0 1".E#>9? -+ *% )*) * G  &*)%@)'&+C ,) + + ))%%% '%* %+ 
6A 1)% '   )) )&C:) *)*  % 5 ($  )+) F%'(*+E 7 &( /5- 
?-2    ' %  & 7 + * %+ 
<>5
>?
>-5
03  35-
9 
4$45

.#D# 

.#

,--

 #B#

%%%%  ,- **

0%D#1 $ $ 44 1 + 
5, 
C<   ,

H % 7*%) &+* *)  ' ( %7 '/  )+ )*)7 +  ,8 + *%' % + ))%%%
* ' 6* %+ %    ,0-

!"

> 9

') &A%****/ +% )** % %/ %/ & ( %!#.

?$ 5- 

%) **  % % '   * )%% %) % & ( *)%** 8)   % & 8  +*)*
%' ' 7 & % *) ' * % ) < %)    
 ( 6A 1 5 (..

"

62  ' &
2324 "453- ..
"
 .
#

&&0 1 + )*  G 7 *  %& ) % + %+& + )%)  %*  %%)%)*( 
??  ' % )& + 1 + 16' 5 (
* %+ %
<$  
3: '-: )&& ) %&0* 1 5- .+ -%   % ) *  *% % & '  :))*    A5 (.+   *: &3 
-7' & +   ' + )% & 6#"=
5- .+ ')'71H*))** % ++ &+  3 @ A ;46)0 1"E#>>  
4$45





 

63

64




&ROOHFWLRQRI$EVWUDFWV

65

66

Oscillator strengths and integral cross sections of the valence-shell
excitations of oxygen molecule studied by fast electron and inelastic
X-ray scattering
Lin-Fan Zhu 1 , Ya-Wei Liu
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, Universityof Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science andTechnology of China, Hefei, Anhui 230026, People’s Republic of China

K 2 → 0, and the ICSs of oxygen have been determined in a wide energy region with the aid of
the newly-developed BE-scaling method.

The oscillator strengths and integral crosssections of the Schumann-Runge(SR) continuum,Longest-Band(LB) and Second-Band(SB) of oxygen molecule have signiﬁcant applications in thestudies of the Earth’s atmosphere and the stellar atmospheres. Recently, molecular oxygen was
detected by the Rosetta spacecraft in the coma of
the comet 67P/CG for the ﬁrst time [1]. Comets such as the comet 67P/CG [1], are the theorized candidates for the building blocks of bodies
like Pluto, this naturally motivates a search formolecular oxygen in the atmosphere of Pluto bymaking use of the data sets acquired by the N ew
Horizons mission during its ﬂyby in 2015 July[2]. In the N ew Horizons, the Alice extreme/far-ultraviolet imaging spectrograph [3] has the
bandpass of 52 nm to 187 nm, which covers the
SR continuum, LB and SB of oxygen. In order toexplain the complex spectra observed, the OOSs
and ICSs of the SR continuum, LB and SB ofmolecular oxygen are the basic and important input parameters for the theoretical modeling.
However, serious discrepancies among the available data for the dynamic parameters still exist.
In this work, the generalized oscillator
strengths (GOSs) of these excitations have been
determined independently by the high-energy
electron-scattering and the high-resolution inelastic X-ray-scattering.
Typical energy-loss
spectra of oxygen are shown in Figure 1 alongwith the excited states assigned. The diﬀerent
experimental techniques provide a strict crosscheck for the present GOSs of oxygen, which
excludes the possibility of any systematic error.
Then, the OOSs of oxygen have been obtainedby extrapolating the present cross-checked GOSs
to the limit of the squared momentum transfer

1

2400

(a)

Intensity(arb.units)

1600

Electron scattering
E0@1500 eV
B
@4°
3

E3 u
v' 0

1

u

800

0

(b) X-ray scattering
E0@10 keV
@38°

100

50

0

7.0

7.5

8.0

8.5

9.0

Energy loss(eV)

9.5

10.0

10.5

Fig. 1. The typical energy-loss spectra of thevalence-shell excitations of molecular oxygen. (a):a electron energy loss spectrum at 4◦ ; (b): a highresolution inelastic X-scattering spectrum at 38◦ ,solid lines are the ﬁtted curves.

The present data can be used as the basic
input parameters of the theoretical models forthe astronomical observations, and are helpful todeepen our understanding of the atmospheres of
the Earth, Venusian, Saturn, Pluto, Europa, andother oxygen-rich planets and satellites.
References[1] A. Bieler et. al., 2015 Nature. 526 678.
[2] J.A. Kammer, S.A. Stern et. al., 2017 Astron. J.
154 55.
[3] S.A. Stern, D.C. Slater et. al., 2008 Space. Sci.
Rev. 140 155.

E-mail: lfzhu@ustc.edu.cn

67

Recent progress in (e,2e) electron momentum spectroscopy
of atoms and molecules
Masahiko Takahashi 1
Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

Over the last half-century an experimental
method has been developed for looking at the
spatial distributions of each electron orbital inmomentum space. The method, called electron
momentum spectroscopy (EMS) [1], is a sort of(e, 2e) spectroscopy and is a kinematicallycomplete electron-impact ionization experiment
under the Compton scattering conditions [2].
The value of EMS lies in the exciting possibilityof measuring Compton profiles associated withtarget electrons at different energy levels
separately. Note that from consideration of thenature of the Fourier transform Compton
profiles are expected to be particularly sensitive
to the behavior of the outer, loosely boundvalence electrons that are of central importancein chemical properties such as bonding,chemical reactivity, and molecular recognition.
One is thus capable to realize momentum spacechemistry by using EMS. Indeed, the idea ofsuch momentum space chemistry can be traced
back to the early 1940’s. For instance, in 1941 aseries of theoretical papers [3] were reported by
C. A. Coulson who greatly contributed tounderstanding of chemical bonding.
In spite of the unique ability, however,application of EMS had largely been limited tostudies on electronic structure of atoms andsimple molecules, due mainly to its inherently
small cross sections. Under those circumstances,
we have joined this research field, in 1992.
Firstly, we have improved the collection
efficiency of EMS measurements, eventually bya factor of nearly 500,000 through a series ofdevelopment of a multi-channel coincidence
technique [4, 5]. We have then started various
kinds of attempts to exploit the unique ability of
EMS for momentum space chemistry [6]. For
instance, measurements of 3-dimensional
electron momentum densities of gaseous,isolated molecules have for the first time been
made [7], as well, such as the first experimental
determination of spatial orientations of theconstituent atomic orbitals in molecular orbitals[8] and studies on distortion of molecularorbitals due to molecular vibration [9].
1Extension of the applicability of EMS totransient species is also one of the challenges to be
tackled, because the change of electron motion isthe driving force behind chemical reactions. We
have therefore developed time-resolved EMS (TREMS) by replacing the continuous incident electron
beam with 5-kHz electron pulses, each having 1 ps
temporal width [10], and applied it to the highest
occupied molecular orbital (HOMO) of a molecular
excited state with a life time of 13.5 ps [11],opening the door to time-resolved orbital imaging
for chemical reactions [12]. Furthermore, we are
additionally developing a time-resolved version of
atomic momentum spectroscopy (TR-AMS) [13],which aims to measure in real time the momentum
distribution of each atom with different mass
numbers in a decaying system. We believe that thejoint use of TR-EMS and TR-AMS would provide acompletely new, momentum-space approach to
studying chemical reaction dynamics.
References[1] E. Weigold, I.E. McCarthy, Electron Momentum
Spectroscopy (Kluwer/Plenum, New York, 1999).
[2] Compton Scattering, ed. by B. Williams (McGrawHill, New York, 1977).
[3] C.A. Coulson and W.E. Duncanson, 1941 Proc.
Cambridge Philos. Soc. 55 67, 74, 397, 406.
[4] M. Takahashi, T. Saito, M. Matsuo, Y. Udagawa,2000 Rev. Sci. Instrum. 73 2242.
[5] M. Yamazaki, M. Takahashi et al., 2011 Meas.
Sci. Technol. 22 075602.
[6] M. Takahashi, 2009 Bull. Chem. Soc. Jpn. 82 751.
[7] M. Takahashi et al., 2005 Phys. Rev. Lett. 94
213202.
[8] N. Watanabe, X.J. Chen, M. Takahashi, 2012
Phys. Rev. Lett. 108 173201.
[9] N. Watanabe, M. Yamazaki, M. Takahashi, 2012
J. Chem. Phys. 137 114301.
[10] M. Yamazaki, M. Takahashi et al., 2013 Rev.
Sci. Instrum. 84 063105.
[11] M. Yamazaki, M. Takahashi et al., 2015 Phys. Rev.
Lett. 114 103005.
[12] Research Highlights, 2015 Nature 59 392.
[13] M. Yamazaki, M. Hosono, Y. Tang,
M. Takahashi, 2017 Rev. Sci. Instrum. 88
063103.

E-mail: masahiko@tohoku.ac.jp

68Ion momentum imaging study of the ion-molecule reactions of Ar+ + NO andAr+ + N2
Shan Xi Tian*
Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, University of
Science and Technology of China, Hefei, 230026, China

Ion-molecule reactions are frequently
observed in plasma, flame, atmosphere, andinterstellar
space.
Althoughdifferent
physicochemical processes such as inelastic
collision leading to the state excitations,fragmentation, and production of new chemicalcompounds can happen, the basics are only
charge exchange or transfer and translational-tointernal energy transfer. These two fundamental
features are strongly dependent on the quantum
state properties of the colliding objects and thecollision energy.
Here we report some new results by using
our recently established ion velocity map
imaging (VMI) apparatus for the low-energy(less than 20 eV) ion-molecule reaction
dynamics study:
1. In the charge exchange reactions of Ar + +NO o Ar + NO+, a resonant charge transfer toform NO+ (a3Σ+) plays a predominant role
through whole collision energy range (2.09-3.71eV) investigated here, while to the higher statesb3Π and w3Δ of NO+ only at the lower collisionenergies. This abnormal translational-to-internalenergy transfer trend is due to the easierformation of (Ar-NO)+ in the slower collisions[1].
2. In the charge exchange reactions of Ar + +N2 o Ar + N2+, X2Σg+ and B2Σu+ states of N2+
can be accessed directly, while A 2Πu state ispopulated by the nonadiabatic couplings
between X and A states and between A and B
states. These two couplings are out of FranckCondon region of the N 2 o N2+ verticaltransitions, and cannot be observed in thephotoionizations. This work (see Fig. 1) is thefirst example about such nonadiabatic processes
in the ion-molecule reaction [2].

Fig. 1. (A) Experimental arrangement of the ionmolecule reactions of Ar+ + N2 o Ar + N2+. Time-sliced
images of N2+ ion velocity distributions at the relative
collision energies of 1.98 eV (B), 2.47 eV (C), 3.73 eV(D), 6.37 eV(E), and 9.21 eV (F). Each image is obtainedby rotating and weighting the measured threedimensional velocity distribution of N2+ ions. Reactant
velocities are indicated by white arrows (N2 along thenegative and Ar+ along the positive x axis). Newton
spheres plotted with broken white circles in the image
correspond to the vibrational states ν’ of N2+ X2Σg+ (outerwhite circles), A2Πu (inner red circles) and B2Σu+ (inner
white circles).

The present study clarifies the previous longstanding arguments about above processes. The ion
momentum images reported here are much clearer
than those obtained in the other groups [3,4], whichlargely benefits from our unique design of a wellconfined pulsed low-energy ion beam source [5].
References[1] J. Hu, C.-X. Wu, Y. Ma, S. X. Tian, 2018 J.
Chem. Phys. (submitted).
[2] J. Hu, et al., (to be submitted).
[3] J. Mikosch, et al., 2008 Science 319 183.
[4] L. Pei, J. M. Farrar, 2012 J. Chem. Phys. 136
204305.
[5] J. Hu, C.-X. Wu, S. X. Tian, 2018 Rev. Sci.
Instrum. 89 066104.

* E-mail: sxtian@ustc.edu.cn

69Soft X-ray emissions from inner-shell excited Li-like ions in chargetransfer collisions of meta-stable He-like ions with neutral gases
Hajime Tanuma∗, 1 and Naoki Numadate∗ 2∗

Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan

In Tokyo Metropolitan University, we have
performed ion-beam collision experiments using
a 14.25 GHz ECR (electron cyclotron resonance)
ion source which produces a plasma of temperature about 106 K. Multiply charged ions produced with this ion source were extracted with
an electric potential of 10–20 kV and the chargestate of the ions was selected by using a doublefocusing dipole magnet.
The ion beam with a single charge state wasintroduced into a collision cell ﬁlled with a target
gas, and photon emissions from the collision cellin an an EUV (extreme ultra-violet) region wereobserved with a compact grazing-incident spectrometer equipped with a gold-plated cylindricalmirror for light condensing and a variable-linespacing (ca. 1200 lines/mm) grating. A CCD(charge coupled device) camera with a Peltiercooling system was installed in the spectrometer.
In this work, we have observed photon emissions in soft X-ray regions in collisions of heliumlike C, N, and O ions with neutral gas targets. If
the incident helium-like ions are in their groundstate 1s2 1 S0 , the photon emissions from lithiumlike ions might be smaller than the ionizationenergies of 1s2 2s ions, namely 64.49, 97.89, and138.12 eV, respectively, because single-electron
captures are the most dominant in collisions ofmultiply charge ions with neutral gases in low energy collisions, and the initial states of emissions
might be 1s2 n. However, we observed emissions
around 300, 400, and 600 eV in collisions of C4+ ,N5+ , and O6+ , respectively.
Therefore, we consider that the emissions
from 1s2sn states produced in charge transfer
collisions of helium-like ions in the meta-stable
triplet states, 1s2s 3 S1 , were observed in our experiments. As it is well-known that the heliumlike ion beam produced with an ECR ion source
is a mixture of the ground state and the longlived excited state and has few percents of themeta-stable state, the formation of 1s2sn statesmight be possible. However, the most probabledecay process of the inner-shell excited state is12!

usually Auger electron emission, and the radiative emission is not strongly expectable.
We have looked for the previous similar studies in the literature, and found a series of experiments in Grenoble, France [1, 2, 3]. In theseexperiments, the results with He and H2 target
gases were reported. But, our new results show
diﬀerence from the previous ones in the emission
spectra. Furthermore, we measured spectra withother target gases, namely Ne, Ar, Kr, Xe, N2 ,O2 , and CO2 , and observed strong target dependence in some cases.
Fig. 1 is shown a typical emission spectrum
observed in collisions of C4+ with He at collisionenergy of 60 keV. These peaks correspond to thetransitions from 1s2s(3 S)3p 2 P, 1s2s(1,3 S)2p 2 P,
and 1s2s2p 4 P states to the ground state oflithum-like C3+ ions (1s2 2s 2 S). The identiﬁcation of transitions was performed with the theoretical calculations [4].




  









 
Fig. 1. EUV emission spectrum in collisions of C4+
with He at ion energy of 60 keV.

References[1] M. G. Suraud et al., 1988 J. Phys. B 21 1219.
[2] L. Guillemot et al., 1990 J. Phys. B 23 3353.
[3] S. Bliman et al., 1992 J. Phys. B 25 2065.
[4] F. F. Goryaev et al., 2017 At. Data Nucl. Data
Tables 113 117.

E-mail: tanuma-hajime@tmu.ac.jp
E-mail: numadate-naoki@ed.tmu.ac.jp70                                             !



  

      
 !!"# $% & '&   "          ( )   % )   %)   *$+$,    %       %     (          - .   (      -/.    %
 %) %  0)    
*123,    &   0          % %       %    %    
0)     (  
&30 0       %           (    
& $ (     )   *$,   %       0)  
            (     &1)    ) 
   ( %% %   % $     %
 ( %
4 
 %
)# 54     0) &  % 
 (          $  0       )  %)    )5 #"6   %
78!! 4  
% 7 8!! 4& 2      % 9  
#:6  #;6 $   %  <%          )   %)  * 2& ,&  ( 5        
0
0   (       
         &&"# $# 3   %          % =/!!!
4 * , /8!! 4 *,  #!!! 4 * ,&    %     #! 4 !! 4 #!! 4
8!! 4  !!! 4         &%
- . >& & ? &  %9 @& @  @&?   A& 2  A& 3  B A& 
C 
 (        %   % & & '& & && 8/) 88* DD:,&-/.E& $5 5 & <% 2&  &
F% 3&   >&$&& 3 &    
F& G   %    9    %  )   1& & '& & D; ;#!!/ */!!",&

3)H 99I%&%&

71

Statistical properties of atomic structures of r-process elements
Daiji Kato*,**,1, Gediminas Gaigalas†, Masaomi Tanaka$,$$*National Institute for Fusion Science, Toki, Gifu 509-5292,Japan
Dept. of Advanced Energy Engineering Science, Kyushu University, Fukuoka 816-8580, Japan†
Institute of Theoretical Physics and Astronomy, Vilnius University, LT-10257 Vilnius, Lithuania$
Astronomical Institute, Tohoku University, Sendai, Miyagi 980-8578, Japan$$
National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588, Japan**

approximatedbytheskewednormaldistribution [8]. The distribution is uniquelyparametrized by a set of statistics, i.e. mean,
standard deviation, and skewness. The atomic
structures of the r-process elements calculated
by HULLAC and GRASP2K are analyzed interms of these statistics. Differences instatistical distributions of oscillator strengths
calculated by the two codes are evaluated byKolmogorov-Smirnov statistical test. We will
also discuss perspectives on the statisticalmethods for atomic structures of heavy
elements.

Gravitational waves by a binary neutron starmerger have been detected on 2017 August 17(GW170817 [1]) for the first time. Ejecta fromthe neutron star merger are expected to containheavy elements created by the r-process, therapid neutron-capture process that makes half ofallelements
heavier
than
iron
[2].
Electromagnetic emission, so called as kilonova,
powered by radioactive decays of thesynthesized r-process nuclei in the ejecta has
also been observed [3]. While properties of theemission are largely affected by opacities in theejected material, available atomic data for rprocess elements are still limited.
In this talk, we present new calculations ofatomic structure for r-process elements: Se (Z =34), Ru (Z = 44), Te (Z = 52), Ba (Z = 56), Nd(Z = 60), and Er (Z = 68) [4]. Due to extremelycomplicated energy level structure and huge
number of transitions, applications of statisticalanalysis assuming stochasticity of the atomic
structures are introduced.

References[1] B.P. Abbott et al.: Phys. Rev. Lett. 119 (2017)
161101.
[2] S. Wanajo et al.: ApJ 789 (2014) L39.
[3] Y. Utsumi et al.: Publ. Astron. Soc. Japan (2017)
psx118, https://doi.org/10.1093/pasj/psx118.
[4] M. Tanaka, D. Kato, G. Gaigalas et al.: ApJ 852(2018) 109.
[5] A. Bar-Shalom, M. Klapisch, J. Oreg, JQSRT, 71(2001) 169.
[6] P. Jönsson, G. Gaigalas, J. Bieroń, C.F. Fischer, I.P.
Grant, CoPhC, 184 (2013) 2197.
[7] A. Kramida, Y. Ralchenko, J. Reader, NIST ASD
Team 2015, NIST Atomic Spectra Database (ver. 5.3)
(Gaithersburg, MD: National Institute of Standards andTechnology) http://physics.nist.gov/asd.
[8] R.D. Cowan, The theory of atomic structure andspectra, Univ. California Press, Berkeley,1981.

For the atomic structure calculations, we use
two different codes, HULLAC [5] and
GRASP2K [6]. The HULLAC code, which
employs a parametric potential method, is used
to provide atomic data for many elements while
the GRASP2K code, which enables more abinitiocalculations
based
on
the
multiconfiguration
Dirac-Hartree-Fock(MCDHF) method, is used to provide
benchmark calculations for a few elements.
Such benchmark calculations are importantbecause systematic improvement of theaccuracies is not always obtained with the
HULLAC code especially when little data are
available in the NIST Atomic Spectra Database(ASD; [7]). By using these two codes, we also
study the influence of the accuracies of atomic
calculations on the opacities.
Due to extremely complicated atomic
structures and quasi continuum spectra,
knowledge of its statistical properties is usefulfor analysis. Statistical weight distribution ofeachelectronic
configuration
is
well

1

72

E-mail: kato.daiji@nifs.ac.jp

Development of electron impact spectroscopy
for directly observing the nuclear motions in molecular systems
Yuichi Tachibana 1, Masakazu Yamazaki 2, Masahiko Takahashi 3
Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan

Figure 1 shows experimental AMS spectra ofH2 and N2. Also included in this figure isassociated theoretical AMS spectra (solid
curves) generated by folding quantumchemistry-predictednuclearmomentum
distributions (chained curves) with the
instrumental response function. It is evident thatthe experimental and associated theoretical
spectra are in satisfactory agreement with eachother, that is, nuclear motions due to molecularvibration can be directly probed by thistechnique.

The importance of wave functions inquantum mechanics has been bringing manyefforts to obtain more accurate wave functions
both experimentally and theoretically. For
instance, shapes of electron wave functions can
now be experimentally observed by several
methodssuchaselectronmomentum
spectroscopy [1]. However, those for observing
shapes of vibrational wave functions are still in
infancy. Here we demonstrate that a newtechnique,calledatomicmomentum
spectroscopy (AMS) [2], enables one toquantitatively measure momentum distributionsof nuclei in a molecule or to observe molecularvibrational wave functions in momentum space.
AMS
employsquasi-elastic
electronbackscattering at large momentum transfer q.
Within the framework of the impulse
approximation, the scattering process is simply
described by a billiard ball-type collision
between the incident electron and a single
nucleus in a molecule. Then, a recoil energy ofthe scattering nucleus with mass M is given by
Erecoil = q2/2M + q·p/M, where p is themomentum of the scattering nucleus before
collision, and Erecoil can be measured byobserving the energy loss of the incident
electrons.
AMS experiments were conducted at anincident energy of 2.0 keV and at an energy
resolution of c.a. 0.6 eV by using ourmultichannel spectrometer [3], which accepts
quasi-elastically backscattered electrons fromthe target at a scattering angle of 135°±0.4°
over an azimuthal angle I range from -72.5° to
72.5° and from 107.5° to 252.5°.We haveobtained an instrumental response function
from experiments on heavy rare gas atoms, andsubsequently employed it to generate theoretical
AMS spectra to be compared with experimentson several diatomic molecules.

Fig. 1. Electron energy loss spectra of H2 and N2.

We believe the present work would be an
important step towards development of timeresolved AMS that provides a completely new,momentum space approach to studying
chemical reaction dynamics.
This work was partially supported by Hatano
Foundation.
References[1] M. Takahashi, 2009 Bull. Chem. Soc. Jpn. 82,751.
[2] M. Vos and M. Went, 2009 J. Phys. B: At. Mol.
Opt. Phys. 42, 065204.
[3] M. Yamazaki, M. Hosono, Y. Tang and M.
Takahashi, 2017 Rev. Sci. Instrum. 88, 063103.

1

E-mail: yuuichi.tachibana.s7@dc.tohoku.ac.jp
E-mail: masakazu@tohoku.ac.jp
3E-mail: masahiko@tohoku.ac.jp
273

 



                
              !"#! $    % $ #&' ((")*)

+         $   !# !, $-$! $ ./01)+   2$ .1# $!    #      3!#  #   2# !$2$$  4! $3#$#       ) 5  $    3  ! -
6 -   .1 3  0 %7     '#  )  #      #2$  3 $!        % !
"#   .01 3    '#     89   :7;) +3     <    !
          #     4! ,  $ 3  # #          #   < 3  !#  )=## !  & 9   $#   ! 8   !2,   







 





















 3 !  #      '#      !  $  3   # $$!! .1 !2$   !  .(1 #  ) +#  !    3 #   $ - ! 3    #  - !  #  
# !!) &!             !! 3B )3#!#          3  3   2$ ) +  3  - -!  !/2#       !  '#    !  )% !  3 - $  )


)

 

  !     '#  

 #  - ! !   #   !  $ 4      , !   $ 9##  ) , 3  2   2$   
$   3 :) ! !      # #   -$!! - 9       ! #   >?@    $#*#.1 ) # -=")*)5 )==)
.1)6 -(")*)8=00E0)
.01*) )("#.1 +)" ! ) %/ /7( ") *)
0=
.=1)")F4  )" $")*)0(>0@(.E1*)8)G  !)A ")*)E
=0.1 )B) <              
.(1A)F)  =( !""$0   &   # ) A $ !    $     ! 3 )
B  #        -      '#      $ # !  ,C,C>@,C> @,C> @,>@!,> @
- ! ## !      9       .1)   $     $  #
3#    #   '#     # !! 3# # ! #   4   ! 2#    -  #     !,>@ !   !/2#    # $-    #)
&!        #  #   !      - ! -  / - $  ! ! B # !) + !     !

  !  
8/$ H,-/#IE0)# $     ! $! -       !*).=1)
D2  #    3! ,C,C ! ,>@   ,    ! - # # 
'#  %     .E1 3      
74

8/$ H<    I2' )!

Optical emission spectroscopy and collisional radiative modeling for Ar plasma
Duck-Hee Kwon*,1, Kil-Byoung Chai*, and Min Park†*

Nuclear Data Center, † Fusion Engineering Center, Korea Atomic Energy Research Institute, Yuseong-gu, Daejeon
305-353, Korea

Some discrepancies for specific transition lines
between modeling and measurement may comefrom the detailed atomic data underlying in the
CRM and the sensitivity of line intensity to theatomic data has been investigated. Effect of electronenergy probability function (EEPF) and radiation
trapping on the CRM has been also discussed.

Optical plasma diagnostic methods such as
optical absorption and emission, laser-induced
fluorescence, Raman and Thomson scattering havebeen extensively used to measure electron/ion
temperature and density, species concentrations inplasmas. Optical emission spectroscopy (OES) is
comparatively simple, versatile, non-intrusive, andhas been widely used in diagnostics for various
plasmas such as magnetically confined fusion
plasma, gas discharge low-temperature capacitively
coupled plasma (CCP), and inductively coupledplasma (ICP). OES determines plasma parameterssuch as electron temperature and density by a
combination with population kinetics modeling.
We have carried out OES and collisionalradiative modeling (CRM) taking into account all
viable collisional and radiative processes of atoms
and ions in plasma [1] for CCP and ICP systems. A
sketch of the experiment setup is shown in Fig. 1.
In present CRM, populations (ni) of the i levels
are obtained by solving the stationary rate balance
equations:Fig. 1. Sketch of the experimental setup.

   D  ¦ K  h
¦
 
 
z

!

¦  D  ¦ K h  D¡   Q S
 z

 

where  is the volume averaged electron density,
D is the electron impact excitation/deexcitation

rate coefficient from ith level to jth level, D¡ is theelectron impact ionization rate coefficient for ith
level, h and K are transition probabilities(Einstein’s A coefficient) and escape factor for
optical transition, from Q is the quenchingprobability per unit time by diffusion to chamber
walls.
Fig. 2 shows the CRM results for our measured
spectra in the CCP. When Te and ne by the probe
measurement is used in the CRM with the effective
plasma length Reff assumed as the chamber radius,
the modeled spectra shows large discrepancy withthe measured spectra shown in Fig. 2 (a) and (c).
When reduced Reff is used in the CRM, theagreement between the measured and the modeled
spectra is improved as shown in Fig. 2 (a) and (d).

1Fig. 2. (a) Measured spectra and (b) electron temperatureand density from our CCP. (c) Our CRM spectra for
Te=3.28 eV and ne=3.62u109 cm-3 determined fromprobe measurement for effective plasma length R eff
assumed as chamber radius R=3.0 cm. (d) Our CRM
spectra for Te=3.28 eV, ne=3.62u109 cm-3 (red line) and
Te=5.0 eV, ne=1.0u109 cm-3 (green line) with Reff =1.0cm.
References[1] S. Iordanova, I. Koleva, 2007 Spectrochimica Acta
Part B 62 344.

E-mail: hkwon@kaeri.re.kr

75

Estimation of photon emission coefficients in tungsten UTA transitions
using LHD plasmas
Shigeru MORITA*,†,1, Yang LIU†,2, Izumi MURAKAMI*,,†,3, Tetsutaro OISHI*,,†,4and Motoshi GOTO*,,†,5*†National Institute for Fusion Science, Toki 509-5292, Gifu, Japan
Department of Fusion Science, School of Physical Sciences, The Graduate University for Advanced Studies(SOKENDAI), Toki 509-5292, Gifu, Japanabundance in ionization equilibrium calculatedwith ADAS code [4].
The value of nW
evaluated from the present CR model seems to
be large, when it is compared with n W estimatedfrom the number of tungsten particles injectedby the pellet. Discussions are made with the n W
evaluated from the photon emission coefficientin CL version of ADAS code.

Tungsten pseudo-continuum spectra called
unresolved transition array (UTA) emitted in
15-70Å have been quantitatively analyzed byobserving the radial profile in neutral-beamheated plasmas of Large Helical Device (LHD).
In our previous result [1], it has been found that
the UTA line at wavelength intervals of 32.1633.32, 30.69-31.71 and 29.47-30.47 Å iscomposed of only a single ionization stage ofW24+, W25+ and W26+, respectively. Based on
the previous result, the ion density of W24+,
W25+ and W26+ is evaluated by observing theradial profile of UTA lines at the specified
wavelength intervals [2].
A photon emission coefficient (PEC) for theW24+, W25+ and W26+ ions is necessary for thedensity evaluation.
At first, the PEC iscalculated using a collisional-radiative (CR)model which has been developed by Murakami[3]. In the CR model, principal quantum
number up to n = 7 and 11753, 13772 and 7515
J-resolved fine-structure levels are taken into
account for W24+, W 25+ and W26+ ions,
respectively, and 19-27 electron configurations
are considered for one ion. Effects of innershell excitation and configuration interaction
are also considered in addition to generalatomic processes.
The photo emission
coefficient at each wavelength interval thenincludes 100 thousands line emissions at eachwavelength interval.
The tungsten density
profile of W24+, W25+ and W26+ ions is thus
obtained from the local emissivity profile andthe photon emission coefficient in addition to
the temperature and density profiles.
A total tungsten ion density, nW, near ρ = 0.7
where the W24+ ion locates is also estimatedfrom the W24+ ion density with the fractional

Fig. 1. Photo emission coefficients from (a) CR model[3] and ADAS (CL version) [4].

References[1] Y. Liu, S. Morita, X.L. Huang, T. Oishi, M. Gotoand H.M. Zhang, 2017 J. Appl. Phys. 122 233301.
[2] Y. Liu, S. Morita, I. Murakami, T. Oishi, M.
Goto and X.L. Huang, submitted to Jpn. J. Appl.
Phys.
[3] I. Murakami, H.A. Sakaue, C. Suzuki, et al.,2015 Nucl. Fusion 55 093016.
[4] H.P. Summers, The ADAS User Manual, version
2.6 http://www.adas.ac.uk (2004).
1

E-mail: morita@nifs.ac.jp
E-mail: liu.yang@nifs.ac.jp
3E-mail: murakami.izumi@nifs.ac.jp
4E-mail: oishi@nifs.ac.jp
5E-mail: goto@nifs.ac.jp
276Experimental evaluation of fractional abundance data for
W23+ − W28+
Keisuke Fujii∗, 1∗

Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University,
Kyoto 615-8540, Japan

calculation by Sasaki et al [2].

The tungsten (W) density in plasmas has
been estimated from the line emission intensityfrom a certain charge state (q) ions and the fractional abundance for this charge state ξq (Te ). Although ξq (Te ) is an essential quantity to the tungsten density measurement in plasmas, its values
reported by sevral groups have been signiﬁcantly
diﬀerent from each other, as shown in Fig. 1.
In this work, we observed Te dependenceof near-ultraviolet emission line intensities forhighly charged tungsten ions for several plasma
experiments in Large Helical Device (LHD) [1].
From the spatially resolved emission intensity
distribution measured with multi-line-of-sight
spectrometer and with the Bayesian statistics
technique, we quantitatively evaluated the fractional abundance proﬁles for W23+ W28+ .

Fig. 1. Fractional abundance data xq for highly
charged tungsten ions. The four panels from the
top show the data sets proposed by Asmussen et al[4], Pütterich et al [3], Sasaki et al [2], and evaluated results in this work, respectively.

Although the absolute values of the fractional
abundance are still inaccessible in our method,
relative proﬁles against Te values were evaluated,
as shown in the bottom row in Fig. 1. The Te
values at the proﬁle peak for q = 23, 24, 25, 26,
27 and 28 states tungsten abundance were evaluated as 0.53, 0.58, 0.65, 0.78, 0.93, and 1.14
keV, respectively (indicated by the vertical arrows in Fig. 1). These results were ≈20% smaller
than those reported by Pütterich et al [3], which
are the theoretical calculations adjusted to match
the quasi-continuum emission by q = 24-35 tungsten ions measured in the extreme ultraviolet region, and ≈60% larger than the pure theoretical

1

References[1] K. Fujii, D. Kato et al., 2017. J. Phys. B: At.
Mol. Opt. Phys 50, 055004[2] A. Sasaki and I. Murakami, 2013. J. Phys. B: At.
Mol. Opt. Phys 46, 175701[3] T. Ptterich, R. Neu et al., 2008.Plasma Phys.
Control. Fusion 50, 085016[4] K. Asmussen, K. Fournier, et al., 1998. Nucl. Fusion 38, 967

E-mail: fujii@me.kyoto-u.ac.jp

77

Estimating the emission spectra of W23+- W30+ by the numerical decompositionof multiple spectra observed from LHD plasmas
Takehiko Esaka*,1, Izumi Murakami†,2, Shigeru Morita†,3, Hasuo Masahiro*,4, Keisuke Fujii*,5*Graduate School of Engineering Kyoto University, Kyoto Nishikyo-ku, Kyoto, 615-8246, Japan†
National Institute for Fusion Science, Toki, Gifu 509-5292, Japan

3. Results and Discussion
Figure 2 (a) shows three of the decomposed resultsof ߶௤ǡ௠ (q = 26, 27 and 28, red curves). Although the୰ୣ୤overall shapes of ߶௤ǡ௠ and ߶௤ǡ௠are similar to eachother, their detailed shapes are different. In Fig. 2 (b),our reconstructed result σ௤ ݊௤ሺ௞ሻ ߶௤ǡ௠ is also shown(red curve). It is suggested that the use of ߶௤ǡ௠୰ୣ୤increases the accuracy of the density
instead of ߶௤ǡ௠
estimation.

1. Introduction
Tungsten (W) was decided to be used as a divertor
material of ITER. To monitor W transport in hightemperature plasmas, spectroscopic observation has
been conducted. Figure 1 shows two W spectra ‫ݕ‬௠measured for LHD plasmas in different two
conditions. m is an index along wavelength direction.
Each spectrum is modeled as follows.
‫ݕ‬௠ ൌ σ௤ ݊௤ ߶௤ǡ௠ ൅ ߝ(1)௤ା
where ݊௤ is the density of  , ߶௤ǡ௠ is its emission
spectrum and ߝ is the noise of the measurement. If
the exact profiles ߶௤ǡ௠ are known, the evaluation of݊௤ is possible. Blue curves in Fig. 2 (a) show three୰ୣ୤
results ߶௤ǡ௠(q = 26, 27 and 28) from one atomic
structure model [1, 2]. ݊௤ has been estimated to
optimize the following equation.
୰ୣ୤௡೜ σ௠ ‫ܦ‬ሺ‫ݕ‬௠ ȁ σ௤ ݊௤ ߶௤ǡ௠ሻ (2)where ‫ܦ‬ሺܽȁܾሻ is a distance measure between a and b.
The squared distance ሺܽ െ ܾሻଶ has been frequently
used. Blue curves in Fig. 2 (b) shows the୰ୣ୤reconstructed result σ௤ ݊௤ ߶௤ǡ௠with the best ݊௤ ,௤ାwhere  (q = 23-30) is assumed to be included inplasmas. As shown in the figure, it is still difficult toreconstruct the experimental data exact enough.
In this work, we evaluate both ߶௤ǡ௠ and ݊௤ bydecomposing the observed spectra based on its
profile variation, considering theoretically predicted
spectra.

Fig. 1 Two examples of the observed W spectra.

2. Method
We use multiple spectra ‫ݕ‬୫ሺ௞ሻ observed with various
experimental conditions, where k = (1, 2, …, 4580)
is the experimental data index. We estimate bothሺ௞ሻ߶௤ǡ௠ and ݊௤ from the following optimization
problem௡ሺೖሻǡథ
೜

೜ǡ೘

ሺ௞ሻ

୰ୣ୤
Fig. 2 (a) Three examples of ߶௤ǡ௠(blue curve) anddecomposed ߶௤ǡ௠ (red curve) for q = 26, 27, and 28.
(b) One example of the observed spectrum ‫ݕ‬௠ ሺ௞ሻ(markers), reconstruction from the atomic structure୰ୣ୤
calculation ߶௤ǡ௠ (blue curve) and that from ourdecomposition (red curve).

ሺ௞ሻቄσ௞ ‫ܦ‬൫‫ݕ‬௠ ȁσ௤ ݊௤ ߶௤ǡ௠ ൯ ൅(3)
The first term represents the goodness ofreconstruction, while the second term represents the୰ୣ୤closeness between ߶௤ǡ௠ to be estimated and ߶௤ǡ௠.ߙ
controls the relative importance of the second term.
We use 250 for ߙ . In this work, we use KullbackLeibler divergence for D. Since Eq. 3 has the same
form to the non-negative matrix factorization (NMF)
problem, it is optimized efficiently [3].
୰ୣ୤ߙ σ௤ǡ௠ ‫ܦ‬൫߶௤ǡ௠ȁ߶௤ǡ௠ ൯ቅ

1

References[1] I. Murakami, et al. , 2015, Nucl. Fusion, vol. 55,
093016.
[2] A. Bar-Shalom, et al. ,2001, J. Quant. Spectrosc.
Radiat. Transfer, vol. 71, pp. 169-188.
[3] D. Lee and H. Seung, 2000, Neural Information
Processing Systems (NIPS), pp. 556-562.

E-mail: esaka.takehiko.86a@st.kyoto-u.ac.jp

2E-mail: mizumi@nifs.ac.jp

3E-mail: morita@nifs.ac.jp

784E-mail: hasuo.masahiro.6u@kues.kyoto-u.ac.jp

5E-mail: fujii@me.kyoto-u.ac.jp

Estimation of density profiles of W43+-W45+ in EAST H-mode plasma
Ling. Zhang*,1, Shigeru Morita†‡,2, Zhenwei Wu*,3, Zong Xu§,4, Xiuda Yang*, Qing Zang*, Haiqing
Liu*, Xianzu Gong*, Liqun Hu**

Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China*Institute of Plasma Physics Chinese Academy of Sciences, Hefei 230026, Anhui, China
National Institute for Fusion Science, Toki 509-5292, Gifu, Japan‡
Department of Fusion Science, Graduate University for Advanced Studies, Toki 509-5292, Gifu, Japan§
Advanced Energy Research Center, Shenzhen University, Shenzhen 518060, China†

EAST tokamak has been equipped withupper tungsten divertor since 2014 to improve
the heat exhaust capability and to examine the
ITER-like divertor configuration [1]. In orderto study the tungsten behavior in EAST
discharges, tungsten spectra has been measured
in EUV wavelength range using fast-timeresponse EUV spectrometers working inwavelength ranges of 20-500Å [2] and 10-130
Å with time resolution of 5ms. Recently, aspace-resolved EUV spectrometer working at
30-500Å has been developed to measure radial
profiles of the tungsten line emission in longpulse H-mode discharges with high heating
power.
Radial profiles of tungsten emissions from
4p-4s and 4p-4p transitions in W42+ – W45+ ions
are successfully obtained at 45-70 Å and 120140 Å in high-temperature discharges(Tet2.5keV), e.g. W43+ at 61.334Å, W44+ at
60.93Å, W45+ at 62.336 Å, W42+ at 129.41Å,W43+ at 126.29 Å and W45+ at 126.998Å. The
radial density profiles of W 43+ – W45+ are
therefore attempted with measured Te and ne
profiles and photon emissivity coefficient (PEC)
from ADAS database when the radial emission
profile is converted into flux surface function
with Abel inversion technique.
Fig.1. shows radial profiles of chordintegrated line intensity of W 45+ at 62.336Å,W44+ at 60.93Å and W43+ at 61.334 Å in steadystate H-mode plasma with Te0=3.3keV (Shot#67682). Fig.2. shows the calculated radial
profiles of W45+ and W44+ ion density in steadystate H-mode phase in Shot #67682.

Fig. 1. Vertical profile of W line intensity.

Fig. 2. Radial profile of W ion density.

References[1] D. Yao, G. Luo, S. Du et al., 2015 Fusion Eng.

Des. 98-99 1692.
[2] L. Zhang, S. Morita, Z. Xu et al., 2015 Rev.
Sci. Instrum. 86 123509.
1

E-mail: zhangling@ipp.ac.cn

32E-mail: morita@nifs.ac.jp

479E-mail: zwwu@ipp.ac.cn
E-mail: xuzong@ipp.ac.cn

Radiation Hydrodynamic Characteristics of Highly Charged
Ions in Laser-Produced Plasmas
Maogen Su*,1, Qi Min*, Shiquan Cao*, Duixiong Sun*, G. O'Sullivan†, Chenzhong Dong**

Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China
ЪSchool of Physics, University College Dublin, Belfield, Dublin 4, Ireland

we developed a dynamic simulation code toinvestigate the complicated spectral features ofhighly-charged ions from LPP. The evolution
diagnosis
ofelectrondensity,plasmatemperature, ion velocity, radiation loss andother parameters in the process of laser plasma
expansion are obtained, and the transient
evolution images of the plasma arereconstructed. The results are helpful for a
detailed understanding of the spectral featuresand hydrodynamics evolution for highly
charged ions of the mid- and high-Z elements.
More importantly, it will be of use to groups
working on ion and light source development.

A laser-produced plasma (LPP) ablated bynanosecond laser pulse is neither homogeneous
nor static in the expanding and cooling process
in vacuum, where electron densities can varyfrom 1017 to 1022 cm-3 and electron temperaturefrom 1 eV to 100 eV. In such plasmas, there aremany competing atomic processes which
depend on electron temperature and electron
density. Electrons, ions and photons take part inthese processes and interact with each other.
The experimental measurements and theoreticalanalysis of LPP spectra can reveal abundant
information on the plasmas, such as electron
temperature, electron/ion density, particle andenergy transport, and the evolution of theseparameters. In recent decades the LPP has
gained universal acceptance as a standard
laboratory ion source1 and pulsed shortwavelength light source2.
Due to the limitation of measurement
accuracy, spectral structure and plasma model,
there are few reports on the radiation anddynamics of highly-charged ions in the EUV
region of mid- and high-Z elements, thedynamics behaviors in the plasma is not yet
clear. Our group built a high precision spatiotemporally resolved spectral measuring device,developed a set of real-time measurement
control and spectral analysis software. And
based on the radiative-hydrodynamics model,
1This work was supported by National Key ResearchandDevelopment
Programof
China(2017YFA0402300); National Natural Science
Foundation of China (NSFC) (11274254,
U1332206, 11364037, 11064012, 11564037).
References[1] N. J. Peacock, and R. S. Pease, 1969 J. Phys. D:
Appl. Phys. 2 1705.
[2] D. T. Attwood, Soft X-Rays and Extreme
Ultraviolet Radiation (Cambridge University Press,
Cambridge, 2000)

E-mail: nwnu_sumg@163.com

80Ultrafast nonequilibrium electron dynamics in a solid-density aluminium
interacting with an ultra-intense ultrafast x-ray pulse
Cheng Gao*,1, Jiaolong Zeng*, and Jianmin Yuan*#*

Department of Physics, College of Liberal Arts and Sciences, National University of Defense Technology, Changsha
410073, Hunan, P. R. China# Graduate School, China Academy of Engineering Physics, Building 9, ZPark II, No. 10 Xiebeiwang Road, Beijing
100193, P. R. China

1600, (c) 1750 and (d) 1830 eV, respectively.
The x-ray pulse has a peak intensity of

The investigation of light-matter interaction is
expanding from long wavelength into shortwavelength with applications of x-ray freeelectron laser (XFEL)[1-2]. Followed by thepioneering experiment of an ultra-intense XFEL
pulse interacting with a neon atom gas [3],many researches are performed to investigate
the interaction of XFEL and complex systems[4-5].澳
Ultrafast nonequilibrium dynamics of freeelectrons in a solid-density aluminium produced
by an ultra-intense ultrafast x-ray pulse isinvestigated by solving Fokker-Planck equation.
Electron energy distribution function (EEDF)
contains two parts: a lower energy part at nearly
equilibrium and a higher energy part at evident
nonequilibrium. The former part accounts forthe most population of the total electron number.
X-ray transmission and bound-bound emissivity
show little difference between the results with
EEDF obtained by solving Fokker-Planck
equation and by Maxwellian distribution
assumption. Yet the bremsstrahlung emissivity
shows great difference.

 u :  FP  with HWHM duration of
40 fs and a bandwidth of 0.5%. The x-ray beam
has a circle spot with radial of 1.3 um.
References[1] P. Emma et al., Nat. Photon. 4, 641 (2010).
[2] C. Bostedt et al., Rev. Mod. Phys. 88, 015007(2016).
[3] L. Young et al., Nature (London) 466, 56 (2010).
[4] S.M. Vinko et al, Nature (London) 482, 59(2012).
[5] H. Yoneda et al., Nat. Commun. 5, 5080 (2014).澳

1

Fig. 1. Time evolution of EEDF at the center ofthe laser spot on the front of aluminium sample(x=0 um). X-ray photon energy is (a) 1550, (b)81E-mail: gaocheng@nudt.edu.cn

Temporal space localization of electrons ejected from continuum atomic
processes in hot dense plasma
Pengfei Liu1, Cheng Gao1, Yong Hou1, Jiaolong Zeng*1, and Jianmin Yuan†,1,2
1

Department of Physics, National University of Defense Technology, Changsha Hunan 410073, China
2
Graduate school of China Academy of engineering Physics, Beijing 100193, China

Continuum atomic processes initiated byphotons and electrons occurring in a plasma are
fundamental in plasma physics, playing a keyrole in the determination of ionization balance,
equation of state, and opacity. Here we propose
the notion of a temporal space localization ofelectrons produced during the ionization of
atoms immersed in a hot dense plasma, which
can significantly modify the fundamental
properties of ionization processes. A theoreticalformalism is developed to study the
wavefunctions of the continuum electrons thattakes into consideration the quantum decoherence caused by coupling with the plasma
environment. The method is applied to thephotoionization of Fe16+ embedded in hot dense
plasmas. We find that the cross section isconsiderably enhanced compared with thepredictions of the existing free-atom model, andthereby partly explains the big difference
between the measured opacity of Fe plasma [1]and the existing standard models for shortwavelengths.
Striking changes induced by localization
may further be seen in the total photoionization
cross sections of the ground and excited levelsof Fe16+ (Fig.1). In panel (a), both contributions
from the direct ionization of 2p and 2s electrons
and indirect ionization from the resonant
processes have been included to give a more
complete picture. The cross section of the free
ion features a series of resonances 2s o np (nt6)superimposed on the continuum background.
The cross section of free ion is in satisfactory
agreement with a recent large-scale R-matrix
calculation[2]. For the embedded ion, however,resonances of higher np disappear for the
principal quantum number n larger than 10, 7,
and 6 at densities of 4.0h1021, 4.0h 1022, and
2.0h1023cm-3,respectively. However, additional
resonances of 2so5p and 2so4p successively
show up at the density of 4.0h1022 and
2.0h1023cm-3. This shows that the bound states
belonging to the configurations of 1s22s2p65p
and 1s22s2p64p in the free ion Fe16+ have
* E-mail: jlzeng@nudt.edu.cn
E-mail: jmyuan@gscaep.ac.cn

become autoionized states because of plasma
screening.

Fig. 1. Total photoionization cross sections.(a) For the
ground level 1s22s22p6 1S of Fe16+ including both direct
ionization of 2p and 2s electrons and indirect resonant
processes at 180.0 eV.(b) For the excited state
1s22s22p53d 1Po of Fe16+, which is assumed to beembedded in an iron plasma at an electron density of
3.0h1022cm-3 and a temperature of 180.0 eV.

References[1]J. E. Bailey et al., A higher-than-predictedmeasurement of iron opacity at solar interiortemperatures. Nature (London) 517, 56 (2015).
[2]S. N. Nahar and A. K. Pradhan, Largeenhancement in high-energy photoionization of Fe
XVII and missing continuum plasma opacity. Phys.
Rev.Lett.116,235003(2016)†82

A consideration on the accuracy of GRASP calculations
Fumihiro Koike,
Faculty of Science and Technology, Sophia University

Accurate and reliable calculations of atomic structures and transition properties areindispensable for understandings of fusion and other plasmas. As for the theoretical methods
based on the variational principle, a number of atomic codes such as FAC, HULLAC, Cowans
code, GRASP family of codes, and others are available for this purpose. Among them the
GRASP family of codes provides us with a non-empirical relativistic method and is believedthat the code gives most reliable result if treated properly. In recent years, an elaborate large
scale calculation has become feasible using the pararrell processing technology and has becomea large amount of numerical values that are usable for plasma analysis.
However, we must note that the theoretical method that is employed by GRASP family ofcodes has its intrinsic difficulties. The method is based on a variational principle with apositive indefinite Hamiltonian, we cannot avoid the possibility of variational collapse in theprocedure of self-consistent iteration. And, furthermore, in case of excited state calculations,similar collapse may occur. The orbital wavefunctions are restricted to the L2 normalizable
functions, which cause the introduction of correlation functions in the MCDF calculations. We
must be careful to treat the correlation functions if we want to calculate the atomic excitedstates.
We want to discuss these difficulties by showing several examples that may cause someerrors in MCDF calculations.
Email: koikef@sophia.ac.jp83Visible spectra of multiply charged heavy ionsobtained with a comapct electron beam ion trap
NAKAMURA Nobuyuki∗, 1 ,∗Inst. for Laser Science, The Univ. of Electro-Communications, Tokyo 182-8585, Japan

Visible transitions in multiply charged heavy
ions are of interest for many applications. For
example, transitions in multiply charged W ions
are in strong demand for the stable operation of
the large scale fusion reactor ITER under construction. Since W is the material of the plasma
facing wall of ITER, sputtered W ions are considered to be the main impurity in the ITER
plasma [1]. Thus it is important to diagnoseand control the W inﬂux and charge evolution
through spectroscopic diagnostics of W ions. Although all the wavelength ranges, including shortwavelength ranges such as EUV and x-rays, areimportant for the diagnostics, transitions in thevisible range are especially important due to theadvantage that a variety of common optical components, such as mirrors, lenses, and ﬁber optics,
can be applied.
As another example, optical transitions in
multiply charged ions have been proposed for a
new type of an optical clock that has a signiﬁcantly enhanced sensitivity to the ﬁne-structure
constant variation due to the strong relativistic
eﬀects [2]. The variation of fundamental constants arises in many theories beyond the Standard Model of particle physics and is hinted by
the astrophysical observations. Recently, it wassuggested that dark matter may lead to oscillations of fundamental constants or transient effects that may be potentially detectable withsuch clocks [3]. It is also an advantage that the
wavefunction of the electron tightly bound in ahighly charged ion is less sensitive to the perturbation such as external ﬁelds.
In this contribution, we present visible spectra of multiply charged ions relevant to suchapplications obtained with a compact electron
beam ion trap, called CoBIT [4]. CoBIT consistsof an electron gun, a drift tube (DT), an electron

1

collector, and a high-critical-temperature superconducting magnet. The DT is composed ofthree successive cylindrical electrodes that act as
an ion trap by applying a positive trapping potential at both ends with respect to the middle
electrode. The electron beam emitted from theelectron gun is accelerated towards the DT while
it is compressed by the axial magnetic ﬁeld produced by the magnet surrounding the DT. The
space charge potential of the compressed highdensity electron beam acts as a radial trap in
combination with the axial magnetic ﬁeld. Multiply charged ions are produced through the successive ionization of the trapped ions. A commercial Czerny-Turner type of visible spectrometer is used for observing Visible emission fromthe trapped ions. The charge state of the ion assigned to the observed lines can be determined
experimentally by studying the electron energy
dependence of the line intensity. Recent results
for tungsten [5] and lanthanide ions [6] and comparisons with theoretical calculations are presented.
References[1] C. H. Skinner, 2008 Can. J. Phys. 86 285.
[2] J. C. Berengut, V. A. Dzuba, and V. V. Flambaum, 2010 Phys. Rev. Lett. 105 120801.
[3] A. Derevianko and M. Pospelov, 2014 Nature
Phys. 10 933.
[4] N. Nakamura, H. Kikuchi, H. A. Sakaue, T.
Watanabe, 2008 Rev. Sci. Instrum. 79 063104.
[5] M. Mita, H. A. Sakaue, D. Kato, I. Murakami,
N. Nakamura, 2017 Atoms 5 13.
[6] S. Murata, T. Nakajima, M. S. Safronova, U. I.
Safronova, N. Nakamura, 2017 Phys. Rev. A 96
062506.

E-mail: n nakamu@ils.uec.ac.jp84Experimental studies on the atomic processes related ICF plasmas at ShanghaiEBIT
Gang Xiong*, †, 1, Zhimin Hu*, 2, Ke Yao†, Jun Xiao†, Yang Yang†, Bo Qing*, Chengwu Huang*, Jiyan
Zhang*, Yamin Zou†, Jiamin Yang**†

Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, China
Shanghai EBIT Laboratory, Institute of Modern Physics, Fudan University, and the Key Laboratory of Applied Ion
Beam Physics, Chinese Ministry of Education, Shanghai 200433, China

Atomic process is crucial for laboratory
plasma physics (Inertial confinement fusion(ICF), Tokomak, Z-pinch, etc.) and astrophysics.
Accurate understanding of the atomic processes
is important to validate the theoretical models
and promote the accuracy of the plasma
diagnostics. In recent years, we resumed
experimental measurements at the updated
Shanghai-EBIT facility focusing on theimportant atomic processes related to ICF
plasmas. The measurements include the open-Lshell dielectronic recombination of argon ions,the open-M shell electron impact excitation and12dielectronic recombination of xenon ions. In
this talk, we are going to report the details ofthese measurements and present the preliminary
results of theoretical analysis.
References[1] G. Xiong, J. M. Yang, J. Y. Zhang et al., 2016
The Astrophysical Journal 816, 36.
[2] G. Xiong, J. Y. Zhang, Z. M. Hu et al., 2013
Phys. Rev. A, 88, 42704[3] Z. M. Hu, X. Y. Han, Y. M. Li et al., 2012 Phys.
Rev. Lett. 108, 73002

E-mail: gangxiong@caep.cn
E-mail: Zhimin.Hu@yahoo.com

85

State-Selective Quantum Interference Studied in the
Photo-Recombination of Ar17+
Kun Ma∗, 1 , Lu-You Xie† ,Xiao-Bin Ding† ,Chen-Zhong Dong† , Hai-Jiang Lv∗ , Feng-Jian
Jiang∗ ,and Zheng Jiao∗∗†

School of Information Engineering, Huangshan University, Huangshan 245041, China
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

imental dielectron recombination (DR) cross section, good agreement is found between available
experimental DR cross section and the present
DR calculate results with FWHM=19eV. Meanwhile, it is found photo-recombination results are
diﬀerent with DR which derived from interference between DR and PC process.

Photo-recombination (PR) is a important
atomic process in many high temperature plasmas. It not only helps to probe quantum electrodynamics in the strong ﬁelds of the ions fromthe energy positions and shapes of the observed
resonance structure, but also reveals the relativistic corrections to the electron-electron interaction from the intensities of the PR cross section. Apart from its fundamental importance,
PR process has practical implications in manyhigh temperature plasmas, PR generates characteristic x-ray lines observed in many high temperature plasmas, such as solar ﬂares, tokamaks] andinertial conﬁnement fusion plasmas, accurate PR
cross sections are essential for plasma diagnostics
and for modeling of astrophysical and laboratory
plasmas. Recently experimental measurements
and theoretical calculation of PR cross sections for few-electron highly charged ions have been
performed.

1E-3

Cross section (Mb)

10
0.300

2s2p 1P1
2p2 1D2

DARC-PR
2p2 1S0(a)2p2 3P2

DARC-PR (Convolved)

2s2p 3P0,1,2(b)2s2p 1P1+2p2 1D2

2p2 3P0

2s2 1S0

2p2 1D2

FWHM=1eV
2p2 1S0
MCDF-DR (Convolved)
FWHM=1eV

0.15
0.00

2p2 3P0,1,2

2s2 1S020(c)2s2 1S02s2p 3P0,1,2

2p2 3P2

2p2 1S0
MCDF-DR (Convolved)
DARC-PC (Convolved)
Exp.

*0.01

0.02

FWHM=19eV

(d)

0.00
2250

2265

2280

2295

2310

Energy energy (eV)

2325

2340

Fig. 1. (a) The total PC cross section of Ar18+ ion
calculated by R-matrix approach; (b) Convoluted
the data of (a) with FWHM =1 eV (c) Convoluted
the DR cross section of Ar18+ ion calculated by MCDF approach with FWHM =1 eV; (d) Convoluted
the data of (a) with FWHM =19 eV and compare
to the experimental results[1] .

In the present work, the total and partial cross sections of the state-selective photorecombination from the ground state 1s (1 S0 ) of
H-like Ar17+ ion to the 1s2 (1 S0 ), 1s2s (1 S0 ,3 S1 )and 1s2p (3 P0,1,2 ,1 P1 ) states of He-like Ar16+ ion
were calculated in detail by using the Dirac atomic R-matrxi code based on a fully relativistic Rmatrix method. The KLL photo-recombination
resonance group are determined and identiﬁedaccording to the calculated transition energies
and probabilities with multi-conﬁguration Dirac
Fock method (MCDF). In the calculations, thequantum interference of direct recombination
and resonant recombination process are well considered. The results indicate that interference
eﬀects strongly inﬂuence the intensity and shapeof the photo-recombination cross sections, especially for the 2s2p (1 P1 ) and 2p2 (1 D2 ) resonant
region. The KLL dielectron recombination crosssections of H-like Ar17+ ion also calculated withMCDF method, results compare with the present
photo-recombination cross section and the exper1

2s2p 3P0,1,2

10
0.1This work was supported by the Natural Science Foundation of Anhui Province (Grant No.
1808085QA22), by the Key Project for Young
Talents in College of Anhui Province (Grant No.
gxyqZD2016301), by Natural Science Foundationof the Higher Education Institutions of Anhui
Province (Grant No. KJHS2015B01), and by the
Natural Science Research Project of Huangshan
University (Grant No. 2016xskq003).
References[1] D. R. DeWitt, D. Schneider, M. W. Clark, M.
H. Chen, D. Church, 1991 Rhy. Rev. A
44 7185.

E-mail: makun0602@163.com

86

(IIHFW RI %UHLW LQWHUDFWLRQ RQ OLQHDU SRODUL]DWLRQ RI UDGLDWLRQ OLQHV IROORZLQJ
HOHFWURQLPSDFW H[FLWDWLRQ RI &D ;H DQG :
& 5HQ = : :X - -LDQJ / < ;LH ' + =KDQJ DQG & = 'RQJ
.H\ ODERUDWRU\ RI $WRPLF DQG 0ROHFXODU 3K\VLFV )XQFWLRQDO 0DWHULDOV RI *DQVX 3URYLQFH &ROOHJH RI 3K\VLFV DQG(OHFWURQLF (QJLQHHULQJ 1RUWKZHVW 1RUPDO 8QLYHUVLW\ /DQ]KRX  &KLQD

5HFHQWO\ -|UJ HW DO >@ PHDVXUHG WKH OLQHDU
SRODUL]DWLRQ RI [UD\V SURGXFHG E\ GLHOHFWURQLF
UHFRPELQDWLRQ RI KLJKO\ FKDUJHG ;H LRQV WKH\
IRXQG WKDW WKH %UHLW LQWHUDFWLRQ KDYH QR HIIHFWV RQ LW,Q RUGHU WR WHVW WKH HIIHFWV RI WKH %UHLW LQWHUDFWLRQ RQ
WKH VDPH [UD\ OLQHV WUDQVLWLRQV EXW IRUPHG IURP WKH
HOHFWURQLPSDFW H[FLWDWLRQ (,( SURFHVV WKH OLQHDU
SRODUL]DWLRQ RI WKH SĺV DQG SĺV HPLVVLRQOLQHV RI KLJKO\ FKDUJHG &D ;H DQG : LRQV
DUH LQYHVWLJDWHG E\ XVLQJ D IXOO\ UHODWLYLVWLF
GLVWRUWHGZDYH SURJUDP 5(,( >@ ,Q WKH SUHVHQWZRUN ZH IRXQG WKDW WKH %UHLW LQWHUDFWLRQ PDNHV WKH
HPLVVLRQ OLQHV FRUUHVSRQGLQJ WR WKH SĺV
WUDQVLWLRQ GHSRODUL]HG ZKLOH LW PDNHV WKH RQHVFRUUHVSRQGLQJ WR WKH SĺV WUDQVLWLRQ PRUHSRODUL]HG 7KH KLJKHU DWRPLF QXPEHU LV WKH PRUH
HYLGHQW WKLV FKDUDFWHULVWLFV EHFRPH 7KHVHFKDUDFWHULVWLFV DUH GLIIHUHQW IURP WKH UHVXOWVREWDLQHG E\ -|UJ HW DO >@ $GPLWWHGO\ 6XFK DGLIIHUHQFH LV FDXVHG E\ GLIIHUHQW SRSXODWLRQPHFKDQLVPV RI WKH H[FLWHG VWDWHV DV ZHOO GLVFXVVHG
LQ 5HI >@
)LJXUH  VKRZV WKH GHJUHH RI OLQHDU SRODUL]DWLRQRI WKH HPLVVLRQ OLQH SĺV RI KLJKO\ FKDUJHG
ERURQOLNH &D ;H DQG : LRQV 11 GHQRWHVWKDW ERWK WKH WDUJHW ZDYH IXQFWLRQV DQG LPSDFWPDWUL[ HOHPHQWV DUH FDOFXODWHG ZLWKRXW WKH %UHLW
LQWHUDFWLRQ LQFOXGHG %1 GHQRWHV WKH IRUPHU DUH
FDOFXODWHG ZLWK DQ LQFOXVLRQ RI WKH %UHLW LQWHUDFWLRQZKLOH WKH ODWWHU ZLWKRXW WKH %UHLW LQWHUDFWLRQLQFOXGHG %% GHQRWHV ERWK RI WKHP DUH FDOFXODWHGZLWK WKH %UHLW LQWHUDFWLRQ LQFOXGHG $V VHHQ FOHDUO\IURP WKH )LJ WKH HIIHFW RI WKH %UHLW LQWHUDFWLRQ RQ
WKH ZDYHIXQFWLRQV RI WDUJHW LRQV KDUGO\ LQIOXHQFHVWKH GHJUHHV RI OLQHDU SRODUL]DWLRQ DW DOO RI WKH
VLWXDWLRQV 7KDW LV WKH FRQWULEXWLRQ RI WKH %UHLW
LQWHUDFWLRQ WR WKH GHJUHHV RI OLQHDU SRODUL]DWLRQFRPHV GRPLQDQWO\ IURP WKH HIIHFW RI WKH %UHLW
LQWHUDFWLRQ RQ WKH (,( PDWUL[ HOHPHQWV(PDLO ]KRQJZHQZX#QZQXHGXFQ(PDLO GRQJF]#QZQXHGXFQ)LJ  7KH GHJUHH RI OLQHDU SRODUL]DWLRQ RI WKH WUDQVLWLRQ
OLQH SĺV IRU KLJKO\ FKDUJHG ERURQOLNH &D ;H
DQG : LRQV$FNQRZOHGJPHQW
7KLV ZRUN KDV EHHQ VXSSRUWHG E\ WKH 1DWLRQDO.H\ 5HVHDUFK DQG 'HYHORSPHQW 3URJUDP RI &KLQD
<)$  = : :X DFNQRZOHGJHV WKH
VXSSRUW RI WKH 6FLHQWLF 5HVHDUFK 3URJUDP RI WKH+LJKHU(GXFDWLRQ ,QVWLWXWLRQV RI *DQVX 3URYLQFH
&KLQD *UDQW 1R $ 

5HIHUHQFHV>@ + -|UJ HW DO  3K\V 5HY $  
>@ - -LDQJ HW DO  3K\V 5HY $  
>@ = : :X HW DO  3K\V 5HY $  

87

The investigation of the anomalous asymptotic behavior of electron
elastic scattering of helium
Ya-Wei Liu 1 , Lin-Fan Zhu 2
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, Universityof Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science andTechnology of China, Hefei, Anhui 230026, People’s Republic of China

SPring-8 with an incident photon energy of about
10 keV and an energy resolution of about 70
meV. The present elastic squared form factors(ESFFs) ζ(q) of helium are shown in Fig. 1 along with the previous electron-scattering results[1-4] and the theoretical calculation [5].
By comparison, it is found that the discrepancies still exist for the electron elastic DCSs, evenat the impact energy of 1500 eV. Because thescattering amplitude between the incident electron and the nuclei almost oﬀsets the ﬁrst Born
scattering amplitude between the incident electrons and the target electrons, the DCSs of theelectron scattering are almost from the contributions beyond the FBA, and the contributions
are enlarged to a large extent in inverse proportion to the fourth power of the momentum transfer. This disagreements between the Born DCS
and the DCS of the electron scattering can judge
sensitively the validity condition of the FBA, especially in the small momentum transfer. The
ESFF is only from the scattering of the target
electrons in the high-resolution X-ray scattering,so it strictly test the wavefunctions in the inner
region, nearby nucleus in the position space.

For the inelastic electron scattering of atoms and molecules, a consensus has been reachedthat the ﬁrst Born approximation (FBA) is easily approached with decreasing the momentum
transfer at the same impact electron energy or increasing the impact electron energies at the same
momentum transfer. This consensus can also be
applied to the elastic electron scattering exceptthat for helium, where the measured elastic diﬀerential cross sections deviate the FBA more
severely with decreasing the squared momentum
transfer at the same impact energy. Since theanomalous phenomenon is found at 40 years ago,
it has not been explained explicitly.

4

1

(

q

)

The present result
Cann et al calcualtion
Jansen et al @ 3000eV
Jansen et al @ 2000eV
Shi et al at @ 1500eV
Jansen et al @ 1000eVBromberg et al @ 700eVBromberg et al @400eV
Kurepa et al @ 150eV
Kurepa et al @ 100eV

0.1

1References[1] J.P. Bromberg, 1974 J. Chem. Phys. 61 963.

102

q (a.u.)[2] R.H.J. Jansen, F.J. de Heer et. al., 1976 J. Phys.
B: At. Mol. Opt. Phys. 9 185.

Fig. 1. The ESFFs ζ(q) of helium.

[3] Q.C. Shi, R.F. Feng et. al., 1997 J. Phys. B: At.
Mol. Opt. Phys. 30 5479.

In the present work, the pure electronic structure of helium is determined directly for the ﬁrst
time by the high-resolution inelastic X-ray scattering at the Taiwan Beamline BL12XU of[4] M.V. Kurepa, and L. Vuskovic, 1975 J. Phys. B:
At. Mol. Opt. Phys. 8 2067.

12[5] N.M. Cann and A.J. Thakkar, 2002 J. Electron.
Relat. Phenom. 123 143.

E-mail: liuyawei@ustc.edu.cn
E-mail: lfzhu@ustc.edu.cn

88

._ M/ h_ `i2 +Q2{+B2Mib Q7 "2@HBF2 *
aX sX qM;∗ - sX sm∗ - wX EX >mM;† - qX ZX q2M† - >X "X qM;† - aX J?KQQ/† - LX
E?M† - GX CX .Qm† - aX SX S`2pH‡ - LX _X "/M2HH - aX a+?BTT2`b - sX J† - R M/ GX 6X w?m∗ k∗.2T`iK2Mi Q7 JQ/2`M S?vbB+b- lMBp2`bBiv Q7 a+B2M+2 M/ h2+?MQHQ;v Q7 *?BM- >2B72B- kjyyke- SX _X *?BM†AMbiBimi2 Q7 JQ/2`M S?vbB+b- *?BM2b2 +/2Kv Q7 a+B2M+2b- djyyyy- GMx?Qm- SX _X *?BM‡.2T`iK2Mi Q7 S?vbB+b M/ bi`QMQKv- lMBp2`bBiv Q7 G2B+2bi2`- lMBp2`bBiv _Q/- G2B+2bi2`- G1R d_>- lE
.2T`iK2Mi Q7 S?vbB+b- lMBp2`bBiv Q7 ai`i?+Hv/2- :Hb;Qr :9 yL:- lE
AX S?vbBFHBb+?2b AMbiBimi- Cmbimb@GB2#B;@lMBp2`bBi i :B2Ľ2M- j8jNk :B2bb2M- :2`KMv

SHbK Bb +QMbB/2`BM; iQ #2 i?2 KQbi #mM@
/Mi 7Q`K Q7 i?2 pBbB#H2 Kii2` BM i?2 mMBp2`b2X
h?mb- ++m`i2 2H2+i`QM@BQM `2+QK#BMiBQM `i2
+Q2{+B2Mib `2 +`m+BH 7Q` bi`QT?vbB+Bbib iQ BM@
i2`T`2i i?2 Q#b2`p2/ s@`v bT2+i`mK Q`B;BMiBM;
7`QK p`BQmb ivT2b Q7 +QbKB+ Q#D2+ib #v THbK
KQ/2HBM;X aiQ`;2 `BM; 2[mBTT2/ rBi? M 2H2+@i`QM +QQH2` Bb T`Qp2/ iQ #2 M B/2H THi7Q`Kb 7Q`
2H2+i`QM@BQM `2+QK#BMiBQM 2tT2`BK2MibX

M/ i`B2H2+i`QMB+ `2+QK#BMiBQM Uh_V `2bQMM+2b
bbQ+Bi2/ rBi? i?2 +Q`2 2t+BiiBQMb Q7 2s2 1 S0 →2s2p 3 P0,1,2 ,1 P1 M/ 2p2 3 P0,1,2 ,1 D2 ,1 S0 X 6`+@iBQMb Q7 8W BQMb i i?2 2s2p 3 P0 K2i@bi#H2 H2p2H
M/ N8W BQMb i i?2 ;`QmM/@H2p2H r2`2 +QMbB/2`2/
BM i?2 +H+mHiBQMX
6Q` i?2 TTHB+iBQM BM THbK KQ/2HBM;THbK `2+QK#BMiBQM `i2 +Q2{+B2Mib 7Q` "2@
HBF2 * r2`2 /2`Bp2/ 7`QK i?2 K2bm`2/ 2H2+i`QM@
BQM `2+QK#BMiBQM `i2 +Q2{+B2Mib M/ +QKT`2/
rBi? i?2 +H+mHi2/ `2bmHib Ub22 6B;X kVX M ;`22@
K2Mi Q7 #2ii2` i?M k8W Bb +?B2p2/ #2ir22M i?2
2tT2`BK2Mi M/ i?2 i?2Q`2iB+H +H+mHiBQM i i?2+QHHBbBQMHHv BQMBx2/ i2KT2`im`2 `M;2X

8
2.0
1.5
1.0

4

0.5

2

0.0
0.0

0.3

0.6

0.9

1.2

1.5

0
0.0

0.5

1.0

1.5

2.0

2.5

Plasma rate coefficient (10-9 cm3s-1)

Rate coefficient (10-9 cm3 s-1)

62
TR:2p2 3PJ (J=0,1,2),1D2,1S0 nl

101

2s2p P1 nl

3

2s2p PJ (J=0,1,2) nl

10

20

30

40

50

Electron-ion collision energy (eV)60

70

6B;X RX S`2b2Mi 2tT2`BK2MiH `i2 +Q2{+B2Mib
U}HH2/@+QMM2+i2/ +B`+H2bV M/ i?2 +H+mHi2/ ._ M/
h_ `i2 +Q2{+B2Mib U;`22M b?/2/ M/ #Hm2 b?/2/+m`p2VX h?2 TBMF b?/2/ +m`p2 /2MQi2b i?2 `i2 +Q@
2{+B2Mib 7Q` i?2 8W T`2Mi BQMb i i?2 K2i@bi#H2
H2p2HX

k

0.1

0.01

1E-3

1E-4
103

104

105

106

107

108

Temperature (K)

6B;X kX h?2 /2`Bp2/ THbK `i2 +Q2{+B2Mib 7`QK
i?2 2tT2`BK2MiH `2bmHi U#H+F HBM2V M/ i?2 l@hPah_l*hl_1 +H+mHiBQM U`2/ HBM2VX h?2 ;`22M/b?2/ M/ #Hm2 /Qii2/ HBM2 /2MQi2 i?2 +H+mHi2/._ M/ h_ `i2 +Q2{+B2Mib- `2bT2+iBp2HvX h?2 2`@`Q` #`b /2MQi2  jyW Q7 2tT2`BK2MiH mM+2`iBMivX*H+BmK Bb QM2 Q7 i?2 KQbi #mM/Mi 2H2@
K2Mi BM i?2 bQH` bvbi2K b r2HH b BM i?2 mMB@
p2`b2X >2`2 r2 T`2b2Mi i?2 K2bm`2/ 2H2+i`QM@
BQM `2+QK#BMiBQM `i2 +Q2{+B2Mib Q7 "2@HBF2* i i?2 *a_K i i?2 AMbiBimi2 Q7 JQ/2`M
S?vbB+b #v K2Mb Q7 K2`;2/@#2K i2+?MB[m2b r2HH b i?2 i?2Q`2iB+H +H+mHiBQM rBi? l@hPah_l*hl_1 +Q/2 Ub22 6B;X RVX h?2 2tT2`B@
K2Mi rb +``B2/ Qmi bm#b2[m2MiHv iQ i?2 bm++2bb@
7mH 2H2+i`QM@BQM `2+QK#BMiBQM 2tT2`BK2Mib rBi?
GB@ M/ "2@HBF2 ` i i?2 *a_K (R- k)X h?2 K2@bm`2K2Mi +Qp2`b i?2 2M2`;v `M;2 Q7 y@8RX33 2o
BM+Hm/BM; i?2 /B2H2+i`QMB+ `2+QK#BMiBQM U._V
R

CollisionallyionizedPhotoionized1_272`2M+2b(R) wX EX >mM;- qX ZX q2M- >X "X qM; 2iX HXkyR8 S?vbB+ a`BTi hRee yR9ykj(k) wX EX >mM;- qX ZX q2M- sX sm 2iX HX- kyR3
bi`QT?vbX CX amTTHX a2`X kj8 ,kX

1@KBH, tXK!BKT+bX+X+M
1@KBH, H7x?m!mbi+X2/mX+M

89

Statistical Analysis of Hydrogen Recycling in the Peripheral Region of LHD
Takuya Osugi*,1, Masahiro Hasuo*,2, Keisuke Fujii*,3*Graduate School of Engineering, Kyoto University, Kyoto Nishikyo-ku, Kyoto 615-8246, Japan

1. Introduction
In magnetic confined fusion plasmas, it is oneof important studies to control particle recyclingat the plasma facing components for the improvement of core plasma properties. For thispurpose, it is necessary to understand the behavior of the peripheral plasma. Although simulation technique by EMC3-EIRENE code [1] hasbeen developed, it is still difficult to quantify relationship between measured data because ofhigh computational cost and many inaccessible
plasma parameters in real experiments.
In this study, we fit a statistical model to experimental data of Large Helical Device (LHD),
and quantified the relationship among multiple
measurement data. We discussed hydrogen recycling near the divertor plate based on the result.

plasmas. The sampling frequency for both measurements is 100 Hz. We assume ݅୧ୱ and ‫ܫ‬ୌ areproportional to ߁୧ and ߁ୌ , respectively, and estimated ߜ߁୧ and ߜ߁ୌ from the AC components(with the frequency larger than 15 Hz) of measured signals.
3. Discussion
Figure 1(a) shows temporal evolution of ݅୧ୱand ‫ܫ‬ୌ measured for the plasma. Fig. 1(b) and (c)show relations between the AC components of݅୧ୱ and ‫ܫ‬ୌ measured at ‫ ݐ‬ൌ ͵Ǥͺͷ̱ͶǤͳͷ and ‫ ݐ‬ൌͶǤ͹ͷ̱ͷǤͲͷ, respectively. The value of the correlation coefficient ‫ ݎ‬in Fig. 1(b) is larger thanthat in Fig. 1(c).
This difference suggests the different generation paths of the neutral hydrogen between these
two timings. At the former timing, since ߪகଶ in
Eq. (5) is smaller than ߪ୧ଶ , ߜ߁୧ in Eq. (1) becomesdominant compared with ߝ. It indicates that neutral atoms are mainly generated from the direct
recombination of ions on the divertor plate. On
the other hand, ߪகଶ is larger than ߪ୧ଶ in the latter
case, suggesting neutral atoms are dominantly
generated by another effect which has little correlation with ߁୧ .

2. Statistical ModelingLet ߁୧ be the ion particle outflux from plasma
to the divertor plate and ߁ୌ be the neutral atom
influx to the plasma. If most of neutral atoms are
generated by the recombination on the divertor
plate, ߁ୌ is expected to be proportional to ߁୧ . We
approximate this relation by the following form,(1)ߜ߁ୌ ൌ ߜ߁୧ ൅ ߝ
where ߜ߁ୌ and ߜ߁୧ are temporal changes in ߁ୌand ߁୧ during small time interval ߜ‫ݐ‬, respectively,
while ߝ approximates the remaining cause of theatom generation, e.g. thermal desorption of atoms from the plate. We further approximate ߜ߁୧and ߝ follow independent Gaussian distribution,(2)ߜ߁୧ ̱ࣨ൫Ͳǡ ߪ୧ଶ ൯(3)ߝ̱ࣨሺͲǡ ߪகଶ ሻଶଶwhere ߪ୧ and ߪக are variance of ߜ߁୧ and ߝ, respectively. With this assumption, ߜ߁ୌ and ߜ߁୧
jointly follow a multivariate Gaussian distribution,‫ ݌‬൬൤ଶߜ߁୧Ͳ ߪ൨൰ ൌ ࣨ ቆቂ ቃ ǡ ቈ ୧ଶ
ߜ߁ୌ
Ͳ ߪ୧

ߪ୧ଶ
቉ቇ
ଶ
ߪ୧ ൅ ߪகଶ

(4)

The correlation coefficient ‫ ݎ‬between ߜ߁ୌ andߜ߁୧ isߪ୧ଶ‫ݎ‬ൌඨ ଶߪ୧ ൅ ߪகଶ

Fig. 1. (a) Measurement data of ݅୧ୱ (green line) and ‫ܫ‬ୌ(blue line) in shot number 137141. (b) and (c) are scatter
diagrams of the AC components of ݅୧ୱ and ‫ܫ‬ୌ . Each variable is normalized to mean 0 and standard deviation 1.

(5)

In this work, we used measurement data of theion saturation current ݅୧ୱ on the divertor plate andthe Balmer- Ƚ emission intensity ‫ܫ‬ୌ for LHD

References[1] Y. Feng et .al, Contrib. Plasma Phys 44, 57 (2004)

1

E-mail: osugi.takuya.85u@st.kyoto-u.ac.jp
E-mail: hasuo@kues.kyoto-u.ac.jp
3E-mail: fujii@me.kyoto-u.ac.jp
290            
  !" # $  %  & ' !  ' #  '  " 
                       
   !"##!$  %&'  ()   *  * $+,,- . %

 ' 0     7   7!:     
 0   *  6       7:%          0     *  7:  7!: * ,$"D    
7: 7 * ,##D% '        78              % 1         /       ))  % 7      0   0    7% ,<> 0 '   *  * *  3*         <   <!>>        %        )))      /     0  7%
,<> 0 *  7!:67     7!:67: (**   * <  <,>>*      *  78!:  
3*  0    7%,<>%)         /   
 *            
   0   % 1    2              *         %   
0   0    *              *    3* 4, !5 0
(       * 6        * %
 78 *    *       * * 0    % )                 *%9  * 78 '     *      '          (*      % )   0 (  6       78!: *%
*    78!:     ,### ;
        0                *  4"5%) 0  0             783: <3="> 
    ' %
9           *       *   *    7  3*  *        * *    7:   7!:% 9 *   (      7    *%
?   /     /     0     0   0            3*        @ ( ( <>   /    78!:      
7:: 7!::7E <> 0            E <> 0    3*     E <> 0    *   *   %78!:7:: 7!::7<,>
78!:7: 7":7:: 7!::7%<!>
)  7% ,<>   /    6      78!:      0     ABC  * *%             )   7% ,<>    '             <  <,>>%0        0    7% ,<> 0     *  7:'  ) 
4,5F%G   %!### ""#+H%
4!5I%   %!##" $$,8$"%
4"5J% %K   %!#,"  L8%
,!",,#%
,91

J6 @'2* M* %*%           !     "# $  % "# &'   (!  )  "$ "  "* # + "* # ,   "# !  "+ # ! # - ".# .  "$ "#  ". "#  / 0#  "( '    

                    ! "#$$"%! &'   (    ! )    * (+#$$$$!     *    (  (                         ,  -'        (            .     .              (        ( -'      ,  (   *       "/   0% 123( 45  -)     .      
6/78     (   ,    7 -  ,
,  1   "/"5         -'       ,
9      /555      ,    -   ( (                    9  /7
"/"5 (       - (             (  "/ (            :;  (( (     :"; (       1         6<=>8  (              "5
"/ -,   ,      <=>
 (                -?          "/"5   (    /79   ,        ,    (        ,      -?              (    (     /7 9 * -    (    1             (    -=  D9 E( -(- ?     ,   1   <=> (        (  4-#  @-+
2- (  (        ,   (  (       - :#;
        "/"5   #  "# - )  ,             ( 0%$"$ , ,   ,    (  7  
= :A;-



















 







    













    

%"121 . /7    (     "/"5   -,3 :;)-<  - "$%A@$00"$:"; - )   - !   - 7    -   B 7-  >- >  -     7- 2  "$$%
 
A#"#@4:#;     =  C        "$$%   "A"$A#@:A;7 ) = C@@#   "A#%.
A"

92                                                  
   ! "#$%%#&  '      "     (')
      " *"  *"           " "    "  +     "                      "       " ,!    -. "    "     + "                       "           " "         "         "    +         "   "  ,      " "      " "          +   "      , /    "              '0-12,  "         ' 3   "        .1   4# ++ "-    012,
5   + 6        .$ "      "  "           "    ,     6 # 1   $  .$       .#               
 "          , 7          .-.   -.       "       (  ) +  3   
 +   "() (),5   
 +      "     " +     " *"    + 3         "    , !   "  "     +   " ()                   + 6   /..8$,9:,",
  /.8#,:1,", +      +   "       0:2,' B3C" D" ,", 93."()    3   "   
#;1   $  +         +       .-.,."() 
"()"        -.,
."() <# ",!  02,7     #%:%=>$#%
0#2?,?    #%1""#%#$#%1
0$2,@A6  #%1$%%:#>
012', ,7    #%&&$9$:
0:2,7,!   ,',"  9:%$1&5HVRQDQFH FRQWULEXWLRQ WR HOHFWURQLPSDFW H[FLWDWLRQ
UDWH FRHIILFLHQWV RI KHOLXPOLNH 6 LRQV
& 5HQ = : :X - -LDQJ DQG & = 'RQJ
.H\ ODERUDWRU\ RI $WRPLF DQG 0ROHFXODU 3K\VLFV )XQFWLRQDO 0DWHULDOV RI *DQVX 3URYLQFH &ROOHJH RI 3K\VLFV DQG(OHFWURQLF (QJLQHHULQJ 1RUWKZHVW 1RUPDO 8QLYHUVLW\ /DQ]KRX  &KLQD(OHFWURQLPSDFW H[FLWDWLRQ RI SRVLWLYH LRQVLV DQ LPSRUWDQW DWRPLF SURFHVV LQ KLJKWHPSHUDWXUH SODVPDV LW FDQ SURFHHG WKURXJKGLUHFW H[FLWDWLRQ '( FKDQQHOV RU LQGLUHFWFKDQQHOV LQYROYLQJ DXWRLRQL]LQJ UHVRQDQFHV WKDWDUH WHUPHG DV UHVRQDQFH H[FLWDWLRQ 5( > @'XH WR LWV DEXQGDQFH LQ PRVW RI DVWURSK\VLFDO
SODVPDV WKH VWUXFWXUH DQG FROOLVLRQ G\QDPLFV RIVXOIXU KDYH EHHQ ZLGHO\ VWXGLHG LQ WKH ODVW \HDUV
7KH SDUDPHWULF VWXGLHV RQ WKH DWRPLF SURFHVV RIVXOIXU DQG LWV LRQV DUH QRW RQO\ EHQHILFLDO WR
SODVPD GLDJQRVLV EXW DOVR FDQ SURYLGH HIIHFWLYH
GDWD VXSSRUW IRU DVWURSK\VLFDO DQG ODERUDWRU\
SODVPD PRGHOLQJ,Q WKH SUHVHQW ZRUN HOHFWURQLPSDFW
H[FLWDWLRQ UDWH FRHIILFLHQWV RI 6 LRQV KDYH
EHHQ VWXGLHG E\ XVLQJ D UHODWLYLVWLF IOH[LEOH
DWRPLF FRGH)$&
WKDW FDQ DFFRXQW
V\VWHPDWLFDOO\ IRU FRQILJXUDWLRQ LQWHUDFWLRQV
0RUHRYHU ZH DOVR FRQVLGHUHG WKH UHVRQDQFH
H[FLWDWLRQ FRQWULEXWLRQV WR WKH UDWH FRHIILFLHQWV,Q WDEOHZH OLVW WKH H[FLWDWLRQ HQHUJLHV LQXQLWV RI .H9 IRU WKH V H[FLWDWLRQV WR WKH V S
DQG V VXEVKHOOV RI 6 LRQV DW WKH FROOLVLRQ
HOHFWURQ HQHUJLHV a .H9

)LJ  VKRZV WKH HOHFWURQ LPSDFW H[FLWDWLRQ
UDWH FRHIILFLHQWV RI 6 LRQV LQ WKH HQHUJ\
UDQJH RI  .H9 7KH VROLG EOXH OLQH
UHSUHVHQWV WKH UHVXOW RI WKH GLUHFW H[FLWDWLRQZKLOH WKH VROLG UHG OLQH GHQRWHV WKH UHVXOWV ZLWKWKH UHVRQDQFH H[FLWDWLRQ LQFOXGHG 7KH
FRQILJXUDWLRQV VOO O V S G DQG VOOO V S G I
FRUUHVSRQG WR WKH UHVRQDQFH
H[FLWDWLRQ SURFHVVHV)LJ  $ V\QWKHVL]HG HOHFWURQLPSDFW H[FLWDWLRQ UDWHFRHIILFLHQWV WKHRUHWLFDO RI 6 LRQV ZLWK WKH '( DQG 5(
FKDQQHOV LQFOXGHG

7DEOH  ([FLWDWLRQ HQHUJLHV LQ XQLWV RI .H9 RI
6 LRQV
6+HOLNH)LQDO VWDWH([FLWDWLRQ HQHUJ\)LQDO VWDWH([FLWDWLRQ HQHUJ\VV 

VS 

VV 

VS 

VS 

VS 

VS 

VS 

VS 

VG 

VS 

VG 

VV 

VG 

VV 

VG 

$FNQRZOHGJPHQW
7KLV ZRUN KDV EHHQ VXSSRUWHG E\ WKH
1DWLRQDO .H\ 5HVHDUFK DQG 'HYHORSPHQW
3URJUDP RI &KLQD <)$  = :
:X DFNQRZOHGJHV WKH VXSSRUW RI WKH 6FLHQWLF
5HVHDUFK 3URJUDP RI WKH +LJKHU(GXFDWLRQ,QVWLWXWLRQV RI *DQVX 3URYLQFH &KLQD *UDQW
1R $ 
5HIHUHQFHV>@ &KHQ=KRQJ 'RQJ -LDQ*XR :DQJ  DQG <L=KL 4X
 &KLQ 3K\V 6RF  
>@ -XQ -LDQJ &KHQ=KRQJ 'RQJ /X<RX ;LH DQG -LDQ*XR :DQJ  3K\V 5HY $  

(PDLO ]KRQJZHQZX#QZQXHGXFQ(PDLO SK\MLDQJ#\HDKQHW(PDLO GRQJF]#QZQXHGXFQ

94

Angular distribution and polarization of x-ray radiation in highly
charged He-like ions: hyperﬁne-induced transition
Zhan-Bin Chen1,2,3 , Chen-Zhong Dong2 1
1

2School of Science, Hunan University of Technology, Zhuzhou 412007, China
Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College ofPhysics and Electronic Engineering, Northwest Normal University, Lanzhou, 730070, China
3
College of Science, National University of Defense Technology, Changsha 410073, China

Precise polarization studies not only enhancepeople, s understanding to the e-e interaction instrong Coulomb ﬁelds, but also help to deeper
elucidate the population mechanism during theimpact dynamics. While most theoretical studies regarding the polarization in the past had justdealt with ions with nuclear spin I = 0, fewer literatures had reported the eﬀect of the hyperﬁneinteraction and how the nuclear spin aﬀected thepolarization of x-ray radiation. Some kinds ofions have a nuclear spin I = 0. Owing to the hyperﬁne coupling, new decay channel will be open,
namely, hyperﬁne-induced transition.
In this study, we present a systematically theoretical investigation on the polarization and angular distribution of x-ray photoemission during the hyperﬁne-induced transition using a fully RDW method [1]. The calculations are performed for the 1s2p3/2 3 P2 F i =3/2→1s2 1 S0
F f =1/2 component of the K α1 decay of highly
charged He-like 119 Sn48+ and 207 Tl79+ ions with
nuclear spin I =1/2 following the impact excitation processes by the incident electron beams of un-polarized and completely longitudinallypolarized, respectively. Two eﬀects, Breit interaction(BI)and E 1-M 2 interference, on the polarization of the emitted radiation are discussed [2].
Our results show that both these eﬀects may signiﬁcantly aﬀect the polarization and angular emission pattern of the transition line. For thecircular polarization, the BI leads to a decreaseby about 20% for 119 Sn48+ ion and a decrease by
about 50% for 207 Tl79+ ion at 1.4X, respectively. The E 1-M 2 mixing results in a increase by
about 41% for 119 Sn48+ ion and in a reduction by
about 97% for 207 Tl79+ ion at 1.4X, respectively.
For the linear polarization, the BI leads to a increase by 15% and 21% for 207 Tl79+ ion at 1.2X
and 1.6X, respectively. The E 1-M 2 mixing reduces the linear polarization by 36% and 21% for
119 Sn48+ and 207 Tl79+ ions at 1.2X, respectively.
We hope that the present results would be useful1

in resolving some disagreement between the theories and experiments related to the polarization
properties of the x-ray radiation.

0.8
E1+M2 (C+B)
119

48+

M2 (C+B)

Circular polarization

Sn

E1+M2 (C)0.7

M2 (C)

0.6

0.5

0.4

0.3

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Incident energy (threshold units)

Fig. 1. The circular polarization of the
1s2p3/2 3 P2 F i =3/2→1s2 1 S0 F f =1/2 hyperﬁneinduced transition for He-like 119 Sn48+ ion
following longitudinally polarized EIE process as afunction of the incident energy in threshold units.
Here, C represents the values with inclusion of only
the Coulomb interaction, and C+B represents theones with the BI included; M2 represents inclusionof the magnetic-quadrupole approximation only,
E1+M2 represents values with inclusion of E1-M2
interference.

This work was supported by the National
Natural Science Foundation of China (Grant
Nos.11504421, U1332206, and 11274254) andInternational Scientiﬁc and Technological Cooperative Project of Gansu Province, China (Grant
No.1104WCGA186).

References[1] Z. B. Chen, C. Z. Dong, and J. Jiang, 2014 Phys.
Rev. A 90 022715.
[2] Z. B. Chen and C. Z. Dong, 2018 Eur. Phys. J.
D (in press)

E-mail: dongcz@nwnu.edu.cn

95Dynamics and density distribution of laser-produced Al plasmas using opticalinterferometry
S. Q. Cao, M. G. Su1, Q. Min, D. X. Sun, P. P. Ma, K. P. Wang, B. Wang, S. Q. He, L. Wu,
H. D. Lu, and C. Z. Dong 2
Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China

The dynamics and state parameter
diagnostics of laser-produced plasmas (LPP)
are very important in developing its applicationsuch as pulsed-laser deposition, extreme
ultraviolet and soft X-ray light sources, laser
ion source and laser fusion. Some techniques
have been employed for related research. Laserinterferometry is widely established in studying
the dynamic evolution and spatio-temporally
resolved density profiles of LPP, particularly
because of the highly accurate spatial andtemporal resolutions.
In this work, dynamic evolution andspatio-temporally resolved density profiles oflaser-produced Al plasmas in air atmosphere
are investigated using optical interferometry. A
series of interferograms are obtained with apulse energy of 35 mJ and delay times from
200 ns to 6.9 Ps are showed in Fig. 1. From Fig.
1, the expansion profiles of the shock wave of
Al plasmas are closed to semicircle all time,
which is different from the situation of air
plasmas in our previous work [1]. The phaseshift and refractive index are calculated using a
two-dimensional fast Fourier transformation
and Abel transformation. The electron densities
of Al plasmas are obtained from the refractive
index have been showed in Fig. 2. ,which givethe 2D expond dimensions and electron
densities distribution of Al plasmas. This work
provide a further understanding of expansion
and dynamic evolution of the laser-produced Al
plasmas and shock wave and the spatiotemporal evolution of the density of plasma in
air atmosphere.

1
2

Fig. 1. Time evolution of optical interferograms of laserproduced Al plasmas (yellow dotted line and blue shaded area
identify regions of shift in interference fringes).

Fig. 2. 2D electron densities distribution of laser-produced
Al plasmas at different delay times.

The work is supported by the National Key
Research and Development Program of China(2017YFA0402300), the Natural Science
Foundation of China (11364037,11274254,
U1332206,11564037).
References[1] S. Q. Cao, M. G. Su, C. Z. Dong et.al, 2018 Phys.
Plasmas 25 063302

E-mail: nwnu_sumg@163.com
E-mail:dongcz@nwnu.edu.cn

96Theoretical study of the dielectronic recombination process of Li-like W71+ ions
L. J. Dou*, ξ, † , L. Y. Xie†,1, Z. K. Huang *, W. Q. Wen*, C. Z. Dong †, and X. W. Ma *, 2
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, Chinaξ
University of Chinese Academy of Sciences, Beijing 100049, China†
College of Physics and Electronic Engineering, NWNU, Lanzhou, 730070, China

Plan of Northwest Normal University (No.NWNULKQN-15-3).
11

s1/2 p1/2

Rate coefficient (10-9cm3s-1)

10

l3/2

30

l5/2 l7/2 j>7/2

25

9
8
7

20

e-+W71+(2s)oW70+(2p1/219l)

6

15

5
4

10

3
2

5

1
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Resonance strength (10-18cm2eV)

Dielectronic recombination (DR) andradiative recombination (RR) spectra of highly
charged Tungsten ions are important formodeling and diagnosing magnetic fusion
plasmas[1,2]. We studied the 'n 0 DR processof Li-like W71+(2s) ions using the flexible
atomic code (FAC) based on the relativistic
configuration interaction (RCI) method [3]. The
detailed resonance energies, widths andstrengths were calculated systematically for thedominated doubly excited states (2p1/2nlj)(n=19~29) and (2p3/2n’lj) (n=7~29) of Be-like
W70+ ions, and the contributions from the higher
Rydberg states with n t 30 , are obtained byextrapolation based on the quantum defecttheory (QDT)[4].The electron-ion recombination
spectra (DR+RR), covering the center-of-massenergy range 0-1700 eV, are presented byconsidering the temperature (120 meV/kB
transverse and 0.1 meV/kB) for purpose of
future storage ring experiments. The present
results would be provide help for investigating
the storage ring DR experiments and diagnosingof ITER plasmas.
Figures 1 and 2 plotted the total rate
coefficients (DR+RR) (black line) for thelowest-energy resonance manifolds (2p1/219lj)Jof 2s-2p1/2 transitions and (2p3/27lj)J of 2s-2p3/2transitions, respectively, where the red dashedline indicate the RR background. The blue
vertical lines give the strengths for each of theindividual resonance with the right blue axis,
and the resonance positions are identified by theblack vertical bars on the top of the figure.
This work is partly supported by the National
Key R&D Program of China under grant No.
2017YFA0402300, the National Natural Science
Foundation of China through Nos. 11320101003,
11611530684, U153014,11464042 and the Strategic
Priority Research Program of the Chinese Academyof Sciences, grant No. XDB21030300 and the Key
Research Program of Frontier Sciences, CAS, grant
No.QYZDY-SSW-SLH006. And
the
Young
Teachers Scientific Research Ability Promotion0
4.0

Resonance energy (eV)Rate coefficient(10-9cm3s-1)

Fig. 1. The detailed rate coefficients for the lowestenergy DR resonance manifold (2p1/219lj)J of W71+
ions.
3.5
5
l1/2
l3/2
l5/2
l7/2 l9/2 j>9/2
4

s1/2

p1/2

3.0

p3/2

2.5

3

-

71+

70+

e +W (2s)oW (2p3/27l)

2

2.0
1.5
1.0

1
0
230 2350.5
0.0

270 275 280 285 290 295
Resonance energy (eV)Fig. 2. Same as figure 1 but for the DR resonancemanifold (2p3/27lj)J of W71+ ions.

References[1] Preval, 2016 Phys. rev A 93 042703[2] Trzhaskovskaya, 2014 At. Data Nucl. Data Tables
100 986[3] M. F. Gu, 2008 Can. J. Phys 86 675[4] Y. Hahn, 1985 Adv. At. Mol. Phys 21 123

1E-mail: xiely@nwnu.edu
E-mail: x.ma@impcas.ac.cn

297Resonance strength (10-18cm2eV)*

Low energy range dielectronic recombination of Fluorine-like Fe17+ at the CSRm
Nadir Khan1,2, Zhong-Kui Huang1, Wei-Qiang Wen1†, Li-Jun Dou1,2, Shu-Xing Wang3, Xin Xu3, Han-Bing
Wang1, Sultan Mahmood1, Chong-Yang Chen 4, Xiao-Ya Chuai1,2, Xiao-Long Zhu1, Dong-Mei Zhao1, LiJun Mao1, Jie Li 1, Da-yu Yin 1, Jian-Cheng Yang1, You-Jin Yuan1, Lin-Fan Zhu 3 and Xin-Wen Ma1‡
1

Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
2
University of Chinese Academy of Sciences, Beijing 100049, China.
3
Hefei National Laboratory for Physical Sciences at Micro scale, Department of Modern Physics, University of Scienceand Technology of China, Hefei 230026, China
4
Institute of Modern Physics, Fudan University, 200433, Shanghai, China

Dielectronic recombination is one of themost important electron ion recombination process
in astrophysical and men made plasma. The absolute
dielectronic recombination rate coefficient of F-like
Fe17+ ions has been measured at the main cooler
storage ring (CSRm), at Institute of Modern Physics
Lanzhou, China [1]. The measured electron-ion
collision energy range 0-6 eV covered the first
Rydberg series of ∆n = 0 core excitations from
2s22p5(2P3/2) nl to 2s22p5(2P1/2) nl from n=18 up to n
= 24.
The FAC code has been used to calculate DR
rate coefficient and compared with experimental
results [2]. Plasma rate coefficient were deduced
from measured and calculated DR rate coefficient.
Overall a reasonable agreement was found between
the experimental results and theoretical results from
FAC. Our results also compared with previously
calculated MCBP, MCDF and measured
experimental results of test storage ring (TSR) as
shown in figure.1. [3,4]. We will present the DR rate
coefficient as well as the obtained plasma rate
coefficient of Fluorine-like Fe17+ ions at theconference.

Fig. 1. Comparison of plasma rate coefficients derived
from the experimental result with the calculated resultsfrom FAC code and also the existed plasma rates
coefficients from literature. The thick solid blue line
denote experimental results from CSRm and thin solid
green line represents FAC calculation. The experimental
result from TSR is displayed by Purple dash-dot line andcorresponding calculations by MCBP and MCDF are
shown by red dashed curve and black dotted curve,
respectively.

References[1] Z. K. Huang et al, 2018 Astrophys. J. suppl. S., 235 2.
[2] Nadir Khan et al, 2018 Chinese Phys. C 42 064001.
[3] O. Zatsarinny et al, 2006 Astron. Astrophys, 447 379.
[4] D. W. Savin et al, 1999 Astrophys. J. suppl. S., 123 687.

†‡

Corresponding author. E-mail: wenweiqiang@impcas.ac.cn
Corresponding author. E-mail: x.ma@impcas.ac.cn

98Dielectronic recombination of Be-like ions: astrophysical plasma applications
and precision spectroscopy
W. Q. Wen *,1, Z. K. Huang*, S. X. Wang†, X. Xu†, H. B. Wang*, L. J. Dou*, N. Khan*, X. L. Zhu*,
D. M. Zhao*, L. J. Mao*, X. M. Ma*, J. Li*, M. T. Tang*, D. Y. Yin*, R. S. Mao*, Y. J. Yuan*,
J. C. Yang*, L. F. Zhu† and X. Ma *,2*†Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Scienceand Technology of China, 230026, Hefei, China

Dielectronic
recombination(DR)
experiments of highly charged ions at thestorage rings have been developed as aprecision spectroscopic tool to investigate
the topics from the atomic structure to
nuclear properties. DR also plays a crucialrole for accurate plasma modeling andspectral analysis in astrophysics and also
man-made plasmas. The atomic levels anddecay modes of Be-like ions is show in Fig.
1. DR of Be-like ions at heavy ion storagerings has been emphazised on different
physical topics, such as first observation oftrielectronic recombination (TR) for Be-like
Cl13+[1], first measurement of hyperfine
induced transition rate of Be-like Ti18+ [2]and precision QED test [3]. In addition, DR
of Be-like ions have been investigated for
applications in astrophysical plasma [4].
Recently, electron-ion recombination of
Be-like 40Ar14+ and 40Ca16+ have beenmeasured by employing the electron-ion
merged-beams method at the cooler storage
ring CSRm [5, 6]. The DR resonances
associated with 2s2→2s2p core transitions
were identified by the Rydberg formulafrom the measured sprectra. In addition,strong TR resonances associated with
2s2→2p2 core transitions were observed.
The plasma rate coefficients for DR+TR
were deduced from the measured electronion recombination rate coefficients tocompare with the previously recommended
atomic data from the literature. The present
results constitute a set of bench-mark datafor use in astrophysical modeling.
In addition, we are preparing to perform
DR experiments of highly charged Be-likeions at the CSRe, the investigation topics

including hyperfine induced transition ratemeasurement with different nuclear spin,
two-photon E1M1 (2s2p 3P0→2s2 1S0)
decay rate measurement for nuclear spin
I=0 and also measurement of the precision
spectroscopy with ions heavier than Xe.
These experiments will open a door for
precision investigation of QED effects,
electron-electron correlation and also
relativity effects. We will present a poster
on this workshop to show the detailed
precision spectroscopy of DR experimentsof Be-like ions at the heavy ion storage ring
CSRe and HIAF [7].

Fig. 1. Level scheme and decay modes of Be-like ion [2].

References[1] M. Schnell et al. 2003 PRL 91, 043001[2] Schippers, et al. 2007 PRL 98, 033001[3] D. Bernhardt, et al. 2015 J. Phys. B 48, 144008[4] D. Savin, et al. 2006, APJ 642, 1275
[5] Z.K. Huang, et al. 2018 APJS 235, 2[6] S.X. Wang, et al. 2018 APJ in press[7] X. Ma, et al. 2017 Nucl. Instr. Meth. B 408, 1699

1E-mail: wenweiqiang@impcas.ac.cn

2E-mail: x.ma@impcas.ac.cn

The simulation of ultrcold neutral plasmas in initial spatial ordered distribution
Zhu Yu-hao*, Wu Yong*,1, Zhou Fu-yang*, Yang Jie†*†

Institute of Applied Physics and Computational Mathematics, Beijing, 100000, China
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, China

dramatically decrease coupling strength, which
agree with the latest simulation[3].

Ultrcold neutral plasmas (UNPs) is astrongly coupled plasma, in which the charged
particles have very low temperature and thepotential energy among the charged particles islarger than its kinetic energy. Disorderedinducing heating is a leading limitation of
coupling strength. We employed the Debye
one-component-plasma model[1] molecular
dynamic to simulate the evolution of UNPs andinvestigate the influence of ordered initial
distribution to disordered-inducing heating.
First of all, we compared the recent
experiment[2] results with our simulation inorder to verify the accuracy of our simulation
model. The fig.1 shows the agreement is good.
It is found in fig.1 that the agreement of process

Fig.2. The evolution of ion temperature and ion couplingstrength in ordered distribution with no expansion.

In addition, we consider the expansion in thecreation of UNPs and Fig.3 shows expansion is able
to induce the disordered-inducing heating, leading
to the reduction of coupling strength.

Fig.1. The evolution of ion temperature and ion
coupling strength. (The blue dot is experiment result,
the red line is simulation result.)of disordered- inducing heating is excellent.
However, the equilibrium temperature in
simulation is lower than the condition ofexperiment. This is due to the expansion
resulting from coulomb potential during thecreation of UNPs. And we also simulated theevolution of coupling strength which is larger
than 1 when it reaches equilibrium.
Under the periodic boundary, we studied
the evolution of UNPs in the initial spatial
ordered distribution. In the Fig.2, we found thatthe spatial ordered distribution of ions could

Fig.3. The evolution of ion temperature and ion couplingstrength in ordered distribution with expansion.

References[1] T.K. Langin, T.C. Killian et.al, 2016 Phys. Rev.
E. 93 023201[2] Y.C. Chen, T.C. Killian et.al, 2004 Phys. Rev.
Lett. 92 143001[3] D. Murphy and B.M. Sparkes et.al, 2016 Phys.
Rev. E. 94 021201(R)1

100

E-mail: wu yong@iapcm.ac.cn

Resonant multiple Auger decay of core-excited 2p-13/24s in argon
Yulong Ma*, Zhenqi Liu*, Fuyang Zhou† and Yizhi Qu*,1*

College of Material Sciences and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing
100049, China†
Data Center for High Energy Density Physics, Institute of Applied Physics and Computational Mathematics, Beijing
100088, China

86This work

4
2
0

Expt. [3]

80

100

120

140

160

40
35
30
25
20
15
10
5
0
180

CountsConvoluted rates (1011 s-1)

Resonant Auger decay of a core-excited state
produced by exciting an inner-shell electron to a
Rydberg orbital, may emit one, two, and evenmore Auger electrons. Multiple Auger (MA)decay is one of the relax processes for an innershell excited atom upon radiationless decays,
which results from many-electron Coulombinteraction. Therefore, investigations of suchprocesses could give important information onelectron correlation effects and many-bodyproblems in atomic processes [1].
Generally, the emission of electrons in the
MA decay can be simultaneous, or it canproceed in a stepwise manner through thecreation and decay of an intermediate
autoionizing state, which are referred to as the
direct and cascade processes, respectively.
Based on multistep approaches, i.e., cascade,knockout and shakeoff mechanisms derived
from many-body perturbation theory (MBPT)[2], we present a detailed theoretical study of
the resonant single (SA), double (DA), triple(TA), and quadruple Auger (QA) for the Ar
atom with a 2p3/2 hole following the resonant
2p3/2→4s photoexcitation.
Resonant Auger decay can be clarified interms of spectator, participator and shakeprocesses, according to the behavior of the
Rydberg electrons, however, a detailed
theoretical investigations of which for MA
decays is still missing at present. Therefore, theimportant one of aim in this work is to explore
the contributions of spectator, participator andshake processes forming the final sates in SA,
DA, TA and QA decays.
The direct TA Auger electron spectra areshown in Fig. 1, in where our theoretical results
reproduce well the experimental measure [3].
The predicted branching ratios of different ionsformed by the SA and MA decays including thecontributions of the cascade and directprocesses are given in Table 1, which show agood agreement with the experimental data [3,4].

Total energy of three Auger electrons (eV)Fig. 1. Theoretical and experimental resonant direct
triple Auger electron spectra of Ar 2p-13/24s.
Table 1. Branching ratios (in percentages) of ionsproduced by single, double, triple and quadruple Auger
decays of Ar 2p-13/24s.
This work
Expt.
Ion
Cascade Direct Total Ref. [3] Ref. [4]
Ar+
65.41
69
66
Ar2+
21.52
9.83 31.35
28
30
3+
Ar
1.08
2.16
3.24
3
4
Ar4+
0.01
0.08
0.09
0.03
0.2

References[1] F. Penent, J. Palaudoux, P. Lablanquie, et al.,2005 Phys. Rev. Lett. 95 083002.
[2] M. Y. Amusia, I. S. Lee, and V. A. Kilin, 1992
Phys. Rev. A 45 4576.
[3] Y. Hikosaka, P. Lablanquie, F. Penent, et al.,2014 Phys. Rev. A 89 023410.
[4] J. A. R. Samson, W. C. Stolte, Z. X. He, et al.,1996 Phys. Rev. A 54 2099.

E-mail: yzqu@ucas.edu.cn

101           ! "# " $ %# & & #  ' # ' ( (#  '            
  
! 
"  #$ %&''%'
/ .  +     +  $   9:   *)     0+ 0<0     0+ 0&<0178 .     (       

>(

>(

,000+<00+0-&

'.''I

'.''0

>(>(,000+<00+0-0'.'0

)'.'0>(>(,000+<00+0-'.'A

)'.'

>(>(,000+<00+0-)'.''

'.''3

/(>(,000+&&<0-0)'.'%'.';

>(>(,000+<00+0-''.'''

'.'''

>(>(,000+<00+0-'.''

)'.''%>(>(,000+<00+0-0)'.';0)'.';0/(>(,000+&&<0-'.'&A

)'.'0









  






















   









 !"   !



 

 

 

 

 $'&







. . >           96  :   9(:>(/()  +      0+0<09++ +:        0+ 0&<0 9 !  +:  178  
+ .

/! 5!++     
( > +    
90'%? '3'0&'':  19  
@;A3'&A%%3070";&'303A3'30:   B "9 B ")#= );)&:.
 

/           )        +   .

  9/(:  2   9=(:                   *)  +  $                  0+0<0     0+0&<0 +  
. / + +    +  $       +      

64/      .#$% !&(        !   )       !    
*                                ++      ,-. /         )   +  
         ,0-.      !          +      +  +  $    *) .1  +  $   *)   +             )        +     + ,&-.
  $    + 
 2     +     +
+,3-.
4 +   ! 5 !     
          *)  +  $         6)5 178   *
 9 :,;-              ++ .
)@*J!..

102,-..6C.D .D. 5 0'&  ))'A0%'A.
,0-./ .6C  D 0'3  *';0%'3.
,&-. 1D  EF 0';  +
'30%'0.
,3-.D4 / 1D D>( /G(14H E " (?0'I.
,;-...0''I. ),A%;.

Measurement and analysis of EUV emission spectrum from laser produced Ni
plasmaS. Q. He, M. G. Su1, Q. Min, S. Q. Cao, L. Wu, H. D. Lu, D. X. Sun and C. Z. Dong*

Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China

Highly charged ions of medium and high-Z
elements exist widely in astrophysical, fusion
plasmas and laboratory plasmas. Spectral structure
analysis of highly-charged ions ablated by the highpower density laser pulse can reveal abundant
information on the plasmas, such as electron
temperature, electron/ion density, particle andenergy transport, and the evolution of theseparameters. More recently, the observation andanalysis of intense quasi-continuous emission
features in the 7.5–14.5 nm spectral region of laserproduced plasmas of Pr have been reported.
In our work, we obtained the EUV spectrum oflaser produced Ni plasma in the 7-14 nm wavelength
range. Lines due to the resonant 3d-4f transition
arrays of Ni6+ up to Ni10+ ions. We have calculated
the resonance 3p6(3d-4f)3d transitions of Ni8+ ionswith the Hartree-Fock method by Cowan codes[1],and find that Gaussian profile is discontinuous andnarrow. We added the 3p5(3d-4f)3d2 transition sothat its Gaussian profile is broad. The result is shownin Fig. 1.
Plasma parameters were estimated bycomparing experimental and simulated spectra,
based on the assumption of a normalized
Boltzmann distribution among excited states anda steady-state collisional-radiative model[2]. The
experimental spectrum, simulated spectra andion fractions are shown in Fig. 2. The results
provide further understanding of radiation
properties of highly charged ions of middle- andhigh-Z elements.
The work is supported by the National Key
Research and Development Program of China(2017YFA0402300), the Natural Science
Foundation of China (11364037,11274254,
U1332206,11564037).

Fig. 1. 3d-4f transition arrays of Ni8+ and Energy
level.

Fig. 2. Comparisons between the experimental
spectrum and simulated spectra.
References[1] Cowan R D 1991 The Theory of Atomic Structure andSpectra(Berkeley, CA: University of California Press).
[2] D. Colombant, G. F. Tonon, 1973 J. Appl. Phys 44 3524.

E-mail: nwnu_sumg @163.com

103

Two-electron one-photon transitions in He-like ions
M. X. Cao*, X. B. Ding*,1, M. W. Zhang†, D. Y. Yu†, Y. L. Xue†, C. Z. Dong**Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China†

Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

The x-rays from the inner shell ionized fewelectron systems provide valuable informationon the temperature, density, and ionization stateof the plasma and hence are useful in thetheoretical modeling of plasmas. Precisetransition properties can act as reference data
for the charge state distribution and averagecharge of plasma. The doubly excited states of
2s2p configuration in He-like ions can decay to
the 1s2 ground configuration through twoelectron one-photon (TEOP) transition. The
TEOP transition is a good example forinvestigation on the electron correlation effects.
The present calculations are carried out by
using GRASP2K code which based on themulticonfiguration Dirac-Fock (MCDF) wave
functions with the inclusion of Breit interaction,
self-energy, and vacuum polarization.
The construction of the atomic statefunctions using systematic expansion of theorbitals in the active space. However, the TEOP
transitions is sensitive to the correlation, theenhancedeffectsofcorrelationaresystematically considered by expanding theactive space from {1s, 2s, 2p} to the set thatconsisted of all orbitals with n = 1 to 6 and l = 0
to 3 so as to ensure the correlation, stability, andconvergence of the observables. We firstconsider the necessary configurations andgenerated
Dirac-Fockwavefunctions
inextended optimal level (EOL) scheme for the
initial doubly excited 2s2p and final 1s2
configurations. Then we consider single anddouble (SD) excitations of electrons and expand
the active space by considering the first layer ofthe set with n = 3 and l = 0 to 2 virtual shells
and optimized the orbital functions while 1s, 2s,
and 2p orbitals were kept fixed. Continue thecycle until the system converges. The optimized
orbitals thus generated were used in theevaluation of MCDF energies and rates.
The E1 transition energy (eV) and probabilities( s − 1) in the He-like Ar are given in Table 1. It canbe seen from table that the results of calculatedtransition energy and rates becomes converged
while the active space increase. The length andvelocity gauges rates are in excellent agreementwith each other for the various transitions to 1S0 and
3
S1 states. The results show a good agreement

between the present calculation and the previous
work. Using the similar correlation model, the
TEOP transition from 2s2p to 1s2 and OEOP
transition from 2s2p to 1s2s were calculated for Helike Ne, Ar, Ca, Fe, Ni, Cu, Zn, Kr, Nb, and Ag
ions. The electron correlation effects, Breit
interaction on the transition energy and rate wereanalyzed. It will be helpful for the experimental
investigation on the decay mechanism of inner shell
doubly hole states.
Table1.Transition energies in eV, length gauge rates（ B ） and velocity gauge rates(C) in sec−1 oftwo-electron one-photon transitions from statesof 2s2p configuration in He-like Ar. The numbersin the parentheses are powers of ten.
3P - 1S
1 - 0

Active set
DF

Energy6395.485{n3l2}

6395.395{n4l3}

6395.414{n5l3}

6395.415{n6l3}

6395.374

Ref
TheoryExpt.

6396.0591

C
B
C
B
C
B
C
B
C
B

1P -1S
10

Rate
8.493 (5)1.684 (8)2.953(8)1.044(8)2.953(8)1.044 (8)2.706 (8)1.298(8)2.785 (8)1.482 (8)1.138(8) 1

Energy6425.420
6425.142
6425.001
6424.645
6424.491
6424.385 1
63992

C
B
C
B
C
B
C
B
C
B

Rate
3.655(5)2.410(10)4.747 (10)1.781(10)4.562(10)2.097 (10)4.445 (10)2.239 (10)4.376(10)2.315 (10)1.568(10) 1
1.534(10)2

63903

Acknowledgment
This work was supported by National Key
Research and Development Program of China(2017YFA0402300).

References[1] R. Kadrekar and L. Natarajan, Phys. Rev. A 84,
062506(2011).
[2] T. K. Mukherjee, T. K. Ghosh, and P. K. Mukherjee,
Z. Phys. D 33, 7 (1995).
[3] H. Tawara and P. Richard, Can. J. Phys. 80, 1579
(2002).

E-mail: dingxb@nwnu.edu.cn

104Relativistic eﬀects in 2p photoelectron spectra of sodium atoms
from the initial state 2p6 3pXiaobin Liu∗, 1 , Yinglong Shi∗ 2∗

Department of Physics, Tianshui Normal University, Tianshui, 741001, China

ﬁne-structure spectra from excited sodium atoms[2, 3]. Usually, the MCDF theory can provide clear and intuitive physical information fromwhich the dynamics of the photoionization process can be interpreted. The present investigation demonstrates the information that may
be obtained regarding the relativistic eﬀects in
subvalence photoionization processes, but theconclusions are by no means limited to excited
sodium atoms.

Photoionization is a fundamental atomic process in which an ion is formed as a result of
the interaction of a photon with an atom. The
need for accurate photoionization cross sections,as well as photoelectron spectra are shared byvarious research ﬁelds such as modeling of astrophysical objects and laboratory plasmas created using a high-energy laser pinch machine or
tokamak. In addition, photoionization calculations together with detailed experimental measurements is a particularly sensitive tool for investigating atomic structure. On the other hand,quasi-one-electron systems are relatively simple
systems which allow precise theoretical description within the framework of quantum theory.
Then, as quasi-one-electron systems with a single electron outside the closed-shell core, alkali
atoms are particularly suited for studies aiming
for a comparison between theory and experiment.
Several investigations of the sub-valence 2p
photoionization from the ground and excitedstates of sodium atoms have been performed boththeoretically and experimentally in the past. Byutilising the high resolution of electron spectrometers and the high brightness of third-generationsynchrotron radiation sources, the ﬁne structureof the photoelectron lines can be resolved. In
this paper, we concentrate primarily on the photoelectron spectra of sodium atoms from the initial state 2p6 3p and investigate the inﬂuence ofrelativistic eﬀects using the multiconﬁguration
Dirac-Fock approximation (MCDF) method andthe corresponding package Grasp92 [1]. For the
relatively light sodium atom, the present MCDF
results agree well or at least reasonable with experimental measurement [2, 3], and we clearlyobserve the manifestation of relativistic eﬀects.
One such eﬀect is a spin-orbit splitting of the
2p photoionization process of sodium atoms. In
the nonrelativistic limit, as generally expected,
the present calculations indicate that the two relativistic channels can be reduced to the single
photoionization process.
Our present work builds upon the experimental measurement of the 2p photoelectron
1
2

Relative intensity

60
2p63p 2P1/2

40

3

20
10

0

13.92

Relative intensity

6

13.96

40

14.00

98 7

4

1

5

14.04
Kinetic energy (eV)

15.5

16.0

2p63p 2P3/2

2

5

20

7
9
10

0

13.92

13.96

14.00

1
8

14.04
Kinetic energy (eV)

6

4

15.5

3

16.0

Fig. 1. The calculated 2p5 3p photoelectron spectra of sodium atoms from the initial states 2p6 3p at
a photon energy of hν=54 eV; the assignments ofphotoelectron peaks are given in terms of the ﬁnal
ionic states. The results in the upper panel are thespectra for the initial state 2p6 3p(2 P1/2 ), and thosein the lower panel are for 2p6 3p(2 P3/2 ). The solidlines are the relativistic calculated spectra, and the(red) dashed lines are the nonrelativistic spectra.

References[1] K.G. Dyall, I.P. Grant, C.T. Johnson et. al., 1989
Comput. Phys. Commun. 55 425[2] A.N. Grum-Grzhimailo, E.V. Gryzlova, D.
Cubaynes et. al., 2009 J. Phys. B: At. Mol. Opt.
Phys. 42 171002[3] D. Cubaynes, S. Guilbaud, F.J. Wuilleumier et.
al., 2009 Phys. Rev. A 80 023410

E-mail: liuxb@tsnu.edu.cn
E-mail: shiyl@tsnc.edu.cn

105                  ! !  " #    $ $% &   "             
      !  "#$%&&$&


106



















 

 !  !" #!$- .'    835%9  +233  (             2&A








































' 
' 
' 
















%









   '  ('     '                     '             '  ' )*                '  (     +     ' ''     '         + '   ) ,      - . '    ('      '             (   )            '  (     #    ('      /
0   .        1          ' 
(    #233      
23-&   ) 0     '   '(   
('                   - . '           )03 1       '                    23-&  
(     233  4 -5    1    6 7. 869  /:;) 0 5               1       
825 2: 2':' 2'5 :5 :'59 <=&  822'
2:'2':::'9 <=3   23-&233  
' ) 0 %   1        5 %>252' 25:' 22'5 22': 22':'
2::' 2:'5 2'5: 2'::' 2':5 :5:'
::'5 %?252': (     ) 0)3 89  89         - .'    835%9   #         @&A   ( ' ' ) 0         '                   - .'    )

 3)
1 K  


























 

& !  !" #!$- .'    835%9  +233  (             @&A*  . ''   4 6'      8)5&3$B &2&5%&&9   -  8)!3:%&32533:@2&%@33$$25>5332@
2&259   C!8C!1
"D13:1%9/3; E. # )5&3?'&?:&&5)
/5;6*-  45&32 ()*@23)
/%; 6A, 0F G45&&:+, -. )/&35$&@)
/2; --  43>>$! +, 0(3&5$
/:;<HIJ )  05&&$  % +, %))) )

Investigation of the expansion dynamics of silicon plasmas
generated by double nanosecond laser pulses
Qi Min, Maogen Su*,1, Duixiong Sun, Shiquan Cao, Chenzhong Dong*,2*Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China

Up to now, there have been numerous
experimental and theoretical studies on theplasma generated by a single pulse (SP).
However, the interaction of two plasmas
generated by the double pulse (DP)configuration and the physical mechanisms
involved in this process constitute a researcharea that has not been sufficiently explored,
though the first experiments were performed in
the early 1970s [1].
A systematic investigation of the expansion
dynamics of plasma plumes generated by two
Q-switched Nd:YAG lasers at 1064 nm
wavelength operating on a silicon target wasundertaken for the inter-pulse delay times of 0,100, 200, and 400 ns using a techniqueinvolving fast-gated intensified charge-coupleddevice imaging [2].
The ICCD images of the expanding plume atdifferent acquisition delay times are given in
Figs. 1(a)–1(f) for the different pulse schemes.
Here, the real dimensions of each image in theseries are 36.67 × 36.67 mm. The pulse energyof each beam for the DP scheme is fixed as 300
mJ. The inter-pulse delay time (Δt) is defined as
the time difference between the arrival of thetwo laser pulses. The acquisition delay time (t a)is the time difference between the arrival of
second laser pulse and the time that the ICCD
begins to acquire data. Our results indicate thatthe plasmas exhibit free expansion in a vacuum
environment at an inter-pulse delay time of 0 ns.
With increasing inter-pulse delay time, theplasma front becomes sharpened and aninteraction boundary is formed.
We can offer a brief explanation on theformation and evolution mechanism of DP plasma
for the inter-pulse delay time is more than 50 ns: (1)When Laser I first interacts with the target surface,
the generated plasma experiences free expansion in
vacuum. (2) When Laser II pulse arrives at a later
time, the second plasma generated thereby expands
in a rarefied high-temperature plasma environment.
The ambient plasma has no influence on the second
1E-mail: nwnu_sumg@163.com

2E-mail: dongcz@nwnu.edu.cn

107

plasma propagation during the initial acquisition
delay time because the pressure of the second
plasma is much higher than that of the ambient
plasma pressure. (3) The second plasma expands
rapidly until its driving pressure has decreased
considerably, then an interaction boundary isformed between the second plasma and ambient
plasma.

Fig. 1. Spatio-temporal Si emission images of plasma
expansion for a single pulse with a pulse energy of (a)300 and (b) 600 mJ, and for a double pulse with a laserdelay between pulses (Δt) of (c) 0, (d) 100, (e) 200 and (f)400 ns. The ICCD acquisition delay time (ta) is noted at
the top of each image column.

This work was supported by National Key ResearchandDevelopment
Programof
China(2017YFA0402300); National Natural Science
Foundation of China (NSFC) (11274254,
U1332206, 11364037, 11064012, 11564037).
References[1] P. T. Rumsby, J. W. M. Paul and M. M. Masoud,1974 Phys. Control. Fusion 16 969.
[2] Q. Min, M. G. Su, B. Wang, et al., 2018 Physics
of Plasmas, accepted.

Investigation of EUV spectra from laser-produced Cr plasmas
Lei Wu, Maogen Su*,1, Qi Min, Shiquan Cao, Duixiong Sun, Chenzhong Dong*,2*Key laboratory of Atomic and Molecular Physics & Functional Materials of Gansu Province, College of Physics andElectronic Engineering, Northwest Normal University, Lanzhou, 730070, China

Spectral data of laser-produced plasmas(LPPs) of middle- and high-Z elements are ofgreat importance for diagnostic studies aboutfusion plasmas, astrophysical and laboratory
plasmas, as well as for interpretation of spectral
structures, conversion efficiencies, and radiativetransport in plasmas [1,2].
In this work, EUV spectra of laser-produced
Cr plasma in the 6.5-15 nm wavelength range
were studied experimentally and theoretically,
where the 3p-4d, 5d, and 3s-4p transitions
dominate the observed emission. The
experiment was performed using a Q-switched
Nd:YAG laser with 10 ns FWHM pulse
durations at a wavelength of 1064 nm. The peak
power density was 2.0×1011 W/cm2.
Theoretical values for wavelengths andweighted radiation probabilities for 3p-4d, 5d,
and 3s-4p transitions were calculated using the
Hartree-Fock method by Cowan codes and theflexible atomic code (FAC), respectively. Fig.1
shows
the
comparison
betweentheexperimental and simulated spectra. A
simulated with Te=38.4 eV and Ne = 5 × 1021
cm -3 is plotted to illustrate spectral features, thedominant fractional contributions arising from
Cr5+-Cr10+ are 5%, 15%, 30%, 30%, 16% and4%.
1E-mail: nwnu_sumg@163.com

2E-mail: dongcz@nwnu.edu.cn

Fig. 1. Comparisons between the experimental andsimulated spectra.

Reference[1] M. J. May, K. B. Fournier, et.al, 2003 Phys. Rev.
E 68 036402.
[2] H. P_epin, B. Grek, F. Rheault, and D. J. Nagel,1977 J. Appl. Phys 48 3312

108       !" #$           
  
! 
"  #$ %&''%'(  )     *+ , -'./-0.012+  !     2/   !      )  /   +    32   4 5)+46        2  
2     2 !       )+47        /  5846   $             
 2        7 9  84      / /
: /  /  4/,      
3
 5 6;<=7  <  ! 84        >
3        ! 2   
84      >3  /    >3    /,    7 ? !  !                 > /3           !  2    7  
4/,  >3    /    7)    >/3         7




















 7<7+ 84       /
  3    / / : /  /  4/,      2  2   7       2  84    3   
2  /      7<7/A $K!77

109

 &3         & 3    2     
2     
 84   4/,  >  3          7 )       > 
3            7  &  3             / /: / /4/,        2   7)    2   2         84       / / : /  /  4/,    !       ! 2  
5  &@6;0=A!           2   7"  2         + <7+
B  5 6  5 6 &  0   325
 <


6


2      84       / /: / /4/,    2 ! <7BC D-E7
+<   2       84      F  7   ;:=  G<':7 /,

/,

: /, /,

4/,

<<7B.>>;/B=

<7B'<>;/%=

B7'%>B;/%=

<7.'%';/%=

&7.''%;/%=

<

<7<B<-;0=

-7'B<&;'=

&7&%<&;<=

B7-%&<;'=

-7<-'H;'=

0

>7>%>0;/B=

>7H-<%;/B=

<7%%'';/%=

%7%.%%;/%=

<70<><;/B=

0

&7>.&B;0=

&7&'.';0=

B7..&B;'=

&70&B';<=

&7--0<;<=

&

B70H<%;/%=

<7B.<-;/B=

-7%B0.;/B=

07.>0.;/B=

-7'->-;/B=

&

>7'%>B;<=

<7'0&-;0=

070%H%;0=

<7'B'0;0=

<7'H.B;0=

>

<7%...;/-=

<70>H>;/-=

07.&%&;/B=

B7%'0H;/B=

<7'->-;/-=

>

07<.-';&=

.7<%&<;0=

.7H.&H;<=

07->>%;0=

07>>.B;0=

-

<7%'.-;/%=

<7>0>B;/-=

070-'H;/-=

<70'&&;/-=

<7->--;/-=

-

-7B''&;'=

<7.%0H;&=

<7%-<>;&=

B7%H%%;0=

B7>>%.;0=

B

<7>&0&;/-=

-70%HH;/%=

<7<H<>;/-=

<7.>-B;/-=

07<0>H;-=

B

<7'H0.;&=

&7<.&&;<=

B7-H.H;0=

<7%'--;&=

<7B.%>;&=

% ;<=770''&  &'(<<&;<=
;0=I*J? 70''%     >'A>0B.

Participant List
 

Name



Tachibana YuichiTakahashi MasahikoEsaka TakehikoFujii KeisukeOsugi Takuya

Kato Daiji



Title
MasterStudent
Prof.
MasterStudent
Assis. Prof.

Affiliation
IMRAM, Tohoku University
IMRAM, Tohoku University
Kyoto University

Emailyuichi@mail.tagen.tohoku.ac.jp
masahiko@tohoku.ac.jp
esaka.takehiko.86a@st.kyo
to-u.ac.jp

Kyoto University

fujii@me.kyoto-u.ac.jp

Kyoto University

t.4.103.tkynt@gmail.com

Assoc. Prof.

National Institute for Fusion Sciencekato.daiji@nifs.ac.jp

Morita Shigeru

Prof.

National Institute for Fusion Sciencemorita@nifs.ac.jp

Koike Fumihiro

Prof.

Sophia University

koikef@sophia.ac.jp



Tanuma Hajime

Prof.

Tokyo Metropolitan University

tanuma-hajime@tmu.ac.jp

Nakamura Nobuyuki

Assoc. Prof.



Kwon Duck Hee

Prof.



Pan Congyuan

Assoc. Prof.



Yuan Jianmin

Prof.



Ding Hongbin

Prof.



Zhao Yuxiang

Assoc. Prof.

Li Shuang

Dr.



Yang Yang

Assoc. Prof.



Lu Qifeng

Ma KunAssoc. Prof.

Huangshan University

makun0602@163.com

Chen Zhan-Bin

Dr.

Hunan University of Technology

253072513@qq.com

He BinProf.



Wu Yong

Prof.



Yuan XiangZhu Yuhao

MasterStudent

MasterStudent

University of The ElectroCommunications
Korea Atomic Energy ResearchInstituteAnhui Universtiy
China Academy of Engineering
Physics
Dalian University of technology
Department of Physics, Tianshui
Normal University
Fujian Agriculture and Forestry
University
Fundan University
Fudan University

Institute of Applied Physics andComputational Mathematics
Institute of Applied Physics andComputational Mathematics

MasterInstitute of Applied Physics andStudent

Computational Mathematics

Phd Student

Institute of Applied Physics andComputational Mathematics

110

n_nakamu@ils.uec.ac.jp

hkwon@kaeri.re.kr
cypan@ahu.edu.cn
jmyuan@nudt.edu.cn
hding@dlut.edu.cn
158381077@qq.com

lishuangwuli@126.com
yangyang@fudan.edu.cn
16210200006@fudan.edu.
cnhebin-rc@163.com

wu_yong@iapcm.ac.cn

yuanxiangjlu@163.com

zhu_yuhao@foxmail.com



Shao Caojie

Prof.

Institute of Modern Physics

c.shao@impcas.ac.cn

Dou Lijun

Phd Student

Institute of Modern Physics, CASdoulijun@impcas.ac.cn

Khan Nadir

Phd Student

Institute of Modern Physics, CASnadirkhan@impcas.ac.cn

Song Zhangyong

Dr.

Institute of Modern Physics, CASsongzhy@impcas.ac.cn



Wang Wei

Dr.

Institute of Modern Physics, CAS

wangwei@impcas.ac.cn



Wen Weiqiang

Dr.

Institute of Modern Physics, CASYang Bian

Dr.

Institute of Modern Physics, CASZhang Mingwu

Dr.

Institute of Modern Physics, CAS

Yu Yanmei

Dr.

Institute of Physics, CAS

ymyu@aphy.iphy.ac.cn

Yang YuJun

Assoc. Prof.

Jilin University

yangyj@jlu.edu.cn

Yuan Haiying

Jilin University

1871952041@qq.com



Li Bowen

Lanzhou University

libw@lzu.edu.cn

MasterStudent
Assoc. Prof.

wenweiqiang@impcas.ac.cnyangbian@impcas.ac.cn
zhangmingwu@impcas.ac.
cn

Laser Fusion Research Center,

Hu Zhimin

Prof.

China Academy of Engineeringzhimin.hu@caep.cn

Physics
Laser Fusion Research Center,

Xiong Gang

Dr.

China Academy of Engineeringgxiong16@fudan.edu.cn

Physics
National University of Defense

Gao Cheng

Assis. Prof.



Liu Pengfei

Phd Student

Zeng Jialong

Prof.



Bakhiet Mohammed

Phd Student

Northwest Normal University

mohanaz777@gmail.com



Cao Shi-Quan

Phd Student

Northwest Normal University

cao_sq@163.com



He Si-Qi

Northwest Normal University

hsq908@126.com

Lu Hai-Dong

Northwest Normal University

luhd_1@163.com

Min QiNorthwest Normal University

mq_lpps@163.com

Tang Zhi-Ming

Wu Lei

Cao Ming-Xin

MasterStudent
MasterStudent
Phd Student
MasterStudent
MasterStudent
MasterStudent

Technology
National University of Defense
Technology
National University of Defense
Technology

Northwest Normal University

gaocheng@nudt.edu.cn

feipeng1050@163.com

jlzeng@nudt.edu.cn

tangzhimingphys@126.com

Northwest Normal University

568128709@qq.com

Nothwest Normal University

763481251@qq.com

111



Cheng Xiao-Shu

Ding Xiaobin

MasterNothwest Normal University

2561129023@qq.com

Assoc. Prof.

Nothwest Normal University

dingxb@nwnu.edu.cn

Dong Chenzhong

Prof.

Nothwest Normal University

dongcz@nwnu.edu.cn



Jiang Jun

Assoc. Prof.

Nothwest Normal University

jiangjun@nwnu.edu.cn



Li Maijuan

Phd Student

Nothwest Normal University

620773990@qq.com



Lu Si-Mei

Nothwest Normal University

1120804082@qq.com



Ma Peng-Peng

Nothwest Normal University

ma_pp08@126.com



Ren Cheng

Nothwest Normal University

18893700913@163.com

Su Maogen

Prof.

Nothwest Normal University

sumg@nwnu.edu.cn



Sun Duixiong

Assoc. Prof.

Nothwest Normal University

sundx@nwnu.edu.cn

Wang Kai-Ping

Nothwest Normal University

wang-kp1993@163.com

Xie Luyou

Nothwest Normal University

xiely@nwnu.edu.cn

Zhang Feng-Ling

Nothwest Normal University

1072023560@qq.com

Zhang Denghong

Assoc. Prof.

Nothwest Normal University

zhangdh@nwnu.edu.cn



Yu JinProf.

Shanghai Jiao Tong University

jin.yu@sjtu.edu.cn



Xiaobin Liu

Assoc. Prof.

Tianshui Normal University

liuxb@tsnu.edu.cnYinglong Shi

Assoc. Prof.

Tianshui Normal University

shiyl@tsnu.edu.cn



Ma Yulong

Phd Student

Qu Yizhi

Prof.



Chen Lei

Phd StudentChen Xiangjun

Prof.



Liu Zhaohui

Phd Student



Liu Yawei

Assoc. Prof.



Shan Xu

Assoc. Prof.



Tian Shanxi

Prof.



Wang Shuxing

Phd Student

Student

MasterStudent
MasterStudent
MasterStudent

MasterStudent
Assoc. Prof.
MasterStudent

University of Chinese Academy of
Sciences
University of Chinese Academy of
Sciences
University of Science andTechnology of China
University of Science andTechnology of China
University of Science andTechnology of China
University of Science andTechnology of China
University of Science andTechnology of China
University of Science andTechnology of China
University of Science andTechnology of China

112

mylphy@Hotmail.com

yzqu@ucas.edu.cn

leichen@mail.ustc.edu.cn

xjun@ustc.edu.cn

chinalzh@mail.ustc.edu.cn

liuyawei@ustc.edu.cn

xshan@ustc.edu.cn

sxtian@ustc.edu.cn

wsx0417@mail.ustc.edu.cn

University of Science and

Wang Qiuping

Prof.



Zhao Xi

Phd Student

Zhu Lin-Fan

Prof.



Zhao Yongtao

Prof.

Xian Jiaotong University

zhaoyongtao@xjtu.edu.cn

Li Yao ZongProf.

Xianyang Normal University

1095036037@qq.com

Liang Chang Hui

Prof.

Xianyang Normal University

1758858011@qq.com

Wang Yi Jun

Prof.

Xianyang Normal University

806605363@qq.com

Wang BaonianProf.

Institute of Plasma Physics, CAS

bnwang@ipp.ac.cn

Institute of Plasma Physics, CAS

shdong@ipp.ac.cn

Technology of China
University of Science andTechnology of China
University of Science andTechnology of China

qiuping@ustc.edu.cn

zx0214@mail.ustc.edu.cn

lfzhu@ustc.edu.cn

Head of

Dong Shaohua

Foreign
Affairs Office

Hu LiqunProf.

Institute of Plasma Physics, CAS

lqhu@ipp.ac.cn



Wu Zhenwei

Prof.

Institute of Plasma Physics, CAS

zwwu@ipp.ac.cn

Wang Liang

Prof.

Institute of Plasma Physics, CASlwang@ipp.ac.cn



Lyu BoProf.

Institute of Plasma Physics, CAS

blu@ipp.ac.cnHuang JuanProf.

Institute of Plasma Physics, CAS

juan.huang@ipp.ac.cn



Xiao Bingjia

Prof.

Institute of Plasma Physics, CAS

bjxiao@ipp.ac.cn



Liu Haiqing

Assoc. Prof.

Institute of Plasma Physics, CAS

hqliu@ipp.ac.cn



Liu Xiaoju

Assoc. Prof.

Institute of Plasma Physics, CASjulie1982@ipp.ac.cn



Gao Wei

Assoc. Prof.

Institute of Plasma Physics, CAS

gw118@ipp.ac.cn

Zhang Ling

Assoc. Prof.

Institute of Plasma Physics, CASzhangling@ipp.ac.cn

Zhang Hongmin

Assis. Prof.

Institute of Plasma Physics, CAS

hmzhang@ipp.ac.cn

Chen Yingjie

Dr.

Institute of Plasma Physics, CAS

bestfay@gmail.com



Xu Zong

Dr.

Institute of Plasma Physics, CAS

xuzhong@ipp.ac.cn

Yang Xiuda

Phd Student

Institute of Plasma Physics, CAS

xdyang@ipp.ac.cn

Cheng Yunxin

Institute of Plasma Physics, CAS

yunxin.cheng@ipp.ac.cn

Li Lei

Institute of Plasma Physics, CAS

lei.li2@ipp.ac.cn

MasterStudent
MasterStudent113