J. Plasma Fusion Res. SERIES, Vol.7 (2006) 190-194

X-Ray Spectral Analysis on Electron Interaction withHighly-Charged Ions in Tokyo-EBIT
KATO Daiji, NAKAMURA Nobuyuki1 and OHTANI Shunsuke1
National Institute for Fusion Science, Toki 509-5292, Japan
1 University of Electro-Communications, Chofu 182-8585, Japan（Received: 14 December 2004 / Accepted: 4 October 2005）

Abstract
Charge state distribution of Xe ions in an electron-beam-ion-trap (EBIT) was studied based on coupled rateequations for ion population density and temperature. A synthetic X-ray spectrum of highly charged Xe ions
was compared with an experimental spectrum measured at the Tokyo-EBIT. The observed spectra containlines from Ne-, Na-, Mg-, Al-, and Si-like ions. Most of those lines have been identified and the wavelengths
have been determined experimentally for elements of Z = 50 − 56.
Keywords:
highly charged ion, electron beam ion trap, X-ray spectrum
1．Introduction
Development of the electron-beam-ion-traps (EBITs) enabled us collision experiments of high-energy
electron beam with cold trapped highly charged ions(HCIs). In previous studies at the Tokyo-EBIT [1], wehave measured 3l − 2p transition wavelengths of Nelike HCIs for atomic numbers Z = 50 − 56 in a X-ray
region, and investigated a configuration mixing of the3l excited levels caused by a strong spin-orbit couplingof the 2p-orbital [2,3].
In this work, we analyze satellite lines of lower
charge states (Na-like to Si-like) observed near by the
Ne-like lines. Charge state abundance of ions in theEBIT does not obey the simple electron collision ionization equilibrium. In the EBIT, axial trapping of
the ions is provided by an electrostatic potential wellat drift tubes, and radial trapping is provided by aspace charge field of the electron beam [4,5]. Theions which gain enough kinetic energies by collision
with the electron beam can escape from the trap (evaporation). Charge state distribution is determined bybalance between rates at which the various detailed
electron-impact ionization, recombination and ion-loss
processes take place.
This paper is organized as follows. In Sec. 2, wecompare experimental and synthetic X-ray spectra of
Xe ions in the EBIT. Calculations of ion population density and temperature are explained in that section. Identification of unknow satellite lines of the lower charge
states for Z = 50 − 56 is presented in Sec. 3. Section 4
is devoted to summarize this work.

2．Experimental and synthetic X-ray spectra of
Xe HCIs in EBITThe X-ray transition excited by a 60 µm-diam electron beam was measured at the Tokyo-EBIT with a flat
crystal spectrometer [6]. The spectrometer consistedof a flat crystal and a position sensitive proportionalcounter (PSPC) [1,6] with a backgammon-type cathode. Two types of crystal were used according to objective wavelength; one was LiF(200) with an area of
120 × 50 mm2 and another was Si(111) with an area of
120 × 70 mm2 . The spectrometer was operated in vacuo(∼ 10−7 torr) to avoid absorption by air. A beryllium
foil with a thickness of 50 µm was used to separate thevacuum of the EBIT (∼ 10−9 torr) from that of the spectrometer. Fig. 1 shows an example of the experimental
and synthetic X-ray spectra for Xe ions.
The synthetic spectrum was obtained using atomic
data of the HULLAC code [7] and a given charge statedistribution. The charge state distribution is predictedusing a set of coupled rate equations for ion population
densities and temperatures,dnqEIRREI= γq,q−1
ne nq−1 − γq−1,q+ γq+1,q
ne nq
dt
RR+ γq,q+1
ne nq+1 − Rloss
q nq ,
3d 
3e−iloss
nq kT q = νq nq δE − Rq nq qeVax + kT q
2 dt
2


i−i 3+ nqkT q − kT q ,νq,q(1)2q q
C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion ResearchCorresponding author’s e-mail: kato.daiji@nifs.ac.jp190

X-Ray Spectral Analysis on Electron Interaction with Highly-Charged Ions in Tokyo-EBIT

C

n=4n=5IP of 2p

3/2

300
1200

3G
10004100 4150 4200 4250 4300 4350 4400 4450 4500 4550 4600

400

Intensity (arb. unit)

n=3

1.2+PVGPVKU[4CVKQVQ&Intensity (arb. unit)

400300&(0CNKMG

)

D/

100

3F
M20.2

E2L

#NNKMG'.

0.6

0.4/INKMG

2000.8E2M5KNKMG '04.5'/

55.566.577.588.5'NGEVTQP$GCO'PGTI[ MG80Fig. 2 Intensity variation as a function of electron energy.
2p3/2 → nl excited level energies and the ionization energy of 2p3/2 orbital are indicated by verticallines in the upper part of the ﬁgure.

4100 4150 4200 4250 4300 4350 4400 4450 4500 4550 4600
X-ray energy (eV)Fig. 1 (a) Experimental X-ray spectrum of Xe ions measured at the Tokyo-EBIT. Electron beam energy
Ee ≈ 5540 eV (below the ionization energy of theNe-like Xe ion), electric current Ie ≈ 97 mA, magnetic ﬁeld strength in the drift tubes B ≈ 4 T,
and axial potential well Vax ≈ 100 eV. (b) Synthetic
spectrum convoluted using the Gaussian distribution function with a full-width-at-half-maximum of 2eV. 3D, 3E, 3F, 3G, E2M, E2L, and M2 lines are ofNe-like ions.

Rloss
≈q

exp[−ω] i−i2νq,q ,√ω
0.922 π(2)where ω = qeVax /kT q , and qeVax is the axial potential barrier. In the RHS of the second rate equation,
the first term represents the electron heating of trappedions, the second term evaporative cooling, and the thirdterm thermal energy exchange. δE = 2 mmei Ee is energy
gain by single electron-collision at electron energy E eprovided Ee > 32 kT q , where me,i are electron and ion
masses, respectively.
In the present calculation, we assumed that neutral
Xe gas was injected continuously into the trap so thatthe neutral density was maintained at 105 cm−3 . At theexperimental condition (see caption of Fig. 1 (a)), thepopulation densities for q = 40, 41, 42, 43, 44 were obtained to be nq ≈ 0.25, 0.38, 0.67, 1.1, 2.1 × 109 cm−3 ,respectively, and the ion temperature kT q ≈ 800 eV for
all the q = 40−44. Charge exchange (CX) with the neutral Xe atoms may aﬀect the charge state distribution tosome extent. However, it was neglected in the present
calculations, since the CX rate was estimated to be several orders of magnitudes smaller than the ion-loss rate
for the neutral density of 105 cm−3 [9].
In Fig. 1 (b), four electric-dipole lines of the Nelike ions are indicated as 3D, 3E, 3F, and 3G.
−1
Their upper levels are (2p−13/2 3d5/2 ) J=1 , (2p3/2 3d3/2 ) J=1 ,where nq and T q stand for density and temperature forions of a charge number q, respectively, γ s are rate coeﬃcients [cm3 s−1 ] for the ion population densities, andν s the Coulomb collision frequencies [s−1 ].
In the right-hand side (RHS) of the first rate equation, four terms are rate of population increase due toelectron-impact ionization (EI) of lower charge stateq − 1, depopulation rate due to EI and radiative recombination (RR) of the current charge state q, rate of population increase due to RR of higher charge state q + 1,and ion-loss rate due to evaporation by electron heating,respectively. The dielectronic recombination (DR) was
omitted in the present study. Since energy distributionof the electron beam is narrow, say 50 eV, the DR would
contribute only at resonance energies. The ion-loss rate
is approximated by a formula for the magnetic-mirror
configuration of a uniform magnetic field [8],191

X-Ray Spectral Analysis on Electron Interaction with Highly-Charged Ions in Tokyo-EBIT

Table 1 Wavelengths of n = 3 to 2 transitions in highly charged Sn, Sb, Te, I, Xe, Cs and Ba ions. The lower levels ofthe transitions are the ground state for all the lines. All values are given in Å. The numbers in the parentheses
represent the experimental uncertainties, e.g. 3.3540 (4) represents 3.3540 ± 0.0004. Key notations by Loulergueand Nussbaumer [10] and Beiersdorfer et al. [11] are used. a) Beiersdorfer et al. [12,13]; b) present; c) Beiersdorfer
et al. [11].
Element(Z)Sn (50)

Sb (51)Te (52)I (53)Xe (54)

Cs (55)Ba (56)Charge
state
Ne
Ne
Ne
Mg
NaNa
Ne
Ne
Mg
NaNe
Ne
Mg
NaNa
Ne
Ne
Mg
Ne
Na
Ne
Ne
Si
Mg
Ne
Na
Ne
Si
AlMg
Ne
Mg
Na
Mg
Na
Ne
Na
Ne
Ne
Ne
Ne
Ne
Na
Ne
Ne

Upper
level
(2p−13/2 3p3/2 )2(2p−11/2 3s)1
(2p−13/2 3d3/2 )12(2p−13/2 3s 3d5/2 )1−1
(2p3/2 3s3d5/2 )3/2
(2p−13/2 3s3d5/2 )1/2
(2p−13/2 3d5/2 )1(2p−11/2 3p3/2 )22(2p−11/2 3s 3d3/2 )1−1(2p1/2 3s3d3/2 )3/2
(2p−13/2 3d3/2 )1(2p−11/2 3s)12(2p−13s3d5/2 )13/2−1(2p3/2 3s3d5/2 )3/2
(2p−13/2 3s3d5/2 )1/2(2p−13/2 3d5/2 )1(2p−13/2 3d3/2 )12(2p−13/2 3s 3d5/2 )1−1(2p1/2 3s)1
(2p−13/2 3s3d5/2 )3/2
(2p−13/2 3d5/2 )1(2p−11/2 3p3/2 )2−1
(2p3/2 3s2 3p21/2 3d5/2 )12(2p−13/2 3s 3d5/2 )1−1(2p1/2 3s)1
(2p−13/2 3s3d5/2 )3/2(2p−13/2 3d5/2 )122
(2p−13/2 3s 3p1/2 3d5/2 )1−12
(2p3/2 3s 3p1/2 3d5/2 )3/2+1/22(2p−13/2 3s3p3/2 )1−1
(2p3/2 3d3/2 )12(2p−13/2 3s 3d5/2 )1−1
(2p3/2 3s3d5/2 )3/22(2p−11/2 3s 3d3/2 )1−1
(2p1/2 3s3d3/2 )1(2p−13/2 3d3/2 )1(2p−13/2 3s3d5/2 )3/2(2p−13/2 3d5/2 )1(2p−11/2 3s)1
(2p−13/2 3p1/2 )2(2p−13/2 3p3/2 )2(2p−13/2 3d3/2 )1(2p−13/2 3s3d5/2 )3/2
(2p−13/2 3d5/2 )1(2p−11/2 3s)1

192

Key

λexpt

E2M
3F
3E

3.3540(4)3.2764(3)3.2695(4)3.2673(3)3.2514(4)3.2416(4)3.2326(4)3.1547(5)3.0931(5)3.0823(5)3.1287(2)3.1253(1)3.1239(2)3.1103(1)3.1005(2)3.0926(2)2.9954(4)2.9902(3)2.9844(3)2.9775(3)2.9608(2)2.8712(3)2.9057(3)2.8640(2)2.8524(2)2.8524(2)2.8370(2)2.7849(2)2.7665(2)2.7596(2)2.7535(2)2.7460(2)2.7358(2)2.5764(3)2.5674(3)2.6427(4)2.6256(4)2.6149(3)2.6076(3)2.6588(5)2.5976(3)2.5398(3)2.5225(3)2.5111(3)2.4995(3)

3D
E2U

3E
3F

3D
3E
3F
3D
E2U

3F
3D

3E

3E
3D
3F
E2L
E2M
3E
3D
3F

Referencelinesa)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-β1 , K-δ1b)
Sn40+ 3D, 3Fb)
Sn40+ 3D, 3Fa)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-β1 , K-δ1a)
Ar16+ K-δ1 , K-1a)
Ar16+ K-δ1 , K-1a)
Ar16+ K-δ1 , K-1a)
Ar16+ K-δ1 , K-1a)
Ar16+ K-δ1 , K-1a)
Ar16+ K-δ1 , K-1c)
Xe44+ M2, E2Lc)
Xe44+ M2, E2Lc)
Xe44+ M2, E2Lc)
Xe44+ M2, E2Lc)
Xe44+ M2, E2Lc)
Xe44+ M2, E2Lc)
Xe44+ E2L, E2Mc)
Xe44+ E2L, E2Mc)
Xe44+ E2L, E2Mc)
Xe44+ E2L, E2Mc)
Xe44+ E2L, E2Mc)
Xe44+ E2M, 3F
c)
Xe44+ E2M, 3F
c)
Xe44+ E2M, 3F
c)
Xe44+ E2M, 3F
c)
Xe44+ E2M, 3F
c)
Xe44+ E2M, 3F
c)
Xe44+ E2U, 3C
c)
Xe44+ E2U, 3C
c)
Xe44+ E2U, 3C
c)
Xe44+ E2U, 3C
c)
Xe44+ E2U, 3Cc)
Xe44+ E2U, 3Cc)
Xe44+ E2U, 3Cc)
Xe44+ E2U, 3Cc)
Xe44+ 3C, 3Bc)
Xe44+ 3C, 3Bc)
Xe44+ 3C, 3Bc)
Xe44+ 3B, 3A

X-Ray Spectral Analysis on Electron Interaction with Highly-Charged Ions in Tokyo-EBIT−1(2p−1Two
1/2 3s) J=1 , and (2p3/2 3s) J=1 , respectively.
electric-quadruple lines E2M and E2L and one
magnetic-quadruple line M2 have upper levels of−1−1(2p−13/2 3p1/2 ) J=2 , (2p3/2 3p1/2 ) J=2 , and (2p3/2 3s) J=2 , respectively. Lower levels for those lines are of theground state (2p6 ) J=0 . As in the figure, relative intensities of the satellite lines obtained using the calculated charge state distribution agree with the experimental measurements. However, significant discrepancies
between the synthetic spectrum and the experimental
spectrum remain for intensity ratios of Ne-like 3F and3G lines to the 3D line. Fig. 2 compares experimental
measurements and theoretical predictions for the line
intensity ratios as a function of the electron beam energy. Sawtooth profiles of the intensity variation are due
to cascade feeding from higher excited levels. The discrepancies are apparent for the 3F and 3G lines, while
good agreement is obtained for other Ne-like lines.

state has strong configuration interaction with the state
which can decay via fast electric-dipole transitions. An
26example is (2p−13/2 3p3/2 ) J=1/2 → 2p 3s in the Na-like sys2tem. In this Z-region, (2p−13/2 3p ) J=1/2 has strong con−1
figuration interaction with (2p3/2 3s3d5/2 ) J=1/2 , whichcan rapidly decay to the ground state 2p6 3s. The twoelectron-one-photon transitions thus occur with relatively strong intensity in this Z-region. The same situation can also be found in the Mg-like system; the2two-electron-one-photon transition, (2p−13/2 3s3p3/2 ) J=1→ 2p6 3s2 , become possible due to the strong con2
figuration interaction between (2p−13/2 3s3p3/2 ) J=1 and2
(2p−13/2 3s 3d5/2 ) J=1 .
4．Summary
We measured n = 3 to 2 transitions in highly charged
ions with Z = 50 to 56 in near Ne-like charge states.
Comparing the experimental spectra with the syntheticspectra, most of the spectral lines have been identified and the corresponding wavelengths were experimentally determined. Discrepancies between the experimental spectrum and the synthetic spectrum remain forthe line intensities of the 3F and 3G. It is noted that wehave omitted the polarization eﬀect of line emission,
whereas the present experimental spectrum was measured at the right angle to the electron beam. If electron
impact excitation makes diﬀerent alignment of magnetic sub-levels for each excited state, the omission ofthe polarization eﬀect would cause error in the line intensity ratios of the synthetic spectrum. We leave investigation of the polarization eﬀect in future studies. Theeﬀects of strong configuration interactions have beenfound as the two-electron-one-photon transition in theNa-like and Mg-like ions.
We owe it to collaborations with JAERI that theHULLAC code was available for this work. D. K. wish
to thank Dr. Yu. Ralchenko and Prof. U. I. Safronova
for comments on this work.

3．Identification of satellite lines
Satellite lines of lower charge states (Na-like to Silike) were observed near by the Ne-like lines. Wavelengths of the satellite lines for Z = 50 − 56 wereexperimentally determined as listed in Table 1. Reference lines which were used for each line are also
listed in the table. The observations for Sn were donewith both LiF(200) and Si(111) to obtain two spectra
which diﬀered in dispersion. At first, a spectrum withwide bandwidth (small dispersion) was observed withSi(111) so that the two reference lines, K-α and Kδ of He-like Ar, appeared in the same spectral range.
From this spectrum the wavelengths of all the lines
26 2
except 3E and (2p−13/2 3s 3d5/2 )1 → 2p 3s were determined. The second spectrum with narrow bandwidth(large dispersion) was obtained with LiF(200) so that
26 23E and (2p−13/2 3s 3d5/2 )1 → 2p 3s could be resolved.
The wavelengths of those lines were then determined byusing the wavelengths of 3D and 3F determined fromthe wide bandwidth spectrum as references. Uncertainties in the experimental wavelengths were estimatedfrom the quadrature sum of three contributions: the uncertainty in the peak position of the reference lines, thatof objective line, and the uncertainties in the reference
wavelengths. The uncertainty in the peak position includes the statistical error and the error arising from thecalibration procedure.
The identification of the lines was done by comparing the measured spectra carefully with the synthetic
spectra. For the Na-like and Mg-like ions, some lines
were identified as two-electron-one-photon transitions.
Although a two-electron-one-photon transitions is usually very weak, it becomes possible when the upper

[1]
[2]
[3]
[4]
[5]
[6]
[7]
193

References
N. Nakamura, D. Kato and S. Ohtani, Phys. Rev.
A 61, 052510 (2000).
T. Kagawa, Y. Honda and S. Kiyokawa, Phys.
Rev. A 44, 7092 (1991).
D. Kato et al., Phys. Scr. T92, 126 (2001).
F.J. Currell et al., J. Phys. Soc. Jpn. 65, 3186
(1996).
H. Watanabe et al., J. Phys. Soc. Jpn. 66, 3795
(1997).
N. Nakamura, Rev. Sci. Instrum. 71, 4065
(2000).
A. Bar-Shalom et al., The HULLAC Package

X-Ray Spectral Analysis on Electron Interaction with Highly-Charged Ions in Tokyo-EBIT

Computer Set of Codes for Atomic Structure andProcesses in Plasmas, unpublished.
[8] R.E. Marrs, Nucl. Instrum. Methods Phys. Res.
B 149, 182 (1999).
[9] B.M. Penetrante et al., Phys. Rev. A 43, 4861
(1991).
[10] M. Loulergue and H. Nussbaumer, Astron. As-trophys. 45, 125 (1975).
[11] P. Beiersdorfer et al., Phys. Rev. A 37, 4153
(1988).
[12] P. Beiersdorfer et al., Phys. Rev. A 40, 150(1989).
[13] P. Beiersdorfer et al., Phys. Rev. A 52, 2693
(1995).

194