J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)425–428
000–000

Soft X-ray Emission Spectra of Capillary Plasma
VRBA Pavel, JANČÁREK Alexander1, VRBOVÁ Miroslava1, SCHOLZOVÁ Lenka1,FOJTÍK Anton1, TAMÁŠ Martin1 and HAVLÍKOVÁ Radka1
Institute of Plasma Physics, AS CR, CZ-18221 Prague 8, Czech RepublicCzech Technical University, Břehová 7, CZ-115 19 Prague 1, Czech Republic

1(Received: 9 December 2003 / Accepted: 3 April 2004)

Abstract
Experimental and computer study of plasma, created in initially evacuated polyacethal and polyethylene capillary,
is reported here. Soft X-ray spectroscopy was used as the diagnostic tool. The time-integrated spectra of plasmameasured correspond to the computer simulated spectra as provided by the NPINCH and FLY codes.
Keywords:
capillary discharge, carbon ion emission spectra, oxygen ion emission spectra, MHD (magnetohydrodynamic)
simulation, ionization state, population kinetics, soft X-ray spectroscopy

1. Introduction
Non-stationary plasma of a fast capillary electricaldischarge was studied as a potential active medium for a soft
X-ray laser. We aim to achieve lasing at 18.2 nm wavelengthwith hydrogen-like carbon ions C 5+ in polyacethal orpolyethylene plasma [1]. In order to obtain conditions
favourable for three-body recombination pumping, thecapillary pulse plasma should be heated initially as the carbon
ions have to be fully ionized. During the next stage, theplasma electrons should be cooled quickly. Details of thecapillary plasma evolution and ion energy level populations
are evaluated by means of MHD (magnetohydrodynamic)
plasma modelling and by ion kinetic post-processor
evaluations. Experimental time-integrated soft X-ray spectra
and calculated ones are compared in this contribution.

Fig. 1Experimental set up: 1-Manual trigger, 2-Pulse
generator, 3-High voltage pulser, 4-Capillary, 5Capacitor bank, 6-Entrance slit of the monochromator,
7- Monochromator, 8-Exit slit of the monochromator, 9CCD camera.

2. Experiment
2.1 Experimental setup
Polyacethal and polyethylene, 5 cm long capillaries eachwith 1.1 mm diameter were used in our experiments. The
pumping energy is stored in a bank of 24 ceramic capacitorsof 15.3 nF total capacity that are mounted in parallel aroundthe capillary between two circular flat plates providing a lowinductance. The applied voltage maximum is 40 kV, so up to12 J energy can be stored and subsequently drained into thecapillary. The main discharge is triggered by a spark between
coaxial electrodes (see Fig. 1). As the discharge plasma
column resistance decreases very quickly and its value
becomes less than 1 Ω, the discharge circuit may be described
as an under-dumped resonant RLC series circuit with quasiperiod about 260 ns. The current peak value Imax is 10 kA.

Time integrated emission spectra in the 10–26 nm
wavelength region are measured with the JOBIN YVON
monochromator PGM-PGS 200, output slit energy of whichis recorded by the Reflex, Ltd. BICCD camera RXBIC 512c
for each shot separately. The two-dimensional image of themonochromator exit slit, as recorded and stored in a computer,provides wavelength resolution of 0.11 nm. The spectralenergies are determined for various wavelengths with 0.02 nm
step. The time integrated spectra are obtained by a simple
processing of the stored data. Each spectral point on figurespresented here is an average of at least five subsequent shotsdata.
©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchCorresponding author’s e-mail: vrba@ipp.cas.cz
1425

Vrba P. et al., Soft X-ray Emission Spectra of Capillary Plasma

2.2 Time integrated spectra
The emission spectra of plasma generated in polyacethal(CH2O)n and polyethylene (CH2)n capillary are depicted atFig. 2 (a), (b). In the selected spectral range, only the lines
corresponding to both carbon and oxygen ions with theionization degree Z > 3 may be found. If the polyacethal
capillary is used, the spectral lines of O4+ and O 5+ aredominant. When comparing these results with themeasurements of Gotou et al. [2], although done underslightly different experimental conditions, a good agreement
can be seen. With polyethylene capillary, the identified
spectral lines correspond namely to C 3+ and C 4+ ions.
Experimental conditions for both types of capillaries were thesame. The dominant oxygen line intensities measured withthe polyacethal capillary are stronger than the dominantcarbon lines observed in the case of polyethylene one.

3. Computer simulations
3.1 Magnetohydrodynamics
Capillary discharge plasma quantities were calculated bymeans of NPINCH code under the one-dimensional, twotemperature, one-fluid MHD approximation [3]. The model
considers the capillary wall material as a dense cold neutralgas (Z = 7, A = 14, and initial mass density ρ0 = 1 g/cm3).
The electrical current pulse time profile is approximated by⎛ πt ⎞⎛ t⎞
I (t ) = I0 sin ⎜⎟ exp ⎜− ⎟ ,⎝ t1 ⎠⎝ 2t0 ⎠where the values used for the calculation: I0 = 14 kA, t0 = 66
ns, t1 = 150 ns, correspond approximately to the measured
current waveform with I max = 10 kA, t max = 54 ns. The
capillary inner volume, initially evacuated, is gradually filled
by a material ablated from the wall. Resulting time-profilesof the electron density and electron & ion temperature axial
values are on Fig. 3. The first axial electron density peak (atN e = 2×10 18 cm -3, t = 20 ns) corresponds to a quick
compression of the plasma created during the leading current
pulse edge. The plasma electron temperature Te is increasing
here due to the increasing local current density. Its peak value
about Te = 130 eV is reached at tmax = 40 ns. Relatively quick
plasma cooling at the end of the first current half period iscaused by the cool plasma coming from the wall. In thecurrent second half period the axial plasma is relatively cold,
Te ≤ 20 eV, and axial electron density grows due to the wall
ablation all the time.

Fig. 2Time-integrated spectra emitted from (a) polyacethal,(b) polyethylene capillary discharge.

Fig. 3Calculated time dependences of axial plasma electron
density Ne , electron and ion temperatures Te , and Ti .

3.2 Ion population density time dependences
C5+ and oxygen ions O5+, O6+ are dominating. The hydrogenlike ion C5+ concentration prevails on the interval of 25 to 90
ns. Concentration of the fully stripped ion, C6+, is negligible
during all that time. Time dependence of the hydrogen-likecarbon ion energy levels population (see Fig. 4b) provides
evidence of a population inversion on the Balmer α transitionstarting at 76 ns. Unfortunately, the absolute value of theThe temporal history of the axial plasma electron density
and temperature, as obtained from MHD simulations (Fig. 3),
were used as input data for the FLY code [4]. Resulting time
profiles of the ionization fractions and energy level population
for lithium-, helium- and hydrogen-like carbon and oxygenions are presented on Fig. 4. During the whole current quasiperiod (i.e. on the time interval 0–260 ns) carbon ions C4+,2426

Vrba P. et al., Soft X-ray Emission Spectra of Capillary PlasmaFig. 4

Time dependences of population densities of (a) carbon ions, (b) excited states of helium- and hydrogen- like carbon ions, (c)oxygen ions, (d) selected excited states of helium- like oxygen ions.

Table 1 Identification of spectral lines in the evaluated time integrated spectra (see Fig. 5)
Label

Wavelength
[nm]

Ion

Configuration

gi

gk

Aki
[s-1]

A

10.48

O5+

1s22s-1s25p

26

6.48×109

B

11.58

O5+

1s22s-1s24p

26

1.23×1010

C

12.98

5+

O

1s 2p-1s 4d610

2.91×1010

D15.01O5+

1s22s-1s23p

17.31

5+

EO

2262.62×1010

226108.78×1010

22

1s 2p-1s 3dF

18.41

O

1s 2p-1s 3s62

1.71×1010

a15.84C4+

1s2s-1s6p

13

1.75×109

b

16.73

4+

C

1s2p-1s5d

9156.56×109

c

18.23

C5+

2-3

8

185.72×1010

d18.644+C

1s2s-1s4p

13

5.77×109

e

19.67

C3+

1s22s-1s212p

268.96×107

f

22.34

3+

C

1s 2s-1s 5p

28

1.21×109

g

24.49

C3+

1s22s-1s24p

262.27×109

h24.754+C

1s2s-1s3p

13

1.28×1010

i

25.95

C3+

1s22p-1s25d

610

2.73×109

26.60

4+

1s2p-1s3d

35

3.95×1010

jC5+222seen from Table 1. The strongest spectral lines in the range
of 8–18 nm belong to O4+ and O5+ ions. The spectral lines ofcarbon ions C 3+ , C 4+, and C 5+ are less intensive, but
dominating in the range 18–25 nm.

hydrogen-like carbon ions density is too low to get detectable
gain factor.

3.3 Time-integrated spectra
Using the subprogram FLYSPEC we evaluated timeintegrated (0–500 ns) emission spectra for the 8–28 nm
wavelength interval (see Fig. 5). The oxygen and carbon ion
spectral lines are denoted by the capital and small letters,
respectively. Corresponding identification of spectral lines is4. Conclusions
In the soft X-ray spectral region studied in this work,
only the spectral lines of C3+, C4+, and C 5+ ions may beessentially found. Consequently, the FLY code that deals with3427

Vrba P. et al., Soft X-ray Emission Spectra of Capillary Plasmacorrespondence between the calculated and measured lineintensities, which may be caused either by the shorter
integration time interval in simulations, or by the inaccurate
estimation of the electron density and temperature axial
profiles, or by an off-axial radiation contribution to themeasured signal. More detailed spectral analysis is in progressin our lab in order to get a proper model of the capillarydischarge for a further system optimization.

Acknowledgements
Fig. 5This work was supported by the Ministry of Education,Youth, and Sports of the Czech Republic grants LN00A100and KONTAKT ME 609.

Time integrated (0–500 ns) spectral line intensities
calculated for ions of oxygen (A–F) and carbon (a–j).

References

lithium-, helium- and hydrogen-like carbon and oxygen ions,is relevant. We show a reasonably good correspondence
between experimentally observed and computer-simulated
time-integrated spectra of the axial plasma (compare Figs. 2and 5). When the polyacethal capillary is used, oxygen ionslines are dominating, while with the polyethylene capillary,
where no oxygen ions may be presented, the carbon ion lines
are identified, but all are less intense. There is no full[1] M. Vrbová et al., Proc. of 8th International Conferenceon X-Ray Lasers, Aspen 2002, AIP Conference
Proceedings 641, 139 (2002).
[2] T. Gotou et al., Jpn. J. Appl. Phys. 40, 995 (2001).
[3] N.A. Bobrova et al., Plasma Phys. Rep. 22, 387 (1996).
[4] R.W. Lee and J.T. Larsen, J. Quant. Spectrosc. Radiat.
Transfer 56, 535 (1996).

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