Lasing mechanism in a capillary discharge

26 September 1994 PHYSICS LETTERS A

PhysicsLetters A 193 (1994) 183-187

ELSEVIER

Lasing mechanism in a capillary discharge H.-J. Kunze, K.N. Koshelev 1, C. Steden, D. Uskov 2, H.T. Wieschebrink Institut fiir Experimentalphysik V, Ruhr- Universiti~t, 44780 Bochum, Germany

Received 22 February 1994; revised manuscript received29 April 1994; acceptedfor publication 22 July 1994 Communicated by B. Fricke

Abstract

The possibility is analyzed that charge exchange between plasma ions preceded by an m = 0 instability is responsible for amplified spontaneous emission observed on the CVI Balmer-alpha line emitted from a capillary discharge.

Research on short-wavelength lasers in the soft Xray region advanced tremendously during the last ten years. A survey of the fundamentals and of the achievements until 1990 are presented in the monograph of Elton [ 1 ], the more recent progress is chronicled in respective conference proceedings [ 2 ]. Lasing usually is generated in elongated laser-heated plasmas and is due to amplified spontaneous emission (ASE) in the direction of the elongation. Collisional excitation and three-body recombination are the most successful pumping schemes so far, but photo-pumping and charge-exchange of ions with neutrals are being investigated too. Plasmas produced by pulsed-power electrical generators offer an alternative route to X-ray lasers and are vigorously investigated [ 3 ] but have not resulted yet in lasing. An extremely simple and low-cost variant are discharges through small-bore capillaries, which are initially evacuated. The discharge starts by surface flashover along the wall and the plasma is Permanent address: Institute for Spectroscopy,Russian Academy of Sciences, Troitzk, Moscow District, 142092, Russian Federation. 2 Permanent address: P.N. Lebedev Physical Institute, Russian Academy of Sciences, Lcninsky Prospect 53, 117924 Moscow, Russian Federation.

made up of ablated wall material. The current pulse leads to fast heating and ionization and it was expected that rapid cooling by radiation and heat conduction to the walls at the end of the current pulse results in lasing according to the recombination scheme. Indeed the emission of the H,~-line of CVI at 18.22 nm displayed features in a discharge through a capillary made of polyacetal (CH20)n which suggested lasing, but surprisingly at the time of the second current maximum [5,6]. It is difficult to advance the recombination scheme at this time since estimated cooling rates do not suffice to produce fast enough the strongly nonequilibrium plasma conditions required for lasing. The situation is further complicated by the fact that similar capillary discharges did not show the same results indicating that discharge parameters might be extremely crucial [7,8]. For these reasons we analyze the possibility that charge exchange between plasma ions preceded by an MHDinstability produces the population inversion. We start with summarizing previous and some new results on the capillary discharge which is briefly described in Refs. [5,6]. The capillaries usually are made of polyacetal since the carbon debris produced is low in comparison with capillaries of polyethylene.

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The capacitance of the circuit is 0.1 IxF, the period of the discharge is 180 ns with a capillary of 1 cm length and 0.5 m m diameter. The observations are: -At the time of the second current maximum we observe a spike on the emission of the H~-line of CVI at 18.22 nm. The jitter of the occurrence of the spike is a few nanoseconds. The spike is not observed on other lines emitted by carbon or oxygen ions. The emission at 18.22 nm from a capillary 0.7 m m in diameter and 5 cm long was shown in Fig. 2 of Ref. [ 6 ]. The charging voltage was 12 kV. - T h e intensity of the spike increases only very weakly with the length of the capillary, i.e. much less than is expected for the case of a constant gain factor. Lengths of 1, 2, 3 and 5 cm have been used, and average gain-length products of 2.7, 3.0, and 3.6 have been deduced [ 5 ]. - T h e narrower the capillary the better is the spiking. As the number of discharges through a capillary increases, the diameter increases due to ablation of the wall, and the current has to be increased in order to retain the spike. - A plane multilayer mirror having a reflectivity of R = 12% at 18.22 nm increased the amplitude of the spike by factors from 1.5 to 1.7 for capillaries of different length. After a few shots this effect disappeared, the multilayer was destroyed. - T h e spikes increased with the length of the capillaries although not exponentially. - T i m e integrated spectra recorded with a grazing incidence spectrograph reveal a directed emission of the Balmer-a transition but not of other lines from carbon or oxygen ions. The divergence of the emission decreases with the length of the capillary. - T h e divergence of the Balmer-a line decreases with the multilayer placed at one end of the capillary. -Time-integrated spectra with a pinhole transmission grating indicated, that the emission from OVI ions, for example, is homogeneous across the capillary whereas the emission from CV and CVI ions is peaked on the axis of the plasma column. This is corroborated by the emission from CV ions at 227 nm, the emission from CIII ions having a minimum on the axis. This suggests a hot plasma channel on the axis. -Time-integrated spectra were also recorded with the grazing incidence spectrograph from a capillary 1 cm long and 0.5 m m in diameter made ofABS poly-

mer (acrylnitril-butadien-styrol-copolymer). At a charging voltage between 7 and 11 kV the intensities of all lines from CV and CVI were considerably enhanced. The Balmer-a to Balmer-~ transitions were clearly seen, even the resonance line of OVII showed up. -Time-resolved measurements of electron density and temperature were carried out by other groups in rather similar capillary arrangements and with comparable discharge currents [7,8]. The obtained average temperatures were so low that it is impossible to ionize an appreciable fraction of the carbon atoms to the bare nucleus or only to excite the heliumlike and hydrogenlike ionization state. This is not consistent with our spectra. In order to explain our observations we advance therefore a model, which relies on an instability of the m = 0 type to produce hot regions in the plasma and on charge exchange between ions as the pumping mechanism for the population inversion [ 9 ]. Charge transfer between ions and neutral atoms has been proposed and investigated already previously [ 1 ] and has attracted again renewed interest only recently [ 10 ], whereas ion-ion charge transfer was dismissed because of small cross-sections [ 1 ]. Lasing on the Balmer-a transition requires that initially most of the carbon atoms are ionized to the bare nucleus independently whether recombination or charge exchange pumping produces the population inversion. Temperatures above 150 eV are necessary, and they are readily obtained in neck regions of an m = 0 instability. The current through the capillary is typically 10 kA at the maximum of the second half-cycle and density and temperature are such that equilibrium described by the Bennett relation is reached. It is usually assumed that such pinch equilibria are stable if the plasma column is surrounded with high pressure gas or even with a wall [ 11,12 ]. Resistivity and viscosity should have further stabilizing effects at our plasma conditions [ 13 ]. However, the effects of heat conduction and of particle flux of ablated wall material on the stability have not been investigated: it is very likely that the particle flux from the wall is rather inhomogeneous along the capillary initiating local perturbations which trigger the instability. The occurrence of such instabilities, although not understood, is corroborated by several observations:

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- The d l / d t signal recorded with a shielded pickup loop clearly displays perturbations during many discharges which are indicative of an instability and occur just at the time of maximum current in the second half-cycle, where lasing is recorded. No such indications are seen during the first half-cycle. Although not relevant to our case, we nevertheless would like to mention the observation of a stable fiber-initiated z-pinch, which turns violently unstable also right at current maximum [ 14]. We cut the capillaries after use, and Fig. 1 shows the inside, which has been slightly stained using a lead pencil: the imprint of an m = 0 instability is unambiguous. For capillaries of length l = 1 cm we observe consistently kao~2.4 for all diameters (2ao) up to about 1.4 mm, where ao is the radius of the capillary and k is the wavenumber of the instability. For capillaries of 2, 3, and 5 cm length we obtain corresponding values for ka0 of 1.6, 0.8, and 1.2, with all wavenumbers deduced from the imprints on the wall. It is amazing that the wavelength of the instability increases with the length of the capillary; no explanation is known at present. Except for the one emission spike we also have no independent proof that all hot regions occur exactly at the same time. -

- The growth time of such an instability is connected with outflow of plasma from the neck regions, and it is typically of the order o f a o / c s , where cs is the ion sound speed [ 15 ]. The initial plasma parameters thus yield a value of 10 ns. The high-temperature phase of the instability, however, is much shorter and typically of the order of 1 ns. This is comparable to the observed jitter of the Balmer-ot spikes and to their duration. Constrictions by factors between 2 and 3 in the neck regions of the instability is all that is needed to reach the temperatures necessary to strip carbon atoms completely. Plasma flows from the neck regions, the velocity being given approximately by the ion sound speed cs [12]. For a plasma of 150 eV with fully stripped carbon atoms one obtains a velocity of the order of 107 cm/s corresponding to a kinetic energy of the carbon nuclei of 600 eV. These ions stream into the cold plasma outside the neck regions of the instability and experience Coulomb collisions, collisional recombination and charge exchange collisions. The electron density ne of this bulk plasma is of the order of 1019 cm -3 at the second current maximum and the temperature is between 10 and 20 eV [7,8]. Carbon atoms will be mainly in the CIII and CIV ionization stages and hence the ion density n i should be around 4 × l0 Is cm 3 for a pure carbon plasma; when polyacetal capillaries are used, the carbon ion density should be 1.25 × 1018cm - 3 instead, if oxygen is ionized to about OV and OVI. Slowing down of the fast ion beam ("test ions") by Coulomb collisions with CIII and CIV ions (or with other ions) may be estimated according to Trubnikov [ 16 ]. Both the slowing down probability and the energy loss probability have the magnitude l010 S-1. This indicates a penetration length of the fast beam into the cold plasma of the order of l0 ~tm. This is certainly a crude model. The interaction region will be larger for several reasons: compression and outflow occur concurrently, the outflow has a strong radial component, and the energy loss by the beam ions and connected heating of the target ions results in average ion energies where charge exchange still takes place. Outflow in radial direction also results in lower beam densities. The probability that a fast ion experiences collisional recombination into all levels above the colli-

Fig. 1. Longitudinalcut of a capillary.

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sion limit is about 109 s- l or lower [ 1,17 ]. The magnitude of charge exchange recombination will be the critical point, therefore. Electron capture by the bare carbon nuclei was studied for collisions with the following target ions: CIV ( ls 2 2p), CIII(2s2), and CIII(2s2p). The energies of CVI (n = 3 ) and of CIV ( I s 2 2p) are very close, and initially a high capture cross-section was expected. However, calculations predict a cross-section of the order of tr~ 10- is cm 2 at energies above 150 eV, which is indeed too small. The cross-sections are much more favorable for collisions with the other ions. A multilevel Landau-Zehner model was used to estimate the cross-section for the collision with CIII(2s2). The cross-section is determined by the crossing at an internuclear distance ofR ~ 12 a.u., and the results are given in Table 1. The overbarrier transition model allows one to estimate capture crosssections for collisions with CIII (2s2p), and they are given by the internuclear distance R ~ 6.5 a.u. Values are also shown in Table I. In both cases the capture process is highly selective into the n = 3 level of CVI. This has been verified by estimating the cross-section for capture into the n--2 level: it is typically smaller than 10-19 c m 2 at our beam energies and approaches l 0 - 1 7 c m 2 for energies above 1 keV. At the electron densities of the capillary plasma the population densities of CIII will be in LTE and hence the 2s2p levels will be most strongly populated because of the higher statistical weight. For the initial energy of the CVII ions of 600 eV we thus obtain a pumping probability of the n = 3 level of CVI of P = n i o v - ~ 9 × 10 l° s-l! (In the case of plasmas from polyacetal capillaries this value will be lower determined by the ratio of the carbon and oxygen frac-

tions, although charge exchange with oxygen ions could be possible too, thus keeping the pumping probability at the above magnitude.) Nevertheless, this pumping probability is nearly two orders of magnitude higher than that by collisional recombination and, most importantly, it is highly selective into the n = 3 level only. The relative dominance of charge exchange recombination will increase towards lower densities. It is further amazing that the cross-section remains high down to energies below 100 eV. Finally, charge transfer collisions with CIV ions in the excited n = 3 states also exhibit a large cross-section of ~ 2 × 10-15 cm 2 in the temperature range 30 to 400 eV and thus contribute, too. At the high electron densities depopulation of the n = 3 level will not only be by radiative decay (A = 1.3 X 10 ~1 s- 1) but also by electron collisions to the n = 4 level. The respective probability is about 3 × 10 ~1 s- ~. Equating populating and depopulating rates yields the population densities of the beam ions in the n = 3 level of CVI, n (3) ~ 0.2n (CVII). Because of the selective population mechanism an inversion factor o f F ~ 1 is most likely, and the peak gain coefficient is simply [ 1 ] G ~ n (3) astim ~ 0.20"stimn (CVII) , where O'stimis the cross-section for stimulated emission. At temperatures of 150 eV and densities of 1019 cm -3, Doppler broadening is still larger than Stark broadening [ 18] and O'stira ~, 1.5 × 10-15 cm 2 is a reasonable value [ 1 ], the uncertainty due to the line shape being probably less than a factor of 2. Beam densities will be also of the magnitude of the ion density of the cold plasma (the electron density will be somewhat larger), and we thus arrive at G ~ 1200

Table 1 Charge transfer cross-sections CVII + CIII ( 2s 2) --}CVI (n = 3 ) + CIV

CVII+ CIII(2s2p) --,CVI(n = 3) + CIV

E (eV)

a (10 - 1 6 c m 2)

E (eV)

tr ( 10-16 cm2)

30 40 50 100 200 800

3.6 5.0 8.0 4.6 3.6 2.0

30 60 100 200 400 800

0 2.5 11.5 18.0 21.0 23.0

H.-J. Kunze et al. / Physics Letters A 193 (1994) 183-187

c m - ~ for pure carbon plasmas. Since the active layer has a depth o f about 10 ~tm or larger, a n d in a capillary o f 1 c m length we have about 14 plasma jets going in one direction, we obtain at total gain-length product o f G L ~ 16. F o r a p l a s m a from polyacetal wc have G L ~ 5, which agrees within the uncertainties with the result derived from the observed increase o f the laser spike when a multilaycr m i r r o r was e m p l o y e d [6]. F o r a capillary o f 3 cm length the wavelength o f the instability increased by a factor o f three giving thus again an estimate o f G L ~ 5 consistent with experimental values o f 2.5 a n d 3.6 in this case. The alignmerit o f the amplifying regions along the axis is not critical since the radial dimension is much larger than the axial extension. Beam spreading has not been considered since the detailed s h a p c o f the amplifying regions is not known. The p r o p o s e d m o d e l for lasing thus also explains the a p p a r e n t failure o f the gainlength product to increase in p r o p o r t i o n to the length o f the capillary as well as the observation that lasing is p o o r for large diameters o f the capillary even i f higher currents are employed: the wavelength o f the instability just is longer for larger diameters a n d the n u m b e r o f neck regions and hence the active p l a s m a jets along the capillary axis thus are lower. In general, driving the discharge through the capillary with higher currents results in an increasing electron density due to higher ablation o f wall material a n d hence will also reduce p o p u l a t i o n inversion duc to increased collisional coupling between u p p e r and lower laser levels. This work was s u p p o r t e d by the Deutsche Forschungsgemeinshchafi. We t h a n k Dr. Danz for supplying the ABS polymer.

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