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AUTOIONIZATION FOR LOWER-LEVEL DE-TRAPPING IN X-RAY LASERS
R. Elton
To cite this version:
R. Elton. AUTOIONIZATION FOR LOWER-LEVEL DE-TRAPPING IN X-RAY LASERS. Journal
de Physique Colloques, 1987, 48 (C9), pp.C9-363-C9-366. �10.1051/jphyscol:1987963�. �jpa-00227381�
AUTOIONIZATION FOR LOWER-LEVEL DE-TRAPPING IN X-RAY LASERS
R.C. ELTON
U.S. Naval Research Laboratory, Washington. D C 20375-5000, U.S.A.
Abstract
--
A novel type of x-ray laser is analyzed in which the population of the lower level is depleted by autoionization instead of spontaneous decay. The intention is to decrease radiative trapping effects that quench the gain and require microscopic plasmas. Two sample systems are described. Proof-of- principle atomic-physics experiments and numerical modeling are needed to verify feasibility, fluorescence and lasing.The trapping of radiation resulting from lower-laser-level decay is a major problem for short-wavelength lasers [I]. Such trapping limits the gain because of the increased population of this level, and also demands micron-scale plasma diameters. This difficulty may be reduced or eliminated if the lower laser level autoionizes at a rate exceeding that for spontaneous emission, thus depleting the
lower-level population by electron rather than by photon emission [1,21. This concept is illustrated in Fig. 1 and represents a novel class of lasers yet to be demonstrated at any wavelength. (In an alternative concept [I] not discussed here, the lasing plasma i s - supplemented with a component that resonantly absorbs the photon through excitation of an autoionizing level, and the radiant energy is transformed to free electrons).
As a guideline for analysis* and identification of potential laser candidates, a set of selection criteria is applied in two steps, initially ignoring any consideration of how the autoionization levels are pumped to inversion, i.e., require that:
1. excitation ( & innershell vacancy) be limited to a single-electron, 2. the lower-laser-level decay predominantly by autoionization, 3. the upper-laser-level be relatively stable against autoionization, 4. and the laser-line-width be limited to Doppler (for maximum gain).
Limiting the analysis to matched-line photoexcitation pumping demands:
5 . an intense pumping line,
6. a good resonance between pumping (p) and absorbing (a) transitions, 7. and a high line strength ( A a ) for the absorbing transition.
'An expanded analysis including graphs showing the trends described here will be published as a NRL memorandum report.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987963
C9-364 JOURNAL DE PHYSIQUE
Additional requirements for high output power are:
8. a strong (high AL lasing transition,
9. a lack of absorption of the laser emission by other lines.
10. p,a atomic species of similar Z , for congruent/adjacent plasmas.
For the portion of the analysis involving decay rates, calculations 2
T~P
by Vainshtein and Safranova [3] and more recently by Chen [4] are used.
For the important transitions here at, Z=26, the theoretical radiative rates for these cases agree to
better than the overall estimate of 1.p
.--..--- ---
-15% given by Chen, so that either
is entirely adequate. However, the
'",'
ARIB,EEs autoionization rates can differ by
several orders of magnitude [41,
and Chen's values were used. -2hlv\.,
The simplest example satisfying criterion #1 is the lithium-like three-electron isoelectronic
sequence, with a 1s vacancy created by, e.g., photon pumping. One possible transition is indicated in Fig. 1. From available data [3,4]
on autoionization rates, it can be shown* that criterion #2 is 1 satisfied at low Z for all three
possible lower-laser configurations,
namely ls2s2, ls2s2p and 1s2pz, Fig. 1. Resonant-photon-pumped and extends to high Z (shortest laser with levels above the wavelength lasing) for the first. ionization potential (I.P.)
and autoionization from the In relating these three lower- lower level.
laser-level possibilities to
promising upper-laser levels, it is
found* that the first option (ls2s2) requires a ls2s3p upper configuration, for which autoionization rates are indeed less than radiative decay rates for 229 and criterion #3 is valid. The second choice, namely a ls2s2p lower level, may combine with either a ls2s3s, a ls2s3d, or a ls2p3p upper configuration. For the first, the single 2S1,z term, criterion 3 is only satisfied for high Z (240) and is not considered further here. For the second choice, namely ls2s3d
~ D ~ / z , B ; z , criterion 3 is met for 2218. For the third choice, namely ls2p3p, the SI 1 2 terms are satisfactory for 2,-14, the 2D3, 2 . s z are suitable for 2222, and the Z P ~ / ~ , 3 / ~ terms are very stable against autoionization for all Z's, by selection rules. Of the third possible lower-laser level, namely ls2p2, upper terms such as ls2p3s 2P~,,z.3 .z satisfy criterion #3 only for 2x32, and are also not considered further. In the ls2p3d upper configuration, the 2 P ~ / 2 , 3 / z terms obey criterion #3 for all Z's considered, while the 2D3/z,s/z terms obey criterion # 3 by a ratio of at least 3 orders-of-magnitude for the .
ratio of radiative to autoionization rates (again limited to Z(16 from criterion 2). For the Z F ~ : ~ , 7 / 2 terms, criterion #3 is obeyed for z,12.
Considering criterion #4, the natural width of the laser line divided by the wavelength can be compared to a corresponding typical ratio of 3 ~ 1 0 - ~ for Doppler broadening. This ratio decreases with Z, and hence provides a lower limit* for 2 .
The results of applying criteria #1-4 are listed in Table 1. The configuration representations in parentheses are those chosen by Chen
[4] with S,P,D subscripts added to mark the present L-values for discussion and for brevity. No distinction is made between singlet and triplet parentages here with expected collisional mixing.
Table 1. Summary of Z-dependence for criteria 1-4.
Lower Lasing ls2s2 2S (F) Is2s2p 2Pi/2 (G)
2Pa/2 (G)
Upper Lasing Is2s3p !P w i , a/2 (J) Is2p3p 2S i /2 (Ms)
2 Pi / 2 , 3 / 2 (Mp )
2D3/ 2 ( MD)
Is2p3p 2Si/2 (Ms )
2 P i / 2, 3/2 (MP )
2 Ds / 2 , 3 / 2 ( M D )
Zm 1 n
12 1 2
8 1 6
1 2 8 1 6
Zm a x 30 1 6 1 6 1 6
36 36 36
Numerous configuration combinations including some described above were ruled out* in forming Table 1 as not having a useful Z-range
(criteria #1-4), or by selection rules, or by a low absorption rate for transitions involving double-electron transitions.
Assuming now that pumping of population density in the upper-laser level will be by photon absorption from an intense line source, we choose (criterion #5) n=2 to n=l "alpha" resonance lines of hydrogenic and helium-like ions and search for good line matches within the widths of the emitting and absorbing transitions (criteribn # 6 ) .
(Other transitions, such as the 3s-2p of neon-like ions are also possibilities [1]). Both the pumping (p) and the absorbing (a) transitions are assumed to be Doppler broadened, so that we desire a maximum wavelength difference (divided by wavelength) of ~3xl6- 4.
In searching for good wavelength matches (Table 2 ) , the hydrogenic Lyman-o(, pumping wavelengths are taken from Erickson [5] and the
corresponding "helium-c<" pumping wavelengths from a recent publication by Vainshtein and Safronova [6]. For the absorbing transitions, again the calculations of Vainshtein and Safronova [3] and Chen [4] are used as indicated, depending on the best match. This is justified, since their data agree within "4x10-4 (wavelength difference/wavelength) for a typical Z=26 example and for the important transitions.
One promising low-Z wavelength (wl) match for each type of pump line is listed in Table 2 as examples*. Also listed is the ratio of the spontaneous radiative decay probability Aa for this absorbing transition to that of the helium-like 3p 1P-2s 'S transition Aae, as a figure of merit for the strength of the absorption (criterion #7) . Strong (criterion #8 above) x-ray laser transitions (TransL) and wavelengths (WIL) are also indicated. The absorption of laser emission at such wavelengths by other species (criterion #9 above), notably Z+l
(e.g., Be-like here), only becomes a problem* at very high Z.
A very promising low-Z combination is for a Lyman- ot pump ion (p) and an absorber (a) ion, both in Z=9 fluorine (the only match with the same Z, offering the decided advantage of a single-element plasma—see
C9-366 JOURNAL DE PHYSIQUE
criterion #10 above). Two possible matches are shown for the two sources [3,4] of absorption data, the first being valid for Z=13-42 and the second for Z=22-42 according to Table 1. Criterion #4 is somewhat violated, resulting in a reduced gain coefficient.
Table 2. Two samples* of possible matches.
Zp Wlp Za Wla A ( w l ) / W l T r a n S a A a / A H e W lL
[ i ] [A] (xlO« ) [ l O ^ s e c -1] [A]
Lyman-c< Pump
9 1 4 . 9 8 2 3 ( S )a 9 1 4 . 9 8 2 2b 0 . 1 3 A - J 0 . 0 7 "105 1 4 . 9 8 2 5 " 0 . 3 3
9 1 4 . 9 8 7 7 ( W )a 9 1 4 . 9 8 2 2 " 3 . 9 1 4 . 9 8 2 5 " 3 . 7
9 1 4 . 8 8 2 3 ( S )a 9 1 4 . 9 9 0c 5 . 3 B-MD O.09 "112 9 1 4 . 9 8 7 7 ( W )a 9 " 1 . 3
H e l i u m - ° < P u m p :
16 5 . 0 3 8 9d 15 5 . 0 3 8 0c l . O B-Mp 0 . 0 5 "36 15 5 . 0 4 0 9c 4 . 8 " 0 . 0 4
aS e e Ref. 5 ; " S e e R e f . 4 ; cS e e Ref. 3 ; " S e e Ref. 6 .
For a helium-°<pump ion, Table 2 shows an excellent match for S (Z=16) pumping P (Z=15) with a B-Mp, J=l/2 and 3/2 absorber that appears to satisfy all of the criteria.
In summary, a new class of quasi-cw x-ray lasers scalable to very short wavelengths and operating on transitions above the normal ionization level is described. It is proposed that the
lower-laser-level decay predominantly by autoionization, with the goal to eliminate quenching due to radiative trapping, and hence lead to large-scale x-ray amplifiers. Much systematic effort is needed to make this a reality. The selective matched-line resonant photon pumping proposed needs to be demonstrated, perhaps first on "optical"
transitons at short wavelengths. Wavelength matches suggested by calculations need to be verified by accurate photo-absorption measurements followed by fluorescence experiments prior to laser demonstrations. Detailed numerical modeling including competing energy levels and collisional mixing is very desireable, once the primary candidates are verified by atomic physics experiments.
This research was supported by the U.S. Strategic Defense Initiative Office.
References
[1] ELTON, R.C., NRL Memorandum Report No. 5906 (1986).
[2] LUNNEY, J.G., Optics Comm. 5_2 (1985) 235.
[3] VAINSHTEIN, L.S., and SAFRONOVA, U.I., Atomic Data & Nuclear Data Tables 2_5 (1980) 311.
[4] CHEN, M.H., Atomic Data & Nuclear Data Tables, 34., (1986) 301.
[5] ERICKSON, G.W., J. Phys. & Chem. Ref. Data 6_ (1977) 831.
[6] VAINSHTEIN, L.S., & SAFRONOVA, U.I., Phys. Scripta 3J, (1985) 519.
