Z-SCALING OF GAIN IN PLASMA X-RAY LASER

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Z-SCALING OF GAIN IN PLASMA X-RAY LASER

J. Apruzese, J. Davis, P. Kepple, M. Blaha

To cite this version:

J. Apruzese, J. Davis, P. Kepple, M. Blaha. Z-SCALING OF GAIN IN PLASMA X-RAY LASER.

Journal de Physique Colloques, 1986, 47 (C6), pp.C6-15-C6-22. �10.1051/jphyscol:1986602�. �jpa-

00225845�

Z-SCALING OF GAIN IN PLASMA X-RAY LASERS(')

J.P. APRUZESE, J. DAVIS, P.C. KEPPLE and M. BLAHA*

Naval Research Laboratory, Plasma Radiation Branch, Code 4720, Plasma Physics Division, Washington, DC 20375-5000, U.S.A.

" ~ e p a r t m e n t of Physics and Astronomy, University of Maryland, College Park, MD 20742, U.S.A.

Resume - L'amplification substantielle de rayons X a Bt6 recemment demontree sur la raie 3-2 du ~ 5 ' et sur des raies 3p-3s du ~ e * ~ + et de Y ~ . ^Nous ~ + considerons comment obtenir une amplification sur les m&mes transitions b plus courte longueur d'onde, en utilisant des elements & num6ro atomique plus

&lev&. Nous trouvons que l'addition d'autres BlBments dans le plasma pour augmenter le refroidissement radiatif est tr+s utile pour acc616rer la recombinaison et l'amplification de transition 3-2 hydrogenoides. Nous presentons aussi une comparaison des caractitristiques atomiques et des conditions d'inversion pour les ions hydrogenoides et n6onoides.

Abstract - Substantial amplification of x-rays has been recently demonstrated on the 3-2 line of ~ 5 ' and on some 3p-3s transitions of seZ4+and Y ~ ~ + . We consider methods of obtaining amplification on these same transitions at shorter wavelength, by using elements of higher atomic number. We find that the addition of other elements to the plasma to enhance radiative cooling is very useful for accelerating the recombination and amplification of the hydrogenic 3-2 line. We also present a comparison of the atomic properties and conditions required for inversion for hydrogenic and neonlike ions.

Introduction.

Several groups have recently succeeded in obtaining gains in excess of 3 cm-I in the soft x-ray region of the spectrum using hydrogenic and neonlike ions in laboratory plasmas. Success with the neonlke ions of selenium and yttrium has been reported at Livermore by Rosen, Matthews, and co-workers [I , 2 ] , leading to lasing at 206 A, 209 A, 155 A , and 157 A.

Three groups have achieved significant gain in the 3-2 transition of hydrogenic carbon ions at 182 A , using recombination in a rapidly cooling plasma. In the experiment of Seely, et al. [31, the cooling was provided by selenium line radiation. The magnetically confined carbon plasma of Suckewer, et al. 141 similarly relied upon radiative cooling, whereas the experiments of Jacoby, Pert, Shorrock, and Tallents 151 utilized expansion as the principal cooling mechanism to bring about recombinative gain in

c5+. Radiative cooling has also been reported to be important in the recombinative inversions achieved in lithiurnlike aluminum and magnesium by Jamelot C61 and co-workers.

("work supported by Strategic Defense Initiative Organization/Innovative Science & Technology Office through the Defense Nuclear Agency.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986602

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Since the viability of both the hydrogenic and neonlike lasing schemes has now been experimentally demonstrated, the natural progression in the search for shorter lasing wavelengths is to scale these schemes to higher-Z elements. In this article we present time-dependent atomic kinetics calculations to suggest specific experimental designs for successful accomplishment of 2-scaling to shorter wavelengths. We have chosen to concentrate on the hydrogenic recomt)Jnation scheme because of its highly favorable wavelength scaling ( A Z Z ). In the final section of this paper, we present a general comparison of the hydrogenic and neonlike schemes as they relate to successful 2-scaling.

1. Z Scaling for Hydrogenic Lasing.

As referred to above, three groups have now achieved significant laboratory gain on the 3-2 transition of hydrogenic carbon at 182 8 . Two of these experiments [3,4] relied upon radiative cooling to drive the recombination, whereas the recombination in the work of Jacoby, et al. [ 5 1 was driven primarily by expansion cooling. In seeking to scale experiments

to 2 > 6, one must choose a cooling mechanism to be employed to drive the recombination. We demonstrate here that use of radiative cooling, by seeding the lasing element with a much higher atomic number "coolant" [ 7 ] is a promising technique to achieve hydrogenic lasing at higher Z.

As has been pointed out by McWhirter and Hearn C81, Pert [ 9 1 and Elton [lo], analytical considerations with regard to the scaling of hydrogenic rates lead to the conclusion that the rate equations maintain their form under Z scaling when the electron density scales as z7. This may be seen by considering the ratio of radiative decay of the lower lasing level, which is proportional to Z4, to the collisional mixing of the lasing levels, which is proportional to Ne z - ~ . This ratio scales as Z7/~,.

Therefore, a s Z increases, Ne may be increased as z7 while maintaining the same kinetic relationship between radiative and collisional processes.

Since the number of electrons donated by the lasing element increases only linearly with Z, use of seeded high Z materials to accelerate radiative cooling becomes more attractive as the atomic number of the lasing element increases. The ion density of the lasant cannot be increased arbitrarily due to undesirable radiative trapping effects.

In their theoretical study of lasing in hydrogenic titanium [lll,

~ a v & and Pert were generally pessimistic with regard to feasibility for a system driven by expansion cooling, but raised the possibility that cylindrical compression of a plasma using techniques developed for inertial confinement fusion might ultimately prove fruitful. I n this paper, we consider the recombination kinetics of such targets, with the difference that they would be seeded with a high-Z material to enhance radiative cooling. In the detailed target design (beyond the scope of these calculations) the driving laser's pulse might be arranged to be truncated at or near peak compression, allowing very rapid cooling by radiation and expansion. In the calculations presented below, we assume that the target density is constant during the period of gain and consider only radiative cooling. Thus the calculation is conservative in that the total cooling, radiation plus expansion, is likely to be greater than that given below.

How much cooling may be realistically expected? In the optically thin limit radative cooling is parameterized by means of a cooling coefficient, expressed in W em3, as a function of temperature. When multiplied by the electron density and the density of coolant ions, a cooling rate in W cm-3 is obtained. Quite a few calculations of such coefficients have appeared in the literature. Such calculations were originally motivated by the problem of impurity radiation in tokamaks. The calculations of Jacobs, et a1 121, for nickel (2=28), show that a peak cooling coefficient of 5 x

W cm3 near 100 eY is obtained in the low-density, optically thin

limit. Jensen, et al. [I31 have utilized an average-ion model for cooling

coefficient calculations for much higher atomic number elements. Their

results for tungsten (Z=74) and gold (2=79), also exhibit cooling

coefficients substantially exceed W cmg for all temperatures between 0.1 keV and 10 keV. Although opacity is unlikely to reduce these rates in x-ray laser plasmas designed to be optically thin along the transverse axis, high density effects are likely to alter the coefficients somewhat.

Therefore, to be conservative we assume in the work that follows a constant cooling rate coefficient of W cm3 for the coolant ion which is mixed with the hydrogenic lasant. The cooling rate is not allowed to exceed 5%

of the blackbody surface-radiator limit in any of the following calculations.

2. Hydrogenic Gain Calculations.

We have calculated the gain to be achieved in the 3-2 transition of radiatively cooled, stationary recombining hydrogenic plasmas of lasant Z

10,12,14,16, and 18. Cooling is achieved by radiation from a seeded

"coolant" ion, with a cooling coefficient of W cm3, as explained above, assumed for the coolant ion. Levels n=l through n=10 are modeled for the hydrogenic stage. The calculations of collisional and radiative rates have been detailed elsewhere [14].

We find numerically that the electron density at which the 3-2 gain coefficient maximizes is given by Ne

4.2 x 1013 z7 ~ m - ~ . The z7 dependence is as expected from the above analytic consideratio s This density is about an order of magnitude lower than the 5 x 1 0 ' ' i7 ^{c i 3}

above which no inversion is possible due to collisional mixing [lo]. We also find that initial stripping of the plasma to 85% bare nuclei is about optimum. More ionization requires more energy with little increase in gain. Less ionization significantly reduces achieved gain. In stripping the plasma we envision compression to densities greater than or equal to twice the above electron density, followed by truncation of the laser pulse and rapid cooling. Our ionization calculations include the effects of electrons donated by the coolant ions and have assumed an electron density of 9.5 x 10'3 z7 cme3. The maximum compression is to a diameter of 10 pm, which has already been achieved in inertial confinement fusion experiments

[151. At this size, the lasing ion density is limited to 1.5 x z ~ ' ~

to avoid spoilage of gain by trapping in the Ly a transition. Collisional- radiative-equilibrium ionization calculations for Z

8-18 are summarized in figures 1 and 2. In figure 1, the fully stripped fraction is plotted against electron temperature in z ~ R ~ . Note that the higher the atomic number, the higher the normalized temperature (i.e., divided by z 2 ) required for ionization. This is due to the fact that radiative recombination scales as Z. The radiative recombination is not offset by photionization in a nearly optically thin x-ray laser plasma. Therefore.

the temperature required to strip to a given fraction of bare nuclei scales upward more sharply than z2. We find that the temperature required to reach 85% stripped nuclei u der the conditions of figure 1 is given approximately by Te

0.24 Z3-' eV.

In figure 2 the ionization data is presented by plotting the temperature in KeV required for 50% and 85% stripping, vs. atomic number.

The substantial difference from strict z2 scaling is apparent. We have accounted for line radiation transport in these calculations by using the velocity-dependent escape probability model of Sobolev C161, assuming a self-similar expansion with the sound velocity at the outer boundary of the cylindrical plasma.

Following cylindrical compression and heating (some deliberate preheat

using photons or hot electrons may be desirable), the plasma cools rapidly

upon truncation of the driving laser pulse. As the lasant Z increases, the

JOURNAL DE PHYSIQUE

F i g . 1 - F u l l y s t r i p p e d i o n i c f r a c t i o n v s . e l e c t r o n t e m p e r a t u r e i n z 2 Ry f o r t h e i n d i c a t e d d e n s i t i e s and s i z e .

F i g . 2 - T e m p e r a t u r e (KeV) r e q u i r e d f o r 50% and 85% i o n i c s t r i p p i n g is shown v s . a t o m i c number. A s t r i c t z2 c u r v e is shown f o r comparison.

Plasma c o n d i t i o n s a r e t h e same a s f i g u r e 1 .

( Z = 1 0 ) , n i c k e l ( Z = 2 8 ) , appears t o be a reasonable coolant choice, with a nickel/neon ion number r a t i o of 0.48 about optimum. For magnesium ( Z = 1 2 ) , s i l i c o n ( Z = 1 4 ) , s u l f u r ( 2 = 1 6 ) , and argon ( Z = 1 8 ) , coolant ion choices of molybdenum ( Z = 4 2 ) , gold ( Z = 7 9 ) , gold ( Z = 7 9 ) , and l e a d ( Z = 8 2 ) , r e s p e c t i v e l y , were made f o r t h e present c a l c u l a t i o n s . The corresponding number r a t i o s of t h e mixed c o o l a n t and l a s a n t ions a r e 1.05, 1.50, 2.43, and 3.66, f o r molybdenum/magnesium, g o l d / s i l i c o n , g o l d / s u l f u r , and lead/argon, r e s p e c t i v e l y . Of course, these s p e c i f i c choices a r e not meant t o be a b s o l u t e l y p r e c i s e . The cooling p r o p e r t i e s vary continuously with Z , and t h e c o o l a n t s may be varied from t h e above suggestions t o avoid l i n e coincidences or f a c i l i t a t e chemical f a b r i c a t i o n of t h e t a r g e t s . Tungsten ( Z = 7 4 ) , f o r example, would work n e a r l y a s well a s gold.

I n f i g u r e s 3 , 4 , and 5 , t h e recombination-gain c a l c u l a t i o n s a r e given f o r neon, s i l i c o n , and s u l f u r l a s i n g ions. The plasmas a r e assumed t o have expanded t o 1 5 um diameter. The time i n t h e f i g u r e s begins with t r u n c a t i o n of t h e d r i v i n g l a s e r pulse. Note t h e drop i n gain a s Z i n c r e a s e s along with t h e time compression of t h e l a s i n g pulse. The l a r g e g a i n c o e f f i c i e n t s predicted imply t h a t t a r g e t s of < ¹ cm l e n g t h could be employed while s t i l l achieving near-saturation. However, swept-gain e x c i t a t i o n would be d e s i r a b l e . The reason f o r t h e reduction i n gain with Z is t h a t , a s d e n s i t y and atomic number i n c r e a s e , t h e recombination occurs f a s t e r than t h e r a d i a t i v e cooling, r e s u l t i n g i n t h e l a s i n g occuring a t a higher temperature. C a l c u l a t i o n s show t h a t , i f t h e c o o l i n g r a t e c o e f f i c i e n t could be doubled t o 2 x W cm3, t h e g a i n f o r Z=16 would a l s o approximately double. The apparent l e v e l i n g of t h e e l e c t r o n temperature i n these t h r e e f i g u r e s is due t o t h e imposition of a l i m i t of 5% of t h e blackbody value on t h e cooling r a t e . We a l s o note t h a t t h e compressions r e q u i r e d do not exceed t h e c a p a b i l i t i e s of such f a c i l i t e s a s NOVA a t Livermore o r OMEGA a t Rochester. A t t h e minimum compressed diameter of 1 0 urn, and maximum

NEON 12-101

n

\

/ \

Fig. 3. - Electron temperature, f u l l y s t r i p p e d i o n i c f r a c t i o n , and 3-2 gain

c o e f f i c i e n t a r e p l o t t e d vs. time f o r a r a d i a t i v e l y cooled, recombining

neon/nickel plasma o f t h e i n d i c a t e d d e n s i t i e s . The diameter of t h e

c y l i n d r i c a l plasma i s 1 5 um.

JOURNAL DE PHYSIQUE

t Ips)

F i g . 4. - A s i n f i g u r e 3 , e x c e p t f o r a s i l i c o n / g o l d plasma.

SULFUR 12-161

laa

-

= 7.0x10'~ cm-3 N. = i.ixlOn cm"

-1.0 - 2 0 -

5

GAIN COEFFICIENT 5 2

+

Z Z

0- 15

6

4 u

E E

-0.5:-10

: _a

z

9 36 40 44 48 52 56 60 t Ips1

F i g . 5 - A s i n f i g u r e s 3 a n d 4 , e x c e p t f o r a s u l f u r / g o l d plasma.

N. = 3 X lo2'

cm?

PLANAR WIDTH 2Oom

F i g . 6 - N e o n l i k e i o n i c f r a c t i o n f o r a r g o n , i r o n , and k r y p t o n is p l o t t e - 3

a g a i n s t e l e c t r o n t e m p e r a t u r e f o r a 20pm p l a n a r plsma o f e l e c t r o n d e n s i t y

3 x 1 0 ~ ' E f f e c t o f n e g l e c t o f l i n e t r a n s p o r t is shown f o r k r y p t o n .

a r g o n - m i c r o b a l l o o n c o m p r e s s i o n s by Yaakobi and co-workers C151. Thus t h e c y l i n d r i c a l compression s u g g e s t e d by S l u t z , e t a l . [ I 7 1 and r e i t e r a t e d by Dave and P e r t [ I 11 may p r o v e f r u i t f u l f o r Z - s c a l i n g of h y d r o g e n i c x-ray l a s i n g when t h e e x p a n s i o n c o o l i n g i s augmented by r a d i a t i o n c o o l i n g from a higher-atomic-number s e e d e d element.

3. Comparison of Hydrogenic and N e o n l i k e Schemes.

Conspicuous s u c c e s s w i t h n e o n l i k e l a s i n g h a s been a t t a i n e d a t Livermore [ l , 2 ] , and c l e a r l y , s h o r t e r w a v e l e n g t h s and h i g h e r a t o m i c numbers s h o u l d a l s o b e a t t e m p t e d f o r l a s i n g i n n e o n l i k e i o n s . We c o n c l u d e by p r e s e n t i n g a few o b s e r v a t i o n s on t h e r e l a t i v e p r o p e r t i e s o f t h e h y d r o g e n i c and n e o n l i k e schemes.

F i r s t t h e wavelength s c a l i n g , haZ -2 , is c o n s i d e r a b l y more f a v o r a b l e f o r t h e h y d r o g e n i c system. The J=O t o 1 3p-3s t r a n s i t i o n (anomalou~]bygweak o r m i s s i n g i n t h e Livermore e x p e r i m e n t s ) is c h a r a c t e r i z e d by XaZ

.

However, t h e J = 2 t o 1 t r a n s i t i o n s s c a l e more f a v o r a b l y , A ~ z - ~ ' 6 1181.

a l t h o u g h n o t a s r a p i d l y a s h y d r o g e n i c i o n s . One must s t i l l pay t h e e n e r g e t i c p r i c e o f s t r i p p i n g f a r more e l e c t r o n s t o o b t a i n l a s i n g i n t h e n e o n l i k e s t a g e a t a comparable wavelength, t h a n i n t h e h y d r o g e n i c s t a g e . For i n s t a n c e , t h e J = O t r a n s i t i o n o f n e o n l i k e s e l e n i u m and t h e 3-2 t r a n s i t i o n o f h y d r o g e n i c carbon b o t h l i e n e a r 1828. However, j u s t s i x e l e c t r o n s must b e s t r i p p e d from c a r b o n , a t a p r i c e o f 1 KeV/ion, whereas 24 e l e c t r o n s need t o b e s t r i p p e d from s e l e n i u m , a t a n e n e r g e t i c p r i c e o f 1 0 KeV/ion. However, t h e r e a r e a d v a n t a g e s t o t h e n e o n l i k e system. L a s i n g c a n be a c h i e v e d e i t h e r by c o l l i s i o n a l e x c i t a t i o n o r r e c o m b i n a t i o n whereas i n h y d r o g e n i c i o n s o n l y r e c o m b i n a t i o n w i l l work due t o t h e weakness o f 1-3 c o l l i s i o n a l e x c i t a t i o n compared t o 1-2. Also, n e o n l i k e l a s i n g is more t o l e r a n t o f r a d i a t i v e t r a p p i n g - t h u s h i g h e r plasma t r a n s v e r s e o p t i c a l d e p t h - t h a n h y d r o g e n i c l a s i n g . F i n a l l y , t h e t e m p e r a t u r e r q u i r e d t o r e a c h t h e n e o n l i k e s t a g e s c a l e s a s z ~ a s opposed t o t h e . ~ Z 3 . ' s c a l i n g f o r f u l l y s t r i p p e d i o n s . T h i s is i l l u s t r a t e d below i n f i g u r e 6 , which p r e s e n t s t h e s t e a d y s t a t e n e o n l i k e f r a c t i o n s f o r a r g o n , i r o n , and k r y p t o n i o n s a s a f u n c t i o n of t e m p e r a t u r e . The e l e c t r o n d e n s i t y o f 3 x 1 0 ~ ' is t h e a p p r o x i m a t e d e n s i t y a t which a p l a n a r t a r g e t s u c h a s t h o s e employed a t Livermore [ I , 2 ] becomes t r a n s p a r e n t t o t h e d r i v i n g l a s e r ' s 0.53um l i g h t . The d o t t e d l i n e d i s t r i b u t i o n f o r k r y p t o n i n d i c a t e s t h a t l i n e photon t r a p p i n g c a n s u b s t a n t i a l l y r a i s e t h e i o n i z a t i o n l e v e l o f t h e plasma by i n c r e a s i n g t h e e x c i t e d s t a t e p o p u l a t i o n s , from which c o l l i s i o n a l i o n i z a t i o n is more p r o b a b l e t h a n from t h e ground s t a t e . -

The g e n t l e r z"" s c a l i n g of t h e t e m p e r a t u r e r e q u i r e d f o r i o n i z a t i o n t o t h e n e o n l i k e s t a g e is i n d i c a t i v e of t h e i m p o r t a n c e of d i e l e c t r o n i c r e c o m b i n a t i o n . The u n f a v o r a b l e Z s c a l i n g o f r a d i a t i v e r e c o m b i n a t i o n - dominant i n t h e h y d r o g e n i c s y s t e m - is a m e l i o r a t e d by d i e l e c t r o n i c r e c o m b i n a t i o n i n t h e n e o n l i k e i o n s . However, t h e t e m p e r a t u r e r e q u i r e d f o r n e o n l i k e i o n i z a t i o n s t i l l s c a l e s s u b s t a n t i a l l y l e s s f a v o r a b l y t h a n z2.

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