X-RAY LASERS : STATE OF ART AND PROSPECT

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X-RAY LASERS : STATE OF ART AND PROSPECT

P. Jaeglé

To cite this version:

P. Jaeglé. X-RAY LASERS : STATE OF ART AND PROSPECT. Journal de Physique Colloques,

1987, 48 (C9), pp.C9-323-C9-334. �10.1051/jphyscol:1987958�. �jpa-00227376�

JOURNAL DE PHYSIQUE

C o l l o q u e C9, s u p p l b m e n t a u n 0 1 2 , Tome 48, d b c e m b r e 1 9 8 7

X-RAY LASERS : STATE O F ART AND PROSPECT

L a b o r a t o i r e d e Spectroscopic A t o m i q u e e t I o n i q u e , U n i v e r s i t e P a r i s - S u d , F - 9 1 4 0 5 O r s a y Cedex, F r a n c e

and G r e c o " I n t e r a c t i o n L a s e r - M a t i e r e " , E c o l e P o l y t e c h n i q u e , F - 9 1 1 2 8 P a l a i s e a u Cedex, F r a n c e

Abstract

Using h o t plasmas f o r making s o f t X-ray amplifiers w i l l lead t o laboratory sources brigther than any others by several orders of magnitude. Population inversions are produced either by collisional pumping due t o plasma free electrons or by f a s t plasma coolins. Gain coefficients between 1 and 5 per cm have been measured i n the 60 A

-

200 A wavelength range.

Introduction

During the l a s t years, one has realized the capability o f h o t plasmas t o act as amplifiers i n the X-ray range /1,2/. A familiar idea i s the basic requirement of any laser t o be the existence o f population inversion between two atomic or molecular states, i n a gaseous or solid material, s o t h a t decay by stimulated emission may yield amplification. The production of population inversion needs pumping energy. I n the case of X-rays, owing t o the short life-time o f excited levels, the d i f f i c u l t y was t h a t a large amount o f pumping energy must be brought i n t o the active medium i n a very short time. Therefore a huge power was required i f the usual pumping techniques were t o be used. Now the fact i s t h a t hot plasmas can give r i s e t o population inversion and stimulated emission just i n consequence o f a suitable matching o f atomic physics and hydrodynamics, i.e. without external pumping. This has kept out the great difficulties associated with the optical pumping o f an X-ray laser. We w i l l explain the main physical mechanisms which make that possible and lead t o t w o major types o f inversion schemes, i.e. the recombination i n cooling plasma and .the free electron collisionnal pumping. Then we w i l l shortly describe the principle o f s o f t X-ray laser experiments and the r e s u l t s obtained so far.

We w i l l conclude i n comparing X-ray lasers with other sources regarding the brigthness and possible applications.

Plasmas f o r s o f t X-rav l a s e r s

I n hot plasmas the electronic temperature i s comprised between 100 ev and several Kev (1 ev corresponds t o 11605'K). The X-ray emission comes from optical transitions between the states o f multicharged ions. Z being the charge o f the i o n core, i.e. the number o f removed electrons, and n the main quantum number, i n the simplest case the energy o f the l e v e l n I s related t o

Z

by:

I n addition t o discrete l i n e radiation (bound-bound transitions), radiative recombination (free-bound transitions) and Bremsstrahlung (free-free transitions) produce a continuous X-UV spectrum.

Admitting t h a t the multicharged ions o f h o t plasmas can work as X-ray emitters, special requirements have t o be met i n order the plasma may effectively amplify radiation. The characteristic feature o f an amplified radiation i s i t s relation intensity w i t h the length covered i n the emitting medium. G being the gain coefficient, L, the length, S the source function, the intensity reads (see figure 1):

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987958

C9-324 JOURNAL DE PHYSIQUE

whereas a t wavelengths where the medium i a absorbing, w i t h a absorption coefficient a , one has :

Figure 1. Illustration of a two level radiative transition i n a medium of finite length L. Nl/gils are the so-called reduced populations, i.e. the total population of level i divided by the statistical weigth of the level.

both expressions reducing each other w i t h the s u b s t i t u t i o n :

Now, l e t i and j be the quantum numbers o f t w o excited levels, the l e v e l j l y i n g above the l e v e l i; l e t v be t h e j-i t r a n s i t i o n frequency, 4V) the p r o f i l e function o f the transition, g- and g j the s t a t i s t i c a l weights. I n thermal equilibrium a t electron temperature Te, the t w o l e v e r population densities, Ni and Nj, are related by:

and the emitted radiation i s re-absorbed inside the plasma, w i t h an absorption coefficient:

where Bi i s Einstein's absorption coefficient. I f we know how t o produce a population inversions!n the plasma, we w i l l have:

where AN i s the inversion density:

I n the 100 ev photon energy range, ( 6 ) leads to:

Plasmas may produce population inversions e i t h e r when a rapid change o f temperature and density o r i f a strong energy f l o w in stationary conditions breaks down the thermodynamical equilibrium. F o r the theoretical prediction o f population inversions as w e l l as t o make simulation o f experiments, t w o computational models are generally used together. The f i r s t provides the time evolution of plasma density and temperature. The second uses these l a s t as parameters in the system of r a t e equations which represents the atomic properties o f the ions.

Now, given the size o f laboratory plasmas and owing t o the lack o f high quality X-ray mirrors, t o reach the gain-length value o f 20

-

30 necessary f a r a n X-ray laser, we must have:

Since the per-level denslty I s a maximum value of A N we can s e e t h a t excited level density around 10gcm-3 is necessary for population inversion t o yield an effective amplification.

Such conditions can be satisfied in laser-produced plasmas. Figure 2 shows the principle of plasma production by cylindrical focusing of the laser beam onto target surface. This realizes a plasma "column" which has approximately constant properties along parallel-to-surface axis, while density and temperature vary in the perpendicular direction. The steepness of these variations depends on the exact target geometry and on the laser shot power. Density and temperature appropriate for lasing plasma are generally found between 50 uand 5 0 0 1 ~ from target surface.

Figure 2. Cylindrical focusing of powerful laser beam onto target produces a hot plasma 'column'. The plasma has constant properties along axis parallel to the surface but varies strongly from the surface to the empty region, as

shown

by the left curves. Density and temperature are suitable for soft X-ray amplification at short distance (1.e. .~10Op) from the target. The plasma life-time i s of a

few

nanoseconds or less.

Recombination laser9

Early considered in hydrogen /3/, the recombination scheme has been extensively studied in H-like ions with a view of

XUV

amplification. Let u s consider a plasma, initially completely ionized. Due t o f a s t cooling, the plasma g e t s out of equilibrium. Three body recombination populates strongly the most excited levels of the recombined H-llke ion. This I s followed by collisional-radiative cascade t o intermediate levels. At the same time, owing t o free-electron low temperature, electron-ion collisions from the ground level can no longer balance the radiative decay of the lowest lying levels. As a consequence, transient population inversions occur between intermediate and lower levels.

In t h i s respect, the group of Hull University has shown the adiabatic expansion of a freely expanding plasma t o be able t o produce a population inversion between 2-3 levels of H-like carbon a t 182 A wavelength./4/. A slightly different scheme, including plasma confinement in a strong sinusoidal magnetic field, has been developped by S. Suckewer e t al. /5/. Besides the emission of radiation from ions having strong resonant lines does also contribute t o plasma cooling. Lithium-like ions are of a special interest because intense is the line emission of the parent ions (He-like).

The case of aluminium is examplified in figures 3 which give the variation of helium-like and lithium-like Ion abundances during a 3 n s l a s e r pulse (3 a) and the 4f

-

3d and 5f

-

3d population inversions (3b) a t fixed distance from the target, with corresponding Ne and Te. These i n ~ e r S l 0 n ~ occur respectively a t 154 A and 105.7 A . / 6 / . One can s e e t h a t the maximum of

~ 0 ~ ~ l a t i 0 n inversion occurs about 3 n s a f t e r the laser pulse. This delay i s typical of recombination mechanism of population inversion production.

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PHYSIQUE

Figure 3 a. Lample of calculated ion abundances as a function of time in aluminium laser-produced plasma. Hatched area, laser pulse; sol

i d

curve, l i thium-l ike ions; dashed curve, he1 ium-l ike ions; dotted curve, electron temperature ( m a x i m at 210 ev). The vertical arrow indicates the predicted moment of the 3d-Sf population inversion outset.

Figure 3

b.

AI~O' ion. Below: time-variation of 5f -

^3d

(solid curves) and 4f - 3d (dashed curves) population inversion densi ties in the space region of their maxima

(

0.35 mm from the target). Above: plasma electron density and temperature at the same

posl

tlon. Pulse duration (displayed in dashed area): 0.6 ns. a) Laser wavelength: 1.06

11 ;

flux density: 12.7 GW/cm.

b)

Laser wavelength: 0.53

lJ

. ^Flux

density: 12.7 GW/cm. c) Laser wavelength: 1.061-1

;

flux density: 21.6 GW/cm.

Princeton experiment

I n Princeton experiment (USA) the plasma i s produced, along the a x i s o f a 4-m radius spherical mirror, by a high power

co2

laser, and i t i s confined by a sinusoi'dal magnetic field.

The t a r g e t may be e i t h e r a gas o r the edge o f a hole i n a s o l i d disc, possibly completed by blades making the plasma more uniform

/7/.

This s e t up i s represented i n figure 4.

E X P E R I M E N T A L A r l R A l G E I E H l W I l I I X U V MIRROR

Figure

4.

Device producing a magnetically confined laser-plasma at Princeton University. Amplified X-rays are detected by the axial monochromator.

I n t h i s system the column length i s n o t measured as precisely as w i t h cylindrical focusing optics. Moreover i t cannot vary without changing other plasma parameters. Therefore the gain

XUV Mirror:% XUV M i r r a r : O p r n

Figure 5. On the left, enhancement of the 3-2 line of

c5+

fran transverse to axial observation. The gain G.L deduced from this measurement i s of 4.3. On the right, additional enhancement due to the XW spherical mirror represented i n figure 4.

i s deduced from line intensities measured simultaneously i n axial and transverse directions, the lasing transition intensity being normalized w i t h the help of another l i n e which must not t o be affected by radiation trapping. Owing t o magnetic confinement, the gain produced by plasma recombination does l a s t a time longer than i n other experiments.

A gain-length product, G.L, as large as 6.5 has been obtained a t 182 A (2-3 transition o f H-like carbon). A further and very impressive proof o f amplification i s given by using an X-UV multilayer spherical mirror. The r e f l e c t i v i t y o f the mirror a t 182 A was measured t o be 12 %, whereas the increasing o f the l i n e i n t e n s i t y along the a x i a l direction, due t o the mirror was about 100 % t8/. Figure 5 gives exampIes o f the results.

Rutherford Laboratory experiment

One o f the f i r s t , the group o f H u l l University (UK) has shown the adiabatic expansion o f a freely expanding plasma t o be able t o produce a population inversion between 2-3 levels o f H-like carbon provided t h a t the expansion rate o f the plasma i s optimized by choosing an appropriate target geometry /4/.

Rutherford Laboratory has developped a laser-beam focusing system especially suitable f o r fibre target irradiation. I n consists i n a combination of focusing lens and off-axis spherical mirror which produces a line focus free o f transverse aberration. Up t o six laser beams can be brought round on the same t h i n fibre o f 7-mm length. Various options i n beam arrangement enable t o choose among d i f f e r e n t lengths. A sketch o f the interaction chamber can be seen i n figure 6. This system has b en successfully used f o r measuring the variation o f intensity w i t h length for the 3-2 line o f Cf+ a t 182 A. The result i s the curve shown i n figure 7 which exhibits an exponential increasing w i t h a gain coefficient about 4 cm-* /9/.

A similar result, with a gain coefficient o f 3 cm-I, has been reported f o r the 80;9 A line of H-like fluor produced from a L i F coated f i b r e target

/lo/.

7 0 U R N A L DE PHYSIQUE

TIME RE SOLVED SPECTROGRAPH

n

P'

.FIBRE TARGET

LASER A=

0

53ym

Figure

6.

Sketch of the Rutherford Laboratory experiment, illustrating the focusing optics designed for thin fibre irradiation.

Figure

7.

Line intensity of the

2-3

transition of carbon 8-like ions (on the right) versus the length of plasma column, as compared to the

3-4

line (on the left).

Palaiseau e x ~ e r i m e n t

Palaiseau experiment

( F f

uses the Greco llInteraction Laser-Mati&reW facilities. The laser beams have 90-mm diameter. Two of them are available for the present X-ray l a s e r experiment.

A

focal line with a length up t o

2

cm

is

produced on the surface of a massive target by a system

of

two crossed cylindrical lenses. The l a s e r energy i s about

200 J

per pulse

/6,i

l/.

The particular way of using here the property expressed

by

relation

(1)

consists in choosing a

couple of two plasma lengths and t o obtain-a relatively extended gain (absorption) spectrum, a t

one go, from the recording of only two emission spectra in the same axial direction. If L and 1

are two plasma column lengths (at same density and temperature), IL and I1 being the

corresponding intensities a t a given frequency, the gain coefficient for t h i s frequency

is

obtained by solving the equation

/12,13/:

Figure 8. Gain a function of time for the 5f

-

3d transition of A l e measured for a 0.7

ca

long plaana column.

L a y ~ - p u k ~

half-maxim duration: 2.5 ns; flux density: 5x10

W/ .

The plasma radiation i s recorded with a streak camera providing a time-resolution about 100 picosecond. I t can be connected with an OMA instead of the usual photographic camera. This provides directly digital data from the time-dependent plasma spectrum /14/.

A typical result achieved by using t h i s proce ure i s presented i n figure 8 which reproduces

%

the time-dependence of the 5f-3d line of ~ l l 'for a plasma column of length L = X cm. The laser-pulse width i s X ns. The investigated plasma section i s located a t a distance X = X mm from the target surface. I n this case a gain with a peak value of X cm-I i s observed a t the center of the line. The peak of gain displayed i n figure 8 has been shown t o occur i n the expanding aluminum plasma about 5 ns a f t e r the top of the Nd-laser pulse.

The shortest wavelength for which a gain has been observed up t o now i n using recombining lithium-like ions i s 65 A. This i s the wavelength of the 3d-5f transitions of $I3+. The value of the gain i s near i cm-l/15/.

For particular multicharged ions species, steady state population inversions are predicted by calculation as a result of the balance between collisionnal ground state excitation produced by plasma free electrons, on the one hand, and f a s t radiative decay of low lying levels, on the other hand /16,17/. The neon-like sequency i s far the most extensively studied up t o date. For rate from the ground level i s approximately the same levels. A t the same time, owing t o selection rules, the 3p t o the ground level i s strictly forbidden, whereas i t i s quite large from 3s level. Moreover there i s a large rate of population transfer from 3d t o 3p level by radiative and collisionnal cascades. As a consequence, population inversion can occur between the 3p and 3s levels provided that plasma free electron density i s chosen i n a suitable range. Rate equation calculations show that population inversions occur only i n a rather narrow range of plasma electron density. A t low density, there i s no collisional pumping and, when the density becomes too large, collisional mixing between the levels leads t o statistical equilibrium for populations. As an example, the gain calculated f o r neon-like strontium i n the range of 160 A wavelength i s shown i n figure ( 9 ) /18/.

N1-like sequency i s also under active consideration. I n t h i s case inversions may appear on 4p-4d transitions /19/.

JOURNAL DE PHYSIQUE

Figure 9. Gain calculated for various 33-3 transitions of neon-like strontium (near 160 A wavelength) versus plasm electron density at fixed temperature (800 ev)

/1W.

Livermore exveriment.

Large gain coefficients have been measured a t Livermore (USA), i n 1985, with neon-like ions /20/. Livermore experiment uses t w o arms o f the giant Nova laser, the beams o f which have 74 cm o f diameter. 2000-5 laser energy, o r more, can be deposlted on the target with a pulse length about 0.5 ns. The target 1s a t h i n foil, f o r instance a 1500-A thick substrate o f formvar coated w i t h a 750-A layer o f selenium. The sketch o f the experimental set up i s shown i n figure 10.

XRL foil on aluminum support structure

Pinhole

r

^On axis McPigs spectrograph

\a-

LTGSS or streaked beam divergence camera or beam divergence camera

Flwre 10. Sketch of the Livermore experlment using tvo a m of the Nova laser for producing a hot plassa column of 1-2

cm

length. Amplification i s observed at 206 A and 209 A i n neon-] ike selenium.

A grazing incidence spectrograph, provided w i t h a gated microchannel plate detector, records the s o f t X-ray signal in the direction o f the axis o f the plasma column. The evidence of amplification i s given by the p l o t o f the signal intensity versus the plasma length. The gain coefficient i s found t o be near 5 cm-l. Figure 1 1 shows a r e s u l t obtained with a Selenium plasma o f 4 cm length. The gain-length product in t h i s experiment i s a s large a s 16 /21/.

Since the f i r s t experiments, a considerabla progress has been made a t Livermore on the way of a true X-ray laser. A succesful attempt o f lasing inside a cavity, which i s made o f a spherical multllayer mirror and a semitransparent multllayer t h i n plate /22/, has been recently performed /23/. In addition, the Ni-1 ke sequency has been proved t o yield amplification a t short wavelengths. A gain about 1 cm-l has been observed a t 66 A with europlum /24/.

Target length lmml

Figure 11. Line intensity of 3p-3s transition of selenium neon-l ike ions versus the length of plasm column /21/.

CEL e x ~ e r i m e n t

Various attempts t o realize collisionnal pumping with more economic means than in Livermore experiment have been made /25,26/. A recent result obtained a t Limeil

(F)

is presented in figure (12). I t shows the large increasing of lines a t 232 A and 236 A according t o plasma length. The lines belong t o the spectrum of Ne-like germanium. The target was a thin meta layer on plastic foil. The irradiation i s made by six beams of the laser Octal, delivering 7x 10 1

d

w/cm2 on the focal line on each side of the target /25/.

ZI

experiment

.

Figure 12. Enhancement of the 3s-3p (551-2) lines of neon-l ike germanium according to plama length L in

CEL

Besides recombining plasmas and collisional excitation, a very different approach i s s t i l l t o be mentionned

.

I t consists in looking for population inversions created by multiphoton absorption of KrF-laser radiation / 7/. This type of l a s e r can de iver powerful g u s t s of five-ev photons.

d

²

a

Starting rom the 4 s 2p ground s t a t e of Kr-like Cdli+ Ions, for Instance. one could p o p ~ l a t e t h e 4s4p 5p s t a t e . Then gain could take place on either the 5p-4d or 4p-4s transitions. Pumping must be done on a picosecond time scale in order t avoid the radiative decay of the upper t o the ground s t a t e . Laser intensity of the order of 10 w/cm2 i s required. P5

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Conclusion

Works described in the previous sections show that hot plasmas o f sufficient density are able t o amplify s o f t X-rays. A s regards the comparison o f X-ray lasers with other sources, a very large enhancement w i l l occur i n t h e i r brightness. ssuming "realistic" experimental conditions i n which the observed emitting area should be I O q cm2, the solid angle a t the entrance o f the meas rement device being

Y

steradian, one f i n d s approximately the same number o f I

-

5x10 photons per pulse or a line a t 100 ev ( =120 A) emitted by laser plasma and tokamak. B u t the pulse duration i s 10 times shorter f o r laser than f o r tokamak, leading t o the same r a t i o

8

between t h e i r brihtnesses, t o laser advantage. I n a similar way, typical photon number and brightness are compared i n table 1 f o r various sources, i n l e t t i n g i n a thermal line broadening of 0.02% f o r plasmas and using the same band width f o r other sources. Although we did .not explain yet how w i l l work an X-ray laser, i t i s interesting t o compare i t s predicted capability t o other devices i n the same photon energy range The estimate displayed i n table I i s made out i n assuming a population inversion density o f l ~ ~ ~ c m - ~ i n a 10 cm long amplifying plasma column.

TabIe 1. Comparison o f s o f t X-rav sources

Source Pulse duration(sec) Photons per p u l s e Briahtness ta.u.)

Tokamak plasma 10-I 1

-

5 x 1 0 ~ 1

Laser plasma

l o +

¹

-

^5x104

l o 8

Storage r i n g 2x10-~O

&lo3 l o 8

Undulator 2x10-lo 2 x 1 0 ~

loi3

S o f t X-rav l a s e r Sxlo-10 1012 d 6

From now onwards, systems involving hydrogenic, lithium-like and neon-like multicharged ions can be used f o r developping amplifiers. A propitiou circumstance i s these systems t o provide f a i r l y large gain coefficients o f the order o f 1 cm-f

-

5 cm-l. Given the moderate reflectivity wich can be expected from s o f t X-ray mirrors, large gain coefficient i s indeed an essential condition f o r achieving X-ray lasers. A great deal o f work i s s t i l l t o be done f o r improving the control o f large gain production.

To succeed i n overtaking the saturation threshold, above which there are approximately as much photons as inverted atoms i n the active medium, the using o f interferential mirrors has t o be extended and, on the other hand, i t i s necessary t o increase the length o f plasma column. In keeping constant the heating flux density on the target, increasing length needs more energy.

A t Palaiseau we w i l l use f i v e laser beams f o r producing 6-cm long plasmas w i t h a few tens o f GW/cm.

D i f f i c u l t i e s f o r achieving large gain i n long plasma can appear from several directions.

Deffects i n laser-target coupling may cause an erratic spatial distribution o f gain coefficient, preventing amplification t o develop completely along the axis. Second, the density gradient perpendicular t o the target surface does produce refraction, which may e n t a i l a simililar consequence i n bending the trajectory o f the radiation. New target designs, minimizing t h i s gradient, are thus necessary, especially f o r systems working a t large density. Finally, increasing o f plasma size tends t o increase also the radiation trapping f o r non-lasing lines. In recombination systems t h i s may reduce the population inversion by photoexcitation from low-lying levels. New constraints f o r target design r e s u l t from this, w i t h a view t o make transverse escape o f radiation as free as possible

.

Shorter wavelengths are under active consideration f o r future X-ray laser experiments. The schemes described above can be extended t o ions o f higher

Z

provided that plasma temperature i s large enough. The wavelength-to-temperature scaling d i f f e r s considerably according t o the population inversion scheme. This i s shown i n terms o f density flux deposited on target surface in figure 13 where the points below 50 A and the lower point o f molybden are calculated.

Figure 13. In order to decrease the lasing wavelength more energy must be spent for producing the plasma. This figure

shows

how the density pcuer onto the target does scale with the wavelength for the col l isional schemes (Ne-l ike and Ni-like ions) and the recabination schemes (H-like and L1-like ions). The dashed vertical lines delimit the uwater-windawB which is of a great interest for blological applications.

Lithium-like ion plasma allows an especially economical extenslon t o short wavelengths b cause, in t h i s case, lasing wavelength and plasma temperature have approximately the same ZS-scaling. The figure displays the "water-windowt1 which is a wavelength range of great interest t o r biological applications. Inside t h i s window, radiation is absorbed by the K-edge of carbon atoms of organic molecules but not by the oxygen K-edge of water molecules. Thus using an X-ray laser in the water-window would make possible, for instance, holography of living samples.

This work has been partially supported by DRET under contract 85/1437.

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Journal de Physique, Vol. 47, Colloque C6, Supplement N o 10, 1986.

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