X-ray spectroscopy and imaging of hot dense plasma created by colliding foils. Simulation of spectra

Pergamon J. Qunnt. Spectrox Radiat. Transfer Vol. 58, No. 4-6, pp. 721-735, 1997

Q 1997 Published by Elsevier Science Ltd. All nghts reserved Pnnted m Great Bntain

PII: 80022-4073(97)00078-2 0022-4073/97 $17.00 + 0.00

X-RAY SPECTROSCOPY AND IMAGING OF HOT DENSE PLASMA CREATED BY COLLIDING FOILS. SIMULATION

OF SPECTRA.

E. LEBOUCHER-DALIMIER_F, P. ANGELO?, P. GAUTHIERt, P. SAUVANt, A. POQUERUSSEt, H. DERFOULt, T. CECCOTTIt,

C. A. BACKS, T. D. SHEPARDS, E. FhRSTER§, I. USCHMANNg and M. VOLLBRECHTg

TPhysique Atomique darts les Plasmas Denses, LULI, CNRS, Universitk Parts VI, 4 place Jussieu, 75252, Paris, cedex 05, France, and Ecole Polytechnique, 91128, Palaiseau cedex, France, ILawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551, U.S.A. and §MPG Research

Unit X-ray Optics, Friedrich Schiller Universitlt, Jena, Germany

Abstract-A simple strategy is presented to create moderately coupled plasmas: it consists in a colliding foil system irradiated by two laser beams. In these correlated plasmas, signatures of transient molecular behaviour are shown. Two studies are intensively developed here: the simulation of the experiment and the X-ray spectroscopic and imaging diagnostics. A reciprocal action between the two studies allows an optimization of both the compression and the associated dense plasma effects. We present accurate fluorine Lyfi spectra as an appropriate example for the exhibition of the non-spherical symmetry of the bound electronic structure. 0 1997 Published by Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

The study of hot-dense plasma physics is stimulated by its connection with inertial confinement fusion (ICF) goals and with astrophysical situations (white and brown dwarfs). In this work our

interest lies more specially on strongly correlated plasma effects such as satellite-like features exhibited in the X-ray emission of dense laser-produced plasmas lm3. Such features have been attributed to transient dicenter emitters resulting from the interaction of the bound states of a monocenter ion with its nearest neighbour ion when the Debye length is being comparable to the interionic spacing 3.4. As shown by Foulis et al 5 and Gauthier et al 3, strongly correlated plasmas require the use of multicenter wavefunctions. When concerning moderately coupled plasmas (i.e. 1 I r I 2), which are our plasmas of interest, only dicenters have to be considered because of their high probability distribution. As a consequence cluster formations and band structures are excluded. Moreover these moderately coupled plasmas are not degenerate.

Such plasma conditions had been previously achieved in the laboratory by irradiation of massive targets with an intense laser beam (IL w 1014W cm-’ at 4 0). These pioneer experiments allowed the exhibition of reproducible red satellite-like features on fluorine Lyfi profile from the densest plasma emission. But as this dense plasma was cold (150 eV), weakly emissive and moreover difficult to access, we worked towards the design of new experiments to confirm the evidence of molecular effects in strongly coupled plasmas. Our idea was to realize an emissive matter compression. We rejected the spherical compression generating a weakly coupled dense plasma because of the high temperature produced (> 1 keV) and held the emissive planar compression scheme which can lead, when precisely driven, to moderate temperatures (30&400 eV) and high densities (1-2.1O23 cme3). In this work we present colliding foil systems devoted to the exhibition of strongly correlated plasma effects and we show that the varying plasma conditions are not deleterious for the exhibition of the satellite features. The evidence of the prominent expected molecular effects has been recently strengthened by a molecular emission code (IDEFIX)3 which shows that the satellite positions do not depend significantly on the electronic density and temperature within the plasma coupling range 1 < r < 2. As a consequence, time and space integrations over such plasma conditions will not smooth the satellite-like features but on the contrary will emphasize their intensities if the transient molecules can be formed.

721

722 E. Leboucher-Dahmier et al

We used two synchronised opposing laser beams of the LULI facilities at 4 o (1 = 0.263 pm), with an energy between 8 and 25 J during a pulse duration 500 ps. These beams were focused onto two thin Al or CF, foils facing each other with initial thickness 1.5 I e < 7 pm and initial separation 50 I d I 200 pm (see Fig. 1). The small focal spots (.a’ 80 to 200 pm) allowed average laser intensities as high as 4.1014 W cm-*. X-ray diagnostics view the system perpendicular to the collision axis: on one side a spectrograph with a spatial resolution along the collision axis, i.e. the laser beam axis (spectrograph 1 PABURCE) and on the other side a spectrograph with a spatial resolution in the transverse direction (spectrograph 2). This second spectrograph can be replaced when required either by a pinhole camera or by an X-ray monochromatic camera.

In the first part we present 2D hydrodynamics simulation results modeling the colliding foil system and leading to estimations of the initial parameters (foil thickness and separation) necessary for an emissive compression drive. In the second part we give time integrated emission diagnostic results and discuss their agreement with the simulations, specially for the optimized compression. The last part is devoted to the exhibition of dense plasma effects in F lyj3. These reproducible effects can be explained by the molecular radiative code 3. In conclusion improvements in the experiment are suggested and the possible exhibition of molecular effects in Lyj3 for different materials is discussed.

2. EMISSIVE COMPRESSION DRIVE BY 2D SIMULATIONS

Our purpose was to generate an emissive plane compression. In order to design the experiment and to estimate the parameter values (the mean laser intensity IL, the focal spot with its gradients, the foil initial thickness and separation) LASNEX 2D hydrodynamics simulations 6 were run. These simulations, using the collision symmetry and neglecting the possible interpenetration of the two plasmas in the colliding zone, compute self-consistently all parameters in a half-space along the collision axis. As a matter of fact for optimal initial conditions leading to a colliding foil regime, there is no interpenetration of the matter in the central plasma created because the electron mean free path is much smaller than the density gradient length.

The LASNEX version performing the calculations for our experiments takes account of two dimensional effects generated by the inhomogeneous laser irradiations: distortion of the foil, plasma lateral expansion ‘.*, plasma lateral thermal conduction, all these defects leading to an absorbed laser energy loss deleterious for the expected compression 9. In our case the laser pulse shape was a gaussian, centered at time t = 0, of full-width-half maximum 0.5 ns. The laser beams were focussed to 80-100 pm diameter spots, yielding peak intensities 10’4+4.10’4 W cm-*.

The starting point in these colliding foil systems is to choose the foil initial thickness and separation in such a way that the remaining matter can collide with a maximum kinetic energy before the end of the pulse. This kinetic energy is favourable for a good compression (high density) and for a strong emission (high temperature). Moreover the foil ablation must be important enough for the foil rear faces to get “hot” before the collision, but not complete for the efficiency of the compression. From this short discussion and from the analysis of the simulation results the best criterion for a good compression is obviously that: the electronic density maximum in the foil rear

/. pinhole camera - X-ray monochromatic

camera - Spectrograph 2

Fig. 1. Implantation of the targets and the diagnostics for colliding foil experiments. The spectrograph 1 ensures a space resolution along the collision axis. The spectrograph 2 gives access to the emission along the transverse direction. This spectrograph could be replaced by a pin-hole camera or an X-ray

monochromatic camera.

X-ray spectroscopy and imaging of hot dense plasma

Foil explosion before laser pulse top : colliding plasma situation

CF, 3 pm, d=lOO urn (16J, 5OOps, focal spot a=80 pm)

1.60

-9 000 -500 0 500 1000

t (ps)

(a)

-0.5 nsec

723

0 0.005 0.010 0 o-.oa5 0.010

LASNEX 2D SIMULATIONS

(b)

Fig. 2. (a) Predictions from LASNEX 1D and 2D for the electronic density and the electronic temperature at the rear face of two CF, foils (e = 3 pm, d = 100 pm) irradiated by two laser beams (16 J, focal spot 0 80 Mm). 0 ps refers to the laser pulse top. The 2D version gives a density maximum before the laser pulse top. The foils explode. (b) LASNEX 2D simulations for CF? foils (e = 3 pm, d = 100 ,um) irradiated by two laser beams (165, focal spot @ 80 pm). One can see the distortion of the foils and the lateral expansion. 0 ns refers to the laser pulse top; distances are in cm. The foils explode 100 ps before the laser

pulse top.

faces must occur at the laser pulse top and just before their electronic temperature maximum. We currently made several simulations by varying initial thickness and separation of the foils. Figure 2 and Fig. 3 give the simulation results for CF? colliding foils for two regimes: the foil explosion (i.e.

the colliding plasma situation) and the emissive compression (i.e. the colliding foil situation), respectively.

Figure 2(a) shows the time evolution of the electronic temperature and density in the rear faces (i.e. the inside surfaces supposed to collide) of CF2 foils (initial thickness 3 pm, initial separation 100 pm) irradiated by laser beams with an energy z 16 J. The time is referred to the laser pulse top (0 ps). One can clearly see from the 2D results that the density exhibits a maximum z 100 ps earlier than the laser pulse top and the electronic temperature gets high enough for the foils to be pierced. At the time reference 0 ps two plasmas will collide. Later the density and the temperature decrease in the colliding zone due to the loss of laser energy through the plasmas.


We also show in Fig. 2(a) that 2D effects are decisive for the compression optimization. A ID code would not allow the foils to explode and would lead to a completely different physical situation: at the laser pulse top the electronic density computed by 1D code is two orders higher than the 2D version prediction; as a consequence at that time the “2D electronic temperature” is much higher than the “1D temperature”, the subcritical plasma being heated by Bremsstrahlung. For that scenario we give in Fig. 2(b) the evolution of the mesh at different times. We have the evidence of the foils distortion and of the lateral expansion. Moreover we can see the explosion of the foils before the laser pulse top.

By increasing the thickness of the foil from 3 to 5 pm, an optimized compression regime is achieved (Fig. 3): the density maximum (l-2 1O23 cme3) is synchronized with the laser pulse top; the corresponding electronic temperature is 400 eV. These predicted optimized conditions (d = 100 pm, e = 5 pm for laser energy 16-20 J) for CF2 foils will be, as we will see, in good agreement with spectroscopic analysis.

3. X-RAY DIAGNOSTICS

All the diagnostics implemented view the X-ray emission merging transversely (i.e. perpendicularly to the collision axis) from the plasmas inside the foils and outside forward the laser beams. These diagnostics are time integrated in order to get an intense signal on the film detector for the compressed central plasma: as a matter of fact, LASNEX simulations show that the emission from this central plasma lasts but a few 10 picoseconds.

1 Optimized compression : colliding foil situation 1

CF2 5 p, d=lOO m (205, SOOps, focal spot @=-.8Oprn)

10 =

10’ q Ne (t=O)= 1-2.1023crn-3

Te (t=O)= 400 eV

Fig. 3. Predictions from LASNEX 2D for the electronic density and the electronic temperature at the rear face of two CFz foils (e = 5 pm, d = 100 pm) irradiated by two laser beams (205, focal spot 0 80 pm). 0 ps refers to the laser pulse top. A density maximum is exhibited at the laser pulse top. The

foils collide and the compression is optimized.

X-ray spectroscopy and imaging of hot dense plasma 725

Al, e=lSpm, d=lOOpm, E=8J Dispersion

b

Spatial resolution along the collision

axis

Hea Hep

LYa LYP

Colliding foil regime

Fig. 4. Al spectrum for a strong compression of the foils. The spatial resolution takes place along the collision axis (spectrograph 1).

3.1. Axial space-resolved diagnostic (spectrograph I)

We used a Johann spectrometer with a gradually bent concave KAP crystal lo allowing the observation of very fine structures thanks to a high resolution (R z 2000 for FLY/J and AlLyfi). An entrance slit 5 pm ensures a space-resolution along the collision axis and a high transversal magnification ratio (CT w 120) favorable for a precise mapping of the plasma characteristics along this axis. As the longitudinal magnification ratio is low (G, z 0.02 for the spectral lines of interest), the plasma extension in the dispersion direction does not affect the line broadening and the spectral resolution.

As predicted by the simulations we observed two regimes according to the collision parameters (foil thickness and separation) and the incident laser intensities. The examples presented here concern aluminum foils leading to very intense spectra.

For a colliding foil situation (d = 100 pm, e = 1.5 pm, E = 8 J) we can see in Fig. 4 the emission in between the foils from their initial position until and after the collision; the two external symmetric zones of the spectrum are due to the emission from the coronas towards the beams and detected through the foils. The emission recorded from the compressed zone inside the foils reveals intense and broadened lines over a distance corresponding to z 10 pm plasma.

Keeping the same foil thickness as previously and increasing the separation and the laser energy, we achieve a colliding plasma situation (Fig. 5): as the foils rapidly explode, the two generated plasmas expand, collide and interpenetrate each other. We observe no breakdown in the emission on the film: only one zone exhibits lines more or less broadened according to the space/time evolution of the plasmas. Such colliding plasma situations have been observed by Chenais I’.

From this axial space-resolved diagnostic we could access the collision parameters optimizing the compression and verify their agreement with the predicted values from the simulations.

3.2. Transverse space-resolved diagnostic (spectrograph 2)

We used a spectrometer with a convex PET crystal allowing a theoretical spectral resolution 5000 (for AlLyP). This resolution is drastically reduced to 2500 due to the non-negligible magnification

726 E. Leboucher-Dalimier et al

Al, e= 1.5pm, d=lSOpm, E=20J Dispersion

Spatial resolution along the collision

axis

Hea Hep

LYa LYP

Colliding plasma regime

Fig. 5. Al spectrum for a plasma collision regime. The spatial resolution takes place along the collision axis (spectrograph 1).

ratio G ,_ z 0.85 in the dispersion direction which is also the plasma extension direction along the collision axis. As a consequence, on each line, we can access a mapping of the plasma along this axis; this characteristic, joined to the transverse space-resolution (ensured by a 30 pm slit and controled with a magnification ratio G, z 6 to 20) leads to a 2D plasma imaging on each line (spectroheliograms). Figure 6 gives a typical result for this diagnostic in the case of an optimized compression: for each line, the emissions from the compressed zone and from the two coronas are reproduced in two dimensions. The longitudinal and transverse dimensions of the compressed plasma emission, 10 pm and 80-100 pm respectively, could be estimated.

Al, e=6pm, d=150pm, E=20J

Dispersion and extension of the plasma along the collision axis

Hea Hep

LYa LYP Fig. 6. Al spectrum for colliding foils. The spatial resolution takes place transversely to the collision axis

(spectrograph 2).


Q BI

I I I I

-lrnOOfl

19Opm

Fig. 7. X-ray 2D waging by using a pin-hole viewing the foils in the transverse direction. The mltial separation 100 pm can be estimated. The compressed zone is emissive.

3.3. X-ray 20 imaging

We implemented a spectrally integrated X-ray 2D imaging by using a filtered pin-hole viewing the colliding foils in the transverse direction. The diameter was 5 pm, the magnification 20 and the filter was a two-layer foil (100 pm Mylar + 0.4 pm,Al). An g-bits CCD camera was used as a detector, its pixel size (about 10 pm) being insignificant when compared to the optical resolution (about 5 pm) and the magnification.

We present in Fig. 7 two typical images for good compressions obtained with aluminum 3 pm foils initially separated by 100 pm and irradiated with laser intensities w lOI W cmm2. Three high emissive zones are recorded: from the back side of the right foil (i.e. towards the collision plane), from the central compressed zone and from the front side of the left foil (i.e. towards the laser

728 E. Leboucher-Dalimler et al

beam). On both images we can see the remaining parts of the foils and can estimate the initial separation. In Fig. 8 are plotted two microdensitometry traces in the two transverse directions A and B giving the emission at the rear side of the right foil and in the central compressed zone respectively. We observe a reproduction of the same hot spots. Moreover there is a correlation between these inhomogeneities and the laser imprinting ones: this fact is obvious in Fig. 9 where we have recorded the colliding foil X-ray imaging next to the imaging of one of the inhomogeneous laser focal spot. As a preliminary observation, we note that the 2D effects which are decisive for the compression optimization cannot be smoothed during the acceleration of the foils due to the short distance between them *. As a consequence there seems to be an efficient compression only for zones in front of the focal “hot spots”. That is also why the transverse geometrical depth of the hot dense central plasma is smaller than the focal spot size.

Trying to explain the less emissive tails exhibited in the central zone (see Fig. 7) we suggest that they could be the imprints of a plasma collision between the exploded thinner foil edges. This last point needs to be strengthened.

3.4. X-ray monochromatic 20 imaging

A 2D monochromatic imaging, integrated over Al Lyfl emission, has been implemented as an independent diagnostic for the measure of the inhomogeneities in both collision axis and transverse direction.

4102 c,, ,,,, ,,,, ‘,,, ,,,, ,,

0 100 150 200 P-lm

0 Q

B A --

til Ki

=90pm

-- 1 OOpmt _

FIN. 8. Mlcrodensitometry traces giving the transverse emission at the rear side of the right foil (section A) and in the central compressed zone (section B). Hot spots are reproducible.


Transverse X-ray imaging

FIN. 9. Correlation between the hot spots

FocaI spot imaging

in the collidmg foil regime and the laser imprinting one5

Two-dimensional bent crystals are commonly used for X-ray imaging by using a single line or narrow continuum range “m’3. The main part of the X-ray monochromatic camera (XMC) used here is a toroidally curved silicon crystal. The crystal is cut parallel to the (111) net-planes, which are used for the reflection. The two bending radii of the torus are chosen to eliminate astigmatism for a single source point, and keep it small for an extended field of view 14. To achieve this, the ratio of the two bending radii R, (in the dispersion plane) and R, (perpendicular to the dispersion plane) has to fulfil the equation RJR,, = sin ‘O,,, where 0, is the Bragg angle: sin @, = IZJ2&, with the lattice spacing dhk, and the emission line wavelength

For Al Ly /I (2, = 0.6053 nm) and Si (2d,,, = 0.6271 nm) we obtain 0, = 74.8”. The selected pair of radii is R,, = 150.2 mm and R, = 139.9 mm. With these radii a magnification of up to 8.3 was possible in the vacuum chamber.

Figure 10 shows the principle of the XMC. As seen in the figure, the incident angle of rays originating from a single source point onto the crystal is not constant. It can be shown that for the direction perpendicular to the dispersion plane the variation A@’ is small and can be neglected for our purpose. By contrast the variation A0 in the dispersion plane is large (valid for magnification K = lb/l, > 1.1). It can be expressed in wavelength scale by using the derived Bragg equation A1 = A.A@/tanO,. We obtain for the wavelength variation in the dispersion plane A& in a first order approximation: A& = (K - 1/K_ ,)(x/R,,tan @)A,, where K is the magnification and x a spatial co-ordinate along the crystal in the dispersion plane 13. With the magnification of 8 and a crystal aperture of 14 mm we have Ai A.lotal = l2 pm.

In Fig. 11 the wavelength variation for two magnifications (6 and 8) is plotted along with a spectral line width AI, (2.4 pm) and the reflection curve width A&(0.06 pm) of the crystal. It can be seen that for such magnifications A& is a few times larger than A,?,. Therefore the image is obtained in the full spectral line. In the case where there are no other emission lines inside the spectral window, we consider the imaging as monochromatic.

To derive the actual magnification and resolution achieved in the experiment, we modified the target arrangement slightly. Only one laser beam was used. It was shifted with respect to the original target position and defocused to irradiate a solid Al target. By this means we created a large Al plasma which illuminated a tantalum grid (100 pm period) from the back that was positioned at the original target position. A densitometer trace of the resulting image is presented in Fig. 12 along with two line scans. From the line scans we derive a resolution of 20 pm in the dispersion plane and 17 pm in the perpendicular direction. Ray tracing calculations predict that a resolution down to 5 pm is achievable in both directions.


In Fig. 13 we show an imaging on Al Lyp for an optimized compression: both primary plasmas (left one attenuated by target foil) and the colliding zone. Numerized microdensitometer traces along the collision axis and the transverse direction (in the compressed zone) are also presented. From the breakdowns in the emission along the collision axis, we can measure the initial foil distance (100 pm). The breakdowns correspond to a reabsorption in the solid and in the cold dense plasma next to the foils before the collision. The same behaviour of the emission (intense core and weak corona emissions) along the laser axis has been simulated; moreover this simulation reveals that the very intense emission from the central zone occurs mostly from the collision time. Since 100 pm is also the focal spot diameter, one can expect that two dimensional effects are not negligible. This can be seen with hot spots reproducing the laser imprinting ones (see figure). From the whole transverse emission size (< 100 pm) and from the hot spot sizes one can check that the optical depth is small when analysing AlLy/3 spectra merging from the compressed zone. This monochromating 2D imaging has strengthened the characteristic values deduced from the spectral integrated 2D imaging. Moreover here the quantitative information is directly useful for AlLyP spectral analysis.

The colliding foil strategy for generating hot-dense plasmas has been accurately driven by simulations joined to several independent X-ray spectroscopic and imaging diagnostics. Therefore, the recorded spectra are available for a comparison with theoretical data.

4. SIMULATION OF SPECTRA

The last part of this paper is focused on the exhibition of dense plasma effects in FLyfi merging from the compressed zone generated by colliding foil systems.

We present in Fig. 14(a) and Fig. 14(b) microdensitometer traces from the densest central plasma obtained for typical colliding parameters (CF, foils, e = 5 pm, d = 100 pm, I, = 2.1014 W cmm2). The spectra are space-integrated over 5 ,um (the entrance slit) and time-integrated over 1.3 ns (the whole emission duration). The shape and broadening of the main line centered at 12.64 A is due to the F*+ monocenter ion emission. On the red wing one satellite referred to [l] is intense and reproducible, it corresponds to a dicenter ion Fs+ -F$+ transition predicted at 12.72 A by the molecular emission code IDEFIX 3. This satellite-like feature, located in the near wing, is spectrally

toroidally curved crystal

dv

image

K*du Fig. 10. Scheme of the X-ray monochromatic camera.

0.612

0.610

0.604

0.602

0.600

0.598

Fig. I I

well-resolved from any He-like dielectronic satellite belonging to the same spectral interval ‘.


I ’ I I I I I I I I I I

- Ah, to,a, (K=8)

I i I I I I I I I I I L I

-8 -6 -4 -2 0 2 4 6 8

crystal extend in dispersion plane / mm

Spectral window of the X-ray monochromatic camera (crystal length 14 mm, AL,,,,‘,, = 12 pm).

Another molecular satellite referred to [2] appears at 12.76 A; this location is in good agreement with the theoretical prediction 3. However, we have to stress that this transition is not resolved from dielectronic satellites with n = 3 spectator electrons in the same wavelength range ‘, therefore it is not a reliable exhibition. On the blue wing of FLY/? another satellite is sometimes exhibited at

vertical trace

horizontal trace

Fig. 12. Image of a test grid (100 pm) and horizontal, vertical line scans through the image


t

transverse direction

collision axis

Collision axis- +,

Transverse direction

Fig. 13. Monochromatic imaging on AlLyP for an optimized Al compression. Densitometer traces giving the emissions along the collision axis and the transverse direction.

12.56 A. It has been recently interpreted in terms of a quadrupolar transition 3 d-l s by Salzmann and Stein Is within the truncated-spheres model,

More precisely for the monocenter F8 + contribution to FLyP line shape, we computed a synthetic line profile involving a time integration over the varying plasma conditions in a spatial window AZ x 5 pm centered in the colliding foil system. At every time step the electronic density Ne(t), the electronic temperature Te(t) and the emissivity c(t) of FLY/~ were averaged over AZ. The code PIM PAM POUM I6 then computed, as a postprocessor, FLyB spectral lineshapes P(Ne(t),Te(t),i) for every coupled density-temperature conditions involved during the emission duration. The synthetic profile I(A) is a time integration of all P(Ne(t),Te(t),l) weighted by the emissivity for the same plasma conditions i.e. Eq. (1)

I(A) = s &(t)P(Ne(t),Te(t),n)dt (1) d,

Here At is the emission duration, typically 1.3 ns. Figure 15 shows a synthetic FLyP profile (the solid line) computed for typical collision

parameters (e = 5 pm, d = 100 pm, IL = 2.1014 W cm-‘). The agreement with the experimental profile (the dotted line) is satisfactory. Concerning the synthetic line profile, it is important to make three comments:

X-ray spectroscopy and imaging of hot dense plasma

CF2 d=lOOpm, e=Spm (Ip2.1014 W.cm-2)

(a)

(4

(b)

733

Fig. 14. FLyb spectra from the densest plasma. Three satellites are exhibited:- the molecular satelhtes located at 12.72 A and 12.76 A on both spectra a) and (b)- the “forbidden” quadrupolar transition

3 d-l s at 12.56 6 on spectrum (a).

1. first, this profile neglects quasimolecule contributions, 2. secondly, while LASNEX simulations take into account transverse inhomogeneities, line

shape profiles are computed here for plasma conditions (Ne(t),T(e)) averaged in the transverse direction (the observation direction),

3. thirdly, the contribution of the highest densities ( 2 1O23 cmm3) in the F*+ monocenter emission lasts but 15ps!

Lower densities will then mostly contribute to FLY/I line shape. On the contrary molecular satellites as well as the forbidden line 3 d-l s are probes of the highest densities achieved in the

12.4 12.5 12.6 12.7 12.8 12.9

(A)

Fig. 15. Comparison between an experimental F Ly/? spectrum and a synthetic one taking account of the monocenter F* l contribution. The agreement is satisfactory for the broadening and the lineshape except

for the satellites (the synthetic profile neglects the quasimolecular contributions).


1

3 g 0.5

$

'F 0

0)

s :s -0.5

5 I=

-1

1 2 3 4 5 6 7 8

R (ad.) R (a.u.)

(a) (b)

Fig. 16. Variation of the transition energies 541 g+210 u (a) and 650 u+lOO g (b) belonging to the spectral range of Ly/3 as a function of the internuclear separation. Evolution of the transition energies

with Z. The transition energy of the unperturbed Ly/3 line is chosen as the reference energy.

central plasma round about the laser pulse top. A recent dicenter radiative property code has been used by Gauthier et al. 3 to predict FE+- F9 + molecular transition locations and intensities. This code gives the emission of one electron diatomic ionic molecule embedded in a plasma by a self-consistent field method. It has been shown that the molecular satellites correspond to electronic transition energy extrema involving short interionic distances.

In Fig. 16(a) and Fig. 16(b) the molecular transition energies are plotted for the two satellites 541 g-*210 u (referred to [l]) and 650 u-+100 g (referred to [2]) belonging to Lyfi spectral range as a function of the internuclear separation. The transition energy of the unperturbed LyB line is chosen as the reference energy and the transitions are referred to the spherical quantum numbers nlm (united atom) and the parity (“g” or “u”). On the same figures the evolution with nuclear charge number Z (9 I Z I 13) is investigated keeping steady the plasma conditions (Ne = 2.1023 cmW3, Te = 300 eV): it is shown that when Z increases the two molecular satellites are shifted towards the red and that smaller internuclear separations are involved. This study could suggest the possible exhibition of molecular satellites in the Ly/? red wing emitted by other materials. But will these satellites be exhibited in anycase? Three more conditions have to be fulfilled: 3

1. first, the interionic distance corresponding to the transition energy extremum must lie near by the one corresponding to the Nearest Neighbour (NN) probability density maximum. The NN probability densities have been computed for our plasma conditions by Molecular Dynamics simulations 3. As shown in Fig. 17(a) and Fig. 17(b), with regard to this criterion, for fluorine, the two molecular satellites within the Lyp spectral range can be exhibited; on the contrary for aluminum, these satellites cannot be exhibited,

0 2 4 6 8 10 R (A.U.) R (A.U.)

Z=9 (Fluorine) Possible exhibition Z=13 (Aluminum) Non-possible exhibition (a) (b)

Fig. 17. Molecular Dynamics simulattons for the Nearest Neighbour (NN) probability densities. (a) for fluorine the molecular satellites [l] and [2] can be exhibited (b) for aluminum the molecular satellites [l]

and [2] cannot be exhibited.


2. secondly, the transition dipolar matrix elements must be non-negligible with respect to the main line,

3. thirdly, the satellites must not be smoothed (i.e. their spectral location must remain steady) by the varying plasma conditions or by other effects such as dynamical effects.

These last issues have been quantitatively addressed in Refs 3 and 17.

5. CONCLUSION

In this work we presented the design of a new experiment devoted to the generation of moderately coupled hot dense plasmas: the colliding foil system. Independent diagnostics have been implemented allowing, with the help of 2D simulations, an accurate drive of the compression. It has been shown that 2D effects are decisive for the optimization. Some of these effects which are not smoothed during the acceleration of the foils are favourable for a good compression: we observed thanks to 2D imaging diagnostics an efficient compression only for zones in front of the focal “hot spots”. That is why, fortunately, the transverse geometrical depth of the hot dense central plasma is smaller than the focal spot size.

These correlated plasmas exhibit effects which have been diagnosed by emission spectroscopy and which can be an indicator of new ionic structures and a test of the self-consistent field method for the treatment of the emitter radiative properties. We have verified that monocenter line broadening and dicenter emission (molecular satellites) give independent measures of the highest density achieved at the laser pulse top. This measure is in agreement with the simulations.

Finally, in the near future we will test Random Phase Plates (RPP) and Phase Zone Plates (PZP) for the possibility of enhancing the emissive compressed volume and then the strongly correlated plasma effects. We will investigate the quasi-molecular radiative properties of hydrogen-like and helium-like dicenters for Z between 8 and 15 and study their associated free-bound continuum.

Acknowledgements-LULI is a CNRS Unite Mixte de Recherche n”100, associated to the Ecole Polytechnique and to the University Paris VI.This work was supported by the Human Capital and Mobility programme (Access to Large Scale Facilities sub-programme, LULI contract number ERBCHGECT 930046) and by the Human Capital and Mobility European network (contract number ERBCHRXCT 930377).The authors acknowledge the expert techmcal assistance of M. Brisard.

REFERENCES

1. Leboucher-Dalimier, E. et al, Phys. Rev. E, 1993, 47, 3, R1467. 2. Leboucher-Dalimier, E. et al, in AZP, Conference proceedings 328, Spectral Line Shape, Vol. 8, 12th

ICSLS, Toronto Canada, 1994. 3. Gauthier, P. et al, JQSRT 1997, 58, 597. 4. Malnoult, P. et al, Phys. Rev. A, 1989, 40, 1983. 5. Foulis, D. L. et al, 7th International Workshop on Atomic Physics for Zon-Driven Fusion, 1995. 6. LASNEX is a radiation hydrodynamics code developed at Lawrence Livermore National Laboratory;

Zimmermann, G. and Kruer, W.L., Comm. Plasma Phys. Controlled Fusion, 1975, 2, 51. Calculations for our experiments have been performed by T.D. Shepard.

7. Key, M. H., Phys. Fluids, 1983, 26, 2011. 8. Cottet, F. et al, LULZ Vol. 133 1984. Fabbro, R. et al, LULZ Vol. 89, 1983. report, report, 9. Faral, B., Phys. Fluids, B, 1990, 2, 371.

10. Poquerusse, A., Opt. Comm., 1986, 58, 108. The spectrograph PABURCE described here has been recently improved by using a Johann geometry.

11. Chenais, C. et al, Phys. Rev. Lett., 1995, 75, 21, 3854. 12. Forster, E. et al, Laser and Particle Beams, 1992, 63, 5012. 13. Uschmann, I PhD thesis, University Jena, 1991 Uschmann, I. et al, Rev. Sci. Instrum., 1995, 66, 734 14. Dirksmoller, M. et al, Opt. Comm., 1995, 118, 379. 15. Salzmann, D. and Stein, J., private communication. 16. Talin, B. et al, Phys. Rev. E, 1995, 51, 1918. Godbert, L., private communication. 17. Gauthier, P. et al, submitted to publication.

Documents

X-ray spectroscopy and imaging of hot dense plasma created by colliding foils. Simulation of spectra