Parameters of a laser produced plasma from XUV line profiles

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Parameters of a laser produced plasma from XUV line profiles

E. Jannitti, P. Nicolosi, G. Tondello

To cite this version:

E. Jannitti, P. Nicolosi, G. Tondello. Parameters of a laser produced plasma from XUV line profiles.

Journal de Physique, 1982, 43 (7), pp.1043-1047. �10.1051/jphys:019820043070104300�. �jpa-00209480�

Parameters of a laser produced plasma ^{from XUV line} profiles

E. Jannitti, ^P. Nicolosi and G. Tondello

Centro Gas Ionizzati, C.N.R., Università di Padova, Italy

(Reçu le 23 novembre 1981, ^{révisé le} 17 février 1982, accepté ^{le 3 mars} 1982)

Résumé.

La région d’interaction entre le faisceau focalisé d’un laser à rubis de 1 GW et une cible plane ^de béryl-

lium a été observée avec un spectrographe stigmatique à incidence rasante de haute résolution. Le profil ^{de la}

raie Ly03B1 ^{de BeIV montre deux} composantes : ^l’une asymétrique ^et large correspond spatialement à la radiation émise _{par la} région à haute densité du plasma qui ^{coincide avec} le cratère et l’autre étroite est émise par le plasma

en expansion. ^{Un modèle} qui ^résout l’équation de transfert radiatif pour ^un plasma qui ^{se détend avec} des para- mètres ajustables reproduit très bien les formes observées. Il est donc possible ^de déterminer un ensemble unique

et réaliste de paramètres ^du plasma, ^en bon accord avec des observations indépendantes précédentes.

Abstract.

The region of interaction between a focused 1 GW ruby laser beam and a plane beryllium target ^has been observed end-on with a high resolution stigmatic grazing ^incidence spectrograph. ^The profile ^{of the} Ly03B1 ^line

of BeIV is made up of ^two components : ^{a broad} asymmetric ^one, spatially corresponding ^to the radiation emitted

by ^the high density ^ablation region ^and a narrow one superimposed, ^emitted by ^the expanding plasma. ^{A model}

that solves the radiative transfer equation ^{for a} moving plasma ^with adjustable parameters reproduces very well the observed features. It is then possible ^{to determine a} unique and realistic set of plasma parameters ⁱⁿ good agree- ment with previous independent observations.

Classification

Physics ^Abstracts

52. 50 - 32. 90

1. Introduction.

Spectroscopic observations of

plasmas produced by laser interaction both .in plane

geometry [1] ^{and for} imploding pellets [2], ^{can be} very useful for the evaluation of plasma parameters. ^In

particular ^line shapes ⁱⁿ optically ^thin sources can

carry the signature ^{of the} plasma density and/or temperature [3]. ^{In the case of} high optical depth

the shape of the lines can be affected also by ^the

motion of the plasma [4]. Velocity ^of expansion [5]

or compression [6] has been derived in this _way.

It is the _purpose of the present paper ^to determine

plasma parameters ^{as electron and ion} densities,

bound state populations and distribution of velo- cities in a laser produced plasma, by comparing ^line profiles observed with a suitable model of the plasma.

Such a model is entirely consistent with all other measurements previously performed ^{on the same}

source.

2. The experiment.

^The plasma ^was produced by focusing ^a ruby ^laser pulse ^of up ^to 10 J of _energy and 15 ns duration with an y/1 aspheric ^{lens of 50 mm}

focal length ^on plane ^massive targets ^of beryllium.

The plasma is observed end-on along ^the target normal, looking ^at the ablation region ^{with a} stig-

matic grazing ^incidence spectrograph. Figure ¹

illustrates the experimental set-up. The laser beam is deflected and focused by mirror A and lens L both

having ^{a hole} through which the XUV radiation emitted by ^the plasma ^{can be collected} by ^{the toroidal}

mirror M. The latter is used for compensating ^the astigmatism ^{of the} spherical ^concave grating ^{G of}

2 m radius, used in the standard grazing ^incidence

Fig. ^1.

Scheme of the experiment : the laser beam is deflected by ^{mirror A} and focused by ^{lens L on} target ^T.

The XUV light ^{is collected} by the toroidal mirror M and sent through ^{the entrance slit S on the} grating ^{G of a 2 m} grazing ^incidence spectrograph. Diffracted stigmatic images

of the plasma ^{are formed on} plate ^P.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019820043070104300

1044

Table I.

Optical parameters of ^the stigmatic spectrograph

Rowland mounting. By properly choosing ^{the radii}

of curvature of mirror M and the angle of incidence

on it, ^a diffracted stigmatic image ^{of the} plasma ^at wavelength Ast ^is produced ^on plate ^P [7]. Space

resolution on one dimension of 20-30 _Ilm is so achieved

over a field of 1 mm for values of the entrance aperture ( z I / 100 rad.) typical ^of grazing ^incidence spectro-

graphs.

As shown previously [8] with this arrangement,

a considerable increase in efficiency ^is possible ^with

respect ^to pinholes previously ^{used for} obtaining spatial resolution. Moreover the ablation region

observed end-on due to its density approaching

the critical density [9] ^{has a} very high brightness.

We could then use a high dispersion grating ^with

2400 lines/mm albeit with relatively ^low efficiency.

Kodak 101-05 plates ^{were used} requiring ^{5-10 shots}

to record a spectrum. ^{Table I} reports ^the optical parameters ^{of the} system used. Plate P could also be removed and a scanning pinhole-scintillator ^coated photomultiplier combination was used to provide

some indications on the time dependence ^{of the}

emitted spectra.

The spectrum ^recorded by ^the spectrograph ⁱⁿ

the 40-150 A region consists of two different parts.

A central _one, on the meridional plane ^{of the} optical system, spatially corresponding ^to the ablation region

of the plasma ^{and z 100} Ilm wide with a continuum emission both of free-free and free-bound type;

and another one, ^on either side of it with the resonance

lines of Belll and BeIV. Figure ^{2 shows the} profiles

of the Lya ^{line of BeIV} corresponding ^{to scans on}

the central region, ^r

^{0 and at 0.1 and 0.2 mm}

away. These represent observations along ^{the axis}

of symmetry, ^{normal to the} target, ^{of the} plasma

and along parallel directions. The profile ^further

away from the central plane quickly approaches

the instrumental spectral broadening indicated in

figure ^{2. The} spatial resolution achieved and marked in figure 2, ^{is also} clearly ^shown by ^the great ^diffe-

rence visible in the shape ^{of the} profiles separated by ¹⁰⁰ pm each and in the intensity ^{of the} underlying

continua.

The Lya profile in the central position ^is clearly

made of two components : ^a very wide asymmetric

one with the blue wing steeper than the red and a narrow one in the central position of the line with

Fig. ^2.

^The profiles of Lya line of BeIV at 75.93 A corres-

ponding ^to three different positions : ^on the central plane ^of

the expanding plasma ^{and at r}

^{0.1 and 0.2 mm away.}

The intensity scale is in relative units. For the central position

r

0 with dotted lines is represented the calculated profile corresponding ^{to the} plasma parameters represented ⁱⁿ figure ^{3. The} position and relative intensity ^{of two dielec-}

tronic satellites at 76.47 and at 76.90 A observed in the

expanding plasma ^are also marked.

self absorption dips ^{on either} side of it. The broad component quickly disappears moving away from the central plane. Very ^similar profiles ^{are observed}

also for the He-like resonance lines of BeIII and,

but with less clarity ^{due to the} decreasing spectral resolution, ^{for the} species BV, ^{CVI and NVII in} targets ^{of the} proper material.

3. Interpretation of the observations.

It is quite

natural to associate the broad component ^{to the}

high density layer ^{in the ablation} region ^{and the}

narrow component ^{to the} expanding ^low density plasma coming towards the observer. Due to the

high optical depth ^{as evidenced} by ^the absorption dips, it is necessary, for ^a complete explanation

of the full profile, ^to solve the radiative transfer

equation ^{for a suitable} plasma ^model.

Previous spectroscopic observations of the same

Fig. ^3.

^The plasma parameters used in the model for

predicting ^line profiles inside and outside the original position ^{of the} target y

^{0. Note} the different scale of dis- tance : negative y (at left) ^{refers to the} inside of the target ; positive y (right) ^{refers to the} expanding plasma. ^In the upper part the electron density ne ^{and the} densities in the ground nl

and upper ^state n2 of Lya ^{of BeIV are} plotted. In the lower part the electron temperature ^{and the} velocity ^{of the} plasma

are shown. The latter is taken positive ^or negative according

to the orientation of the y ^axis.

plasma ^{can be} summarized as follows; ^{see also} figure ^{3 :}

i) ^{in the} expanding plasma ^the electron and the

hydrogen-like ^ion densities measured side-on as

average ^over the plasma depth, decrease from ne

^{5 x} 102 ° and n 31 = 5 x 1019 cm-3 at the target position to ne

1018 and n 31 = 1017 cm-3

at a distance of 2 mm. The electron temperature correspondingly goes from Tr

^{100 eV to} Te

¹⁰ eV; ^the expanding velocities are approxi- mately constant at 1.6 x 107 cm S- 1 [6] ;

ii) ^the plasma expands ^{in a cone-like} shape ^with

rotational symmetry around the normal to the target ^{but with} pronounced holes, ^i.e. minima in the ionic population ^{near the axis} [10]. Consequently,

when observing ^{end-on on} axis, ^{one has} relatively

little material and low optical depth ^{from the} expand- ing plasma ^{and can therefore see} through ^{the inner}

part ;

iii) direct observations of the ablation layer ^with

lower spectral resolution [9] have shown that in

beryllium ^the depth ^{of the} emitting region ^is

15 J.1m, the electron density equals the critical density ^for ruby ^laser light, ne

2.2 x 1021 cm- 3, the ion den-

sity ^{n 31 = 2 x 1020 cm-3 and} Te = 100 eV ;

iv) ^from analysis of the laser radiation back- scattered from the plasma [11] ^{it was} derived that the critical layer ^moved during laser irradiation inside the target ^{with a} velocity, deduced from the

Doppler shift, ^{of 5 x} 10’ cm s-’. Assuming ^the

same behaviour for the ablation region ^a receding,

from the observer, velocity ^{of the same order can be} expected. The radiative transfer equation ^{in our case}

can be written as [12] :

where I (A, y) is the total intensity, (W cm-2 ^A- 1 sr-l)

emitted by ^the plasma ⁱⁿ the direction of sight y at wavelength A, x (cm -1) ^{and J} (W ^{cm - ’ A -1} sr-l)

are the absorption and emission coefficients for radiation with wavelength A ^{at the} point y ^{inside the} plasma. They include both line and continuum contributions

The line contribution can be written as [13] :

where K and K’ are two constants, gl and _g2 the statistical weights ^{of levels 1} (lower) ^{and 2} (upper)

of BeIV, n 1 ( y) ^and n2(y) ^{are the} population ^densities

of such levels, A21 is the transition probability ^of Lya, §(h, y) ^{is the} local normalized line profile.

o(A, y) ^{was taken as a} Voigt function i.e. a convo-

lution of a Lorentzian Stark component ^{and a thermal} Doppler ^one. The FWHM of the Lorentzian com-

ponent ^{for BeIV} Lya ^was determined by interpolation

of the predictions of Stark broadened Lyman ^lines

made by Kepple ^{and Griem} [14]. ^In the continuum contribution to the emission coefficient both the free-free and free-bound components ^{of BeIV are} included

where Fff ^and Ffb characterize the spectral depen-

dence of the free-free and free-bound emission and

are also functions of the electron temperature [15].

The absorption coefficient _Xc is, ^{in the} neighbourhood

of Lya, always very small.

A program ^{was set} up [13, 16] ^that integrates equation (1) ^{in a} plasma whose local parameters, like electron and ion densities, temperature, streaming velocity, density of the lower and _upper state of the

line, ^can be varied widely ^{both in value and} spatial

distribution along ^the plasma. Obviously ^{for those}

parameters previously measured the adopted ^value

is the experimental ^{one. For} practical ^{purposes it is}

convenient to divide the plasma ^{into two} parts : ^the

inner one 15 pm deep ^{and the outer} part ^{1 mm} deep.

1046

4. The plasma ^model.

^{The most} noteworthy

feature of the broad component ^{is its} asymmetry.

As shown by ^Irons [4] ^and experimentally ^found by

Tondello et al. [5] and Yaakobi et al. [6], ^an asym- metric line profile ^{in a} moving plasma ^can be obtained

only ^{if the source function} S(A, y)

J(A, y)IX(A, y) ^oc n2(y)/nl(y) ^is not constant along ^the plasma depth.

The direction of the asymmetry, i.e. blue or red

wing enhanced is determined by the distribution of the velocities of the elements of plasma. ^{In an} expanding plasma ^{the blue} wing is enhanced i.e. the red _appears steeper; ^the opposite ^{in a} plasma ^under- going compression. ^For matching the observed profile,

we have adopted consequently the value and distri- bution of the plasma densities, temperature ^and velocities shown on the left side of figure ^3. Precisely

the electron density ne and the ion density n 31 ;: -- n 1 were taken constant and in agreement ^with previous experiment : ^see iii) ^of paragraph ^3.

For obtaining ^{a non uniform source} function the distribution of population n2(Y) is assumed higher

towards the interior of the target. The absolute value of n2(y) ^controls, according ^to equation (4),

the intensity of the line that must be in a fixed ratio with the underlying continuum, ^the intensity ^{of the}

latter as shown by equation (5) is determined by ^the product n,,(y).nl(y). ^The adopted distribution of velocities in the ablation region is consistent with

a receding motion of the critical layer ^{from the}

observer with a velocity that is maximum in absolute value near the unperturbed position ^{of the} target and gradually ^{decreases as the} layer stops ^{at some}

depth inside the massive target. Its average value is in accordance with iii) ^{of the} paragraph ^{3. In this}

way the velocities are as in a compressing pellet ^i.e.

higher ^{in the} peripheral, ^less emitting region ^and

smaller in the central, high emitting ^{one. Evidence}

of compression ⁱⁿ plane targets ^have previously

been reported [17] although using ^different diagnostic techniques. ^In figure ^{2 with} dotted lines is shown the profile ^{for the} Lya ^{line as} predicted by ^{the model}

with the set of parameters given ⁱⁿ figure 3 : for the wide component ^the agreement ^is very good ^both

as regards ^{to the total} width, determined mainly by

the opacity

^{note that} 0 (A, y)

^0.15 A - and also as regards ^{to the} degree ^of asymmetry ^{and the} relative intensity ^{of the} underlying continuum. It turns out that the precise ^value of the electron tempe-

rature is unimportant ⁱⁿ affecting ^the profile ^as

well as the detailed shape of the distribution of velocities and population n2(y) inside the target.

The narrow profile arising ^{from the} expanding plasma ^{can be} similarly modelled. The right part of figure ^{3 shows the} parameters adopted, ^{most of}

them in agreement ^with previous experiments. ^Here

the most critical finding that arises from the best fit is the low value of the ground ^state density nl ( y) ;

this is in agreement with observation ii) ^of paragraph ³ indicating ^a hole in the expanding plasma. If, ^{on the}

contrary, ^the density ^{is taken at} the full value as i)

of paragraph ^{3 the} integration ^of equation (1) along

1 mm depth produces ^a spectrally ^wide component that interacts with the emission from the crater.

A wide flat hole or a wide flat maximum is then _pro- duced on top ^{of the} profile according ^if n2 (Y) ^is

small or large. Only assuming ^a relatively ^low density plasma ^on axis it is possible ^{to see} through ^{at fre-} ,quencies ^{not too} far from the central frequency.

Again ^{here the} optimization ^of nZ ( y) ^is governed by

the ratio of the intensities of the central peak ^{to the} wings. ^{For the} expanding plasma ^the temperature and the precise value of the expanding velocity ^as

well as the details of the distribution of the popula-

tions are unimportant ^{for the} resulting shape ^{of the}

line. Figure ^{4 shows the} optical depth ^{in the} neigh-

bourhood of Lya ^{for the} plasma ^model adopted;

it is clear how the contribution of the expanding plasma is small and also that the plasma ^is optically

thin for the continuum emission only.

Fig. ^4.

^The optical depth ^{in the} Lya ^{of BeIV as} predicted by the model. With solid line is represented ^the optical depth corresponding ^to integration ^{over the total} plasma depth;

with dotted lines the optical depth ^{for the} expanding plasma only. The shift in wavelength ^{of the two curves is due to the} Doppler effect of the expanding plasma.

5. Discussion.

It is quite important ^{to notice}

that in the framework of the plasma ^model adopted,

whose consistency ^{in turn} has been tested on several

previous experiments, ^the plasma parameters ^as shown in figure ^{3 are} unambiguously determined, ^i.e.

the solution of the radiative transfer problem ^is unique; any variation produces remarkable effects

on the line profile. ^For example larger electron and ion densities in the ablation region although ^not compatible ^with previous observations [9] ^{could in} principle ^be possible inside the target. The effect of such assumption however is to broaden, through

the increased opacity, ^{too much the} profile ^{of the}

line.

It is also interesting ^to compare the values of the

population of the excited state n2(y) ^determined

in this work with what can be predicted by ^{the often}

used LTE or corona models in the two regions

inside and outside the target. ^{For the} region ^inside

the target ^and immediately outside the value of

n2 (Y) ^{is within a factor of two in} agreement ^{with an} LTE model assuming collisional coupling ^{of the}

n

2 level of BeIV and the bare nuclei. Further outside the target the value of n2 lay ^{between the} predictions of LTE and corona models. These findings

are in quite good agreement ^with previous ^observa-

tions of similar plasmas [18]. Consequently ^{it can be}

said that the adopted population densities, ^inde- pendently determined, ^{are in} good agreement ^with the densities expected ^from reasonably valid atomic models.

The velocity ^{of the} expanding plasma ^{does not}

affect the shape ^{of the narrow} profile ^but only ^its

shift in wavelength ^with respect ^to the broad one.

Since a precise wavelength measurement was not

made, the value corresponding ^{to the} peak ^{of the} profile ⁱⁿ figure ^{2 was} assigned ^as predicted by ^the

code to 75.89 A i.e. to the Doppler shifted value

corresponding ^{to the} expanding velocity ^with respect

to the « rest » value of 75.93 A [19].

The time and space resolved observations made with the photomultiplier, although ^affected by ^a

lack of reproducibility, indicated that the emission of the Lya line outside the central plane ^{arose later}

than the emission from the broad component spa-

tially coincident with the focal spot. These observa- tions are also supporting ^the adopted model of the

plasma.

Observations of asymmetry ^{of the same} type ^as reported here have been noted for imploding pellets by ^{Hauer et al.} [20] ^{in ArXVII} Is’-I.E3p ^{and inter-} preted ^{as due to a forbidden} component present ^on

the low-energy wing. ^{While no forbidden} component

can clearly ^be present ^{for the} Lya, there is the possi- bility of inner shell ^or dielectronic satellites to enhance the red side of the line. In figure ^{2 we} have marked the position ^{of such} satellites as observed in a less dense expanding plasma [21]. They correspond ^to

1 s 31-2p ³¹ configurations. Many ^{more of the same}

type and ^also for the 1 s 41-2p ⁴¹ configuration ^are predicted [22] ^{that lie} closer to the resonance line

although ^with relatively ^low intensity. ^{While this} explanation ^{for the} asymmetry of the line and also others like Zeeman effect due to the high magnetic

fields present ^{at the} region of interaction between the laser light ^{and the} plasma ^{cannot be ruled out,}

it is important ^{to stress that the} proposed explanation

is the simplest ^{one and} clearly consequent ^{with all} the previous observations. Compression ^{in a} target is after all a necessary consequence of ^momentum conservation and the present observations provide ^a spectroscopic evidence of such ^an effect.

Acknowledgments.

The authors desire to thank Dr. A. M. Malvezzi for having provided the radiative transfer code in advance of publication.

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