Inner shell satellite transitions in dense short pulse plasmas

Pergamon

J. Qum. Spectrosc. Radrat Transfer Vol. 58, No. 4-66, pp. 859-878, 1997 0 1997 Elsewer Science Ltd. All rights reserved

Printed m Great Bntain PII: s00224073(97)ooo92-7 0022X)73/97 $17.00 + 0.00

INNER-SHELL SATELLITE TRANSITIONS IN DENSE SHORT PULSE PLASMAS

F. B. ROSMEJt, A. YA. FAENOVI, T. A. PIKUZS, F. FLORA/I, P. DI LAZZAROII, S. BOLLANTIII, N. LISIII, T. LETARDIII, A. REALE&

L. PALLADINO$, D. BATANIT[, S. BOSSIT, A. BORNARDINELLO?, A. SCAFATI,6tt L. REALE,6tt A. ZIGLER,‘$t M. FRAENKEL,‘$$

and R. D. COWAN*@ TRuhr-UniversitLt Bochum, Institut fiir Exp. Phys. V, D-44780, Bochum, Germany, SMCISDC

VNIFFTRI, 141570, Mendeleevo/Moscow, Russia, IIENEA, INN. Fis. P.O. Box 65, 00044, Frascati (RM), Italy, §Dip-Fisica Universita a dell’ Aquila e INFN, g.c. LNGS, L’ Aquila, Italy, TDip. Fisica Universita dl Milan0 e INFN, Sezione di Milano, Italy, ifLab. Fisica, Instituto Superiore di Sanita e

INFN, Sezione Samta, Rome, Italy, ‘Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel and #Los Alamos National Laboratory, Los Alamos, NM 87545,

USA

Abstract-Soft x-ray spectra originating from dense plasmas, generated by a laser irradiating a solid target with ns- and fs- laser pulses, have been obtained with simultaneous high spectral (i/S2 x 10 000) and spatial resolution (6x z 10 pm). Interesting structure of the He-like resonance line together with strong emission of the Li-like n = 2 satellites have been observed very close to the target surface. We show here that the resonance line structure is strongly influenced by higher order satellites of the type ls*nl’-ls21nl’ which overlap for n > 2. For plasmas created with short pulse duration lasers there are high density and low temperature regions near the target that give rise to three body recombination into Rydberg satellite levels leading to substantial intensity at the position of the resonance transition. Atomic data necessary for spectra simulations have been calculated with inclusion of configuration interaction and relativistic effects and these results are cross-checked with other calculational methods. Time-dependent simulations of the spectra including the effects of optical thickness, energetic electrons and numerous high order Rydberg satellites (up to n = 7) are found to be in good agreement with experimental data. 0 1997 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

X-ray spectroscopy as a diagnostic tool for hot plasmas provides information about the plasma parameters. In numerous cases x-ray spectroscopy is the only tool able to deliver sufficient information, in particular, for dense hot plasmas where active diagnostics fail due the high electron densities, > 10” cmm3, short time scales, z < 1 ps, and small spatial extent, L < 100 pm. Some of these conditions can be found, e.g., in inertial confinement fusion implosion cores, hot spots in pinching plasmas, and short pulse laser target interactions.

The analysis of soft x-ray spectra from highly charged ions for plasma diagnostics I4 is often based on the use of resonance lines from H- and He-like ions Is-np and ls2-lsnp and their adjacent dielectronic satellites 1 snl-2lnl’ and ls21nl’-1 s221’ for Stark broadening investigations and line intensity ratios. Among these the H-like Ly, line ls-2p, its dielectronic satellites, ls21-2121’, the He-like resonance and intercombination lines, ls2-ls2p ‘,3 PI, called W and Y, respectively, and their associated dielectronic satellites, 1~~21-1 s2121’, have received particular interest. This is due to the fact that line identification is simple and the necessary atomic data is available and highly accurate. This is particularly true for highly charged ions due to the results of several atomic structure codes: HFR 5, SUPERSTRUCTURE 6, ATOM ‘, MZ ‘3*, GRASP ‘,‘O, HULLAC ‘I.

In the present laser target interaction experiments we obtain x-ray spectra with a spherically bent mica crystal technique 12-14 that provides simultaneous high spectral (n/&4 x 10,000) and spatial resolution (6x x 10 pm), finding interesting structure near the position of the He-like resonance line. Close to the target, where the electron temperature (T,) is low and the electron density (N,) is high, enhanced recombination leads to Rydberg satellites originally has been proposed by Rosmej

859

860 F. B. Rosmej et al

and Faenov “. In the present work we give a detailed analysis of the physical mechanisms involved, calculate the atomic data necessary for transient spectral modeling, and show systematic experiments carried out at two different facilities.

2. EXPERIMENTAL SETUP AND DIAGNOSTICS

A high intensity laser focused on massive Mg targets provides soft x-ray spectra from resonance and satellite transitions which is recorded by means of the spherically bent mica crystal technique ‘2-‘4. Crystals with radii of curvature equal to 100 and 186 mm have been used. Crystal, plasma and photographic film are placed to enabled a simultaneous high spectral (n/&l w 10,000) and spatial (6x x 10 pm) resolution. A schematic view of the experimental setup at the two facilities is given in Fig. 1.

In Frascati, Italy, ns-laser experiments have been performed at the Hercules facility, a XeCl laser with wavelength 1 = 0.308 mm, giving 2 J in a 12 ns pulse length. The laser was focused to a diameter of 40-70 pm giving a flux density of 4-8.10’* W cm-*. This laser worked in a pulse-periodic regime at 10 Hz allowing 20 to 40 shots, each on a fresh target surface, to be accumulated to provide high quality spectra.

Fs-laser experiments, carried out at the Racah Institute, Israel employed a laser producing 120 fs pulses with 20 mJ per pulse at 10 Hz. The prepulse was N 10-5-10A of the main pulse, with a duration about 1 ns. A spot size of 20 pm provides flux density of 5.1016 W cm-*. Typically 600 shots were accumulated each from a fresh target to obtain a spectrum.

3. ATOMIC DATA AND SPECTRAL MODELING

Transient spectra simulations have been carried out with the “MARIA”-code 16. This is based on transient metastable resolved multilevel collisional radiative model with inclusion of optical depth and energetic electrons. The time-dependent level populations are obtained from the system of rate equations (Eq. (1)):

Spherically bent crystal

Space resolution D X = 10pm Spectral resolution h/Ah = 10.000

Laser - beam

X

Fig. 1. Schematic view of the experimental arrangement between laser, target and spectrometer.

Inner-shell satellite transitions m dense short purse plasmas 861

where the matrix W,, contains all collisional radiative processes from level i to level j: dielectronic recombination, dielectronic capture, autoionization, collisional excitation/de-excitation, ionization/

Is21 3L

r DC

c

DC

4 I

Tr 1

l 1s 21 nl’

ES-IS

I

Tf r

ES-IS

D I s*nl

Fig. 2. Schematic energy level diagram showing some of the principal collisional radiative processes of the Li-like ls2lr-J autoionising levels. Ionization/three-body recombination and collisions between the different “n” configurations have been included: A = spontaneous radiative decay, r = autoionizing rate, DC = dielectronic capture, IS = inner-shell excitation, ES-IS = inner-shell excitation from excited states,

C = collisional excitation, I = ionization, T, = three body recombination.


three-body recombination, radiative recombination, spontaneous radiative decay, and charge exchange. The solution of Eq. (1) involves the simultaneous solution of the ionization balance together with all excited states “. Due to different time scales in the relaxation times, l/W,,, the problem is stiff, requiring the evaluation of the Jacobian matrix J, for each time step to provide adaptive step sizes for each transition i-j (Eq. (2)):

In optically thick plasmas, the system of differential equations becomes non-linear in the level populations n,.

For the generation of synthetic spectra Voigt line profiles cp for all transitions have been used: the Gaussian part, TG, determined by the ion temperature, T,, the Lorentzian part, TL, is given by the inverse lifetime of the upper and lower level including radiative and collisional processes

(Eq. (3)):

the FWHM (full width at half maximum) is given by (Eq. (4))

FWHMG = 2.&%-y

and 0%. (5))

(4)

r: = CA,, + c, + c,, + 14, + r,, + c,, / I

with the FWHM (Eq. (6))

FWHML = I-; (6)

TG and I: are, respectively, the Gaussian and Lorentzian widths for the transition i+j, A is the number of nucleons, 1,, is the wavelength, A,, the radiative decay, I,, the autoionizing rate and C,, are the total collisions out of the level i. Eqs. (3-6) allow the approximate inclusion of Stark-broadening processes both for intrinsic line profiles and opacity calculations. The inclusion of the full Voigt line profile in the opacity calculations is crucial, because for high optical depth and/or high collisional broadening the asymptote of the photon escape probability, 0, with respect to the line center optical depth z, is (Eq. (7))

@a&

& (7)

whereas ignoring of the collisional line broadening results in the quite different asymptote for a Gaussian profile (Eq. (8)):

OCc r03i;;;y (8)

For the calculation of appropriate optically thick line profiles, inhomogenities and velocity effects are included. Each optically thick emission line profile O(o) is subject to a normalization procedure

(Eq. (9))

701 s S(q,)e-'md7,

O Rxm(~) = (9)

s “1 @(w)do

L’I

Inner-shell satellite transitions in dense short pulse plasmas 863

with (Eq. (10))

s

v2 @“orm(0)dW = 1 (10)

“I

to provide a consistent intensity calculation. Here S is the source function and dt, the frequency dependent differential optical thickness. In Eq. (11)

&,(@) = a n:(m) f A,,(s-‘)n,(cm_4cp,,(w)dl(~Lm) (11) J

I is the wavelength, A the radiative decay, np the absorbing ground state density, and dl the differential photon path length. In particular for source functions that vary due to density variations or velocity fields, the normalization procedure provides a self consistent approach for integrated intensities and spectral distribution 16.

The introduction of the effective photon path length, LCr, is very convenient for the representation of results and understanding of the physical mechanisms of opacity broadening. With the geometrical path length L Leff is defined by (Eq. (12))

Further we define the line center optical depth r, as (Eq. (13)):

T 0 = !+A 4 ” g,

!,%cp,,(~ = DOLT (13)

The generation of energetic electrons due to the high intensity laser interactions is required because energetic electrons considerably influence the ionization balance and inner-shell processes. Moreover, dielectronic satellite spectra and forbidden lines are seriously influenced by energetic electrons ‘8-22 due to different high energy excitation cross section asymptotes. In the high energy limit, resonance lines are excited through direct excitation (Eq. (14))

1nE ddcc -

E (14)

while the excitation of forbidden lines are excited through exchange which has the asymptote

(Eq. (15))

1 at.oc _j E (15)

This is strictly valid only in LS-coupling, and in intermediate coupling the mixing of allowed and forbidden states creates admixtures of Eq. (14) and Eq. (15). According to Vainshtein’s theorems ‘, the excitation cross-section can be represented as a sum of direct and exchange contributions, i.e.

(Eq. (lb)),

0 = QA + Qeoc (16)

For example, for He-like Mg we have for the W and Y transitions, using MZ-mixing coefficients, Qd(W) = 0.9983, Qc(W) = 0.25 and Qd(Y) = 3.32*10m3, Qe(Y) = 0.25, so that the admixture of the direct cross section for the excitation of the Y transition is small. On the other hand, dielectronic capture is a resonance process concerning only the low energy part of the electron distribution function.

To model the energetic electrons we assume that the distribution can be approximated by two Maxwellians with different temperatures 23.24 This is incorporated into the model by means of effective rate coefficients Reff given by (Eq. (17)):


where TbulL is the bulk-electron temperature and Tbcam is the beam-electron temperature, f is the beam fraction given by (Eq. (18)):

Ne(Tbulk) is the bulk-electron density and N,(T,,) is the density of energetic electrons. For the present investigation particular attention is paid to the atomic structure of autoionizing

levels of Li-like and Be-like ions excited by the following channels: Dielectronic capture (DC) ? 1s’ + e+ ls2lnl’ 1~~2s or 2p + e-* ls2x2ynz

Inner-shell excitation (ISES), 25:ls22s or 2p + e+ls2lnl’ 1~~2121’ + e+ls2x2ynz Inner-shell excitation from excited states (ES-ISES) ?ls2nl + e+ ls2lnl’ ls221nl’ + e+ ls2x2ynz

For Li-like ions, dielectronic satellite transitions ls2lnl’+ ls2nl’ + hv have been included for n = 2-7. Figure 2 shows the level scheme and some collisional radiative processes connected with the Li-like satellites.

It will be shown below with the analysis of experimental spectra that the inclusion of higher order satellites is crucial for the interpretation of the He-like resonance line. We therefore checked the consistency of the current method of data generation with other methods. Complete sets of atomic data necessary for investigation of the spectra have been calculated for the spectral interval from the He-like resonance line to the Be-like n = 2 satellites. This spectral interval involves the satellite transitions from the Li-like and Be-like ions with the transitions ls2lnl’-ls’nl” and ls2x2ynz-ls22x’nz’. All calculations have been carried out with the Hartree-Fock method including relativistic corrections up to second order ‘. Pure ab initio calculations of atomic data for spectra simulations have been made in the following way. 27 For Li-like autoionizing levels each calculation involves the configurations 1~2121’ (16 levels), 1~2131’ (66 levels), 1~2141’ (98 levels), 1~2151’ (130 levels), 1~2161’ (162 levels), 1~2171’ (194 levels). Both parities include the 1 s2nl levels for n = 2-7 and the 1~2121’ levels. The second parity includes also the ls2lnl’ levels for n = 3-7. This includes configuration interaction through all ls2lnl” levels. For Be-like autoionizing levels, a similar approach has been chosen with configurations up to n = 5. After numerous comparisons with existing data 27m36 we find that the current method is quite accurate.

Figure 3(a) demonstrates the accuracy level of the atomic data for spectral simulations by comparing an experimental spectrum from a ns-laser produced plasma 36 and theoretical spectra generated using the current HFR data. It is clear from Fig. 3(a) that all significant features in the experimental spectrum including the resonance lines and dielectronic Li-like satellites are well modeled. Figure 3&--h) show the separate contributions of the dielectronic satellites.

As the autoionizing rates are very important we checked our autoionizing rates with calculations from Chen and Nilsen based on MCDF (multi-configuration Dirac Fock) methods 37.2* and the SUPERSTRUCTURE code 6l 33 and found that the present autoionizing rates are in very good agreement with all other codes, the agreement being typically within 5-10%.

Thus, based on the extensive comparisons with other calculations and with experiment we conclude that the set of present HFR atomic data, including configuration interaction with all high n-states, provides sufficient accuracy for spectral simulations and diagnostics of highly charged ions.

4. OPTICALLY THICK LINE SPECTRA FROM NS LASER EXPERIMENTS

Figure 4 shows the space resolved X-ray spectra obtained from the ns-laser experiments. Far from the target the spectrum is dominated by the W and Y transitions, while close to the target surface the spectrum is dominated by dielectronic satellites. Analysis shows that the dielectronic Li-like n = 2 satellite spectrum is effected by optical thickness. Those dielectronic satellites that depopulate the upper level due to the autoionization must be included in the escape probability, then dielectronic transitions that are formed by electron capture result in decreased intensity, as the autoionizing rate is N lOI s-’ and plays the dominant role up to densities of N 1O23 cme3 38.


A generalization of this is understood by defining the probability p that after photo absorption the photon is re-emitted is given by (Eq. (19))

(a)

A P=

~A+~l-+~C

5.0

4.0

3.0 lw

2.0

1.0

1~2131’ + 1~2141’

\ I 1~2131’

hlnm

0.916 0.920 0.924 0.928

-____ ISES

W

Li-like satellites n = 2

Y

. . .

St .,

(19)

0.916 0.920 0.924

hlnm

Fig. 3(a) and (b). Caption on p. 868.

0.928

866

(cl

F. B. Rosmej et al

Li-like satellites II = 3

Y

k

I s23p 2P -

0.916

W

0.920 0.924 0.928

hlnm

(4

I

I Li-like satellites n = 4

Y

““,I”“‘I”“‘I”” 0.920 0.924 0.928

hlnm

0.916

Fig. 3(c) and (d). Caption on p. 868.

For the Li-like j-satellite of Mg we have

A = 9.5*10i3 s-‘, Cl- = 1.3.1014 s-‘, CC w lo-* cm3s-’

so that in the coronal limit, i.e., N,+O, we have the low re-emission probability, p = 0.42, while at very high densities, e.g. N, = 1O22 cmm3, p has the slightly lower value of 0.29.


Due to the ability to resolve satellite transitions, effects of opacity can be estimated by comparing the intensity of satellites with low and high radiative decay rate and low and high autoionizing rates. From a theoretical point of view the n, m, s, t, k, and j-satellites are suitable due to their different combination of radiative decay and autoionizing rates. The present experimental spectra are obtained with spectral resolution of - 10,000, so that mn and even st are separated from the

(e)

W ,

1.0 -

Li-like satellites n = 5

0.916 0.920 0.924 0.928

hlnm

Be-like II = 2 satellites

Y

0.916 0.920 0.924 0.928

h/nm

Fig. 3(e) and (f) Cuprion overleaf.

868

(g)

F. B. Rosmej et al

7.0

1

Be-like satellites n = 3

q*

5.0 -

7 0 :

3.0 -

1 .o 1 W

0)

Be-like satellites n = 4

L 2.0

1.0

k

0.624 0.428

Unm

qr a

n k

j, , , , , ( , , , , , , I , I , , , , , , ,m, , , , , , , , , , , , , , ,g, , , . , , , * , , , , 5

0.916 0.920 0.924 0.928

hlnm

Fig. 3(g) and (h)

Fig. 3. (a) Comparison of an experimental spectrum I6 of He-like Mg with its resonance line W = Is’-ls2p ‘P,, intercombination line Y = is’-ls2p ‘PI and its Li-like satellites ls2nl’-ls21nl’ with the theoreticai spectrum simulation employing entirely HFR atomic data. The plasma parameters are T, = 180-280 eV, N, = 1-3.102’ cm-‘, L,, = 100 pm and a non-equilibrium ratio of He-like and Li-like population of n(lsz2s,2p)/n(ls’) = 0.14, T, = T,, and apparatus function with resolution of A/U = 4000. (b) The contribution of the Li-like n = 2 satellites only. (c) The L&like n = 3 satellites only. (d) The Li-like n = 4 satellites only. (e) The Li-like n = 5 satellites only. (f) The Be-like n = 2 satellites only. (g) The Be-like

n = 3 satellites only. (h) The Be-like n = 4 satellites only.

Inner-shell satelhte transitions in dense short pulse plasmas 869

Far from target

Y

L1-sat n=2

x = 280 pm

x=40pm

Fig. 4. Space resolved soft x-ray Mg spectra of the He-like resonance line W, intercombination line Y and its satellite structure obtained from a massive Mg target irradiated with a 12 ns laser. Far from the target surface the spectrum is dominated by the W and Y line, while close to the target surface dielectronic

satellites are dominating in the entire spectrum.


8

E e : z

6 c Mg T, = 80 eV

41 I I I I lllll I I I1 lllll I I I I III,

0.01 0.1 I

z ti)

Fig. 5. Diagnostic of optical thickness using Li-like dielectronic satellites nm and jkl. The dependence on the line center optical thickness t. is very strong between 0.2-2 and practically independent on the electron

density.

Y transition. Using the dielectronic satellites enables determination of small optical depth, due to low p-value, of order z, N 0.2-2, whereas optical depth in resonance lines can be seen directly only at much higher values.

Figure 5 shows the optical depth diagnostics realized with the mn and jkl satellites. It can be clearly seen that a sensitivity is obtained for r0 N 0.2-2, where the optical depth of the j-satellite has been chosen as representative. The diagnostic ratio does not depend strongly on the N,, as seen

jkhm

\ j/W

t I I I I I I

50 100 150 200 250 300

T, (eV)

Fig. 6. Intensity ratio of the nm and jkl showing the weak dependence on the electron temperature T,. For comparison the strong T,-dependence of the W-line and the satellites are shown.


Fig. 7. Spectra simulation of the experimental spectrum at X = 40 pm of Fig. 4. The Inclusion of numerous dielectronic Li-like satellites up to n = 7 results in an excellent agreement with the experiment:

T, = 80 eV, N. = lo*’ cm-‘, LeR = 100 pm, V, = IO6 cm s’, fbm = 5.10W6, Tbcam = 1 keV.

in Fig. 5. This insensitivity is an important property because the optical thickness is connected through the ground state np to N, by (Eq. (20))

N, z,ansa - Ztl (20)

where ZFR is the effective charge of the one-component plasma. The weak dependence is due to the fact that their ground state is 1~~21 independent of their excitation channel. Redistribution effects inside the autoionizing levels are also weak for satellites with high autoionizing rates. These conditions are met using the mn and jkl satellites. Figure 6 demonstrates the weak dependence of the diagnostic ratio on the T,. For comparison the T, dependence between the W transition and the satellites is shown. The weak dependence on the T, is a result of the high autoionizing rates of these selected satellite transitions resulting in a high population from the dielectronic capture channel and a weak from the inner-shell excitation channel (see also Fig. 3(b)).

Inspection of the experimental spectra, Fig. 4, indicates that the jkl to nm-satellite intensity ratio is a factor of 2 lower than in optically thin plasmas. The results of Fig. 5 implies this may be due to optical depth effects. In Fig. 7 the experimental spectrum at x = 40 pm (see Fig. 4) is shown with the theoretical simulation. Agreement is found for a T, = 80 eV, N, = lo*’ cme3, an effective photon path length of L,, = 100 pm, corresponding to a spot size of 70 pm, with a differential plasma motion corresponding to V, = lo6 cm s”. Under these parameter conditions, line center optical depths are: z,(n) - 0.49, r,,(m) - 1.2, r,,(s) -0.58, z,(t) - 0.38, z,(k) - 2.3, r,(j) - 3.8, r,(Y) - 0.60, and r,(W) - 320. This range of optical depths indicates the importance of radiation transport to the interpretation.

872 F. R. Rosmej et al

An addition of a small fraction of energetic electrons of f&,,,,, = 5 x 10e6 with Tbeam = 1 keV improved the agreement. The influence of energetic electrons on the final theoretical spectrum in shown in Fig. 8, where the simulation is shown for “no beam” and “with beam” cases.

No beam

With beam

I I I I I I I

0.915 0.925

hlnm

Fig. 8. Spectra simulation showing the influence of energetic electrons. The upper spectrum contains no energetic electrons, the lower one contains a very small fraction of fb, = 5.10d6 with Tbm = 1 keV.


NO sa1elhtes

Wtth sate111tes

> L 1 L a 1 b 0915 0.925 0 935

A.lnm

Fig. 9. Spectra simulation showing the strong influence of dielectronic satellites. Upper spectrum: no satellites, lower spectrum with inclusion of Li-like satellites with n = 2-7. The upper spectrum contams only the He-like resonance line W and intercombination line Y. The asymmetric broad structure of the W-line is due to optical thickness in connection with differential plasma motion. Simulation parameters

like in Fig. 7.

Figure 9 demonstrates the influence of the dielectronic satellites on the interpretation of the experimental spectrum, the lower spectrum shows the simulation with satellites, the upper spectrum shows the same simulation without satellites. It is interesting that the satellites dominate close to the target surface due to the low T, and high N, resulting in a large optical depth in resonance line and satellite transitions. At the position of the resonance line, high order satellite transitions contribute because their transition energy asympotically approaches that of the He-like resonance line.

The optical depth effects on the resonance line can most clearly be seen in the upper spectrum of Fig. 9. The broad asymmetric structure is a result of high optical depth in conjunction with differential plasma motion. The experimental spectrum near the target indicates a shift corresponding to a relative plasma motion with a velocity of -V, = lo6 cm s’.


Finally we note that the parameters obtained from purely spectroscopic interpretation, i.e., N,, T,, LeR, V,,, are in excellent agreement with MHD calculations 39. It is interesting to note that a very small fraction of energetic electrons seem to provide a better fit in ns-laser produced plasmas.

5. RELAXATION AND RYDBERG SATELLITE FORMATION IN FS-LASER EXPERIMENTS

The study of fs-laser pulses interacting with solids is intriguing as the time scales of atomic processes and relaxation constants are no longer short compared to the time scale of the variations in N,(t) and T,(t). Thus a fully time-dependent approach is required because excited states relaxation and collisional mixing of relaxation times ‘7.‘9,2’ are extremely important on this time scale. Moreover, even at extremely high densities where the collisions are much larger than the radiative decay rates, the Boltzmann relation for the relative populations becomes invalid because the time required to establish the statistical distributions is longer than the rate of change in the plasma parameters.

In these 120 fs experiments a massive Mg target was irradiated and observed for approximately 600 shots at an angle between 30 degrees to the target surface. Figure 10(a) shows the spectra emitted from plasmas near the target surface, while Fig. 10(b) represents a more distant position. In Fig. 10(b) we observe a spectrum dominated by W transition without the Y transition due to the higher density found in the fs experiment. This can be seen by comparing spectra at x = 280 pm, Fig. 4 and x = 165 pm, Fig. 10(b). Nearer the surface dielectronic satellites dominate, in particular, the spectrum closest to the surface show a dramatic influence of dielectronic satellites. At the position of the W transition a unusual structure is present, designated as the W-line structure in Fig. 10(a). This structure is mainly due to the contributions of Rydberg satellites in a transient three-body recombination regime.

For the time dependent simulation of the X-ray spectra we employ a simplified time-dependence that enables a parameter study using the spectroscopic observables “O. Figure 11 shows schematic time-dependence, where the meaning of the indices 1, 2, and 3 is: 1) corresponds to the prepulse

(a) W-lure

a-d

qrl II

15 urn

30 pm

45 urn

(b) w

Li-sat n = 2

165 urn

150 urn

135 urn

120 pm

115um

100 pm

Fig. 10. (a) Space resolved soft x-ray spectra from fs-laser pulses irradiating a massive Mg target. Close to the target surface the influence of the satellite structure is dramatic. The spectrum closet to the target (x = 0) shows satellite intensities higher than the W-line structure. The anomalous W-line structure is due to accumulated Li-like Rydberg satellites. (b) Spectra obtained far from the target where the most distance

spectrum is composed primarily of the He-like resonance line W.


T, (2)

f.

ne (1)

T, (3)

f *

Fig 11. Parameter test function dependence on time, electron temperature T,, fraction of energetic electrons f, electron density N,.

plasma, 2) corresponds to plasma during interaction of the main pulse with the prepulse-plasma, and 3) represents the cooling plasma. Due to the laser intensity of 5.1016 W cm-’ energetic electrons are generated and this is taken into account by specifying a bulk-temperature, beam-temperature, and a beam fraction according to Eq. (1’7) and Eq. (18).

Figure 12(a) shows the theoretical streak spectrum. Until t = 200 fs, strong emission of the Li-like n = 2 satellites takes place. The Li-like dielectronic captured jkl satellites are excited due to the high temperature of 150 eV, the inner-shell satellites qr are excited by energetic and bulk electrons with T, = 150 eV. At later times, recombination occurs so that the jkl- and qr- satellites disappear rapidly. For higher order Li-like satellites strong emission of Rydberg satellites with n > 2 takes place. Their influence can be directly seen from Fig. 12(b) where all satellites have been artificially turned off. The large emission is due to a three body recombination regime (Eq. (21)):

ls21+ e + e+ ls21nl’ + e (21)

which is three-body recombination into the first excited states 1~21. At N, = 1O22 cmm3 and very low temperatures, the three-body recombination rates are large, and due to optical depth in the He-like resonance line, the 1~21 states do not radiatively decay. Under such conditions even the Li-like n = 3 satellites are optically thick.

Figure 13 shows the time integrated spectrum obtained by integrating the streak spectra of Fig. 12(a). Comparing these with the space resolved spectra from Fig. lO(a,b) good overall agreement for the spectra at distances of m 45 pm is found despite the schematic time-dependence.

We now discuss the influence of different parameters chosen for the time dependence. T,(l) determines the plasma generated from the prepulse. As the prepulse is high, the temperature is also rather high. The lower T,(l), the more pronounced the Li-like inner-shell n = 2 satellites, e.g., qr,


(a) ISE-2

(b) .5E-2

.OE-2

.OE-3

0.915 0.925 0.915 0.925

h/nm h/nm

Fig. 12. (a) Theoretical streak spectrum (each spectrum is a snap-shot) showing the strong role of the 3-body recombination regime after 200 fs in the Li-like n > 2 satellites near the W-line center position. The parameters of this simulation are: @“(1,2, and 3) = IO** cm-3, 2(l) = 50 eV, T,(2) = 150 eV, T,(3) = 50, NP” (1) = 0, Np”” (2) = lo*’ cme3 which according to Eq. (18) corresponds tof= 0.091, Np” (3) = 0, T,,(l - 3) = 10 keV, At = 200 fs, Lcff = 20 pm. (b) Spectra without satellite transitions. It is

clearly seen that dielectronic satellites play a major role in the interpretation.

because the ionization is too slow. The lower T,(2), the higher the relative intensity of the dielectronic captured Li-like n = 2 satellites, e.g., jkl, because of the increasing role of dielectronic recombination. The presence of energetic electrons increases inner shell excited satellites and the W transition because the energetic electrons enhance the ionization. Density variations determine the influence of the three body recombination regime, the lower N, the lower the three body recombination. Lower density also increases the W transition because with fixed effective photon path length, i.e., Lefi = spot size, the optical depth decreases. We note that at high density the plasma potential gives rise to ionization potential depression causing the disappearance of the higher-n levels and one must limit the possible Rydberg satellites. The detailed number of the cut-off is not critical for the final simulation, in the present case we limited n to nlnst = 7.

6. CONCLUSION

In the present work we have investigated experimentally and theoretically the important role of dielectronic satellite spectra for the interpretation of soft x-ray spectra. By means of simultaneous high spectral and spatial resolution we obtained x-ray spectra with high quality very close to the target surface.

The theoretical analysis was based on transient spectral simulations including optical depth effects, energetic electrons and numerous satellite configurations. Atomic data calculations for spectral simulations which take into account configuration interactions and relativistic effects have been carried out. Detailed data comparison and cross-checking has been performed with various other calculational methods.

We have demonstrated the role of dielectronic satellites in the overall spectrum and in the interpretation of resonance line emission. In cold and dense plasmas near the target Rydberg


0 008

0.006

0.004

0 002

0 000

W - line structure

L

9.10E-010 9.15E-010 9.20E-010 9.258-010 9.30E-010

a/m

Fig 13. Time integrated spectra obtained from the summation of the streak spectra of Fig. 12(a).

satellites contribute near the resonance line position. Generalization leads to the concept of higher order Be-like satellites merging into the Li-like satellites, B-like satellites merging into the Be-like satellites and so on.

Acknowledgemenrs-One of us (F.B.R.) greatly acknowledges fruitful discussions over many years with L.A. Vainshtein and U.I. Safronova and partial financial support by the Deutsche Forschungsgemeinschaft. Part of the work was also supported by the Russian Fundamental Science Foundation under grant No. 96-02-16111.

1. 2. 3.

4. 5. 6. 1.

8. 9.

10. 11. 12.

13.

14.

15.

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Inner shell satellite transitions in dense short pulse plasmas

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