X-RAYS FROM HIGH-DENSITY PLASMAS

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X-RAYS FROM HIGH-DENSITY PLASMAS

R. More

To cite this version:

R. More. X-RAYS FROM HIGH-DENSITY PLASMAS. Journal de Physique Colloques, 1987, 48

(C9), pp.C9-343-C9-353. �10.1051/jphyscol:1987960�. �jpa-00227378�

JOURNAL DE PHYSIQUE

Colloque C9, suppl6ment au n012, Tome 48, decembre 1987

X-RAYS FROM HIGH-DENSITY PLASMAS

R.M. MORE'"

Ecole P o l y t e c h n i q u e , F-91128 P a l a i s e a u Cedex, France

Les trois dernieres annbes ont vu des progrhs remarquables dans la recherche des plasmas de haute densite cr&s par laser, en particulier l'obtention des premiers lasers produisant des rayons X mous, la spectroscopie X d'implants pour l'etude d'ions simples et complexes, l'etude systematique de la conversion de l'energie du laser en rayons X, et la premiere spectroscopie d'absorption de la matiere cornprime par chocs A des densites bien au dela de celle du solide. Nous resumons ces developpements et considerons les implications qu'ils one pour la theorie des processus atomiques dans les plasmas de haute densitb.

ABSTRACT

The past three years have seen remarkable progress in research on high-density laser-produced plasmas including the first lasers producing soft x-rays, microdot x-ray spectroscopy of simple and complex ions, systematic study of conversion of laser energy to x-rays, and the first absorption spectroscopy of shock-compressed matter at densities well above the normal solid density. We summarize these exciting developments and consider their implications for the theory of atomic processes in high-density plasmas.

("on leave from Lawrence Livermore National Laboratory, Livermore. CA 94550. U . S . A

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987960

Overall, there are two continuing themes in the recent experimental work on laser plasmas: (1.) improved understanding of plasma x-ray production, achieved as a result of ( 2 . ) better control over plasma density-temperature conditions.

A-nay Lasers

Following the Livermore experiments on neon-like selenium"', gain has been found with various ions for photons of energies of 60-190 eV with gain-length products as large as 16.'=' Some laser schemes are described in detail by ~aeg16.'~' Demonstration of gain for soft x-rays has galvanized research on atomic physics in the USA and elsewhere; the potential importance of x-ray laser technology has motivated the.assembly of large groups 0.f researchers, and there is no shortage of challenging problems such as the missing or reduced gain for the transition J=0 to J=l at 182 A in the Livermore experiments on neon-like selenium.

One result of this activity is the development of detailed numerical models for various ion species, especially for He-like, Li-like, Ne-like and now Ni-like

ion^.'^*^'

The codes include rate coefficients for most of the relevant atomic processes and generation of this data has required a major effort in numerical calculation. The codes are being tested against laser and other spectroscopic experiments.

Most x-ray laser experiments involve low-density plasmas and strong density effects do not occur. This is not accidental because density effects such as Stark broadening of the laser line are likely to be detrimental to laser gain.

Rosen et al."' emphasize that in order to observe x-ray lasing, it is necessary to understand and control the plasma hydrodynamics.

Obviously one must heat ions to the desired charge state, but in addition, the gain is easily lost by x-ray refraction Or by absorption in cold regions at the end of the plasma column (the "laser rod"), so the plasma geometry must be controlled. There is now detailed and quantitative agreement between theoretical LASNEX calculations and experimental plasma expansion profiles measured by pulsed holographic interferometry.

'='

X-ray refraction is a density effect, although the interesting phenomena of anomalous refraction near lines and photoelectric edges do not occur in x-ray laser experiments because one deliberately seeks a plasma with low x-ray absorption in order to keep the gain as high as possible.

Absence of gain predicted for the J=O lines of Ne-like Se has stimulated consideration of various hypothetical density effects, especially screening effects which might interfere with the monopole electron-impact excitation mechanism. To date it appears that these density effects are not able to explain the experiment and other mechanisms are still being sought.

An interesting theoretical picture suggested by H. Griem illustrates the possibilities.'" In this scenario, the Doppler width of the laser lines is assumed to be reduced by a process called Dicke narrowing: when the ion-ion collision time is comparable to the inverse Doppler line-width, a given ion can change directions several times while emitting and the Doppler line-profile is greatly narrowed. The magnitude of the Dicke effect is determined by the ion mean free path and therefore by the ion temperature, which unfortunately is not measured in the current experiments.

For the J=2 lines, Griem argues that the Dicke effect is largely removed by quadrupolar fields encountered in ion-ion collisions, but these do not affect the singlet upper states of the J 4 lines. This reasoning implies a narrower line for the J 4 transition, which would naively imply a higher gain and a larger mystery. However with sufficient plasma turbulence, a line that is too narrow will suffer from refractive losses that would not affect a broader line; for a plausible turbulence level one can match the observed gain of J = 0 and J=2 lines.

Some other representative subjects of current research on x-ray lasers include (1.) plasma density fluctuations and their effect on refraction and beam divergence, ( 2 . ) effects of non-Maxwellian free electrons, and (3.) effects of missing levels in atomic rate equations, especially levels near the continuum, and new descriptions which would be more sophisticated than simply forming and inverting the large matrix representing all atomic transitions between all atomic levels.

Microdot S p e c t r o s c a

One of the characteristic difficulties of laser plasmas is the spatial inhomogeneity in the plasm produced by ablati-g a solid target.

This spatial inhomogeneity means that the recorded x-rays originate over a range of density-temperature conditions and any densitg effects are blurred or averaged. The new technique of plasma microdot spectroscopy shows how to solve this pr~blem.'~'

In the microdot method, a small spot of high-Z material of interest is placed in the center of a disk of plastic or other low-Z material.

When the laser irradiates this composite target, the high-Z dot expands as an axially confined plasma column, like a smoke signal. Looking from the side, one sees emission from a section of this column which has a unique density and temperature (which, of course, remain to be determined). There is also a technical improvement in the reduced source size and reduced optical depth.

In addition to plasma diagnosis using H-like and He-like line spectra, the microdot technique has been used for detailed studies of Neon-like and Nickel-like spectra principally for X-ray laser development.<J° There are also experiments using two nearby micro-dots for the measurement of hot plasma x-ray absorption coefficients.Cs>

High-Charge Periodic Table

Some of the most recent x-ray laser experiments involve Ni-like

ions< s > and the UTA spectra discussed in the next section are also

obtained from ions near the nickel-like configuration. Why are Ni-like ions so important?

In ordinary matter Ni is an itinerant-electron ferromagnet with a 3ds4s2 configuration, a consequence of its position in the second half of the 3d transition series, i.e.,

H Li 4 11 12 19 20 37 38 55 56

21 22 23 24 25 Fe Co Ni Cu Zn 39 40 41 42 43 44 45 Pd 47 48

5 13 31 49

6 14 32 50

7 15 33 51

8 16 Se 52

He 9 Ne 17 Ar 35 Kr 53 Xe

Here, we give only atomic numbers except for a few elements, especially the noble gas elements (He, Ne, Ar, Kr, and Xe) which have closed-shell configurations as neutral atoms.

For high-charge ions, the nuclear potential (= Ee/r) is increasingly important relative to the electron contribution and the energy-levels rearrange into essentially hydrogenic order. Therefore, the chemistry of

C9-347 high-charge ions is better described by a "High-Charge" periodic table:

H He Li 4 11 12 Cu Zn

61 62 5 13 31 63

6 14 32 64

7 8 9 Ne 15 16 17 Ar 33 34 35 Kr

47 48 49 50 65 ...

19 37 51

20 38 52

21 39 53

22 40 Xe

23 41 55

24 42 56

25 43 57

Fe 44 58

Co 45 59

Ni Pd Nd

This table describes Ne-like, Ni-like ions of high-charge elements. The grouping indicates the sequential filling of shells (Is, 2s, 2p, 3s, 3p, 3d, 4s, etc). For example, high-charge nickel-like ions have a closed-shell configuration,

ls22s22p*3s23p*3d10

As a consequence Ni-like ions have unusual stability in the plasma and a relatively simple spectrum. For very high-Z ions the grouping should reflect spin-orbit splitting so that the 2s, 2p shells become (2s-2p j-1/2), <2p j=3/2), etc.

Unresolved Transition Arrays

High-Z spectra from many-electron ions are often too complex for the usual line-by-line analysis, and various statistical methods have been developed. The most elaborate is the method of unresolved transition arrays (UTAs), developed by Bauche, Bauche-Arnoult, and Klapisch.<9> This approach has permitted the clear identification of certain transitions in high-charge ions near the nickel-like configurations.

In simplest terms, a UTA is a cluster of lines resulting from allowed transitions between a given initial and final configuration. The pair of configurations (differing in the placement of one electron) generate one UTA, which is characterized by a mean energy S E and a width determined by the moments

<SE> = E Wij (Ei - Ej) / z wi;j

< S E2> - r Wjj (Ei - E j )2 / s Wjj

Here w^j is the oscillator-strength of the transition i — > j. The sum runs over all states in initial and final configurations.

The idea of the UTA method is to directly calculate <SE> and <SE2>

by operator techniques instead of evaluating them by laboriously diagonalizing the Hamiltonian, finding the many eigenstates, and forming the averages. The moments involve the direct and exchange electron-electron interactions (in the form of Slater integrals F and G ) , spin-orbit matrix-elements, and angular coefficients which are fixed for a given pair of configurations and which are tabulated by Bauche et al.

Klapisch, Zigler et a l .C l o > analyze a palladium laser-plasma spectrum and find a series of nine well-defined UTA peaks near 500 eV, beginning with the Ni-like 3d94f — > 3d1 0 transition. The spacing is about 27 eV. Each peak is attributed to a successively higher ionization stage, e.g., Co-like 3ds4f — > 3d5", Fe-like 3dr4f — > 3ds , etc. Although there are more and more transitions in these arrays, the widths do not grow with the ion charge state. A hydrogenic screening model reproduces the spacing in a rough way:

a(E„ - E3)/ap3 = (Qe2/a0) (1/32 - 1/42) = 24 eV

To observe such an UTA spectrum the plasma must be near the Ni-like ionization stage, and the width of the UTA line-cluster must be less than the spacing of peaks. It is somewhat surprising that this occurs, because the width contains contributions from spin-orbit, direct and exchange energies while the spacing is mainly the 1 = 0 direct interaction as indicated by the hydrogenic estimate. Of course, it is also necessary that background emission produced by satellite electrons not obscure the UTA spectrum, and this constraint evidently means that the best UTA series correspond to high angular momenta (e.g., 3d-4f or 3d-5f transitions).

A second type of UTA spectrum is observed for gold.c 11_,*:> In this case ~there are strong spin-orbit splittings, so that one sees interlaced groups of line clusters, e.g.,

A4 : 3 d %/ 2 5 f7 / 2 (4s)n — > 3d1 0 (4s)»

B4 : 3 d9 3 / 2 5 fs / 2 (4s)n — > 3d1 0 (4s)n

Four peaks are seen in most cases, corresponding to Ni-like (n=0), Cu-like (n=l), Zn-like (n=2) and Ga-like (n=3) ions. For gold these peaks occur at about 2.5 keV with a spacing of 36 eV; in this case the hydrogenic model predicts a spacing of 30 eV. There are also well-defined UTAs corresponding to the 3d-5f transitions at about 3.3 keV.

This interpretation of the Au spectrum is convincingly supported by precise calculations of the line positions by Bauche et al."" and Busquet et al."" It is in marked contrast to a verydifferent interpretation of similar spectra given by Kiyokawa et a1.'I3' Spin-orbit split Ni-like UTA spectra are identified for Ta, W, Re, Pt, Hg and Pb by Tragin et a1.'14'

The 3d-4f UTAs are superposed upon an interesting background emission which is known to increase with plasma density. This so-called red wing is not yet unambiguously interpreted.""

X-Ray Conversion Efficiency

Next we mention experiments which look at the total X-ray production from a laser-irradiated target. The quantity measured is the conversion efficiency,

CE(Z,I,x) = (Total x-ray energy out)/(Laser energy in)

One must specify the spectral range of x-rays collected, for example, the range ^{h u} ) 1 keV.

Optimizing the conversion efficiency is very important for potential practical applications such as inertial fusion via indirect drive, where the x-ray energy itself implodes the capsule, or lithography using soft x-rays.

Laser energy absorbed by the target goes into various degrees of freedom including ionization energy, thermal energy (3/2 kT per free electron), ion internal excitation energy and plasma kinetic energy. Much of the radiated energy escapes from the plasma. In general there are comparable amounts of energy in each form and it is difficult to calculate the partition. Therefore it 1s useful to directly measure the x-ray yield as a function of laser wavelength A, laser intensity I, and target atomic number 2.

The recent work takes a systematic approach: many target materials are irradiated under similar conditions and the entire periodic table is sampled.

Experiments performed at the Ecole Polytechnique by H. Pepin et a1.'15' show peaks in the conversion efficiency at Z = 22(~i) , 42(Mo) ,

and near 79(Au), with minima near Cu(Z = 79) and Gd(Z=64). Similar experiments done in Japan also show maxima at Z = 22, 42, and 80.''~'

We can easily understand this behavior on the basis of the

"high-charge periodic table" and two key assumptions:

i.) The CE is largest for ions with half-filled shells.

ii.) The ion charge Q is determined by

with 5 = 6. I is the ionization pokential and n is the principal quantum number.

Using this formula with a temperature kT = 130-160 eV, one finds a half-filled L-shell at Z = 22, half-filled M-shell at Z = 42, and a half-filled N-shell near Z = 75.

Experiments by Eidmann et a1.'17' give emission spectra for Be, C , Al, Ti, Cu, Mo, Sn, W, Au and Pb targets; these experiments illustrate the successive emission of K,L, M, N and 0-shell lines in agreement with the above estimates. For the high-Z elements one is dealing precisely with the emission of UTA spectra.

A more complete theoretical analysis is difficult because there is a large uncertainty in the spatial density profile, uncertainty in the temperature profile and therefor in the heat conduction, uncertainty in the calculation of non-LTE ionization for complex ions, and uncertainty in the extent and consequences of non-Maxwellian free-electron distributions. These questions are strongly interrelated.

'"'

For example, if the experiments were modelled with a non-Ifaxwellian distribution f(E) having a reduced electron population at energies E > 6 kT, one could explain the observed strong inhibition of electron heat conduction without making any large change in plasma energy-content.

However the reduction of f(E) would also have a large effect on the ionization rate and therefore on the charge state. In turn, loss of electrons at energies ) 6 kT to ionization may help explain their absence. All of this seems logical, but satisfactory numerical modelling has not yet been performed. The recent experimentalsC"-'" will certainly stimulate new theoretical effort.

Absorption Spectra from Beyond Solid Density

Yith a hot source plasma producing a continuous emission spectrum, one can examine absorption caused by a target plasma. For example, in implosion experiments, the hot fuel core serves as a source for absorption by materials in the pusher (Hauer et a1. " 9 ' ) . However, in these experiments the absorbing plasma is not even approximately homogeneous, and so while the data can help diagnose plasma conditions they do not rigorously test fundamental models of the density effects. A different type of absorption experiment is giving data about the strongest density effects: absorption spectroscopy of shock-compressed matter (Bradley et a1. '20-2" and Hall et a1.'22').

In these experiments, the plasma is produced by one (or two) planar shock-waves in a solid target. In principle, this technique produces a large region of homogeneous plasma at an approximately known density of 4 (or 6) times the initial solid density. Again the geometry gives the required control over the plasma density and teinperature conditions.

The shocked sample is irradiated by a bright continuous spectrum from the nearby backlighting target and the absorption spectrum reveals time-dependent features associated with arrival of the shock wave(s). In practise there are uncertainties in plasma conditions produced by preheat, by two-dimensional effects and by nonuniformity of the laser focal-spot. The backlighting x-rays themselves may perturb the target, for example raising its temperature or causing transient ionization.

In one experiment, the K-shell absorption edge of chlorine contained in a chlorinated plastic target material is observed to be red-shiftsd by about 10 eV. One expects such a shift to be produced by a change in the atomic potential due to the increased average electron density and tha proximity of neighbor ions, and due to changes in the free-electron distribution function; the Fermi-energy is raised by compression and also the shocked material has a high enough temperature that some states are open at energies below the Fermi surface. While these considerations produce results generally like those seen experimentally, there is probably a need for a more detailed and realistic picture of the chemical bonding environment of the chlorine, especially in the normal initial state.

A second innovative experiment sees a shift (and loss of definition) of the EXAFS structure near the aluminum K-edge.'22' In this case one has

again a reasonably good idea of the hydrodynamic compression of the target, and so a nontrivial high-density effect is being observed from a plasma of known thermodynamic state.

Summary

The author hopes that this brief survey has brought out one central point: research on laser plasmas has matured, a greater number of laboratories are performing interesting experiments, and much of this progress is a result of improved control over the hydrodynamic motion of the laser plasma.

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