K. Eidmann

An approximate method for calculating Planck and Rosseland mean opacities in hot, dense plasmas

Abstract A method is described for computing the Rosseland and Planck mean opacities of an element as a function of temperature and density. The method is based on the average ion representation for calculating the occupation numbers of the various electronic levels. The photoabsorption coefficients are calculated in the hydrogenic approximation. To account for the important contribution of line absorption, a simple phenomenological method has been developed, which takes into consideration effects such as broadening of the upper electronic levels into bands and band overlapping in the heaviest of the elements. Calculations are presented for various elements and compared with the results of more elaborate methods. Power-law scaling relations for the dependence on temperature and density are derived for a number of elements of practical importance.

XUV OPACITY MEASUREMENTS AND COMPARISON WITH MODELS

The opacities of aluminium, iron and holmium were measured spectrally resolved in the energy range of 70 to 280 eV. For this purpose the iodine laser ASTERIX IV at the MPQ (200J0.4 ns at 440 nm) was focused into a spherical gold Hohlraum with a dia of 3 mm. The generated radiation with a temperature of 60 eV heated thin tampered absorber foils. The transmission was measured spectrally and temporally resolved by means of a backlighter source with a delay of 0.8 ns to the main beam. At this delay time the density in the sample material is about 0.01 g/cm3 and the temperature is about 20 eV. We have compared the experimental data with the opacity codes IMP, JIMENA, OPAL, SAPHIR and STA.

Absolutely measured x‐ray spectra from laser plasmas with targets of different elements

Soft x‐ray spectra emitted by laser‐produced plasmas in the wavelength range 10 A<λ<250 A were absolutely measured with a transmission grating and calibrated Kodak 101‐01 film. Laser pulses with a length of 3 ns and a wavelength of 0.53 μm were focused at an intensity of 3×1013 W/cm2 on planar targets of various elements with atomic numbers ranging from 4 to 82. The overall conversion of incident laser energy into x‐ray energy increases from 2% for Be to nearly 50% for the heaviest elements.

MULTI-fs – A computer code for laser–plasma interaction in the femtosecond regime

Abstract The code MULTI-fs is a numerical tool devoted to the study of the interaction of ultrashort sub-picosecond laser pulses with matter in the intensity range from 10 11 to 10 17 W cm −2 . Hydrodynamics is solved in one-dimensional geometry together with laser energy deposition and transport by thermal conduction and radiation. In contrast to long nanosecond pulses, short pulses generate steep gradient plasmas with typical scale lengths in the order of the laser wavelength and smaller. Under these conditions, Maxwellʼs equations are solved explicitly to obtain the light field. Concerning laser absorption, two different models for the electron–ion collision frequency are implemented to cover the regime of warm dense matter between high-temperature plasma and solid matter and also interaction with short-wave-length (VUV) light. MULTI-fs code is based on the MULTI radiation-hydrodynamic code [R. Ramis, R. Schmalz, J. Meyer-ter-Vehn, Comp. Phys. Comm. 49 (1988) 475] and most of the original features for the treatment of radiation are maintained. Program summary Program title: MULTI-fs Catalogue identifier: AEKT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKT_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 49 598 No. of bytes in distributed program, including test data, etc.: 443 771 Distribution format: tar.gz Programming language: FORTRAN Computer: PC (32 bits and 64 bits architecture) Operating system: Linux/Unix RAM: 1.6 MiB Classification: 19.13, 21.2 Subprograms used: Cat Id: AECV_v1_0; Title: MULTI2D; Reference: CPC 180 (2009) 977 Nature of problem: One-dimensional interaction of intense ultrashort (sub-picosecond) and ultraintense (up to 10 17 W cm −2 ) laser beams with matter. Solution method: The hydrodynamic motion coupled to laser propagation and several transport mechanisms is solved in one-dimensional geometry using a fractional step scheme. Fluid motion together with heat diffusion is solved by using an implicit Lagrangian method. Transport by thermal conduction and radiation as well as electron–ion energy transfer are treated in a two-temperature (electron and ion) model covering the wide range from solid state to high temperature plasma. Laser propagation is calculated from the one-dimensional Maxwell equations. Radiation transfer is solved by using the forward-reverse method for a discrete number of frequency groups. Matter properties are interpolated from tables (equations-of-state, ionization, opacities, and emissivities) generated by external codes. An alternative WKB laser deposition package is available to be used for long pulse lasers. Restrictions: The code has been designed for typical conditions prevailing in short pulse (fs–ps time scale) laser–matter interactions at moderate intensities (10 12 –10 17 W cm −2 ). Although a wider range of situations can be treated, extrapolations to regions beyond this design range need special care. Additional comments: A graphical post processor is included in the package. Its use requires the previous installation of code MULTI2D (see “Subprograms used” above). Running time: 4.8 seconds for the example supplied.

Generation of hot plasma at solid density by high-contrast ultra-short laser pulses

Abstract We have generated a high-density plasma by focusing frequency-doubled Ti-Sapphire laser pulses at λ=395 nm and a duration of 150 fs on flat solid targets at an intensity of ≈10 17 W / cm 2 . Using solid Al targets tamped by a thin surface layer of MgO we measured the Al K-shell emission. The measured resonance lines ( Ly α , He α and Heβ) and their Li-like and He-like satellites are extremely broad. In addition, we observed clear center of gravity red shifts of the main lines by using the cold Kα line as a reference. The temporal duration of the K-shell emission, measured by an X-ray streak camera, is ≈2.5 ps. Analysis of the spectra yields an effective electron temperature of ≈300 eV and an electron density of ≈(7–10)×10 23 cm −3 . A very weak emission of cold Al Kα indicates a low level of energy deposited by fast electrons in the solid. Essential for achieving these results is the suppression of early time expansion of the Al target by using both, a high-contrast laser pulse and a tamped target.

Radiative heating of B, Al and Ni thin foils at 15–25 eV temperatures

Several thin foils have been heated by X-ray radiation emitted by a small gold cavity irradiated with the LULI facility Nd glass laser. The foils were heated to moderate temperatures (10–25 eV) in conditions near local thermodynamic equilibrium. Measurements of the absorption of Kα transitions of aluminum, of the K-shell transitions of boron, and of the n=2–3 and 4 transitions of nickel are reported. A 5000 l/mm transmission grating spectrograph recorded the boron data, and a flat thallium hydrogen phthalate (TlAP) crystal was used for aluminum and nickel absorption measurements. The nickel and aluminum spectra indicate a higher temperature (22–25 eV) than the boron case (14 eV), explained by a difference in the absorption spectra of these elements. In the Ni case the measured 2p-3d spin–orbit–split absorption structures compared well with theoretical spectra obtained with the SCO superconfiguration code using the spin orbit split transition arrays formalism (SOSA). The heating of the foils as calculated with radiative hydrodynamic simulations is very similar to the experimental data.

Absolute calibration of a flat field spectrometer in the wavelength range 10–70 Å

We characterize an x-ray spectrometer in the wavelength range 10–70 A. The instrument has been designed for the study of the soft x-ray emission from plasmas generated with intense sub-ps laser pulses. It uses a flat field reflection grating with 2400 lines per mm as dispersing element and an x-ray charged coupled device (CCD) as detector. The sensitivity of the spectrometer and CCD detector has been absolutely calibrated by means of a ns-laser generated gold plasma of well known x-ray conversion efficiency. The calibration procedure is explained in detail. Finally, we present examples of spectra emitted by a sub-ps laser plasma. From the spectra follows a resolving power of 150–350 and a low conversion efficiency into the second diffraction order of the flat field grating of only a few %. The measured frequency averaged total conversion of laser energy into x-ray energy emitted into 2π is in the range of 2.4×10−4 up to 6.2×10−3 depending on the material of the solid targets.

Comparative study of laser acceleration of thin foils at wavelengths 0.44 μm and 1.3μm

Abstract The acceleration of thin plastic foils irradiated with frequency-triplet ( λ = 0.44 μm ) and fundamental ( λ = 1.3 μm ) iodine laser light was investigated. Rear-side velocities and two-dimensional behaviour of the foils were recorded with a novel 6-frame photographic diagnostic. Core velocities were inferred from calorimetry and X-ray backlighting. Unlike at 1.3 μm, the rear-side and core velocities were found to be quite different at λ = 0.44 μm . An explanation is offered in terms of lack of lateral smoothing at 0.44 μm. The ablation pressure scales as P abl ≈ I 0.6 abs λ -0.4 .

Absorption measurements of radiatively heated multi-layered Al/Ni foils

Abstract Mixtures of light and mid- Z elements have been used to measure the absorption of the mid- Z element Ni, the temperature is inferred from the K-shell absorption of the light element Al. Here we test this method by comparing the temperatures deduced from Al K α transitions and nickel L-shell absorption spectra in Al/Ni multilayers and bilayers. The ionisation state is obtained by comparison of the Al and Ni spectra with calculations assuming local thermodynamic equilibrium. The temperatures obtained from the experiment are compared with hydrodynamic simulations predictions. Simulation code results show that the density differs by a factor of 2 in the two elements. This has to be taken into account in the determination of the temperature.

Transmission grating spectroscopy in the 10 keV range

We demonstrate the feasibility of transmission grating spectroscopy in the 10 keV range. The diffraction efficiency of a 5000 l/mm free-standing gold transmission grating was measured at the three photon energies of 1.49, 5.4, and 8.04 keV (Kα of Al, Cr, and Cu). At 1.49 keV, the measured efficiencies agree well with efficiencies calculated by standard grating theory. At 5.4 and 8.04 keV, the measured efficiencies significantly exceed the theoretical ones. For Cu Kα, the absolute efficiency into first order is still as high as 3.3%. We present spectra of fs laser plasmas generated by irradiating Al, Cr, and Cu targets.