Longitudinal coherence length in x-ray lasers depends strongly on the shape of the amplified line. We have modeled an experiment performed at the Lawrence Livermore National Laboratory. The experiment was devoted to the study of the temporal (longitudinal) coherence of the transient x-ray laser at 14.7 nm in Ni-like palladium (4<i>d</i>-4<i>p</i> transition). Only electron (collisional) and Doppler broadening play a role in the line profile of the 0-1 4<i>d</i>-4<i>p</i> transition. This allows us to use the Voigt shape in conditions where the amplifier, <i>i.e.</i>, the plasma produced by the interaction of a high intensity laser with a slab target, is neither stationary nor homogeneous. Our calculations use a ray trace code which is constructed as a post-processor of the hydro-atomic code EHYBRID. In the saturation regime, there is need to account properly for the interaction between the x-ray laser field and the lasing ions. This is done in the framework of the Maxwell-Bloch formalism. The FWHM of the spontaneous emission profile is ~28 mÅ, while the width of the amplified x-ray line ~4 mÅ. Comparison with experiment is discussed.
We present a detailed analysis of an experiment carried out recently in which the temporal coherence of the Ni-like silver transient X-laser at 13.9 nm was measured. Two main consequences of this measurement will be discussed and interpreted with numerical calculations. First we show that the high temporal coherence length measured corresponds to an extremely narrow spectral width of the X-ray laser line. Second we show that the high temporal coherence helps to explain the presence of small-scale structures observed in the cross-section of all transient X-ray laser beams.
Large amplification at 25.5 nm in neon-like iron has been demonstrated in experiments where prepulses are used. We show that the interaction between the x-ray laser beam and the amplifying medium must be taken into account in a reliable modeling of the saturation regime. Two approaches for intensity calculations are presented in this contribution. The first one combines the radiative transfer equation and the population rate equations. This approach is fully consistent, in the sense that beam amplification and population kinetics are treated simultaneously. A formalism based on a paraxial Maxwell-Bloch approach is presented. The Maxwell-Bloch calculations give the variation with length of intensity, local gain...Moreover, in the small-signal regime, it is possible to define an effective gain which is comparable to the measured gain. The second approach is based on a raytrace calculation where the saturation effect has been introduced empirically. The two codes need the electron density and the electron and ion temperatures as inputs. These quantities are given by the hydrocode EHYBRID. The two approaches give similar results.
Recent high temporal resolution Ni-like x-ray laser experiments have yielded important insights into the output characteristics of picosecond pumped x-ray lasers. However, current experimental observations do not fully explain the plasma dynamics which are critical to the gain generation within the x-ray laser medium. A theoretical study of the Ni-like Silver x-ray laser has therefore been undertaken to compliment our experimental results, in an attempt to further our understanding of the processes at play in yielding the observed x-ray laser output. Preliminary findings are presented within this paper.
A numerical code COLAX solving the Maxwell-Bloch equations has been developed and applied to the modeling of soft X-ray lasers in hot laser-produced plasmas. First results in the case of Ne-like Zn from solid targets are presented, including refraction, saturation, coherence properties, and the effect of a half-cavity mirror.
We investigate the polarization state of x-ray beams in collisionally pumped lasers, and compare our results to experimental data on Ne-like Ge lines. The plasma polarization properties are studied in terms of the orientation and alignment, using irreducible tensors of the density matrix. It is shown that the elastic electron-ion collisions tend to equalize the quantum-states populations of each level, and then lessen or even eliminate the polarization of the medium, that is induced by the x-ray beam.
Line profiles taking into account ion (Stark) broadening, ion dynamic effect, and electron collisions are calculated for the Al<SUP>10+</SUP> lines at 154.7 and 105.7 angstrom, and for the S<SUP>13+</SUP> line at 206.5 angstrom in recombination lasers. The first two lines are formed of three fine structure components, while the third is constituted of nine components, and the resulting gain may be defined accordingly. The electron collisions yield an homogeneous broadening, while the Stark interaction with neighboring ions is responsible for an asymmetry of the whole profile. Consistently with the experimental determination of the gain, we calculate the total intensity involving the population inversions of the set of components which contribute to the lasing radiation, and deduce an effective small-signal gain coefficient. We discuss our results and compare them to experimental gains.
We present our recent efforts to produce X-ray lasers in the 200 angstroms range by using the moderate power drive of the LULI facility in Palaiseau. The 4 - 5 transitions of Li-like sulfur exhibit large gain-length products in recombining plasmas, and appear to be less sensitive to plasma non-uniformity than the 3 - 4 and 3 - 5 transitions previously studied. From numerical simulations this is likely due to smaller radiative and collisional excitation from 4f than from 3d levels. In collisional scheme, neon-like zinc gives analogous results to similar works on other elements for the 3p - 3s, J equals 2 yields 1 transitions, but the J equals 0 yields 1 transition shows a surprisingly large gain coefficient of 4.9 cm<SUP>-1</SUP>. From a detailed comparison of time-dependent intensities of the J equals 0 yields 1 and the J equals 2 yields 1 lines, we conclude that transitions from J equals 0 and from J equals 2 are not emitted in the same region of the plasma.