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Atomic Structure Theory.

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We have observed both effects separately noticed in Refs. Indeed our model, based on rate and transport equations including the solid-density plasma state of the target, accounts for both observed mechanisms that are the privileged direction for the stimulated emission of the Mg L 2,3 characteristic emission 3sd-2p electron transition as reported in Ref. The presented theoretical framework provides the basis for the development of novel coherent pulsed EUV and x-ray sources characterized by negligible spectral jitter and unprecedented intensity.

The Its bandwidth is 0. The FEL beam intensity before the sample is monitored through a calibrated ionization chamber. The FEL beam can be focused on the sample at normal incidence. For a given detection angle, hundreds of single-shots are carried out on different neighboring places of the sample.

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The MgO target sample is a single crystal supplied by Neyco; the sample was polished with a 0. The crystal is cut along the plane whose reticular distance is around 0.


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So Bragg scattering diffraction of the incident Each point corresponds to the mean of the measurements following hundreds of FEL shots, where each measurement is normalized by the energy in the FEL shot. The errors bars represent 3 standard errors. The experimental distribution displays some modulations which are likely actual structures considering the statistics of the measurements.

Our model does not reproduce these oscillations. An explanation should be that the outgoing radiation is partially backscattered at the interface between the target and vacuum, resulting in interferences between the direct and backscattered radiations giving rise to these structures. We also measured the output intensity of the generated emission as a function of the pump intensity or the number of photons in a FEL shot, Fig. The result of the simulation see below is also shown in this figure. As mentioned in Refs. The large intensity increase observed above the threshold cannot be ascribed to the generation of satellite lines following the creation of double core holes.

Number of characteristic photons detected by the avalanche photodiode, as a function of the number of photons in a FEL shot and of the pump intensity: points experimental values; blue dashed line region of the slightly increasing plateau; red dashed line linear fit according to Eq. A9 and A The energy of the photons in the FEL beam is Under low intensity exposure, the MgO sample remains in a cold solid state and emits the Mg L 2,3 band, different in MgO and metallic Mg.

In the oxide, the spectrum presents two maxima located at 41 and Electron transitions involving valence and conduction bands for the three relevant processes are as follows:. Core holes decay by both spontaneous and stimulated emissions. In competition with these two radiative decay channels, the Auger effect also reduces significantly the lifetime of the core holes.

Nevertheless, core holes decay by stimulated emission more efficiently than by the Auger effect, 3 so that under intense FEL pumping, the number of Auger processes is considerably reduced with respect to the small excitation regime excitation with x-ray tube or synchrotron for instance for which stimulation is irrelevant.

The potential X corresponds merely to the bottom of the valence band. The electronic band structure typical of the crystalline solid state tends to disappear as shown in Fig. Somehow, X is the 2p ionization potential of the isolated atom decreased by the density-induced continuum lowering effect. Energetic diagram of a solid in the cold state a and in the state of a warm plasma with solid density b. In the cold solid state, the less tightly bound electrons are distributed within a valence band [dashed surface in a ], whereas in the warm state, the electrons are distributed at discrete levels [horizontal lines in b ].

At temperatures corresponding to the solid-density plasma and for times less than about 1 ps, the ionic lattice remains weakly altered but the electronic distribution can no longer be described by the density of states DOS of a cold crystalline solid. As shown in Fig.

Atomic Properties in Hot Plasmas

Let us note that owing to the difference between the densities of Mg and MgO, the number of magnesium atoms per volume unit is similar in both materials. In the simulation, we consider a degenerated free-electron gas and not the cold valence DOS which is supposed to disappear quickly as the electronic temperature increases. Depth variation of the electron temperature inside a Mg sample as a function time for the FEL pulse of 65 fs duration whose photons have an energy of The FEL beam arrives from the right at the depth of nm corresponding to the sample surface. The maximum of the pulse occurs at 84 fs.

The change in the FDS creates free space below the Fermi energy and allows ionization at lower energy, see Fig. In the heated solid, the potential X is always the ionization potential of the ion in the solid-density plasma and can be fixed by. Since the ionization potential of the solids is very well known, 16 it is easily possible to deduce X from Eq.

EUV stimulated emission from MgO pumped by FEL pulses

This shift is then handled with the use of Pauli-blocking factor. At intermediate temperatures, the factor blocks only partially the transfer of electrons and the threshold extends between X s and X plasma , and at high temperature, the factor has no effects leaving the potential at X plasma.

The DOS evolves rather quickly with the temperature, so it is the same for the chemical potential, which can be approximated by the DOS of a Fermi free-electron gas. In our case for magnesium, one has numerically.

Plasma Physics Division, U.S. Naval Research Laboratory

The last term r is the stimulated recombination rate from the valence band given by. In our case,. A discussion concerning the micro-reversibility relations can be found in various textbooks. The initial condition, meaning that no core holes are present before the arrival of the FEL pulse. In fact, we adopt a simplified quasi-analytical model where a volume integral 3D is reduced to a one-dimensional problem see Methods. Geometry of the experiment. From Eqs. This geometry presents a close analogy with the pencil-like geometry adopted in some models of amplification of spontaneous emission ASE with transverse pumping.

In this geometry, Fig. The set of coupled differential equations governing the growth in intensity reads. This formula, where r is given by Eq. On the right side of Eq. Following Ref. The rate and transport equations, Eqs. The computation is carried out by means of the refractive index values from the Centre for X-Ray Optics database. For high intensities of the exciting FEL pulse, an absorption saturation effect occurs. Physical quantities and experimental parameters used in the model for the MgO target. Values without reference are experimental parameters or calculated with our model.

Above threshold, both core hole density and gain become clamped near their threshold values and the stimulated intensity varies linearly with the exciting photon intensity. The pump intensity at the beginning of the plateau 2.