**4. The laser-produced soft X-ray source**

The setup of a standard soft X-ray source based on gas targets is used [8]. It basically consists of a piezoelectrically operated Proch–Trickl gas valve [38] mounted on a vacuum chamber, and a driving Nd:YAG laser that emits radiation at the fundamental wavelength of 1064 nm with a pulse energy of 800 mJ and a pulse duration of 6 ns (InnoLas SpitLight 600), see **Figure 7**. The intensity profile of the unfocused laser beam, measured by a CCD camera (Lumenera Lu160M), reveals a beam diameter of 5.9 mm (determined through 1/*e*<sup>2</sup> decay), corresponding to a mean power density of 4.9 × 108 W/cm2 . Plasma production takes place as soon as a critical power density of ≈ 1012 W/cm2 is reached in the focused beam at a sufficiently large particle density [39]. This initiates the first ionization of the target gas followed by avalanche ionization, creating large numbers of free electrons.

**Figure 7.** Pinhole camera images of the plasma at a stagnation pressure of *p*<sup>0</sup> = 11 bar for various background pressures *pb* as given below the individual figure. The average of 30 single shots is shown.

The target gas is expanded through a divergent nozzle of conical shape. Over a length of *ln* = 1 mm, its diameter increases from the throat diameter *d*\* = 0.3 mm to the exit diameter *de* = 0.5 mm. The nozzle is opened for a period of 1 ms, generating an underexpanded supersonic jet that expands from stagnation pressure *p*0 = 11 bar into vacuum, i.e., the background pressure *pb* is as low as 10−4 mbar. The laser is focused into the gas as soon as the jet flow is steady. The position where the plasma is produced is located in a distance of 500 μm, i.e., one diameter *de* behind the nozzle exit (see the typical plasma position indicated in **Figure 8**). Although the density is highest at the nozzle exit, the plasma should not be generated closer to the nozzle because of growing degradation effects. By employing different target species, various spectra can be obtained in the EUV and soft X-ray range. Noble gases with high atomic numbers such as xenon, argon, or krypton are broadband emitters, while oxygen or nitrogen each produces several narrow lines. The corresponding spectra can be found in **Figure 9**, produced by a system comparable to that described above and captured with a soft X-ray spectrometer, which is described in detail in [8]. Here, nitrogen is used in combination with a titanium filter, resulting in a monochromatic emittance at *λ* = 2.88 nm in the water window, corresponding to the transition 1*s*<sup>2</sup> − 1*S*2*p* of the valence electron of the N5+ ion [40].

axis of the nozzle. Here, without ambient gas the jet is even more rarefied and with ambient

The setup of a standard soft X-ray source based on gas targets is used [8]. It basically consists of a piezoelectrically operated Proch–Trickl gas valve [38] mounted on a vacuum chamber, and a driving Nd:YAG laser that emits radiation at the fundamental wavelength of 1064 nm with a pulse energy of 800 mJ and a pulse duration of 6 ns (InnoLas SpitLight 600), see **Figure 7**. The intensity profile of the unfocused laser beam, measured by a CCD camera (Lumenera Lu160M), reveals a beam diameter of 5.9 mm (determined through 1/*e*<sup>2</sup> decay),

large particle density [39]. This initiates the first ionization of the target gas followed by

**Figure 7.** Pinhole camera images of the plasma at a stagnation pressure of *p*<sup>0</sup> = 11 bar for various background pressures

The target gas is expanded through a divergent nozzle of conical shape. Over a length of *ln* = 1 mm, its diameter increases from the throat diameter *d*\* = 0.3 mm to the exit diameter *de* = 0.5 mm. The nozzle is opened for a period of 1 ms, generating an underexpanded supersonic jet that expands from stagnation pressure *p*0 = 11 bar into vacuum, i.e., the background pressure *pb* is as low as 10−4 mbar. The laser is focused into the gas as soon as the jet flow is steady. The position where the plasma is produced is located in a distance of 500 μm, i.e., one diameter *de* behind the nozzle exit (see the typical plasma position indicated in **Figure 8**). Although the density is highest at the nozzle exit, the plasma should not be generated closer to the nozzle because of growing degradation effects. By employing different target species, various spectra can be obtained in the EUV and soft X-ray range. Noble gases with high atomic numbers such as xenon, argon, or krypton are broadband emitters, while oxygen or nitrogen each produces several narrow lines. The corresponding spectra can be found in **Figure 9**, produced by a system comparable to that described above and captured with a soft X-ray spectrometer, which is described in detail in [8]. Here, nitrogen is used in combination with a titanium filter,

W/cm2

. Plasma production takes place as

is reached in the focused beam at a sufficiently

gas the shock structure is present.

84 High Energy and Short Pulse Lasers

**4. The laser-produced soft X-ray source**

corresponding to a mean power density of 4.9 × 108

avalanche ionization, creating large numbers of free electrons.

*pb* as given below the individual figure. The average of 30 single shots is shown.

soon as a critical power density of ≈ 1012 W/cm2

**Figure 8.** Photograph of experimental setup for plasma generation. The laser beam is focused by a lens into the vac‐ uum chamber and generates the plasma right below the gas nozzle, which appears here in bluish color in the center of the chamber.

**Figure 9.** Principle of plasma generation employing jet targets: typically the plasma is generated close to the nozzle under vacuum conditions. Applying a background pressure *pb* induces the barrel shock structure, which enhances plasma generation due to a local density increase.

In the approach pursued in this work, the background pressure *pb* is increased to several tens of mbar in order to generate a barrel shock in the supersonic jet. For this purpose, helium is utilized as a background gas due to its high transmissivity of photons generated by the plasma. In addition, the optical path length of the resulting soft X-rays through helium is minimized by differential pumping. Another advantage of using helium as a surrounding gas is its large first ionization energy (24.6 eV) compared to that of nitrogen (14.5 eV) [41]. Thus, the critical power density to drive ionization by the incident laser beam is higher for helium, which ensures that only the target species nitrogen is ionized. Right behind the shock system generated in the jet, the particle density increases. In this manner, regions involving high densities of the target gas are obtained at comparably large distances from the nozzle. Thus, the plasma can be generated further away from the nozzle exit, and degradation effects are minimized.
