## 1 Introduction  
The Ne-like Ar capillary-discharge laser (CDL) represents a compact, handy device that emits intense monochromatic radiation with a wavelength of 46.9 nm delivered in nanosecond pulses [1]. The extreme ultraviolet laser promises great potential for use in the field of holographic imaging [2], microscopy [3] and materials processing [4; 5; 6; 7; 8; 9; 10] including nanostructure manufacturing, benefitting from the short wavelength of its radiation. For numerous applications it is important that even a single photon carries the energy that exceeds the band gaps and the cohesive energies of almost all common materials. It is also important that such energetic photons (their energy is 26.4 eV) are strongly absorbed in the material almost solely by the photoelectric effect. Thus, the intense short-wavelength radiation can create ultra-fine structures via a direct ablation of dielectric materials that would be transparent to long-wavelength lasers, i.e., those working in UV, visible (Vis) and IR spectral ranges.  
Patterning of the surface of materials can be performed with intense coherent electromagnetic radiation in two ways. Ripples are formed either spontaneously (so called LIPSS, first observed in the middle sixties [11]--frequently caused by an interference of incoming laser radiation with the front of the pulse scattered on an imperfect surface [12]) or by an externally modulated (e.g., in an interferometer, by reflection/transmission masks)wavefront of the laser beam (for such experiments with XUV-CDL radiation see refs [7; 8; 9; 10]). In this article, we shall concentrate on the spontaneous LIPSS formation on XUV-CDL irradiated surfaces. It has been demonstrated earlier that the LIPSS associated with interference phenomena on the surfaces exposed to XUV radiation (radiation with wavelengths shorter than 100 nm here referred to as XUV [13]; EUV is now usually attributed to 13.5-nm radiation routinely engaged in EUV Lithography--EUVL [14]) occurring only rarely [15; 16]. This scarcity is likely caused by the absence of back-reflected XUV radiation under normal incidence conditions. However, LIPSS of other kinds may quite often be found on the XUV-exposed surfaces.  
In this article, barium fluoride (BaF\({}_{2}\)) was exposed to focused XUV-CDL radiation as it is a typical UV-Vis transparent inorganic dielectric material widely used as a scintillator and in the manufacture of various optical elements (for more details on this material see ref [17]). It crystalizes (similarly to the more popular CaF\({}_{2}\)) in an 8-coordinated fluorite structure [18]. In our initial experiments, reported in ref. [19], we indicated a spontaneous formation of grating-like nanostructures with a spatial period of 400 nm on the BaF\({}_{2}\) surfaces exposed to a focused 46.9-nm laser beam delivered by the CDL that was developed and operated at the Harbin Institute of Technology in China. This was quite a surprising finding because of a high abundance of such uniform ripples registered in the ablated area with no external modulation of the laser wavefront. Here, we made use of the CDL device available at the Institute of Plasma Physics in Prague, which is more powerful than the CDL source engaged in the earlier Harbin irradiation experiment, to characterize the grating-like nanostructures under wider irradiation conditions to test the possibility of tailoring their properties and to shed light on their formation mechanisms.