## 2 Experiment  
### Scheme for the Formation of QPM Conditions in Plasma  
The experimental setup consists of Ti:Sapphire laser, traveling-wave optical parametric amplifier (OPA) of white-light continuum, and HHG scheme using the propagation of two pulses (the amplified signal radiation from OPA and 800 nm radiation, as well as their second harmonics) through the extended LPP. We used the mode-locked Ti:Sapphire laser (TSUNAMI, Spectra\(-\)Physics Lasers) pumped by diode-pumped, cw laser (MILLENIA Vs, Spectra\(-\)Physics Lasers) as the source of 803 nm, 55 fs, 82 MHz, 450 mW pulses for injection in the pulsed Ti:sapphire regenerative amplifier with pulse stretcher and additional double-pass linear amplifier (TSA\(-\)10, Spectra\(-\)Physics Lasers). The output characteristics of uncompressed radiation from this laser were as follows: central wavelength 800 nm, pulse duration 370 ps, pulse energy 4 mJ, 10 Hz pulse repetition rate. This radiation was further amplified up to 22 mJ in the home-made three-pass Ti:Sapphire linear amplifier. Part of the amplified radiation with pulse energy of 5 mJ was separated from the whole beam and used as a heating pulse for homogeneous extended plasma formation using cylindrical lens of 200 mm focal length installed in front of the 5-mm long target placed in the vacuum chamber (Figure 1). The intensity and fluence of the heating pulse on the target surface were varied up to \(4\times 10^{9}\) W cm\({}^{-2}\) and 1.4 J cm\({}^{-2}\), respectively. We used 5-mm-long targets for ablation and formation of extended homogeneous and structured plasmas. The ablation area was \(5\times 0.08\) mm\({}^{2}\). The remaining part of the amplified radiation was delayed with respect to the heating pulse in such a way that, after compression and pump of OPA, the signal pulse from parametric amplifier propagated through the plasma plume 40 ns after the beginning of target irradiation by heating pulses, which is assumed to be optimal for ablation of used samples and harmonic generation. After propagation through the compressor stage, laser pulses of 810 nm central wavelength, 8 mJ energy, 50 fs duration, 10 Hz repetition rate, and pulse bandwidth of 17 nm were produced. This radiation pumped the OPA (HE-TOPAS Prime, Light Conversion). The signal and idler pulses from the OPA allowed tuning in the 1200-1600 nm, and 1600-2600 nm ranges, respectively. In our HHG experiments we mostly used the signal pulses, which were \(\sim\)1.5 times stronger than the idler pulses. Most of the experiments were carried out using the 1 mJ, 70 fs signal pulses tunable in the range of 1200-1600 nm; and 3 mJ, 50 fs, 810 nm pulses. The spectral bandwidth of the tunable near infrared (NIR) pulses was 40 nm. The intensity of the 1310 nm pulses, showing the highest yield from OPA, was \(2\times 10^{14}\) W cm\({}^{-2}\). The driving pulses were focused onto the extended plasma at a distance of \(\sim\)100-150 \(\upmu\)m above the target surface. The harmonic yield was maximized by adjusting the position of target with regard to the optical axis of propagation of two driving pulses and by varying their focusing positions relative to the extended plasma. The harmonic emission was analyzed using an XUV spectrometer containing a cylindrical mirror and a 1200 grooves/mm flat field grating with variable line spacing. The spectrum was recorded on a micro-channel plate detector backed by phosphor screen, which was imaged onto a CCD camera. The multi-slit mask (MSM) was installed between the cylindrical lens and the target to produce multi-jet plasma (MJP, Figure 1). The width of each slit was varied between 0.3 and 0.8 mm with similar distance between slits. The electron density of plasma (\(7\times 10^{16}\) cm\({}^{-3}\)) was estimated using the hydrodynamic code HYADES [25]. Similar estimates were reported in [26]. We also estimated the electron density using the  
Figure 1: Experimental setup for high-order harmonic generation (HHG) in MJP.