## 3 Results  
Figure 1 shows the time evolution of the electron density \(n_{e}\), the electron temperature \(T_{e}\) (obtained as a ratio of the local kinetic energy density of electrons to their concentration) and the transverse component of the magnetic field \(B_{z}\) at different times for a pulse with a duration of 700 fs and an intensity of \(10^{20}\) W/cm\({}^{2}\). It can be seen that at the beginning (Figure 1d,e) the target is deformed under the action of radiation and a noticeable pre-plasma layer is formed in the region \(x<0\), which enhances absorption of radiation. Later the interaction takes the form of a so-called \"hole-boring\" which enhances the absorption even more. On the rear side of the target, the expulsion of the energetic electrons is observed. It triggers the expansion of the plasma and the formation of the plasma sheath. At a later moment in time (Figure 1g-i), an increase in the azimuthal magnetic field is observed in the formed plasma sheath. With increasing intensity, the magnitude of the generated magnetic field also grows, reaching a maximum at the moment when the maximum of the laser pulse arrives at the target (Figure 1j-l). At this moment, the magnetic field at its peak reaches a value of the order of 400 MG, and is of the order of 100 MG in most of the plasma sheath. Note that the electron concentration in the same region is in the range \(10^{20}\)-\(10^{21}\) cm\({}^{-3}\). As for the electron temperature, a high-energy electron current is observed on the sheath axis; however, to the side of it, the electron temperature is much lower, and in a significant region near the target, it is significantly below the relativistic value \(kT_{e}<mc^{2}\). Due to the fact that in such a plasma there are no effective mechanisms for cooling electrons, then, most likely, these cold electrons were drawn out by a cold reverse current to compensate for the charge of hot electrons that had sufficient energy to leave the interaction region. At later times, the plasma continues to expand and cool down a little, but the magnetic field is dissipating slowly and changes in magnitude insignificantly. An interesting feature is that, as follows from the performed calculations, the magnitude of the magnetic field at later times is practically independent of the intensity of the laser radiation. This can be seen from Figure 2, which shows a time dependence of the peak value of the magnetic field for different intensities of the laser pulses with fixed duration. Although the field value at  
Figure 1: Distributions of electron concentration (left column), electron temperature (central column) and transverse magnetic field (right column) at **(a–c)**\(t=0\) fs, **(d–f)**\(t=500\) fs, **(g–i)**\(t=1000\) fs, **(j–l)**\(t=1500\) fs, and **(m–o)**\(t=2000\) fs after start of the simulation. The parameters of the simulation are in the text. the maximum of the laser pulse increases with intensity, it relaxes to an almost identical value of about 100 MG after the pulse leaves. Let us now turn to an analysis of the main parameters of the resulting plasma. Figure 3 shows the distributions of the previously introduced parameters \(\beta=\mu_{0}n_{e}kT_{e}/B_{2}^{2}\) and \(\sigma=B_{2}^{2}/\mu_{0}n_{e}mc^{2}\), and also a quantity \(\delta=R_{L}/(B_{z}/|\
abla B_{z}|)\), equal to the ratio of the Larmor radius \(R_{L}=\sqrt{kT_{e}/m_{e}B_{2}^{2}}\) to a characteristic scale of the magnetic field variation \(L_{B}=B_{z}/|\
abla B_{z}|\). The analysis of \(\delta\) is important because for effective plasma magnetization it is not enough to have a sufficiently large magnetic field, but it is also required that the electrons can make a full revolution in the magnetic field before they leave the region of their localization. This can be a limiting factor in femtosecond laser plasma due to the small interaction volume and high gradients of the generated magnetic field. In particular, this is one of the limiting factors for the generation of magnetized plasma by pulses with a duration of less than 100 fs.