In our previous research (Zhao et al., 2016), we focus on the transport processes from hot electrons to K α X-ray emission in a copper foil and nanobrush target when the electron refluxing effect is not taken into account. In this work, considering the refluxing effect, the transport of hot electrons in a solid target is studied by adding the electric fields both at the front and rear surfaces of the target with Monte Carlo code Geant4. Simulation results show that the electron refluxing has an important influence on K α photon yield and the size of K α radiation source. K α yield from the 10-μm-thick target with the electron refluxing effect is 2.7–3.7 times more than that without the refluxing for the electron temperatures from 0.4 to 1.4 MeV. The laser-to-K α photon energy conversion efficiency ${\rm \eta} _{L \to K_{\rm \alpha}} $ with the refluxing effect is always higher than that without the refluxing, and both of them decrease gradually with laser strength Iλ2. Considering the electron refluxing effect or not, the variations of K α yield with the target thickness d are very different. A critical thickness of the target d c (~30 μm) is achieved to confirm whether the refluxing effect is valid for the target. For the target with the thickness d less than d c, the refluxing effect can enhance K α yield with several times, while for the target with the thickness d larger than d c, the refluxing effect is not so effective. The full-width at half-maximum increases from 23 to 56 µm after including the refluxing effect by the electron beam with the radius of 10 µm and the temperature of 400 keV.

The heating of the titanium foil in a recent femtosecond laser plasma experiment is investigated theoretically in two different ways. In the first, the energy content and thus the heating efficiency of the central volume of the foil is derived by integrating the transverse temperature profiles obtained in this experiment, using specific heats based on the average atom model. In the second approach target heating by the fast electrons, both by direct energy deposition and by resistive heating is investigated. The latter approach makes use of a specially devised electron flow model which includes a simplified quantitative treatment of multi-refluxing as a crucial component. In all, the calculated results of electron beam heating are consistent with experiment within the limitations of the modeling. Finally, a prediction for the temporal dependence of the Kα pulse from the central volume of the foil based on our electron flow model is given.