Spatial and pulse shape dependence of K$\alpha$ source from high contrast fs laser plasmas in regime of Relativistic Engineering

Interaction of intense Ti: Sapphire laser with Cu foil targets has been studied by measuring hard X-ray generation. Hard x-ray spectroscopy and K$\alpha $ X-ray conversion efficiency (\textit{$\eta $}$_{K})$ from Cu plasma have been studied as a function of laser intensity via pulse duration scan (\textit{60 fs $\sim $ 600 fs}), laser pulse energy scan (\textit{60 mJ $\sim $ 600 mJ}) and target displacement scan from best focus. For intensity \textit{I $>$ 1x10}$^{17}$\textit{ W/cm}$^{2}$, the Cu \textit{$\eta $}$_{K}$ keep on increasing to reach a maximum value of $1x10^{-4}$ at an intensity $I = 1x10^{18}$\textit{ W/cm}$^{2}$. The focusing was varied widely to give a range of intensities from $10^{15}$\textit{ W/cm}$^{2}$\textit{ $\sim $ 10}$^{18}$\textit{ W/cm}$^{2}$. Two individual emission peaks are obtained, one is at best focal spot and the other is at larger target offset corresponding to \textit{$\sim $ 10}$^{15}$\textit{ W/cm}$^{2}$. Each peak is corresponding to different energy absorption mechanism. In addition, when we introduce slightly detuning of compressor gratings at the best focal condition, it shows \textit{$\eta $}$_{K}$ generated by negatively skewed \textit{100 fs} pulse width laser irradiation reach $5x10^{-4}$ and almost $7$ times greater than the case of positively skewed pulse. Vacuum Heating is greatly stimulated in this case and preciously control of pre-plasma is the key factor in tuning control of X-ray emission in relativistic \textit{fs} regime.