Short-pulse high-intensity laser-generated fast electron transport into thick solid targets

The transport of fast electrons generated by 1 ps, 1 $\mu \mathrm{m}$ wavelength laser pulses focused to spot diameters of 20 $\mu \mathrm{m}$ and peak intensities of up to $2\times {10}^{18}$ W ${\mathrm{cm}}^{-2}$ on to solid aluminum targets is considered using a relativistic Fokker-Planck equation, which is solved by reducing it to an equivalent system of stochastic differential equations. The background is represented by $\mathbf{E}=\eta {\mathbf{j}}_b,$ where $\eta$ is the resistivity and ${\mathbf{j}}_b$ is the background current density. Collisions, electric and magnetic fields, and changes in resistivity due to heating of the background are included. Rotational symmetry is assumed. The treatment is valid for fast electron number densities much less than that of the background, fast electron energies much greater than the background temperature, and time scales short enough that magnetic diffusion and thermal conduction are negligible. The neglect of ionization also limits the validity of the model. The intensities at which electric and magnetic fields become important are evaluated. The electric field lowers the energy of fast electrons penetrating the target. The magnetic field reduces the radial spread, increases the penetration of intermediate energy fast electrons, and reflects lower energy fast electrons. Changes in resistivity significantly affect the field generation. The implications for $K\alpha$ emission diagnostics are discussed.