[en] When fs laser pulses interact with solid surfaces at intensities Iλ² > 10¹⁸ W/cm² microm², collimated relativistic electron beams are generated. These electrons can be used for producing intense X-radiation (bremsstrahlung or K_α) for pumping an innershell X-ray laser. The basic concept of such a laser involves the propagation of the electron beam in a material which converts electron energy into appropriate pump photons. Using the ATLAS titanium-sapphire laser at Max-Planck-Institut fuer Quantenoptik, the authors investigate the generation of hot electrons and of characteristic radiation in copper. The laser (200 mJ/130 fs) is focused by means of an off-axis parabola to a diameter of about 10 microm. By varying the position of the focus, they measure the copper K_α - yield as a function of intensity in a range of 10¹⁵ to 2 x 10¹⁸ W/cm² while keeping the laser pulse energy constant. Surprisingly, the highest emission is obtained at an intensity of about 10¹⁷ W/cm². However, this result is readily explained by the weak scaling of the hot-electron temperature with intensity. An efficiency of 2 x 10^-4 for the conversion of laser energy into copper K_α is measured. Simulations of the interaction of the hot electrons with the cold target material and the conversion into X-rays are carried out by means of the TIGER/ITS code, a time-independent, coupled electron/photon Monte Carlo transport code. The code calculates the propagation of individual electrons and the generation of photons in cold material. Comparison of the code predictions with the data shows an efficiency of 15% for the generation of electrons with energies in the 100 keV range. A second experiment involves the demonstration of photopumping of an innershell transition in cobalt by the copper radiation. Comparing the emission with the one of nickel, which is not photopumped by copper K_α photons, an enhancement of more than a factor of two was obtained. An essential part of this experiment is the use of a 1 mm carbon sheet to block the electrons from the material to be photopumped