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Abstract The discovery of laser-driven rescattering and high harmonic radiation out to a maximum photon energy of 3.17 times the ponderomotive energy ( U p ) laid the groundwork for attosecond pulse generation and coherent X-rays. As the laser field drives the interaction to higher energies, relativity and the Lorentz force from the laser magnetic field enter into the dynamics. We present the results of recent studies of laser rescattering, including these effects, to give a quantitative description of rescattering dynamics in the high-energy limit, ie, recollision energies of order 1,000 hartree (27 keV). The processes investigated include inner K- and L-shell excitation and the ultimate limit of high harmonic generation via rescattering bremsstrahlung. The results indicate the path to the frontier area of x-ray strong field processes. 

We address the challenge of finding the optimal laser intensity and wavelength to drive high-energy, strong field rescattering and report the maximum yields of K-shell and${\mathrm{L}}_{\mathrm{I}}$-shell hole creation. Surprisingly, our results show laser-driven rescattering is able to create inner shell holes in all atoms from lithium to uranium with the interaction spanning from the deep IR to x-ray free electron laser sources. The calculated peak rescattering follows a simple scaling with the atomic number and laser wavelength. The results show it is possible to describe the ideal laser intensity and wavelength for general high-energy laser rescattering processes.