Dynamics of the AXE at the C 1s→ <em>X</em> transition for an ensemble of pre-aligned CO molecular with 〈cos <sup>2</sup>ζ〉 = 0.64: XFEL pump intensity (a) and AXE intensity (b) in W cm<sup>−2</sup>, population of the intermediate core-ionized state ∑ρ<sub><em>ii</em></sub>/<em>N</em> (c), and normalized AXE intensity (d) in the frame of the retarded time <em>t</em>' = <em>t</em> − <em>z</em>/<em>c</em> (relative to the maximum of the pump pulse) and interaction length <em>z</em>

<p><strong>Figure 6.</strong> Dynamics of the AXE at the C 1s→ <em>X</em> transition for an ensemble of pre-aligned CO molecular with 〈cos <sup>2</sup>ζ〉 = 0.64: XFEL pump intensity (a) and AXE intensity (b) in W cm<sup>−2</sup>, population of the intermediate core-ionized state ∑ρ<sub><em>ii</em></sub>/<em>N</em> (c), and normalized AXE intensity (d) in the frame of the retarded time <em>t</em>' = <em>t</em> − <em>z</em>/<em>c</em> (relative to the maximum of the pump pulse) and interaction length <em>z</em>. The XFEL pump pulse parameters are the same as in figure <a href="http://iopscience.iop.org/0953-4075/46/16/164017/article#jpb465580f5" target="_blank">5</a>.</p> <p><strong>Abstract</strong></p> <p>We theoretically demonstrate the feasibility of x-ray lasing in the CO molecule by the core ionization of the C K- and O K-shell by x-ray free-electron laser sources. Our numerical simulations are based on the solution of generalized Maxwell–Bloch equations, accounting for the electronic and nuclear degrees of freedom. The amplified x-ray emission pulses have an extremely narrow linewidth of about 0.1 eV and a pulse duration shorter than 30 fs. We compare x-ray lasing transitions to the three lowest electronic states of singly ionized CO. The dependence of the lasing efficiency on the spectral width of the x-ray fluorescence band, value and orientation of the electronic transition dipole moment, lifetime of the core-excited state and the duration of the pump pulse is analysed. Using a pre-aligned molecular ensemble substantially increases the amplified emission. Moreover, by controlling the molecular alignment and thereby the alignment of the transition dipole moment polarization, the control of the emitted x-ray radiation is achievable. Preparing the initial vibrational quantum state, the x-ray emission frequency can be tuned within the fluorescence band. The present scheme is applicable to other diatomic systems, thereby extending the spectral range of coherent x-ray radiation sources based on stimulated x-ray emission on bound transitions.</p>