(a) Propagation geometry: <strong>E</strong>

<p><strong>Figure 2.</strong> (a) Propagation geometry: <strong>E</strong><sub>L</sub>, <strong>E</strong><sub>XFEL</sub> and <strong>E</strong> mark the electric field polarization vectors of the optical laser used for impulsive alignment, XFEL and AXE radiation, respectively. All three pulses propagate along the <em>z</em>-axis direction, as is shown by the corresponding wave vectors <strong>k</strong><sub>L</sub>, <strong>k</strong><sub>XFEL</sub> and <strong>k</strong><sub>AXE</sub>. (b) Degree of molecular alignment 〈cos <sup>2</sup>ζ〉 as a function of the delay time <em>t<sub>a</sub></em> computed using initial rotational temperature <em>T</em> = 100 K (\full) and 300 K (−− − −). The insets show the angular density distribution β(ζ) of CO molecules at times related to the maxima and minima of the 〈cos <sup>2</sup>ζ〉 curves.</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>