The relative error (32), for Gaussian and exponentially correlated noises, as a function of Omega _s^{(0)}/Gamma _2, for various bandwidths of the field

<p><strong>Figure 5.</strong> The relative error (<a href="http://iopscience.iop.org/0953-4075/46/16/164010/article#jpb462676eqn32" target="_blank">32</a>), for Gaussian and exponentially correlated noises, as a function of \Omega _s^{(0)}/\Gamma _2, for various bandwidths of the field. (a) γ = 6.67Γ₂; (b) γ = 3.33Γ₂; (c) γ = 1.67Γ₂; (d) γ = 1.11Γ₂. Other parameters: Gaussian pulse profile, Γ₂τ = 3, 5000 random pulses, Δ_<em>s</em> = 0, <em>t</em> = <em>t</em>₀.</p> <p><strong>Abstract</strong></p> <p>Motivated by recent experiments pertaining to the interaction of weak SASE-free-electron-laser (FEL) pulses with atoms and molecules, we investigate the conditions under which such interactions can be described in the framework of a simple phase-diffusion model with decorrelated atom–field dynamics. The nature of the fluctuations that are inevitably present in SASE-FEL pulses is shown to play a pivotal role in the success of the decorrelation. Our analysis is performed in connection with specific recent experimental results from FLASH in the soft x-ray regime.