We show that noise enhances the trapping of trajectories in scattering systems. In fully chaotic systems, the decay rate can decrease with increasing noise due to a generic mismatch between the noiseless escape rate and the value predicted by the Liouville measure of the exit set. In Hamiltonian systems with mixed phase space we show that noise leads to a slower algebraic decay due to trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands. We argue that these noise-enhanced trapping mechanisms exist in most scattering systems and are likely to be dominant for small noise intensities, which is confirmed through a detailed investigation in the Hénon map. Our results can be tested in fluid experiments, affect the fractal Weyl's law of quantum systems, and modify the estimations of chemical reaction rates based on phase-space transition state theory.PACS numbers: 05.40.Ca,05.40.Fb,05.60.Cd,82.20Db The responses of nonlinear dynamical systems to small uncorrelated random perturbations (noise) can be surprising and seemingly contradictory. Noise usually destroys fine structures of deterministic dynamics, e.g. it fattens fractals [1-3], but it can also combine constructively with the nonlinearities and increase the order of the system [4]. In chaotic Hamiltonian systems, investigations focused on the effect of noise on anomalous transport [5,6] and, very recently, on chaotic scattering [7][8][9].Chaotic scattering is a basic process of Hamiltonian dynamics [2,10,11], with fundamental applications in classical [12] and quantum [2,13] systems, and recent applications ranging from plankton populations [3] to blood flows [14] and even the origin of life [15]. Chemical (dissociative) reactions of simple molecules are also scattering processes where chaos is essential in the microcanonical phase-space formulation of transition state theory (TST) [16]. Scattered trajectories perform transiently chaotic motion while trapped by fine structures of the phase space, such as fractal nonattracting sets and chains of Kolmogorov-Arnold-Moser (KAM) islands [2,10]. Noise destroys the small scales of these structures [7], modifies the temporal decay of trajectories in time from algebraic to exponential [8,9] with an exponent that increases with noise [8], and create otherwise forbidden escape paths [9]. All these effects weaken the deterministic trapping.In this Letter we show that noise also plays a constructive role in chaotic scattering, enhancing the trapping of trajectories. First we introduce and scrutinize two different mechanisms responsible for this surprising effect, arguing that they exist in very general circumstances. The first mechanism acts in fully chaotic systems and reduces the escape rate of particles by blurring the natural measure of the system. The second mechanism acts on mixed-phase-space systems and enhances trapping by throwing trajectories inside KAM islands. We confirm the generality of these mechanisms through simulations in the conservative Hénon map, and we explore the implications ...

The present work revisits the subjects of mixing, saturation, and space-charge effects in free-electron lasers. Use is made of the compressibility factor, which proves to be a helpful tool in the related systems of charged beams confined by static magnetic fields. The compressibility allows to perform analytical estimates of the elapsed time until the onset of mixing, which in turn allows to estimate the saturated amplitude of the radiation field. In addition, the compressibility helps to pinpoint space-charge effects and the corresponding transition from Compton to Raman regimes. V C 2013 AIP Publishing LLC. [http://dx

We investigate the occurrence of extreme and rare events, i.e., giant and rare light pulses, in a periodically modulated CO_{2} laser model. Due to nonlinear resonant processes, we show a scenario of interaction between chaotic bands of different orders, which may lead to the formation of extreme and rare events. We identify a crisis line in the modulation parameter space, and we show that, when the modulation amplitude increases, remaining in the vicinity of the crisis, some statistical properties of the laser pulses, such as the average and dispersion of amplitudes, do not change much, whereas the amplitude of extreme events grows enormously, giving rise to extreme events with much larger deviations than usually reported, with a significant probability of occurrence, i.e., with a long-tailed non-Gaussian distribution. We identify recurrent regular patterns, i.e., precursors, that anticipate the emergence of extreme and rare events, and we associate these regular patterns with unstable periodic orbits embedded in a chaotic attractor. We show that the precursors may or may not lead to the emergence of extreme events. Thus, we compute the probability of success or failure (false alarm) in the prediction of the extreme events, once a precursor is identified in the deterministic time series. We show that this probability depends on the accuracy with which the precursor is identified in the laser intensity time series.

In the present work, we extend results of a previous paper [Peter et al., Phys. Plasmas 20, 12 3104 (2013)] and develop a semi-analytical model to account for thermal effects on the nonlinear dynamics of the electron beam in free-electron lasers. We relax the condition of a cold electron beam but still use the concept of compressibility, now associated with a warm beam model, to evaluate the time scale for saturation and the peak laser intensity in high-gain regimes. Although vanishing compressibilites and the associated divergent densities are absent in warm models, a series of discontinuities in the electron density precede the saturation process. We show that full wave-particle simulations agree well with the predictions of the model. V C 2014 AIP Publishing LLC. [http://dx

We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate κ and dimensions D of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of κ and D, and show that the improvement of the precision of the estimations with the number of trajectories N is extremely slow (∝ 1/ ln N ). We also argue that the finite-size D estimators are typically biased. General theoretical results are combined with analytical calculations and numerical simulations in area-preserving baker maps.