Andrea Antoniazzi

Maximum entropy principle explains quasistationary states in systems with long-range interactions : The example of the Hamiltonian mean-field model

A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytic expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected, which is consistent with Gaussian tails of velocity distributions. A dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.

Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation

We here discuss the emergence of quasistationary states (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian mean-field model, numerical simulations are performed based on both the original N-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bells theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particle correlations.

Statistical mechanics and Vlasov equation allow for a simplified Hamiltonian description of Single-Pass Free Electron Laser saturated dynamics

Abstract.A reduced Hamiltonian formulation which reproduces the saturated regime of a Single Pass Free Electron Laser, around perfect tuning, is here discussed. Asymptotically, Nm particles are found to organize in a dense cluster, that evolves as an individual massive unit. The remaining particles fill the surrounding uniform sea, spanning a finite portion of phase space, approximately delimited by the average momenta ω+ and ω-. We propose a theoretical framework in which the external parameters Nm, ω+ and ω- are self-consistently determined. To this aim, we make use of a statistical mechanics treatment of the Vlasov equation, that governs the initial field amplification process. Simulations of the reduced dynamics are shown to successfully capture the oscillating regime observed within the original N-body picture.

Wave-particle interaction: from plasma physics to the free-electron laser

We discuss the analogies between two classical models of the single-pass free electron laser dynamics and of the beam-wave plasma instability. Moreover, a formal bridge between the two areas of investigation is established. This connection is here exploited to derive a reduced Hamiltonian formulation for the saturated regime of the free electron laser.

The Hamiltonian Mean Field model: anomalous or normal diffusion?

We consider the out‐of‐equilibrium dynamics of the Hamiltonian Mean Field (HMF) model, by focusing in particular on the properties of single‐particle diffusion. As we shall here demonstrate analytically, if the autocorrelation of momenta in the so‐called quasi‐stationary states can be fitted by a q‐exponential, then diffusion ought to be normal for q<2, at variance with the interpretation of the numerical experiments proposed in Ref. [1].

Enhancement of particle trapping in the free electron laser

Abstract The saturated dynamics of a Single Pass Free Electron Laser is here considered within a simplified mean field approach. A method is proposed to increase the size of the macro-particle. This approach is based on the reconstruction of invariant tori of the dynamics of test particles. To this aim a dedicated control term is derived, the latter acting as a small apt perturbation of the system dynamics. Implications of these findings are discussed in relation to the optimization of the laser source.