Phase-space Fluctuations Research Articles

Momentum transfer driven by fluctuations in relativistic counter-propagating electron beams

A semi-Lagrangian relativistic Vlasov–Maxwell solver is used to describe the non-linear momentum transfer between electron beams, which is driven by spontaneous fluctuations in the oblique filamentation instability (a type of Weibel mode) in two-dimensional plasmas. For counter-streaming plasmas, these filamentation instabilities may strengthen the generation of a fine structure of the distribution function in phase space. Properties of such counter-streaming beams are investigated using full-kinetic simulations and a Hamiltonian reduction technique based on the invariance of the transverse canonical momentum, the so-called multi-stream model. In the regime where , being the wavevector and d e the electron skin depth, a momentum transfer takes place when a mesoscale current filamentation mode couples with microscopic phase-space fluctuations. This regime is characterized by the appearance of filamentation modes with large wavenumbers and large amplitude fluctuations, which induce variations of the L 2-norm of the plasma in link with the self-organization of counter-streaming electron beams. We also discuss some theoretical aspects of information theory that highlight the role of the (reversible) entropy production in momentum transfer, thus by clarifying the connections between (microscopic) fluctuations of the distribution function and the fundamental aspects of the filamentation in Vlasov theory. The momentum transfer between beams is quantitatively analyzed by means of both theoretical estimations and numerical experiments.

Low- and high-frequency nature of oblique filamentation modes. II. Vlasov–Maxwell simulations of collisionless heating process

The nonlinear regime of electromagnetic oblique instabilities is investigated by means of a “noiseless” semi-Lagrangian Vlasov–Maxwell solver. Starting from an initial equilibrium configuration with two counterstreaming electron beams, qualitatively different nonlinear regimes are shown to exist depending on the nature of the solutions of the linear dispersion relation, whose properties have been discussed in the companion paper I [Ghizzo et al., Phys. Plasmas 27, 072103 (2020)]. This behavior is in contrast with existing theories of the oblique instability, which are based on the excitation of a single eigenmode at a time: nonlinear transitions toward regimes dominated by low-frequency modes are generally shown to be possible. The emphasis here is on gaining a better understanding of the multiplicity of electromagnetic oblique unstable modes and on modeling their back-reaction on plasma wave-particle interactions and energy conversion mechanisms. The latter are shown to depend on the saturation scenario of the different regimes of the oblique instability. A new regime is discussed, in which a stochastic heating occurs at the expenses of the magnetic energy first amplified by the oblique modes and in which a (reversible) violation of entropy conservation is made possible by large amplitude phase-space fluctuations of the distribution function.

Continuous-variable random-number generation from an amplified spontaneous emission light source

An amplified spontaneous emission (ASE) light source using an Er-doped fiber is an ideal random-number source in principle because ASE originates from vacuum fluctuations. Interferometrically measured ASE light directly reflects vacuum fluctuations in phase space; the interferometer does not need to be stabilized because the phase is completely random, and measurable random numbers are a continuous variable because vacuum fluctuations are continuous. These characteristics make the random-number source practical and ideal. Evaluated randomness was sufficiently ideal at the accuracy level of measurements and evaluations.

Comparison of heavy-ion transport simulations: Collision integral in a box

Simulations by transport codes are indispensable to extract valuable physics information from heavy ion collisions. In order to understand the origins of discrepancies between different widely used transport codes, we compare 15 such codes under controlled conditions of a system confined to a box with periodic boundary, initialized with Fermi-Dirac distributions at saturation density and temperatures of either 0 or 5 MeV. In such calculations, one is able to check separately the different ingredients of a transport code. In this second publication of the code evaluation project, we only consider the two-body collision term, i.e. we perform cascade calculations. When the Pauli blocking is artificially suppressed, the collision rates are found to be consistent for most codes (to within $1\%$ or better) with analytical results, or completely controlled results of a basic cascade code after eliminating the correlations within the same pair of colliding particles. In calculations with active Pauli blocking, the blocking probability was found to deviate from the expected reference values. The reason is found in substantial phase-space fluctuations and smearing tied to numerical algorithms and model assumptions in the representation of phase space. This results in the reduction of the blocking probability in most transport codes, so that the simulated system gradually evolves away from the Fermi-Dirac towards a Boltzmann distribution. As a result of this investigation, we are able to make judgements about the most effective strategies in transport simulations for determining the collision probabilities and the Pauli blocking. Investigation in a similar vein of other ingredients in transport calculations, like the mean field propagation or the production of nucleon resonances and mesons, will be discussed in the future publications.

Dynamical description of heavy-ion collisions at Fermi energies

Descriptions of heavy-ion collisions at Fermi energies require to take into account in-medium dissipation and phase-space fluctuations. The interplay of these correlations with the one-body collective behaviour determines the properties (kinematics and fragment production) and the variety of mechanisms (from fusion to neck formation and multifragmentation) of the exit channel. Starting from fundamental concepts tested on nuclear matter, we build up a microscopic description which addresses finite systems and applies to experimental observables.

Frustrated fragmentation and re-aggregation in nuclei: A non-equilibrium description in spallation

Heavy nuclei bombarded with protons and deuterons in the 1 GeV range have a large probability of undergoing a process of evaporation and fission; less frequently, the prompt emission of few intermediate-mass fragments can also be observed. We employ a recently developed microscopic approach, based on the Boltzmann-Langevin transport equation, to investigate the role of mean-field dynamics and phase-space fluctuations in these reactions. We find that the formation of few IMF's can be confused with asymmetric fission when relying on yield observables, but it can not be assimilated to the statistical decay of a compound nucleus when analysing the dynamics and kinematic observables: it can be described as a fragmentation process initiated by phase-space fluctuations, and successively frustrated by the mean-field resilience. As an extreme situation, which corresponds to non-negligible probability, the number of fragments in the exit channel reduces to two, so that fission-like events are obtained by re-aggregation processes. This interpretation, inspired by nuclear-spallation experiments, can be generalised to heavy-ion collisions from Fermi to relativistic energies, for situations when the system is closely approaching the fragmentation threshold.

Bifurcations in dissipative fermionic dynamics

The Boltzmann-Langevin One-Body model (BLOB), is a novel one-body transport approach, based on the solution of the Boltzmann-Langevin equation in three dimensions; it is used to handle large-amplitude phase-space fluctuations and has a broad applicability for dissipative fermionic dynamics. We study the occurrence of bifurcations in the dynamical trajectories describing heavy-ion collisions at Fermi energies.The model, applied to dilute systems formed in such collisions, reveals to be closer to the observation than previous attempts to include a Langevin term in Boltzmann theories. The onset of bifurcations and bimodal behaviour in dynamical trajectories, determines the fragment-formation mechanism. In particular, in the proximity of a threshold, fluctuations between two energetically favourable mechanisms stand out, so that when evolving from the same entrance channel, a variety of exit channels is accessible.This description gives quantitative indications about two threshold situations which characterise heavy-ion collisions at Fermi energies. First, the fusion-to-multifragmentation threshold in central collisions, where the system either reverts to a compact shape, or splits into several pieces of similar sizes. Second, the transition from binary mechanisms to neck fragmentation (in general, ternary channels), in peripheral collisions.

New Thermodynamical Force in Plasma Phase Space that Controls Turbulence and Turbulent Transport

Physics of turbulence and turbulent transport has been developed on the central dogma that spatial gradients constitute the controlling parameters, such as Reynolds number and Rayleigh number. Recent experiments with the nonequilibrium plasmas in magnetic confinement devices, however, have shown that the turbulence and transport change much faster than global parameters, after an abrupt change of heating power. Here we propose a theory of turbulence in inhomogeneous magnetized plasmas, showing that the heating power directly influences the turbulence. New mechanism, that an external source couples with plasma fluctuations in phase space so as to affect turbulence, is investigated. A new thermodynamical force in phase-space, i.e., the derivative of heating power by plasma pressure, plays the role of new control parameter, in addition to spatial gradients. Following the change of turbulence, turbulent transport is modified accordingly. The condition under which this new effect can be observed is also evaluated.

Probing the nuclear EOS with fragment production

We discuss fragmentation mechanisms and isospin transport occurring in central collisions between neutron rich systems at Fermi energies. In particular, isospin effects are analyzed looking at the correlations between fragment isotopic content and kinematical properties. Simulations are based on an approximate solution of the Boltzmann-Langevin (BL) equation. An attempt to solve the complete BL equation, by introducing full fluctuations in phase space is also discussed.

A new approach to solve the Boltzmann–Langevin equation for fermionic systems

We present a new method to introduce phase-space fluctuations in transport theories, corresponding to a full implementation of the Boltzmann–Langevin equation for fermionic systems. It is based on the procedure originally developed by Bauer et al. for transport codes employing the test particle method. In the new procedure, the Pauli principle is carefully checked, leading to a good reproduction of the correct fluctuations in the “continuum limit” ( h → 0 ). Accurate tests are carried out in one and two dimensional idealized systems, and finally results for a full 3D application are shown. We stress the reliability of this method, which can be easily plugged into existing transport codes using test particles, and its general applicability to systems characterized by instabilities, like for instance multifragmentation processes.

Signals of fragment structures from a semiclassical transport equation in heavy-ion collisions

Phase space bound structures generated from the semi-classical Landau-Vlasov (LV) description of the nuclear dynamics are analyzed. To this purpose a new approach has been implemented for sampling configurations with fixed number of nucleons from the LV solution, on which the most bound density fluctuations in phase space are searched. The method is shown to reproduce correctly the global experimental trends on 36Ar on 58Ni at 32, 52 and 95 MeV/nucleon incident energies. This results open a new view of one body descriptions.

Onset of fragment formation in periodic expanding systems.

The problem of the time evolution of the process of fragment formation is investigated in the framework of expanding periodic systems. We focus on the fragmentation of small (100 constituents) systems. We use a molecular-dynamics method that simulates the behavior of condensed matter under homogeneous adiabatic expansion. Fragment formation is studied using a generalized version of the early cluster formation model (GECFM) which searches for the most bound density fluctuations in phase space. We show that the asymptotic fragment spectra is early realized in phase space not only for the total multiplicity but also for the populations of different mass ranges. In order to map the evolution of the system on the phase diagram of the small cell periodic one, its equation of state is calculated. It is shown that the fragmentation of the system cannot be unambiguously related to spinodal decomposition or nucleation processes. \textcopyright{} 1996 The American Physical Society.

Fluctuations of one-body observables: Comparison between exact predictions and numerical simulation

Within the framework of a stochastic transport equation, we discuss a theoretical approach in order to derive the general covariance matrix of phase-space fluctuations and the dispersion of one-body variables at equilibrium. We compare with the independently obtained numerical results of Chomaz, Burgio and Randrup. The analysis proves the validity of the general approach.

From stochastic phase-space evolution to brownian motion in collective space

Within the framework of stochastic transport equations in phase space, we study the dynamics of fluctuations on collective variables in homogeneous fermion systems. The transport coefficients are formally deduced in the relaxation-time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations: respectively, the BUU/Landau-Vlasov equation for the average phase-space trajectories and the equations for the averages and dispersions of the observables. Independently, we derive the general covariance matrix of phase-space fluctuations and then by projection, the dispersion on collective variables at equilibrium. Detailed numerical applications of the formalism are given; they show that the dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy, whatever is its degree of thermalization.

Phase space fluctuations and dynamics of fluctuations of collective variables

Within the framework of theoretical approaches based on stochastic transport equation of one-body distribution function, a numerical treatment of the fluctuations of collective observables is studied and checked in comparison with analytical results either at equilibrium or close to it.

Method of identification of a fluctuating emitter under the conditions of inadequate statistical coverage of measurements

The natural fluctuations of a radiation field have an amplitude that stands at the limit of the sensitivity of modern detectors; it is therefore necessary to enhance the statistical coverage of the detection process. This is usually accomplished by counting over a sufficiently large column of the phase space of the field. The statistical coverage of measurements in such intervals is extremely low, however, and the solution of the identification problem thus requires that the most representative parameter of the appearance of fluctuations be selected and that it be optimally averaged over the entire volume of the phase space. In this paper, such a parameter is chosen on the basis of the principle of synchronous manifestation of fluctuations in phase space. As an example the authors identify, using this parameter, natural fluctuations of the cosmic and bismuth components of gamma radiation of the atmosphere over water, carried out using NaI detectors. A similar method is employed for K 40, Be 7, and Cs 137.

Computer simulations of fragmentation in nuclear reactions: A semiclassical model.

A semiclassical model is used to perform numerical simulations of the production of nuclear fragments in both proton- and heavy-ion-induced reactions. The Pauli principle is incorporated by means of a collision term, as it is in the Vlasov-Uehling-Uhlenbeck equation. The model goes beyond the Vlasov-Uehling-Uhlenbeck equation by propagating on an event-by-event basis the phase space fluctuations which develop during a nuclear reaction. Both the Coulomb and isospin-dependent interaction terms are included. For proton-induced reactions at intermediate energies, fragment production is found to be a fairly infrequent process, as is observed experimentally. Heavy-ion reactions show much greater fragment yields. For these latter reactions, we have compiled sufficiently many events so as to be able to compare the predicted fragment yields with experiment. The isotopic distribution of products, as well as their distribution in momentum space, are also examined. The events are used to generate a two-particle correlation function. Analysis of the energy-summed two-proton correlations indicates a large source region. The coordinate and phase space reaction trajectories are followed for a central collision, and preliminary evidence is found in the simulations for the onset of mechanical instability.