arXiv subjects

Renato Fedele

Publications and source records attributed to Renato Fedele.

At least 19 recordsLinked to original sources

arXiv2023

Hydrodynamic regime and cold plasmas hit by short laser pulses

We briefly report and elaborate on some conditions allowing a hydrodynamic description of the impact of a very short and arbitrarily intense laser pulse onto a cold plasma, as well as the localization of the first wave-breaking due to the plasma inhomogeneity. We use a recently developed fully relativistic plane model whereby we reduce the system of the Lorentz-Maxwell and continuity PDEs into a 1-parameter family of decoupled systems of non-autonomous Hamilton equations in dimension 1, with the light-like coordinate $ξ=ct\!-\!z$ replacing time $t$ as an independent variable. Apriori estimates on the Jacobian $\hat J$ of the change from Lagrangian to Eulerian coordinates in terms of the input data (initial density and pulse profile) are obtained applying Liapunov direct method to an associated family of pairs of ODEs; wave-breaking is pinpointed by the inequality $\hat J\le 0$. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons, which have very important applications.

physics.plasm-ph↗

arXiv2023

On the impact of short laser pulses on cold diluted plasmas

We analytically study the impact of a short laser pulse onto an inhomogeneous cold diluted plasma at rest, in particular: the duration of the hydrodynamic regime; the formation and the features of plasma waves (PWs); their wave-breakings (WBs); the motion of test electrons injected in the PWs. If the pulse is a plane wave travelling in the $z$-direction, and the initial plasma density (IPD) depends only on $z$, then suitable matched bounds on the maximum and relative variations of the IPD, as well as the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid during its whole interaction with the pulse, while ions can be regarded as immobile. This evolution is ruled by a family (parametrized by $Z\ge 0$) of decoupled systems of non-autonomous Hamilton equations with 1 degree of freedom, which determine how electrons initially located in the layer $Z\le z<Z+dZ$ move; $ξ=ct-z$ replaces time $t$ as the independent variable. This family of ODEs is obtained by reduction from the Lorentz-Maxwell and continuity PDEs for the electrons' fluid within the spacetime region where the change of the pulse is negligible. After the laser-plasma interaction the Jacobian of the map from Lagrangian to Eulerian coordinates is linear-quasi-periodic in $ξ$. We determine spacetime locations and features of the first wave-breakings of the wakefield PWs, the motion of test electrons (self-)injected in the PWs. The energy of those trapped in a single PW trough grows linearly with the distance gone, where the IPD is constant. If the pulse has cylindrical symmetry and a not too small radius, the same conclusions hold for the part of the plasma enclosed within the causal cone swept by it. This computationally light approach may help in a preliminary study of extreme acceleration mechanisms of electrons (LWFA, etc.), before 2D or 3D PIC simulations.

physics.plasm-ph↗

arXiv2022

Hydrodynamic impacts of short laser pulses on plasmas

We determine conditions allowing to simplify the description of the impact of a short and arbitrarily intense laser pulse onto a cold plasma at rest. If both the initial plasma density and pulse profile have plane simmetry, then suitable matched upper bounds on the maximum and the relative variations of the initial density, as well as the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid (without wave-breaking or vacuum-heating) during its whole interaction with the pulse, while ions can be regarded as immobile. We use a recently developed fully relativistic plane model whereby the system of the (Lorentz-Maxwell and continuity) PDEs is reduced into a family of highly nonlinear but decoupled systems of non-autonomous Hamilton equations with one degree of freedom, with the light-like coordinate $ξ=ct\!-\!z$ instead of time $t$ as an independent variable, and new apriori estimates (eased by use of a Liapunov function) of the solutions in terms of the input data (initial density and pulse profile). If the laser spot radius $R$ is finite but not too small the same conclusions hold for the part of the plasma close to the axis $\vec{z}$ of cylindrical symmetry. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons.

physics.plasm-ph↗

arXiv2020

Dust-acoustic wave electrostatic and self-gravitational potentials in an opposite polarity dusty plasma system

An opposite polarity dusty plasma system (containing a few micron size massive opposite polarity dust species and singly charged ion species following Boltzmann law) is considered. The nature of dust-acoustic (DA) wave electrostatic and self-gravitational potentials are correctly found by the numerical analysis of two coupled second-order nonlinear differential equations for electrostatic and self-gravitational potentials associated with the DA waves in such an opposite polarity dusty plasma medium. These coupled nonlinear differential equations are derived from the continuity and momentum equations for positive and negative dust species, and the Boltzmann law for ion species. The basic features of the DA wave self-gravitational potential are compared with that of the DA wave electrostatic potential. The relevance of our results to space and laboratory opposite polarity dusty plasma systems is mentioned.

physics.plasm-ph↗

arXiv2017

Modulation instability of lower hybrid waves leading to cusp solitons in electron-positron-ion Thomas Fermi plasma

Following the idea of three wave resonant interactions of lower hybrid waves it is shown that quantum -modified lower hybrid (QLH) wave in electron positron ion plasma with spatial dispersion can decay into another QLH wave ( where electron and positrons are activated whereas ions remain in the background) and another ultra low frequency QULH (where ions are mobile). Quantum effects like Bohm potential, exchange correlation and Fermi pressure on the lower hybrid wave significantly reshaped the dispersion properties of lower hybrid waves. Later a set of nonlinear Zakharov equations have been derived to consider the formation of QLH wave solitons with the nonlinear contribution coming from the QLH waves. Further, modulational instability of the lower hybrid wave solitons is investigated and consequently it's growth rates are examined for different limiting cases. Since the growth rate associated with the three-wave resonant interaction are generally smaller than the growth associated with the modulational instability, therefore only latter have been investigated. Soliton solutions from the set of coupled Zakharov and NLS equations in the quasi-stationary regime have been studied. Ordinary solitons are attribute of nonlinearity whereas a cusp soliton solution featured by nonlocal nonlinearity have also studied. Such an approach to lower hybrid waves and cusp solitons study in Fermi gas comprising electron positron and ions is new and important. The general results obtained in this quantum plasma theory will have widespread applicability, particularly for processes in high energy plasma-laser interactions set for laboratory astrophysics and solid state plasmas.

physics.plasm-ph↗

arXiv2017

The REsonant Multi-Pulse Ionization injection

The production of high-quality electron bunches in Laser Wake Field Acceleration relies on the possibility to inject ultra-low emittance bunches in the plasma wave. In this paper we present a new bunch injection scheme in which electrons extracted by ionization are trapped by a large-amplitude plasma wave driven by a train of resonant ultrashort pulses. In the REsonant Multi-Pulse Ionization (REMPI) injection scheme, the main portion of a single ultrashort (e.g Ti:Sa) laser system pulse is temporally shaped as a sequence of resonant sub-pulses, while a minor portion acts as an ionizing pulse. Simulations show that high-quality electron bunches with normalized emittance as low as $0.08$ mm$\times$mrad and $0.65\%$ energy spread can be obtained with a single present-day 100TW-class Ti:Sa laser system.

physics.plasm-ph↗

arXiv2017

Self consistent hydrodynamic description of the plasma wake field excitation induced by a relativistic charged-particle beam in an unmagnetized plasma

A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam, for a typical plasma wake field acceleration configuration in an unmagnetized and overdense plasma. The random component of the trajectories of the beam particles as well as of their velocity spread is modelled by an anisotropic temperature, allowing the beam dynamics to be approximated as a 3-D adiabatic expansion/compression. {It is shown that even in the absence of the {nonlinear plasma wake force}, the localization of the beam in the transverse direction can be achieved owing to the} nonlinearity associated with the adiabatic compression/rarefaction and a coherent stationary state is constructed. Numerical calculations reveal the possibility of the beam focussing and defocussing, but the lifetime of the beam can be significantly extended by the appropriate adjustments, so that transverse oscillations are observed, {similar to those} predicted within the thermal wave and Vlasov kinetic models.

physics.plasm-ph↗

arXiv2017

Stability properties of a thin relativistic beam propagation in a magnetized plasma

A self-consistent nonlinear hydrodynamic theory is presented of the propagation of a long and thin relativistic electron beam through a plasma that is relatively strongly magnetized, $|Ω_e|\simω_{pe}$ and whose density is much bigger than that of the beam. In the regime when the parallel phase velocity in the comoving frame is much smaller than the thermal speed and the beam electrons are thermalized, a stationary solution for the beam is found when the electron motion in the transverse direction is negligibile and the transverse localization comes from the nonlinearity of its 3-D adiabatic expansion. Conversely, when the parallel phase velocity is sufficiently large to prevent the heat convection along the magnetic field, a helicoidally shaped stationary beam is found whose transverse profile is determined from a nonlinear dispersion relation and depends on the transverse size of the beam and its pitch angle.

physics.plasm-ph↗

arXiv2014

The slingshot effect: a possible new laser-driven high energy acceleration mechanism for electrons

We show that under appropriate conditions the impact of a very short and intense laser pulse onto a plasma causes the expulsion of surface electrons with high energy in the direction opposite to the one of propagation of the pulse. This is due to the combined effects of the ponderomotive force and the huge longitudinal field arising from charge separation ("slingshot effect"). The effect should also be present with other states of matter, provided the pulse is sufficiently intense to locally cause complete ionization. An experimental test seems to be feasible and, if confirmed, would provide a new extraction and acceleration mechanism for electrons, alternative to traditional radio-frequency-based or Laser-Wake-Field ones.

physics.plasm-ph↗

arXiv2014

Ultrarelativistic regime in the propagation of an ultrastrong, femtosecond laser pulse in plasmas

The interaction of a multi-Petawatt, pancake-shaped laser pulse with an unmagnetized plasma is studied analytically and numerically in the regime of fully relativistic electron jitter velocities and in the context of the laser wakefield acceleration scheme. The study is applied to the specifications available at present time, or planned for the near future, of the Ti:Sa Frascati Laser for Acceleration and Multidisciplinary Experiments (FLAME) in Frascati. Novel nonlinear equation is derived by a three-timescale description, with an intermediate timescale associated with the nonlinear phase of the laser wave. They describe on an equal footing both the strong and moderate laser intensity regimes, pertinent to the core and the edges of the pulse. These have fundamentally different dispersive properties since, in the core, the electrons are almost completely expelled by a very strong ponderomotive force and the electromagnetic wave packet is imbedded in a vacuum channel and has (almost) linear properties, while at the pulse edges the laser amplitude is smaller and the wave is dispersive. The nonlinear phase provides a transition to a nondispersive electromagnetic wave at large intensities and the saturation of the previously known nonlocal cubic nonlinearity, without the violation of the imposed scaling laws. The temporal evolution of the laser pulse is studied by the numerical solution of the model equations in a two-dimensional geometry, with the spot diameter presently used in the self-injection test experiment (SITE) with FLAME. The most stable initial pulse length is found to be around 1 $μ$m, which is several times shorter than presently available. A stretching of the laser pulse is observed, followed by the development of a vacuum channel and a very large electrostatic wake potential, as well as the bending of the laser wave front.

physics.plasm-ph↗

arXiv2013

Wave theories of non-laminar charged particle beams: from quantum to thermal regime

The standard classical description of non-laminar charge particle beams in paraxial approximation is extended to the context of two wave theories. The first theory is the so-called Thermal Wave Model (TWM) that interprets the paraxial thermal spreading of the beam particles as the analog of the quantum diffraction. The other theory, hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of the single beam particle (uncertainty principle and spin) and provides the collective description of the beam transport in the presence of the quantum paraxial diffraction. QWM can be applied to beams that are sufficiently cold to allow the particles to manifest their individual quantum nature but sufficiently warm to make overlapping-less the single-particle wave functions. In both theories, the propagation of the beam transport in plasmas or in vacuo is provided by fully similar set of nonlinear and nonlocal governing equations, where in the case of TWM the Compton wavelength (fundamental emittance) is replaced by the beam thermal emittance. In both models, the beam transport in the presence of the self-fields (space charge and inductive effects) is governed by a suitable nonlinear nonlocal 2D Schroedinger equation that is used to obtain the envelope beam equation in quantum and quantum-like regimes, respectively. An envelope equation is derived for both TWM and QWM regimes. In TWM we recover the well known Sacherer equation whilst, in QWM we obtain the evolution equation of the single-particle spot size, i.e., single quantum ray spot in the transverse plane (Compton regime). We show that such a quantum evolution equation contains the same information carried out by an evolution equation for the beam spot size (description of the beam as a whole). This is done by defining the lowest QWM state reachable by a system of overlapping-less Fermions.

physics.acc-ph↗

arXiv2011

Propagation of ultrastrong femtosecond laser pulses in PLASMON-X

The derivation is presented of the nonlinear equations that describe the propagation of ultrashort laser pulses in a plasma, in the Plasmon-X device. It is shown that the Plasmon-X scheme used for the electron acceleration uses a sufficiently broad beam ($L_\bot\sim 130\,\,μ{\rm m}$) that justifies the use of the standard stationary 1-D approximation in the electron hydrodynamic equations, since the pulse width is sufficiently bigger than the pulse length ($\sim 7.5\,\,μ{\rm m}$). Furthermore, with the laser power of $W\leq 250$ TW and the $130\,\,μ{\rm m}$ spot size, the dimensionless laser vector potential is sufficiently small $|A_{\bot_0}|^2/{2} = ({W}/{c^2ε_0})({λ^2}/{8 π^2 c})({4}/{πL_\bot^2})({e}/{m_0 c})^2 \sim 0.26$, the nonlinearity is sufficiently weak to allow the power expansion in the nonlinear Poissons's equation. Such approximation yields a nonlinear Schr\" odinger equation with a reactive nonlocal nonlinear term. The nonlocality contains a cosine function under the integral, indicating the oscillating wake. For a smaller spot size that is used for the Thomson scattering, $L_\bot = 10\,\, μ$m, the length and the width of the pulse are comparable, and it is not possible to use the 1-D approximation in the hydrodynamic equations. With such small spot size, the laser intensity is very large, and most likely some sort of chanelling in the plasma would take place (the plasma gets locally depleted so much that the electromagnetic wave practically propagates in vacuum).

physics.plasm-ph↗

arXiv2011

Self consistent thermal wave model description of the transverse dynamics for relativistic charged particle beams in magnetoactive plasmas

Thermal Wave Model is used to study the strong self-consistent Plasma Wake Field interaction (transverse effects) between a strongly magnetized plasma and a relativistic electron/positron beam travelling along the external magnetic field, in the long beam limit, in terms of a nonlocal NLS equation and the virial equation. In the linear regime, vortices predicted in terms of Laguerre-Gauss beams characterized by non-zero orbital angular momentum (vortex charge). In the nonlinear regime, criteria for collapse and stable oscillations is established and the thin plasma lens mechanism is investigated, for beam size much greater than the plasma wavelength. The beam squeezing and the self-pinching equilibrium is predicted, for beam size much smaller than the plasma wavelength, taking the aberrationless solution of the nonlocal Nonlinear Schroeding equation.

physics.plasm-ph↗

arXiv2011

Quantumlike description of the nonlinear and collective effects on relativistic electron beams in strongly magnetized plasmas

A numerical analysis of the self-interaction induced by a relativistic electron/positron beam in the presence of an intense external longitudinal magnetic field in plasmas is carried out. Within the context of the Plasma Wake Field theory in the overdense regime, the transverse beam-plasma dynamics is described by a quantumlike Zakharov system of equations in the long beam limit provided by the Thermal Wave Model. In the limiting case of beam spot size much larger than the plasma wavelength, the Zakharov system is reduced to a 2D Gross-Pitaevskii-type equation, where the trap potential well is due to the external magnetic field. Vortices, "beam halos" and nonlinear coherent states (2D solitons) are predicted.

physics.plasm-ph↗

arXiv2011

Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach

Using the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions.

nlin.SI↗

arXiv2009

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schrödinger equation and a one-dimensional (1D) nonlinear Schrödinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.

cond-mat.quant-gas↗

arXiv2009

Soliton solutions of 3D Gross-Pitaevskii equation by a potential control method

We present a class of three-dimensional solitary waves solutions of the Gross-Pitaevskii (GP) equation, which governs the dynamics of Bose-Einstein condensates (BECs). By imposing an external controlling potential, a desired time-dependent shape of the localized BEC excitation is obtained. The stability of some obtained localized solutions is checked by solving the time-dependent GP equation numerically with analytic solutions as initial conditions. The analytic solutions can be used to design external potentials to control the localized BECs in experiment.

nlin.SI↗

arXiv2009

Some mathematical aspects in determining the 3D controlled solutions of the Gross-Pitaevskii equation

The possibility of the decomposition of the three dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schrödinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, solutions of the 3D controlled GPE can be constructed from the solutions of a 2D linear Schrödinger equation (transverse component of the GPE) coupled with a 1D nonlinear Schrödinger equation (longitudinal component of the GPE). Such a decomposition, called the 'controlling potential method' (CPM), allows one to cast the above solutions in the form of the product of the solutions of the transverse and the longitudinal components of the GPE. The coupling between these two equations is the functional of both the transverse and the longitudinal profiles. The analysis shows that the CPM is based on the variational principle that sets up a condition on the controlling potential well, and whose physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control operation.

nlin.SI↗