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The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. Then, we reduce such a problem to the study of spatiotemporal evolution of the wave packet in an inertial frame in the presence of a homogeneous force field but with an arbitrary time dependence. We demonstrate the existence of a Gaussian wave packet solution, for which the position and momentum uncertainties are unaffected by the uniform force field. This implies that, similar to in the case of a force-free motion, the uncertainty product is unaffected by acceleration. In addition, according to the Ehrenfest theorem, the wave packet centroid moves according to classic Newton’s law of a particle experiencing the effects of uniform acceleration. Furthermore, as in free motion, the wave packet exhibits a diffraction spread in the configuration space but not in momentum space. Then, using Radon transform, we determine the quantum tomogram of the Gaussian state evolution in the accelerated frame. Finally, we characterize the wave packet evolution in the accelerated frame in terms of optical and simplectic tomogram evolution in the related tomographic space.

We carry out a stability analysis of a relativistic nonlaminar electron beam which is experiencing the self-consistent plasma wake field excitation. This is done in overdense regime (i.e. plasma density much greater than beam density) in a cold plasma. We adopt the self-consistent kinetic model for the plasma wake field excitation, that is based on the pair of Vlasov-Poisson-type equations. The latter governs the phase-space spatiotemporal evolution of the beam and its linearized form leads to a Landau-type approach to the beam stability analysis. Thereby, the analysis, performed for the case of a Gaussian electron beam distribution, shows the existence of the unstable modes for both cold and warm beams, respectively.

European physical journal special topics 229(24), 3675 - 4284 (2020). doi:10.1140/epjst/e2020-000127-8, This report presents the conceptual design of a new European research infrastructure EuPRAXIA. The concept has been established over the last four years in a unique collaboration of 41 laboratories within a Horizon 2020 design study funded by the European Union. EuPRAXIA is the first European project that develops a dedicated particle accelerator research infrastructure based on novel plasma acceleration concepts and laser technology. It focuses on the development of electron accelerators and underlying technologies, their user communities, and the exploitation of existing accelerator infrastructures in Europe. EuPRAXIA has involved, amongst others, the international laser community and industry to build links and bridges with accelerator science — through realising synergies, identifying disruptive ideas, innovating, and fostering knowledge exchange. The Eu-PRAXIA project aims at the construction of an innovative electron accelerator using laser- and electron-beam-driven plasma wakefield acceleration that offers a significant reduction in size and possible savings in cost over current state-of-the-art radiofrequency-based accelerators. The foreseen electron energy range of one to five gigaelectronvolts (GeV) and its performance goals will enable versatile applications in various domains, e.g. as a compact free-electron laser (FEL), compact sources for medical imaging and positron generation, table-top test beams for particle detectors, as well as deeply penetrating X-ray and gamma-ray sources for material testing. EuPRAXIA is designed to be the required stepping stone to possible future plasma-based facilities, such as linear colliders at the high-energy physics (HEP) energy frontier. Consistent with a high-confidence approach, the project includes measures to retire risk by establishing scaled technology demonstrators. This report includes preliminary models for project implementation, cost and schedule that would allow operation of the full Eu-PRAXIA facility within 8—10 years., Published by Springer, Heidelberg

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., Comment: 7 pages, 6 figures

Figure 20.1 was not correct in the published article. The original article has been corrected. The published apologizes for the inconvenience.

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., 16 pages

The interaction of an ultrashort (femtosecond), pancake-shaped laser pulse with underdense unmagnetized plasma is studied analytically and numerically in a regime with ultrarelativistic electron jitter velocities. The adiabatic evolution of the quasistationary electron distribution function is resolved by following particles along their nonlinear trajectories in phase space. It is estimated that under typical laser-plasma accelerator conditions, the quasistationary distribution is established after the pulse has penetrated . 1mm into the plasma. The main particle eect is found to be the beam loading associated with the electrons re ected from the maxima of the eective potential, a fraction of which can also be entrapped in the time dependent potential minima. Owing to the relativistic mass increase, their participation in the plasma dynamics is reduced. The number density of re ected particles is exponentially small for nonrelativistic electron temperatures, but at the wavebreak it can become comparable to the density of the background plasma if the temperature of electrons exceeds several percent of their rest energy m0c2. Numerical calculations in the presence of beam loading and in the strong intensity regime, based on the three-timescale approximation [1], reveal the creation of a bubble in the electron density, along with the steepening and the breaking of the nonlinear Langmuir wake that occurs simultaneously with the creation of a sharp spike in the distribution function and a peak in the electron density, located at the position of the wavebreak.

25th International Conference on the Application of Accelerators in Research and Industry, CAARI 2018, Texas, USA, 12 Aug 2018 - 17 Aug 2018; AIP conference proceedings 2160(1), 040012-1 - 040012-9 (2019). doi:https://doi.org/10.1063/1.5127692, Plasma accelerators present one of the most suitable candidates for the development of more compact particle acceleration technologies, yet they still lag behind radiofrequency (RF)-based devices when it comes to beam quality, control, stability and power efficiency. The Horizon 2020-funded project EuPRAXIA (“European Plasma Research Accelerator with eXcellence In Applications”) aims to overcome the first three of these hurdles by developing a conceptual design for a first international user facility based on plasma acceleration. In this paper we report on the main features, simulation studies and potential applications of this future research infrastructure., Published by AIP Publishing, Melville, NY

A numerical investigation on the spatiotemporal evolution of an electron beam, externally injected in a plasma in the presence of a plasma wake field, is carried out. The latter is driven by an ultra-short relativistic axially-symmetric femtosecond electron bunch. We first derive a novel Poisson-like equation for the wake potential where the driving term is the ultra-short bunch density, taking suitably into account the interplay between the sharpness and high energy of the bunch. Then, we show that a channel is formed longitudinally, through the externally injected beam while experiencing the effects of the bunch-driven plasma wake field, within the context of thermal wave model. The formation of the channel seems to be a final stage of the 3D evolution of the beam. This involves the appearance of small filaments and bubbles around the longitudinal axis. The bubbles coalesce forming a relatively stable axially-symmetric hollow beam structure., 6 pages, 9 figures

Within the framework of the Vlasov–Maxwell system of equations, we describe the self-consistent interaction of a relativistic charged-particle beam with the surroundings while propagating through a plasma-based acceleration device. This is done in terms of the concept of coupling (longitudinal) impedance in full analogy with the conventional accelerators. It is shown that also here the coupling impedance is a very useful tool for the Nyquist-type stability analysis. Examples of specific physical situations are finally illustrated.

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. Such situation is encountered when the gyro-frequency is comparable to the plasma frequency, i.e. |Ω e | ~ ω pe . In addition, it is assumed the plasma density is much bigger than that of the beam. In the regime when the solution propagates in the comoving frame with a velocity that is much smaller than the thermal speed, a nonlinear stationary beam structure is found in which the electron motion in the transverse direction is negligible and whose transverse localization comes from the nonlinearity associated with its 3-D adiabatic expansion. Conversely, when the parallel velocity of the structure is sufficiently large to prevent the heat convection along the magnetic field, a helicoidally shaped stationary solution is found that is governed by the transverse convective nonlinearity. The profile of such beam is determined from a nonlinear dispersion relation and depends on the transverse size of the beam and its pitch angle to the magnetic field.

Recently a new injection scheme for Laser Wake Field Acceleration, employing a single 100-TW-class laser system, has been proposed. In the Resonant Multi-Pulse Ionization injection (ReMPI) a resonant train of pulses drives a large amplitude plasma wave that traps electrons extracted from the plasma by further ionization of a high-Z dopant (Argon in the present paper). While the pulses of the driver train have intensity below the threshold for the dopant's ionization, the properly delayed and frequency doubled (or more) ionization pulse possesses an electric field large enough to extract electrons, though its normalized amplitude is well below unity. In this paper we will report on numerical simulations results aimed at the generation of GeV-scale bunches with normalized emittance and {\it rms} energy below $80\, nm \times rad $ and $0.5\, \%$, respectively. Analytical consideration of the FEL performance for a $1.3\, GeV$ bunch will be also reported., EAAC 2017 Conference, Elba, Italy

Laser Wake Field accelerated electrons need to exhibit a good beam-quality to comply with requirements of FEL or high brilliance Thomson Scattering sources, or to be post-accelerated in a further LWFA stage towards TeV energy scale. Controlling electron injection, plasma density profile and laser pulse evolution are therefore crucial tasks for high-quality e-bunch production. A new bunch injection scheme, the Resonant Multi-Pulse Ionization Injection (RMPII), is based on a single, ultrashort Ti:Sa laser system. In the RMPII the main portion of the 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 energies in the range 265MeV −1.15GeV , normalized emittance as low as 0.08 mm·mrad and 0.65% energy spread can be obtained with a single 250 TW Ti:Sa laser system. Applications of the e-beam in high-brilliance Thomson Scattering source, including 1.5 - 26.4 MeV γ sources with peak brilliance up to 1 · 1028ph/(s · mm2 • mrad2 • 0.1%bw), are reported.

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 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 x mrad and 0.65% energy spread can be obtained with a single present-day 100TW-class Ti: Sa laser system. Published by AIP Publishing.

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.

Recent investigations indicate that sufficiently long beams of charged particles, travelling in a plasma, experience the phenomenon of self-modulation. The self-modulation is driven by the plasma wake field excitation due to the beam itself, and it may become unstable under certain conditions. A preliminary theoretical investigation of the self-modulation of a relativistic charged-particle beam in overdense plasma in the presence of a preformed plasma wave is carried out, within the quantum-like description of charged particle beams provided by the Thermal Wave Model. A simple physical model for the self-modulation is put forward, described by a nonlinear Schrodinger equation coupled with the Poisson-like equation for the plasma wake potential (so-called Fedele–Shukla equations). The physical mechanism is based on the interplay of three concomitant effects, the radial thermal dispersion (associated with the emittance e ), the radial ponderomotive effects of a preexisting plasma wave (which provides the guidance for the beam), and the self-interaction of the plasma wake field generated by the beam itself.

The interaction of an ultrashort (femtosecond), pancake-shaped laser pulse with underdense unmagnetized plasma is studied analytically and numerically in a regime with ultrarelativistic electron jitter velocities. The adiabatic evolution of the quasistationary electron distribution function is resolved by following particles along their nonlinear trajectories in phase space. It is estimated that under typical laser-plasma accelerator conditions, the quasistationary distribution is established after the pulse has penetrated ≲ 1 mm into the plasma. The main particle effect is found to be the beam loading associated with the electrons reflected from the maxima of the effective potential, a fraction of which can also be entrapped in the time dependent potential minima. Owing to the relativistic mass increase, their participation in the plasma dynamics is reduced. The number density of reflected particles is exponentially small for nonrelativistic electron temperatures, but at the wavebreak, it can become comparable to the density of the background plasma if the temperature of electrons exceeds several percent of their rest energy m 0 c 2. Numerical calculations in the presence of beam loading and in the strong intensity regime, based on the three-time scale approximation[Jovanovic et al., Phys. Plasmas 22, 043110.1 (2015)], reveal the creation of a bubble in the electron density, along with the steepening and the breaking of the nonlinear Langmuir wake that occurs simultaneously with the creation of a sharp spike in the distribution function and a peak in the electron density, located at the position of the wavebreak.

A theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derived under the Hartree mean field approximation, coupled with a Poisson-like equation for the wake potential. These two coupled equations are subsequently reduced to a nonlinear, non-local Schrödinger equation and solved in a strongly non-local regime. An approximate Glauber solution is found analytically in the form of a Hermite–Gauss ring soliton. Such non-stationary (‘breathing’ and ‘wiggling’) coherent structure may be parametrically unstable and the corresponding growth rates are estimated analytically.

Parametric instabilities induced at the plasma edge by lower hybrid wave power externally coupled to tokamak plasmas have, via broadening of the antenna spectrum, strong influence on the power deposition and current drive in the core. For modeling the parametric instabilities at the tokamak plasma edge in lower hybrid current drive experiments, the effect of the collisions has been neglected so far. In the present work, a specific collisional parametric dispersion relation, useful to analyze these nonlinear phenomena near the lower hybrid antenna mouth, is derived for the first time, based on a kinetic model. Numerical solutions show that in such cold plasma regions the collisions prevent the onset of the parametric instabilities. This result is important for present lower hybrid current drive experiments, as well as in fusion reactor scenarios.

We present an analytical and numerical study of the interaction of a multi-petawatt, pancake-shaped laser pulse with an unmagnetized plasma. The study has been performed in the ultrarelativistic regime of electron jitter velocities, in which the plasma electrons are almost completely expelled from the pulse region. The calculations are applied to a laser wake field acceleration scheme with specifications that may be available in the next generation of Ti:Sa lasers and with the use of recently developed pulse compression techniques. A set of novel nonlinear equations is derived using a three-timescale description, with an intermediate timescale associated with the nonlinear phase of the electromagnetic wave and with the spatial bending of its wave front. They describe, on an equal footing, both the strong and the moderate laser intensity regimes, pertinent to the core and to the edges of the pulse.

A novel approach, based on Fresnel tomography, to determine the entropy of two-dimensional optical Laguerre-Gaussian beams is presented and discussed. Numerical evaluations of the entropy distribution in the phase space associated with Laguerre-Gauss modes are presented. It is shown that the concept of Fresnel entropy provides a general criterion for studying and characterizing the vorticity of Laguerre-Gauss modes. (C) 2010 Elsevier B.V. All rights reserved.

The Fresnel tomograms of Laguerre-Gaussian beams are found and the relation of the two-point spatial correlation function with the tomographic map is discussed. The spatial distribution and signature of vorticity of Laguerre-Gaussian modes is analyzed by measuring the two-point spatial correlation function of the one-dimensional projection of the vortex field. An interferometric approach, based on a Fourier projection algorithm, for the experimental determination of the two-point correlation function of the full complex vortex field at the cross-section plane of the recorded interference pattern is also described; this approach allows one to characterize the vortex structure and spatial coherence along the direction of propagation.

The possibility of the decomposition of the three-dimensional (3D) Gross–Pitaevskii equation (GPE) into a pair of coupled Schroedinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schrödinger equation coupled with a 1D nonlinear Schrödinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

A correspondence between the families of generalized nonlinear Schrodinger (NLS) equations and generalized KdV equations was recently found using a Madelung fluid description. We similarly consider a special derivative NLS equation. We find a number of solitary waves and periodic solutions (expressed in terms of elliptic Jacobi functions) for a motion with a stationary profile current velocity. We study the stability of a bright solitary wave (ground state) by conjecturing that the Vakhitov-Kolokolov criterion is applicable.

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schrödinger soliton [JETP Lett. 80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically, taking initialy a controlled soliton whose “effective mass” is several times bigger than the critical value for a weak collapse in the absence of a potential well, and allowing for reasonably large errors in the experimental realization of the trapping potential required by the theory. For repulsive and sufficiently weak attractive interactions, the controlled state is shown to remain stable inside a breathing potential well, for a time that is an order of magnitude longer than the characteristic periods of the forced and eigenoscillations of the soliton. The collapse is observed only for attractive interactions, when the nonlinear attraction exceeded the appropriate threshold.

Istituto di Cibernetica “Eduardo Caianiello” del CNR Comprensorio “A. Olivetti” Fabbr. 70, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy Dipartimento di Scienze Fisiche, Universit`a “Federico II” di Napoli, INFN, Sezione di Napoli, ComplessoUniversitario di M. S. Angelo, Via Cintia, I-80126 Napoli, Italy Lebedev Physical Institute, RAS, Moscow, Russia

The interaction of a multi-petawatt, pancake-shaped laser pulse with an unmagnetized plasma is studied analytically and numerically in a regime with ultrarelativistic electron jitter velocities, in which the plasma electrons are almost completely expelled from the pulse region. The study is applied to a laser wakefield acceleration scheme with specifications that may be available in the next generation of Ti:Sa lasers and with the use of recently developed pulse compression techniques. A set of novel nonlinear equations is derived using a three-timescale description, with an intermediate timescale associated with the nonlinear phase of the electromagnetic wave and with the spatial bending of its wave front. They describe, on an equal footing, both the strong and the moderate laser intensity regimes, pertinent to the core and to 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, thus having (almost) linear properties. Conversely, at the pulse edges, the laser amplitude is smaller, and the wave is weakly nonlinear and dispersive. New nonlinear terms in the wave equation, introduced by the nonlinear phase, describe without the violation of imposed scaling laws a smooth transition to a nondispersive electromagnetic wave at very large intensities and a simultaneous saturation of the (initially cubic) nonlocal nonlinearity. The temporal evolution of the laser pulse is studied both analytically and by numerically solving the model equations in a two-dimensional geometry, with the spot diameter presently used in some laser acceleration experiments. The most stable initial pulse length is estimated to exceed 1.5–2 microns. Moderate stretching of the pulse in the direction of propagation is observed, followed by the development of a vacuum channel and of a very large electrostatic wake potential, as well as by the bending of the laser wave front.

The propagation, in a shallow water, of nonlinear ring waves in the form of multisolitons is investigated theoretically. This is done by solving both analytically and numerically the cylindrical (also referred to as concentric) Korteweg-de Vries equation (cKdVE). The latter describes the propagation of weakly nonlinear and weakly dispersive ring waves in an incompressible, inviscid, and irrotational fluid. The spatiotemporal evolution is determined for a cylindrically symmetric response to the free fall of an initially given multisoliton ring. Analytically, localized solutions in the form of tilted solitons are found. They can be thought as single- or multiring solitons formed on a conic-modulated water surface, with an oblique asymptote in arbitrary radial direction (tilted boundary condition). Conversely, the ring solitons obtained from numerical solutions are localized single- or multiring structures (standard solitons), whose wings vanish along all radial directions (standard boundary conditions). It is found that the wave dynamics of these standard ring-type localized structures differs substantially from that of the tilted structures. A detailed analysis is performed to determine the main features of both multiring localized structures, particularly their break-up, multiplet formation, overlapping of pulses, overcoming of one pulse by another, ``amplitude-width'' complementarity, etc., that are typically ascribed to a solitonlike behavior. For all the localized structures investigated, the solitonlike character of the rings is found to be preserved during (almost) entire temporal evolution. Due to their cylindrical character, each ring belonging to one of these multiring localized structures experiences the physiological decay of the peak and the physiological increase of the width, respectively, while propagating (``amplitude-width'' complementarity). As in the planar geometry, i.e., planar Korteweg-de Vries equation (pKdVE), we show that, in the case of the tilted analytical solutions, the instantaneous product $P\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}(\mathit{maximum}\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathit{amplitude})\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{(\mathit{width})}^{2}$ is rigorously constant during all the soliton spatiotemporal evolution. Nevertheless, in the case of the numerical solutions, we show that this product is not preserved; i.e., the instantaneous physiological variations of both peak and width of each ring do not compensate each other as in the tilted analytical case. In fact, the amplitude decay occurs faster than the width increase, so that $P$ decreases in time. This is more evident in the early times than in the asymptotic ones (where actually cKdVE reduces to pKdVE). This is in contrast to previous investigations on the early-time localized solutions of the cKdVE.

Self modulated dynamics of a relativistic charged particle beam is reviewed within the context of the theory of plasma wake field excitation. The self-consistent description of the beam dynamics is provided by coupling the Vlasov equation with a Poisson-type equation relating the plasma wake potential to the beam density. An analysis of the beam envelope self-modulation is then carried out and the criteria for the occurrence of the instability are discussed thereby., Comment: This is a 10 pages manuscript which contain 4 figures. This manuscript is recently submitted in 'Nuclear Instruments and Methods in Physics Research Section A' as a proceeding of the conference 'EAAC 2015'

Entropic uncertainty relations for Shannon entropies associated with tomographic probability distributions of continuous quadratures are reviewed. New entropic uncertainty relations in the form of inequalities for integrals containing the tomograms of quantum states and deformation parameter are obtained.

We introduce a new type of tomographic probability distribution containing complete information about the density matrix (wave function) related to the Fresnel transform of the complex wave function. We elucidate the relation to the symplectic tomographic probability distribution. We present a multimode generalization of the Fresnel tomography and give examples of applications of the present approach. © 2005 Springer Science+Business Media, Inc.

Tomographic-probability representation for soliton solutions of Gross-Pitaevskii equation is introduced. Tomograms of the wavefunction describing bright soliton states of Bose-Einstein condensate are obtained in the presence of a quadratic external potential. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003.

An investigation to deepen the connection between the family of nonlinear Schrödinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schrödinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schrödinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x - u0s (s being a time-like variable). This novel method in solving the nonlinear Schrödinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented.

Within the Vlasov’s kinetic theory, describing the plasma wake field interaction, the collective transport of a warm nonlaminar relativistic charged particle beam is analyzed in the strongly nonlocal regime, where the beam spot-size is much less than the plasma wavelength. This is done in the overdense regime, i.e., the beam density is much less than the plasma density. The beam is supposed to be sufficiently long to experience the adiabatic shielding by the plasma. In these conditions, we neglect the longitudinal beam dynamics and focus on the transverse one only.We derive the virial description (envelope description) from the 2D Vlasov-Poisson-type system of equations that governs the transverse self-consistent plasma wake field excitation. The resulting envelope equation is then reduced, in the aberration-less approximation, to a differential equation for the beam spot size, where the role of the ambient magnetic field is evaluated in both laboratory and astrophysical environments. An analysis of the beam envelope self-modulation is then carried out and the criteria for the occurrence of the instability are found.

An analysis of the transverse plasma wake field dynamics excited by a long relativistic electron beam is carried out in a purely local regime, in which the transverse beam spot-size is much bigger than the plasma wavelength. This is done by using the Vlasov equation, that governs the kinetic spatiotemporal evolution of the transverse paraxial beam transport. A self-consistent description of the beam dynamics is then provided by coupling the Vlasov equation with a Poisson-type equation. Furthermore, the latter relates the beam density with the plasma wake potential energy. Remarkably, the approach here proposed seems to be suitable for describing the beam self-modulation and the prediction of the beam collapse.

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., Talk presented at International Topical Conference on Plasma Science: Advanced Plasma Concepts, 24-28 September, Faro, Portugal Submitted to Journal of Plasma Physics

The nonlinear dynamics of the concentric shallow water waves is described by means of the cylindrical Korteweg-de Vries equation, often referred to as the concentric Korteweg-de Vries equation (cKdVE). By using the mapping that transforms a cKdVE into the standard one – hereafter also referred to as the planar Korteweg-de Vries equation (KdVE) – the spatiotemporal evolution of a cylindrical surface water wave, corresponding to a tilted cylindrical bright soliton, is described. The usual representation of a tilted soliton is 'non-physical'; here the cylindrical coordinate and the retarded time play the role of time-like and space-like variables, respectively. However, we show that, when we express such analytical solution of the cKdVE in the appropriate representation in terms of the two horizontal space coordinates, say X and Y, and the 'true' time, say T, this non-physical character disappears. The analysis is then carried out numerically to consider the surface water wave evolution corresponding to initially localized structures with standard boundary conditions, such as bright soliton, Gaussian and Lorentzian profiles. A comparison among those profiles is finally presented.

A tutorial presentation is given of the interaction between a high frequency electrostatic wave and a plasma. The analysis is carried out in several consecutive simple steps, starting from electrostatic plasma waves in a cold plasma and successively introducing complications like streaming electrons, the two stream instability and eventually the Landau damping phenomenon. The analysis is based only on cold plasma fluid theory and does not involve kinetic Vlasov theory. (C) 2001 American Association of Physics Teachers.

By using a recently-proposed quantum-like approach in semiclassical approximation, the equilibrium state of the particle distribution is given in a simple 1-D model of a nested trap. This result is used to evaluate the antihydrogen recombination rate in a nested trap containing antiprotons and positrons.

A generalization of the Vlasov-Poisson system describing the collective dynamics of stored, high-energy hadron beams under the influence of a complex wall impedance is derived in the highly relativistic beam limit γ≫1. A coherent electric field structure Ez(r,z) is found to affect the beam dynamics in O(γ-2), giving rise to an updated feedback between line density (respectively, beam current) and self-fields. Propagating solitary wave solutions as special solutions of this system are obtained by the potential method known from plasma physics. Various parameter regimes are investigated and wave structures are found which are characterized by notches (respectively, humps) in the resonant part of the distribution function. These coherent waves typically travel with thermal velocities and below (kinetic solitary waves) but also structures moving with larger phase velocities (hydrodynamic solitons) are found. Dory's conjecture about mass conjugation is approved a posteriori in the purely reactive case but is found to be substantially altered in the strongly resistive case. Hydrodynamic Korteweg-de Vries solitons are shown to exist in the purely reactive case and for beams above transition energy and for weak space charge effects only. © 2000 American Institute of Physics.

The study of CPT invariance with the highest achievable precision in all particle sectors is of fundamental importance for physics. Equally important is the question of the gravitational acceleration of antimatter. In recent years, impressive progress has been achieved at the Low Energy Antiproton Ring (LEAR) at CERN in capturing antiprotons in specially designed Penning traps, in cooling them to energies of a few milli-electron volts, and in storing them for hours in a small volume of space. Positrons have been accumulated in large numbers in similar traps, and low energy positron or positronium beams have been generated. Finally, steady progress has been made in trapping and cooling neutral atoms. Thus the ingredients to form antihydrogen at rest are at hand. We propose to investigate the different methods to form antihydrogen at low energy, and to utilize the best of these methods to capture a number of antihydrogen atoms sufficient for spectroscopic studies in a magnetostatic trap. Once antihydrogen atoms have been captured at low energy, spectroscopic methods can be applied to interrogate their atomic structure with extremely high precision and compare it to its normal matter counterpart, the hydrogen atom. Especially the 1S-2S transition, with a lifetime of the excited state of 122 ms and thereby a natural linewidth of 5 parts in 1016, offers in principle the possibility to directly compare matter and antimatter properties at a level of 1 part in 1018. Additionally, comparison of the gravitational masses of hydrogen and antihydrogen, using either ballistic or spectroscopic methods, can provide direct experimental tests of the Weak Equivalence Principle for antimatter at a high precision.

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., Comment: File RevTex, 12 pages, 8 figures

Recently, a theoretical investigation of the collective and nonlocal quantum effects has been carried out within the framework of a quantum approach to the relativistic charged particle beam travelling in a cold, collisionless, strongly magnetized plasma. This has been done taking into account both the plasma wake field excitation and the quantum paraxial approximation. On the basis of this theory, here we carry out a preliminary study of the transverse effects experienced by a cold relativistic beam through a thin plasma slab (plasma lens). In the strongly nonlocal regime, in which the beam experiences a very strong focusing effect, the scheme of plasma lens is reviewed in terms of the wave description provided by the above quantum theory.