1,721,114 research outputs found
Envelope solitons versus solitons
No full textA theory involving a correspondence between envelope solitonlike solutions of the generalized nonlinear Schrödinger equation (GNLSE) and solitonlike solutions of the generalized Korteweg-de Vries equation (GKVdE) is developed within the context of the Madelung's fluid description (fluid counterpart description of the GNLSE). This correspondence, which, under suitable constraints, can be made invertible, seems to be very helpful for finding one family of solutions (whether envelope solitonlike solutions of the GNLSE or solitonlike solutions of the GKdVE) starting from the knowledge of the other family of solution (whether solitonlike solutions of the GKdVE or envelope solitonlike solutions of the GNLSE). The theory is successfully applied to wide classes of both modified nonlinear Schrödinger equation (MNLSE) and modified Korteweg-de Vries equation (MKVdE), for which bright and gray/dark solitonlike solutions are found. In particular, bright and gray/dark solitary waves are determined for the MNLSE with a quartic nonlinear potential in the modulus of the wavefunction (i.e. q1|Ψ|^2 + q2|Ψ|^4) as well as for the associated MKdVE. Furthermore, the well known bright and gray/dark envelope solitons of the cubic NLSE and the corresponding solitons of the associated standard KdVE are easily recovered from the present theory. Remarkably, this approach opens up the possibility to transfer all the know how concerning the instability criteria for solitonlike solutions of the MKdVE to the instability theory of envelope solitonlike solutions of the MNLSE
From Maxwell's theory of Saturn's rings to the negative mass instability
No full textThe impact of the Maxwell's theory of Saturn's ring, formulated in Aberdeen around 1856, is discussed. One century later, Nielsen, Sessler and Symon formulated a similar theory to describe the coherent instabilities (in particular, the negative mass
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A wave theory for the negative mass instability
No full textCharged particle beam transport has been recently described in terms of a quantum-like model, called Thermal Wave Model (TWM). Within the framework of TWM, the longitudinal dynamics of a relativistic charged particle beam in an accelerating machine is presented. It is shown that this dynamics is governed by a nonlinear Schrodinger-like equation for a complex function (the beam wave function) whose squared modulus is proportional to the beam number density. This way it is shown that such a description provides a wave theory for negative mass instability which is fully similar to the one used for describing oscillating two stream instability in plasma physics
Spherical aberrations in the thermal wave model for luminosity estimates in particle accelerators
No full textAn approach for estimating the luminosity in linear colliders in the presence of spherical aberrations is developed within the framework of the recently proposed thermal-wave model for relativistic-charged-particle-beam propagation. By taking into account a quadrupolelike lens with octupole deviations, the transverse beam motion is governed by a two-dimensional Schrödinger-like equation, with an anharmonic potential. To first order in perturbation theory and in the thin-lens approximation, we analytically find the transverse beam density, the spot size, and the luminosity reduction factor at the interaction point in terms of the initial conditions. Some numerical estimates are also given.
© 1992 The American Physical Societ
Coupling between nonlinear Langmuir waves and electron holes in quantum plasmas
No full textThe nonlinear effects on a slow timescale, compared with the electron plasma frequency, are studied using the Wigner-Poisson system, in the plasma regimes characterized by the overlapping of the wavefunctions of individual electrons, by the presence of a large amplitude Langmuir pump wave, and whose temperature is higher than the Fermi temperature. It is shown that the electron trapping on closed orbits in phase space is strongly affected both by the classical nonlinear ponderomotive effects and by the quantum super-diffusion. A solution in the form of a quantum corrected electron hole is found in terms of a generalized energy in the Wigner equation that contains higher derivatives in velocity space. In the classical limit, the high-frequency pump hampers the electron trapping due to the unfavorable sign of the ponderomotive potential and due to deformation of their distribution function by the diffusion. Conversely, in the modulational regime the leading quantum effect is shown to be related with the effective super-diffusion in the velocity space associated with the quantum effects on the high-frequency pump, which facilitates the electron trapping and allows the creation of holes with smaller amplitudes. © 2006 Elsevier B.V. All rights reserved
A quantum-like Landau Damping of an Electromagnetic Wavepacket
No full textBy using the Wigner transform, it is shown that the propagation of an electromagnetic (EM) wavepacket in a nonlinear medium, governed by nonlinear Schrödinger equation, can be described, in phase space, by a kinetic-like theory similar to the one based on the Vlasov equation which is used for describing the collective longitudinal dynamics of charged-particle bunches in accelerating machines. In this framework, the modulational instability of the wavepacket corresponds to the coherent instability of the particle bunch. Remarkably, a Landau damping of the EM wavepacket is predicted and put forward for a future investigation. Furthermore, the concept of coupling impedance associated with the EM wavepacket propagation is also introduced in analogy to the one of charged-particle bunches. This approach provides stability charts similar to the ones describing charged-particle beams in accelerating machines
A Thermal Wave Model for relativistic-charged-particle beam propagation
No full textWe show that the well-known analogy between electromagnetic beam optics (EBO) and relativistic-charged-particle beam optics (RCPBO) in paraxial approximation is deeper than it would usually appear in the literature. This analogy is understood by suggesting a wave model of thermal nature for particle-beam propagation. This is done using a parabolic equation for a wave function whose modulus squared is proportional to the number of particles per unitary transverse section, and the emittance represents the diffraction parameter as the wavelength in monochromatic EBO. Since the particle beam is described by a Schrodinger-like equation, we get a further formal analogy between RCPBO and nonrelativistic quantum mechanics (NQM). The emittance plays now the role corresponding to Planck's constant. The wave model for RCPBO is completely new and gives a formal unified description of RCPBO, EBO and NQM. This equivalence allows us, using quantum mechanics, to obtain in a simple way all the already known results of RCPBO. Furthermore, it provides in perspective a useful framework for a more accurate study of several applications, such as those in particle accelerators, in FEL and particle beam-plasma interaction
A NOVEL APPROACH FOR DETERMINING SOLITARY WAVE SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATIONS
No full textQuantum methodologies in beam, fluid and plasma physics
No full textThe quantum methodologies useful for describing in a
unified way several problems of nonlinear and collective dynamics
of fluids, plasmas and beams are presented. In particular, the
pictures given by the Madelung fluid and the Moyal-Ville-Wigner
phase-sp
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