A theory involving a correspondence between envelope solitonlike solutions of the generalized nonlinear Schro« dinger equation (GNLSE) and solitonlike solutions of the generalized Korteweg^de Vries equation (GKVdE) is developed within the context of the Madelung's £uid description (£uid counterpart description of the GNLSE). This correspondence, which, under suitable constraints, can be made invertible, seems to be very helpful for ¢nding 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 modi¢ed nonlinear Schro« dinger equation (MNLSE) and modi¢ed 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. q 1 jCj 2 þ q 2 jCj 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.
A statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrödinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave fields are shown to exist for a wide class of nonlinear media.
Summary. --We 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 SchrSdinger-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.PACS 41.80 -Particle beams and particle optics. PACS 42.10 -Propagation and transmission in homogeneous media.
The focusing of particles by a thin plasma lens is analyzed with physical, linearized fluid and particle-in-cell computational models. For parameters similar to next-generation linear colliders, the plasma lens strength can exceed 100 MGcm, and the luminosity can be enhanced by an order of magnitude by passing each beam through an appropriate plasma slab. The plasma electrons affect the focusing by shifting so as to (partially or completely) charge neutralize the beam. Both overdense and underdense plasma lenses are described (plasma density n0 greater or less than beam density nb). The former case applies equally well to e+ and e- beams, while the latter has distinct advantages for e- beams (including smaller aberrations and background). The effects of spherical and longitudinal aberrations, emittance, plasma boundaries, and non-linear-plasma dynamics on the final spot size are discussed. © 1990 The American Physical Society
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