Millimeter-Wave Beam Scattering by Field-Aligned Blobs in Simple Magnetized Toroidal Plasmas.

The first direct experimental measurements of the scattering of a millimeter-wave beam by plasma blobs in a simple magnetized torus are reported. The wavelength of the beam is comparable to the characteristic size of the blob. In situ Langmuir probe measurements show that fluctuations of the electron density induce correlated fluctuations of the transmitted power. A first-principles full-wave model, using conditionally sampled 2D electron density profiles, predicts fluctuations of the millimeter-wave power that are in agreement with experiments.

Interaction of charged particles with localized electrostatic waves in a magnetized plasma.

Charged particle interaction with localized wave packets in a magnetic field is formulated using the canonical perturbation theory and the Lie transform theory. An electrostatic wave packet characterized by a wide range of group and phase velocities as well as spatial extent along and across the magnetic field is considered. The averaged changes in the momentum along the magnetic field, the angular momentum, and the guiding center position for an ensemble of particles due to their interaction with the wave packet are determined analytically. Both resonant and ponderomotive effects are included. For the case of a Gaussian wave packet, closed-form expressions include the dependency of the ensemble averaged particle momenta and guiding center position variations on wave packet parameters and particle initial conditions. These expressions elucidate the physics of the interaction which is markedly different from the well known case of particle interaction with plane waves and are relevant to a variety of applications ranging from space and astrophysical plasmas to laboratory and fusion plasmas, as well as accelerators and microwave devices.

Breathers in a nonautonomous Toda lattice with pulsating coupling.

We study a nonautonomous Toda lattice, with a periodically switched on-off coupling coefficient, describing a pulsating strength of neighbor particle interaction. It is shown that when the uncoupled oscillations are linear and under appropriate conditions for the duration of the time intervals where the coupling is switched off, breather solutions can be obtained analytically. Their dynamics and collisions are related to the soliton dynamics of the corresponding autonomous Toda lattice, while a "ratchet" effect is shown to result in breather deceleration, providing a mechanism for breather velocity and collision control.

Kinetic theory for distribution functions of wave-particle interactions in plasmas.

The evolution of a charged particle distribution function under the influence of coherent electromagnetic waves in a plasma is determined from kinetic theory. For coherent waves, the dynamical phase space of particles is an inhomogeneous mix of chaotic and regular orbits. The persistence of long time correlations between the particle motion and the phase of the waves invalidates any simplifying Markovian or statistical assumptions--the basis for usual quasilinear theories. The generalized formalism in this Letter leads to a hierarchy of evolution equations for the reduced distribution function. The evolution operators, in contrast to the quasilinear theories, are time dependent and nonsingular and include the rich phase space dynamics of particles interacting with coherent waves.

Universal probability distribution function for bursty transport in plasma turbulence.

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.

Power-dependent reflection, transmission, and trapping dynamics of lattice solitons at interfaces.

Surface soliton formation and lattice soliton dynamics at an interface between two inhomogeneous periodic media are studied in terms of an effective particle approach. The global reflection, transmission, and trapping characteristics are obtained in direct analogy to linear Snell's laws for homogeneous media. Interesting dynamics related to soliton power-dependent formation of potential barriers and wells suggest a spatial filtering functionality of the respective structures.

Power dependent soliton location and stability in complex photonic structures.

The presence of spatial inhomogeneity in a nonlinear medium results in the breaking of the translational invariance of the underlying propagation equation. As a result traveling wave soliton solutions do not exist in general for such systems, while stationary solitons are located in fixed positions with respect to the inhomogeneous spatial structure. In simple photonic structures with monochromatic modulation of the linear refractive index, soliton position and stability do not depend on the characteristics of the soliton such as power, width and propagation constant. In this work, we show that for more complex photonic structures where either one of the refractive indices (linear or nonlinear) is modulated by more than one wavenumbers, or both of them are modulated, soliton position and stability depends strongly on its characteristics. The latter results in additional functionality related to soliton discrimination in such structures. The respective power (or width/propagation constant) dependent bifurcations are studied in terms of a Melnikov-type theory. The latter is used for the determination of the specific positions, with respect to the spatial structure, where solitons can be located. A wide variety of cases are studied, including solitons in periodic and quasiperiodic lattices where both the linear and the nonlinear refractive index are spatially modulated. The investigation of a wide variety of inhomogeneities provides physical insight for the design of a spatial structure and the control of the position and stability of a localized wave.

Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model.

A novel method for obtaining analytical solitary wave solutions of the nonlinear Kronig-Penney model in periodic photonic structures with self-defocusing nonlinearity is applied for providing generic families of solutions corresponding to the gaps of the linear band structure. Characteristic cases are shown to be quite robust under propagation.

Transient dynamics of charged particles interacting with localized waves of continuous spectra.

A modified canonical perturbation method is employed for analyzing the charged particle dynamics as they interact with localized waves with continuous spectrum. In contrast with periodic Hamiltonian models, where the method has already been applied in a multitude of respective systems, the system in hand is inherently aperiodic. The localized waves have the form of amplitude modulated electrostatic fields, ranging from ordinary wave packets to ultrashort pulses. The analytically obtained approximate invariants of the motion contain rich information for the structure of the phase space and the respective distribution functions.

Multichannel pulse dynamics in a stabilized Ginzburg-Landau system.

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasielastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasielastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semiquantitative agreement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasielastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed transmission system.

Stabilization of dark solitons in the cubic ginzburg-landau equation

The existence and stability of exact continuous-wave and dark-soliton solutions to a system consisting of the cubic complex Ginzburg-Landau (CGL) equation linearly coupled with a linear dissipative equation is studied. We demonstrate the existence of vast regions in the system's parameter space associated with stable dark-soliton solutions, having the form of the Nozaki-Bekki envelope holes, in contrast to the case of the conventional CGL equation, where they are unstable. In the case when the dark soliton is unstable, two different types of instability are identified. The proposed stabilized model may be realized in terms of a dual-core nonlinear optical fiber, with one core active and one passive.

Dissipative solitons under the action of the third-order dispersion.

We study the evolution of a solitary pulse in the cubic complex Ginzburg-Landau equation, including the third-order dispersion (TOD) as a small perturbation. We develop analytical approximations, which yield a TOD-induced velocity c of the pulse as a function of the ratio D of the second-order dispersion and filtering coefficients. The analytical predictions show agreement with the direct numerical simulations for two distinct intervals of D. A new feature of the pulse motion, which is a precursor of the transition to blowup, is presented: The pulse suddenly acquires a large acceleration in the reverse direction at D>D(cr) approximately -1.5 and without the reversal at D