Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. II. Energetic Analysis of Certain Types of Monoenergetic Beam-Plasma Interactions Based on the Čerenkov Resonance Condition

The energy and momentum balance equations for a potential wave in a monoenergetic electron beam-plasma system are considered in the linear approximation, when the wave is in ?erenkov resonance with the beam particles. An energetic analysis of certain types of beam-plasma instabilities is given. It is shown that the energy and momentum balance equations are consistent with the dispersion relation for all unstable waves. From this fact follows that the energy and momentum densities of all linear unstable waves in reactive beam-plasma systems are equal to zero. An interpretation and a possible classification of beam-plasma instabilities are given.     

On shock waves and phase-transition fronts in continua

A R I - The canonical formalism that considers simultaneously the second law of thermodynamics and the balance of canonical momentum is used to incorporate the case of shock waves among those...     

Reversal of momentum relaxation

A new phenomenon of momentum relaxation reversal has been discovered experimentally and explained theoretically for dipolar spin waves in magnetic garnet films. It is shown that the process of momentum relaxation, caused by the scattering of a signal wave on defects, can be reversed, and the signal can be restituted after it left the scattering region. The reversal of momentum relaxation is achieved by frequency-selective parametric amplification of a narrow band of scattered waves having low group velocities and frequencies close to the frequency of the original signal wave. The phenomenon can be used for the development of a new type of active microwave delay lines.     

Parallel velocity shear driven electrostatic waves in a very dense nonuniform magnetoplasma

It is shown that the parallel (magnetic field-aligned) velocity shear can drive the low-frequency (in comparison with the ion gyrofrequency) electrostatic (LF-ES) waves in an ultracold super-dense nonuniform magnetoplasma. By using an electron density response arising from the balance between the electrostatic and quantum Bohm forces, as well as the ion density response deduced from the continuity and momentum equations, a wave equation for the LF-ES waves is derived. In the local approximation, a new dispersion relation is obtained by Fourier transforming the wave equation. The dispersion relation reveals an oscillatory instability of dispersive drift-like modes in super-dense quantum magnetoplasmas.     

Energy and angular momentum transfers from an electromagnetic wave to a copper ring in the UHF band

Electromagnetic waves could carry orbital angular momentum. Such momentum can be transferred to macroscopic objects and can make them rotate under a constant torque. Based on experimental observations, we investigate the origin of orbital angular momentum and energy transfer. Due to angular momentum and energy conservation, we show that angular momentum transfer is due to the change in the sign of angular momentum upon reflection. This leads to a rotational Doppler shift of the electromagnetic wave frequency, ensuring energy conservation.     

Bifurcation and stability of dynamical structures at a current instability

We investigate bifurcation and stability of nonuniform current states at a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The system is described by balance equations for momentum and energy densities of the carriers. These transport fields are coupled to Maxwell's equations. The uniform stationary current state is unstable against long-wavelength dielectric relaxation modes at a critical field. We find that the softening of these modes gives rise to a family of periodic travelling waves and to a solitary solution (dipole domain). We show that the periodic travelling waves are unstable, wheras the dipole domain can be stabilized by coupling the sample to a suitable external circuit, if the static impedance of the sample in the domain state is negative. The model describes therefore a discontinuous nonequilibrium transition to a large amplitude domain state.Work Supported by the Swiss National Science Foundation     

Momentum transfer in crystal lattices with vibrating atoms

A momentum transfer equation previously used to describe non-elastic deformation in crystalline solids represented by point masses at fixed lattice positions is extended to take into account the existence of intrinsic (e.g. thermal) small amplitude vibrations of the masses about their mean positions in a lattice. Use of the time-dependent Schroedinger equation to describe momentum transfer and deformation is also discussed in terms of this vibrating point-mass lattice model. The result is that a modified and identical differential equation for momentum transfer is obtained from each approach; some solutions to this equation are presented. The previous particle momentum wave frequency dependence on wave vector and resulting applications to non-elastic deformation are unchanged, but these particle momentum waves can now be considered as modulating the usual high-frequency waves associated with the elastic modes of a crystalline solid.     

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.     

Quadrupole test particle as a detector of gravitational waves

In this paper it is shown that in general relativity the theory of motion of quadrupole test particles (QTP's) can be used to describe the energy and angular momentum absorption by detectors of gravitational waves. By specifying the form of the quadrupole moment tensor Taub's [7] equations of motion of QTP's are simplified. In these equations the terms describing the change of the mass and of the angular momentum of a QTP due to external gravitational waves are found to occur. The limiting case of the flat space-time is also briefly discussed.     

Nonlinearly controlled angular momentum of soliton clusters

We demonstrate an original approach, to the best of our knowledge, to acquire nonlinear control over the angular momentum of a cluster of solitary waves. We show that the angular momentum can be adjusted by acting on the global excitation of the system. The effect is verified in liquid crystals by observing power-dependent rotation of a two-soliton cluster.     

Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.     

Theoretical Study of Deflection of Reflected and Refracted Electromagnetic Waves from Incident Plane

An equation for the orbital angular momentum of electromagnetic waves in the process of reflection and refraction is deduced from the generalized variational principle, which shows the transverse shift of reflected and refracted waves and predicts that the deflection of reflected and refracted waves from the incident plane can occur.     

A comparison of generalized hybrid Monte Carlo methods with and without momentum flip

The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.     

Dirac Particle in an Aharonov-Bohm Potential: The Structure of the First Order S-matrix

The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order components (eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number.     

Radiation force on multilayer media

It is shown that the force exerted by plane electromagnetic waves on multilayer media can be evaluated in terms of the changes in momentum flow that take place at the planes of discontinuity. The expression obtained is relevant to radiation pressure experiments.     

Elastic scattering loss of atoms from colliding bose-einstein condensate wave packets

Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.     

Dynamics of solitary wave scattering in the Fermi-Pasta-Ulam model

In this Letter, we study the scattering dynamics of a pair of solitary waves in the Fermi-Pasta-Ulam model with interaction potential V(x)=alphax(2)/2+x(4)/4 and establish a quantitative connection between the scattering property and the energy transport behavior. The energy and momentum conservation laws are obtained and the scattering rates of solitary waves are calculated. Our studies suggest that the anharmonic limit model with alpha=0 can be taken as a paradigm model for studying lattice solitary waves.     

Classical probability waves

Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, described by the probability density and the generating function of the Hamilton-Jacobi theory. It is shown that by introducing a minimum distance in the coordinate space, the action distributions aquire the phase-space dispersion specific to the quantum objects. At finite temperature, probability density waves propagating with the sound velocity can arise as nonstationary solutions of the classical Fokker-Planck equation. The results suggest that in a system of quantum Brownian particles, a transition from complex to real probability waves could be observed.     

Optical and sound helical structures in a Mandelstam-Brillouin mirror

It is shown theoretically that the phase conjugation of a speckle optical field in a Mandelstam-Brillouin mirror is accompanied by the excitation of helical hypersonic waves with a step equal to one-half of the optical wavelength. The excitation of these waves violates the initial isotropy of the dielectric medium. The predicted effect admits clear physical interpretation based on the angular momentum conservation. The angular momentum transfer from the light to the medium occurs in the vicinity of an optical singularity (optical vortex line) due to reversal of the light orbital angular momentum by the phase-conjugation mirror. The excitation of hypersonic waves transferring the angular momentum is the necessary condition for the reversal of the angular momentum of the reflected light.