Short-wavelength Approximations Research Articles

Evanescent escape from the dielectric ellipse

The evanescent wave outside a whispering gallery mode of an elliptic dielectric cavity is described using the extension to complex phase space of the underlying family of rays. Evanescent waves outside dielectric cavities supporting whispering gallery modes are of practical importance in applications such as microlasers, wavelength filters and sensors. The elliptical case is interesting because it shares key topological features with generically deformed nonintegrable resonators but allows all the required ray data to be computed explicitly. This is in contrast to generic perturbations where natural boundaries can prevent direct computation of the required ray data for arbitrarily small deformations. It is found that while natural boundaries do intervene in the elliptical case, they do so at higher order in the short-wavelength approximations and only for sufficiently large deformations. Before natural boundaries intervene, complex WKB methods provide a good description of emission patterns.

Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom

In this review we summarize and amplify recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short-wavelength, semiclassical limit. Focusing on the correspondence between quantum and classical physics, we mathematically formulate and attempt to answer three fundamental questions. (i) How can one drive a small dynamical quantum system to behave classically? (ii) What determines the rate at which two single-particle quantum-mechanical subsystems become entangled when they interact? (iii) How does irreversibility occur in quantum systems with few degrees of freedom? These three questions are posed in the context of the quantum-classical correspondence for dynamical systems with few degrees of freedom, and we accordingly rely on two short-wavelength approximations to quantum mechanics to answer them: the trajectory-based semiclassical approach on the one hand, and random matrix theory on the other hand. We construct novel investigative procedures towards decoherence an...

Kink oscillations in magnetic tubes with twisted annulus

Aims. We study kink waves in a magnetic flux tube modelled as a straight core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field, and derive the dispersion relation for this configuration. Methods. The existence and behaviour of the kink modes are examined with specific attention to the effect that the addition of magnetic twist has on phase speeds and periods. Analytic expansions to the short and long wavelength approximations are also considered. Results. The magnetic twist is found to introduce of an infinite set of body modes into solutions of the dispersion relation not present in the untwisted case. Moreover, for the kink modes, the width of interval of this infinite set, generally found to occupy phase speeds around the annulus' longitudinal Alfven speed, increases for longer wavelengths. Two surface modes are also present in the solution, one at each surface: the internal and the external edges of the annulus. The magnetic twist is found to increase or decrease the phase speeds of these surface modes that are depending on the ratio of internal and external Alfven speeds in the flux tube. Conclusions. The magnetic twist of the annulus region of a flux tube is found to have a marked effect on the phase speeds of occurring modes. A straight annulus layer increased (or decreased) the periods of the surface modes for a tube modelled as a density (magnetic) enhancement. The addition of twist reduces the periods of the modes in both cases.

Sausage and kink oscillations in incompressible annular magnetic cylinders

Aims. The propagation of MHD waves in a structured magnetic flux tube embedded within a straight magnetic environment is studied analytically. The motivation for this analysis comes from the observations of damped loop oscillations indicating the possibility that only part of the loop is homogeneous in the radial direction and from the observation of two simultaneous waves with different speeds in the same magnetic loop in the solar atmosphere. Methods. The general dispersion relation of longitudinal wave propagation is derived for a flux tube configuration consisting of a core, annulus and external region each with straight distinct magnetic field. Modes of oscillation are examined from the general dispersion relation that is suitable for obtaining information not just on oscillations but also on some instability properties of this complex tube structure. Specific attention is given to the modification of the phase speeds and oscillation periods caused by the annulus structure, compared to a single monolithic tube. Results. It is shown that two purely surface modes arise. The relative change in periods due to the additional annulus layer is shown to be rather significant (up to 20% in some cases). In particular we found that in photospheric type annular tubes, periods are less than their counterparts in a monolithic loop while for a dense flux tube in the majority of cases the period was greater than the period of the counterpart monolithic flux tube. Both short and long wavelength approximations are considered for both the symmetrical (sausage) and kink modes. Conclusions. Annular structuring of a magnetic flux tube will reduce or increase periods of the allowed oscillations depending on the type of flux tube considered (either as a magnetic or as a density enhancement). The results are relevant to further our knowledge of solar magneto-seismology. In particular, the obtained results for the kink oscillations may be applicable from photosphere to corona, while the case for the sausage mode is more relevant in the lower part of the solar atmosphere.

Structure and Stability of Phase Transition Layers in the Interstellar Medium

We analyze the structure and stability of the transition layer (or front) that connects the cold neutral medium and warm neutral medium in the plane-parallel geometry. Such fronts appear in recent numerical simulations of a thermally bistable interstellar medium. The front becomes an evaporation or condensation front depending on the surrounding pressure. The stability analysis is performed in both long- and short-wavelength approximations. We find that the plane-parallel evaporation front is unstable under corrugational deformations, whereas the condensation front seems to be stable. The instability is analogous to the Darrieus-Landau instability in combustion front. The growth rate of the instability is proportional to the speed of the evaporation flow and the corrugation wavenumber for modes with wavelength much longer than the thickness of the front, and it is suppressed at scales approximately equal to the thickness of the front. The timescale of the instability is smaller than the cooling timescale of the warm neutral medium ($\sim 1$ Myr), and can be as small as the cooling timescale of the cold neutral medium ($\sim 0.01-0.1$ Myr). Thus, this instability should be one of the processes for driving the interstellar turbulence.

Sausage MHD Waves in Incompressible Flux Tubes with Twisted Magnetic Fields

Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general. This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts.

Wave propagation in incompressible MHD wave guides: the twisted magnetic Annulus

The propagation of MHD waves in a structured magnetic flux tube embedded within a straight vertical magnetic environment is studied analytically. The motivation of this analysis comes from the observations of damped loop oscillations showing that possibly only part of the loop is homogeneous in the radial direction. The general dispersion relation of longitudinal wave propagation is derived for a fully magnetically twisted configuration consisting of a core, annulus and external region each with magnetic field of uniform, yet distinct, twist. Next, a simplified case representing coronal loops is analysed in detail considering magnetic twist just in the annulus, the internal and external regions having straight magnetic field. Modes of oscillations are examined from the general dispersion relation that is suitable for obtaining information on not just oscillations but also on some instability properties of this complex tube structure. It is shown that there are purely surface (i.e. evanescent) and hybrid (spatially oscillatory in the twisted annulus, otherwise evanescent) modes. Except for small wavenumbers, the surface waves show little dispersion; a property making them more suitable for observations. The hybrid modes show a more complex character. Though the frequency range seems to be rather limited, there is a continuum band of frequencies for a given wavenumber. Both short and long wavelength approximations are considered for the symmetrical (sausage) mode and with small twist in particular.

Features of the nonlinear dynamics of domain walls in ferrimagnets

The nonlinear motion of a 180° domain wall with two inequivalent sublattices in the field of a sound wave propagating orthogonally to the plane of the domain wall is investigated. The dependence of the drift velocity of the domain wall on the polarization and the parameters of the sound wave is found. An analysis of the long-wavelength and short-wavelength approximations is carried out. The conditions for drift of the stripe domain structure in ferrites are determined.

On the instability of plane liquid sheets in two gas streams of unequal velocities

This paper reports a linear stability analysis of plane liquid sheets in gas streams of unequal velocities. It is found that there exist two independent unstable modes, named herein as para-sinuous and para-varicose. They resemble, but certainly differ from, the well-known sinuous and varicose modes found for equal gas velocities. The gas velocity difference may increase or decrease the growth rate for the para-varicose mode, and for the para-sinuous mode at high Weber numbers. At Weber numbers slightly larger and less than unity, gas velocity enhances significantly the degree of instability for the para-sinuous mode. For the practical interest of large Weber numbers such as related to liquid atomization, the para-sinuous mode is always more unstable. Liquid viscosity has complicated dual effects on the instability, and surface tension is always stabilizing. Long and short wavelength approximations indicate that instability is due to the velocity jump across the two liquid-gas interfaces and from one gas stream to the other, hence is related to the classical Kelvin-Helmholtz instability, and from the disturbance energy equation that the mechanism of instability is due to the interfacial pressure fluctuations.

Barrier penetration in the presence of coupling to intrinsic degrees of freedom

The barrier-penetration problem in the presence of couplings to intrinsic degrees of freedom is discussed in a framework suitable for describing heavy-ion fusion reactions. The inward-outward integration formulation with an ingoing-wave boundary condition leads to an efficient algorithm for numerical calculations. Short-wavelength approximations are introduced to obtain semi-quantal equations. These are used to derive the leading-order effects of the coupling on the barrier-penetration probability for the general case and to solve a coupled-harmonic-oscillator problem to all orders. The characteristic enhancement of the penetration due to the coupling in the barrier region and the interference between the inside and outside regions are discussed.

Ray method for scattering by small discontinuities in a waveguide

As an improvement on the conventional induced-dipolemoment calculation, a ray-optical method is advocated which provides for obstacle-wall interaction and is not invalidated by short-wavelength approximations. Possible applications to other propagation problems are listed.