Exponentially self-similar impact ionization waves

The existence of generalized self-similar solutions to the system of continuity and Poisson equations is analyzed for the problem of evolution of impact ionization waves (IIWs). It is shown that, for any physically reasonable electric-field dependence of the impact ionization coefficients, there exist only exponentially self-similar (“limiting”) asymptotic solutions. These solutions describe IIWs whose spatial scales and propagation velocities increase exponentially with time. Conditions are found for the existence of plane, cylindrical, and spherical waves of this type; their structure is described; analytical relations between the key parameters are derived; and effects of recombination (or attachment) and tunnel ionization are analyzed. It is shown that these IIWs are intermediate asymptotics of numerical solutions to the corresponding Cauchy problems. The most important and interesting type of exponentially self-similar IIWs are streamers in a uniform electric field. The simplest comprehensive and explicit model describing their evolution is a spherical IIW.     

Transverse instability of line defects of period-2 spiral waves

Spiral waves that arise in period-2 oscillatory media extended in space generically bear "line defects" along which the local kinetics exhibits a period-1 oscillation. Locally, these defect structures can be viewed as a front separating two period-2 oscillatory domains oscillating 2pi out of phase. Here we show that their shape can become sinusoidal with a transverse instability as in bistable fronts. This instability eventually leads to a line-defect filled spatiotemporal chaotic state having erratic proliferations, annihilations, and regenerations of line defects. The same sequence of phenomena is observed in a model reaction-diffusion system as well as in an experimental system.     

Transverse instability of solitary waves in the generalized kadomtsev-petviashvili equation

The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable.     

Transverse magnetic scattering of two incident plane waves by a dielectric coated cylindrical reflector

Scattering characteristics of two plane waves are investigated for a circular cylinder covered by a dielectric substance. Fields are assumed to be transverse magnetic (TM) and represented in an exponential series form. The diffracted radiations are found by applying the boundary conditions to the wave functions. The wave transformation method and the orthogonality of the exponential functions are respectively employed to obtain an infinite series in the solution. Numerical results are evaluated by reducing the infinite series to a finite number of terms and comparing estimates with the single plane wave scattering situation.     

Transverse instability of dunes

The simplest type of dune is the transverse one, which propagates with invariant profile orthogonally to a fixed wind direction. Here we show, by means of numerical simulations, that transverse dunes are unstable with respect to along-axis perturbations in their profile and decay on the bedrock into barchan dunes. Any forcing modulation amplifies exponentially with growth rate determined by the dune turnover time. We estimate the distance covered by a transverse dune before fully decaying into barchans and identify the patterns produced by different types of perturbation.     

Current layers and filaments in a semiconductor model with an impact ionization induced instability

Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.     

Transverse waves in a relativistic rigid body

We present relativistic elasticity as a scalar field theory. We apply it to rigid bodies, i.e., relativistic bodies with a nonlinear elastic law and a definite longitudinal wave velocity _l equal to the light velocity,c. We obtain the transverse wave equation with a definite velocity _t , and the relation between _l , _t , and the Poisson coefficient is the classical one. This is an indication that we have the relativistic extension of a classical Hooke elastic law.     

Transverse coupling of chemical waves

The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.     

Three-body coupling for electron impact ionization of helium in the perpendicular plane geometry

Dynamically screened three-Coulomb-wave (DS3C) model is applied to study single ionization of helium by 102 eV electron impact. Fully differential cross sections (FDCS) are calculated at different scattering angle of (8°, 10°, 15°, 20°) in the perpendicular plane asymmetric geometry. The results are compared with experimental data and theoretical predictions from a three-Coulomb wave function (3C) approach, convergent close-coupling calculation (CCC), as well as second-order distorted-wave Born method (DWB2). It is shown that three-body coupling effects are important for the perpendicular plane geometry.     

Transverse instability of magnetized electron holes

We study a transverse instability of the nonlinear equilibria known as electron phase-space holes in the presence of a magnetic field. The instability is intrinsically two dimensional and is determined by the dynamics of the trapped electrons. It depends on hole amplitudes, ambient magnetic fields, and the perpendicular velocity spread. The long-standing hole stability problem in multiple dimensions can be characterized by the gyro-to-bounce frequency ratio. A low ratio associated with a small perpendicular velocity spread results in a disintegration of the positive potential spikes.     

Imaging a tunneling ionization front by using a schlieren method

A schlieren method was used to generate time-resolved images of the tunneling ionization front produced when an ultrashort high-power laser pulse irradiates He gas. By superimposing sequential schlieren images, we obtained information about the laser propagation and found that the ionization front propagated farther with decreasing density of the target gas. Ray-tracing suggested that this density dependence is a result of the spatial distribution of the laser intensity. Received: 20 May 1999 / Revised version: 19 August 1999 / Published online: 27 January 2000     

Effect of diffusion on the velocity of stationary impact ionization waves in semiconductors

The known theory of stationary plane impact ionization waves in gases [U. Ebert et al., Phys. Rev. E 55, 1530 (1997)] has been generalized to the bipolar case characteristic of semiconductors, where a medium is ionized by hot charge carriers of both signs. In this case, the velocity u of bipolar waves (in contrast to monopolar waves) is determined by the processes in the leading region of the front at any nonzero impact ionization rates and for any propagation directions. This property makes it possible to derive analytical formulas for u as a function of material parameters, initial perturbation, and external field strength by analyzing a boundary value problem linearized near an unstable state. In the highest achievable fields (e.g., in streamers), diffusion must give rise to an increase in u by a factor of about 3 as compared to the average drift velocity at typical parameters of semiconductors.     

Electromagnetic waves in a plane wave background

Source-free Maxwell equations are equivalent to the scalar wave equation. Most of its solutions are singular at infinity. If the nail eigenvector of the background metric is an eigenvector of the Maxwell field, too, the e.m. field is not changed by the plane wave.     

Small-scale instability of a pulse front traversing a resonant saturable absorber

Wave front of a light pulse is shown to be unstable as it propagates through a resonant saturable absorber, if its frequency is higher than the resonance frequency of the absorber. When ΔωT ₂∼1, a small-scale transverse instability with the dimension of (λl _abs)^1/2 grows rapidly. Its growth-rate is of the order of the small-signal-absorption length of the medium.     

Scattering of plane waves on a nonstationary potential

We study scattering of plane waves on a nonstationary potential. The nonstationary potential is considered as either a rectangular well with constant depth or a rectangular barrier with constant height, both with the transverse dimension increasing linearly. We obtain the dependences of the final momenta of the wave as functions of the initial ones.