Igor Rutkevich

Ray trajectories in an absorbing ionosphere

Abstract The present paper deals with the simulation of electromagnetic ray propagation in a cold collisional ionosphere in the presence of the Earths magnetic field. This subject has been extensively studied in the past. The novel aspect here is our attempt to assess the effect of absorption on the ray trajectories, not merely the field intensity. In addition to the theoretical interest in this problem, practical questions, such as target location by means of Over The Horizon Radar (OTHR) systems, in the presence of high losses, provide the motivation. The analytical investigation of such problems is limited by the complexity of the wave propagation field problem and the physics of the ionosphere, which combine to yield a complex dispersion relation, and the restricted capability of available computers and mathematical software packages for handling the ray tracing model. The present model is based on the familiar Appelton-Hartree, sometimes called the Appelton-Lassen, dispersion equation for the cold, collisional, magnetized ionosphere. The way that the ray tracing is performed (ray tracing being an approximation) and the model chosen by the researcher predetermines the resultant ray trajectories. Thus, in the presence of losses, certain decisions regarding the use of the Hamiltonian ray tracing model have to be made. Unlike some studies which first compute the lossless trajectories, and then add on a posteriori the attenuation along these trajectories, as a perturbation of the lossless solution, here the Hamiltonian ray tracing formalism is extended in order to include the absorption effects in the formalism a priori. For small absorption all models yield more or less the same results; therefore, in the present study high losses are considered in order to emphasize the effects. However, the present study contributes to our understanding of the basic problem of ray propagation in the presence of arbitrary losses. The extended Hamiltonian ray tracing formalism used here assumes complex space, and an additional constraint that guarantees real space and time subspace for the ray trajectories, as well as for the group velocity, whereas the propagation vector and the frequency may be complex. Other formulations for the ray equations formalism exist too. At this time it remains an open problem whether ray trajectories computed by those models will agree with the results obtained here or not. Furthermore, in the absence of sufficient direct ray trajectories empirical data, where high absorption cases are compared to lossless cases, the question as to which model better describes the physical reality must remain open. The variation of the ray paths with frequency, launching angle, collision frequency, electron density profile and other variables, are examined for Chapman type E and F layers. By using typical F layer parameters, it is found that, in certain cases, a high collision frequency affects the ray path by as much as 500 km. This result is important for sub-ionospheric propagation and for target location tracking.

Thermodynamic properties and stability of shock waves in metals

A thermodynamic description of metals in the range of high pressures and temperatures is obtained and applied to the problem of the stability of strong shock waves under spontaneous emission of sound. A three-term form of the equation of state is employed to describe the contributions of the cold elastic pressure, the thermal atomic pressure, and the thermal pressure of the free electrons to the total pressure. The full determination of the equation of state is performed from the experimental Hugoniot data and from a model (such as the Slater–Landau model) connecting the atomic Gruneisen parameter and the atomic cold pressure. From the equation of state, the behavior of the Mach number, the temperature, and the entropy along the Hugoniot adiabatic is obtained and analyzed. The calculation of the sound velocity behind the shock enables the application of the Kontorovich criterion for the spontaneous emission of sound from the shock’s front. It is shown that metals with a relatively low slope of the shock v...

Spontaneous acoustic emission from strong shocks in diatomic gases

The stability properties of strong shock waves in diatomic ideal gases are investigated. Shock instabilities in diatomic gases may play a role in the dynamics of astrophysical molecular clouds, hypersonic flight applications, and inertial confinement schemes. It is shown that the dissociation processes alone do not give rise to shock instabilities. It is further demonstrated that the shock’s front becomes unstable under spontaneous acoustic emission due to the ionization processes and only for those perturbations that are characterized by thermal nonequilibrium between the electrons and the heavy particles (atoms, ions, and molecules). To show that, the classical Dyakov–Kontorovich stability criterion is modified in order to take into account the effects of the perturbed electronic temperature. Numerical calculations for diatomic nitrogen indicate that the spontaneous acoustic instability occurs on the descending portion of the Hugoniot curve in the density–pressure plane. In addition, it is found that th...

Polyurethane in plane impact with velocities from 10 to 400 m/sec

Shock response of the rubber-like polyurethane (PU) samples in the plane impact experiments with the impactors made of the same PU has been studied within the impact velocity range 10–400 m/sec. The experiments were performed with 25-mm pneumatic gun. The free surface velocity of the samples was measured by VISAR. The shock response of PU is not perfectly elastic and this can be connected with a complicated rheology of the material. The non-elastic behavior is well observed with the lowering of the velocity of impactor.

Ray trajectories in an absorptive ionosphere

Simulates EM ray propagation in a cold collisional ionosphere in the presence of the geomagnetic field. A novel aspect is our attempt to assess the effect of absorption on the ray trajectories, not merely the field intensity. The present model is based on the familiar Appelton-Hartree dispersion equation for the cold, collisional, magnetized ionosphere, where slow variation (on the scale of a wavelength) of the terrestrial magnetic field is assumed. Unlike some studies which first compute the lossless trajectories, and then add on a posteriori the attenuation along these trajectories, as a perturbation of the lossless solution, here the Hamiltonian ray tracing formalism is extended in order to include the absorption effects in the formalism a priori. High losses are considered in order to emphasize the effects. The present study contributes to our understanding of the basic problem of ray propagation in the presence of arbitrary losses. The variation of the ray paths with frequency, launching angle, collision frequency, electron density profile and other variables, are examined for the Chapman type F layer. Results for various conditions are displayed. By using typical F layer parameters, it is found that, in certain cases, high collision frequency affects the ray path by as much as 500 km. The paper is motivated by over-the-horizon radar.

Stability of strong shocks in metals

The stability of strong shock waves in metals with respect to spontaneous emission of acoustic and entropy-vortex waves is investigated theoretically. The analysis employs the empirical Hugoniot adiabatic (HA) which is commonly represented as a straight line in the plane (U,D) where U is the particle velocity behind the shock and D is the shock velocity. The criterion for spontaneous emission depends on the sound velocity in a shock-compressed medium which is determined from the three-term equation of state. The latter takes into account contributions of atoms and electrons to the total pressure. The atomic Gruneisen parameter and the cold elastic pressure are calculated from a system of coupled differential equations which is based on the empirical HA and the Slater–Landau approach. It has been found that spontaneous emission may occur in metals with relatively low values of the Hugoniot adiabatic slope S=dD/dU such as molybdenum and tantalum.

Ionization waves in the pre-breakdown phase of a pulsed capillary discharge

We present experimental observations of ionization waves in pulsed hollow cathode capillary discharges. When the capillary shield is at the anode potential, an anode directed ionization wave, with characteristic speed ∼107 m/s, is observed. When the capillary shield is at the cathode potential, a cathode directed slower ionization wave, with characteristic speed ∼104 m/s, is observed. The several orders of magnitude difference in the ionization wave speed can be attributed to the different initial electric field configuration in both polarities.

Wave Packets and Group Velocity in Absorbing Media: Solutions of the Telegrapher's Equation - Abstract

The propagation of high-frequency wave packets and solitary pulses in absorbing media, for which the process of wave propagation is governed by the telegraphers equation, is investigated. The group velocity W for elementary wave solutions of telegraphers equation is real and larger than the speed of light c for real wave numbers exceeding some critical value. The group velocity is real also for purely imaginary wave numbers and in this case W < c. The case W < c appears when the long-time asymptotics of wave packet solutions is considered, while the case W > c appears for finite times and short traveling distances. Both analytical and numerical studies of the evolution of high-frequency wave packets and aperiodic solitary pulses have been performed. This is done by analyzing and calculating the convolution integral representing a causal solution in a half-space. It has been found that the maximum of the wave packets envelope begins to propagate from the boundary with superluminal velocity and after relatively short traveling distances its velocity becomes sublumi- nal. The maximum of a solitary pulse propagates with a subluminal velocity. Numerical calculations demonstrate strong reshaping of a solitary pulse at distances of the order of several absorption lengths. The conjunction of the local group velocity concept and superluminal propagation speeds is to be perceived as kinematical phenomenon closely related to the definitions used and does not imply a falsification of special relativity theory.