Edward Liverts

Present status of theoretical modeling the magnetoelectric effect in magnetostrictive-piezoelectric nanostructures. Part I: Low frequency and electromechanical resonance ranges

Mechanical deformations of a magnetostrictive-piezoelectric bilayer result in the interaction between the magnetic and electric subsystems. This review reports the models for describing the distinctive features of magnetoelectric (ME) interactions in ferrite-piezoelectric nanostructures at low-frequencies and in electromechanical resonance region. Expressions for ME coefficients are obtained using the solution of elastostatic/elastodynamic and electrostatic and magnetostatic equations. The ME voltage coefficients are estimated from known material parameters. The models take into account the clamping effect of substrate, flexural deformations, and the contribution of lattice mismatch between composite phases and substrate to ME coupling. Lattice mismatch effect has been taken into account by using the classical Landau–Ginsburg–Devonshire phenomenological thermodynamic theory. For a nickel ferrite-lead zirconate titanate nanobilayer on SrTiO3 substrates, the strength of low-frequency ME interactions is show...

Present status of theoretical modeling the magnetoelectric effect in magnetostrictive-piezoelectric nanostructures. Part II: Magnetic and magnetoacoustic resonance ranges

We presented here the theoretical analysis of high frequency magnetoelectric (ME) effects for a ferrite-piezoelectric bilayer and a detailed treatment for electric field induced resonance field shift for ferromagnetic resonance (FMR) in layered structures. ME effects in a single-crystal ferrite-piezoelectric bilayer in the magnetoelastic resonance region are considered. The theory predicts a giant ME effect at magnetoacoustic resonance. The enhancement in ME effect predicted by our theory arises from interaction between elastic modes and the uniform precession mode, resulting in magnetoelastic modes. The peak ME voltage coefficient appears at the coincidence of acoustic resonance and FMR frequencies. In our calculations, we suppose that the layer thickness is sufficiently large to neglect the influence of strain relaxation on average stresses in the structures that determine the ME voltage coefficient. The work presented here will certainly be of interest for the design and analysis of electrically contro...

Demagnetizing factors for two parallel ferromagnetic plates and their applications to magnetoelectric laminated sensors

An analytical expression is derived to approximate the magnetometric demagnetizing factors for two parallel ferromagnetic plates having the shape of rectangular prisms. The magnetometric demagnetizing factors relate the average magnetic fields within the plates’ volumes to an external magnetic field. Knowing this relationship is essential for describing the response of magnetoelectric sensors comprising two parallel magnetostrictive plates. It is shown that two separate ferromagnetic layers provide better field sensitivity than a single layer with a doubled thickness. The obtained results are in a good agreement with numerical calculations and experimental data.

Integration of the electronics and batteries inside the hollow core of a search coil

A novel design of a miniature search coil magnetometer is proposed based on the integration of the electronics and batteries within the hollow core of the search coil. In contrast with conventional designs, where the search coil and its electronics have individual housings and electrostatic shields, this paper presents a design in which the core of the search coil serves both as the housing and the magnetic shield for the electronics and batteries. Moreover, the electrostatic shield of the search coil also shields the electronics and batteries. We found that a thin-wall tube core with sufficient permeability is able to replace a solid rod core without decreasing the average flux sensed by the coil winding. In addition, the outer diameter of the tube core can be increased beyond its optimum size to provide more space for the electronics and batteries without considerably affecting the search coil resolution. To validate the effectiveness of this new design, a miniature search coil magnetometer was built an...

Hall Instability of Thin Weakly Ionized Stratified Keplerian Disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio . The leading order of the asymptotic expansions in is applied to both equilibrium and perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial perturbations and unstable to vertical short-wave perturbations. The marginal stability surface was found in the space of the local Hall and inverse plasma-β parameters, as well as the free parameter of the model related to the total current. To estimate the minimal values of the equilibrium magnetic field that leads to the instability, it was constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by the distributed electric current.

The Hall instability in accelerated plasma channels

The Hall instability of a perfectly conducting plasma is studied. The two-dimensional magnetohydrodynamic equations for systems with large Larmor radius for a two-fluid model in which the Hall term is taken into account in Faraday’s law, are investigated. By using a linearized theory it is shown, that the plasma may become unstable under small perturbations. This instability is driven by the plasma acceleration in channel. The most unstable perturbations propagate in the direction where the wave vector is orthogonal to the magnetic field.

Evolution of initially localized perturbations in stratified ionized discs

A detailed solution of an initial value problem of a vertically localized initial perturbation in rotating magnetized vertically stratifled disk is presented. The appropriate linearized MHD equations are solved by employing the WKB approximation and the results are verifled numerically. The eigenfrequencies as well as eigenfunctions are explicitly obtained. It is demonstrated that the initial perturbation remains conflned within the disk. It is further shown that thin enough disks are stable but as their thickness grows increasing number of unstable modes participate in the solution of the initial value problem. However it is demonstrated that due to the localization of the initial perturbation the growth time of the instability is signiflcantly longer than the calculated inverse growth rate of the individual unstable eigenfunctions.

ANGULAR MOMENTUM TRANSPORT IN ASTROPHYSICAL DISKS

The evolution of astrophysical disks is dominated by instabilities of gravity perturbations (e.g., those produced by a spontaneous disturbance). We develop a hydrodynamic theory of nonresonant Jeans instability in a dynamically cold subsystem (identified as the gaseous component) of a disk. We show analytically that gravitationally unstable systems, such as disks of rotationally supported galaxies, protoplanetary disks, and, finally, the solar nebula are efficient at transporting mass and angular momentum: already on a timescale of on the order of 2-3 rotational periods an unstable disk sees a large portion of its angular momentum transferred outward, and mass transferred both inward and outward.

Nondissipative saturation of the magnetorotational instability in thin disks.

A new nondissipative mechanism is proposed for the saturation of the axisymmetric magnetorotational (MRI) instability in thin Keplerian disks that are subject to an axial magnetic field. That mechanism relies on the energy transfer from the MRI to stable magnetosonic waves. Such mode interaction is enabled due to the vertical stratification of the disk that results in the discretization of its MRI spectrum, as well as by applying the appropriate boundary conditions. A second order Duffing-like amplitude equation for the initially unstable MRI modes is derived. The solutions of that equation exhibit bursty nonlinear oscillations with a constant amplitude that signifies the saturation level of the MRI. Those results are verified by a direct numerical solution of the full nonlinear reduced set of thin disk magnetohydrodynamics equations.

The Hall Instability of Weakly Ionized, Radially Stratified, Rotating Disks

Cool weakly ionized gaseous rotating disks are considered by many models to be the origin of the evolution of protoplanetary clouds. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Thus, a hierarchy of successive fragmentations into smaller and smaller pieces as a part of the Kant-Laplace theory of formation of the planetary system remains valid also for contemporary cosmogony. Traditionally, axisymmetric magnetohydrodynamic (MHD) and, recently, Hall-MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum and of radial density stratification. In the current work, the Hall instability against nonaxisymmetric perturbations in compressible rotating fluid in external magnetic field is proposed as a viable mechanism for the azimuthal fragmentation of the protoplanetary disk and, thus, perhaps initiates the road to planet formation. The Hall instability is excited due to the combined effect of the radial stratification of the disk and the Hall electric field, and its growth rate is of the order of the rotation period. This family of instabilities is introduced here for the first time in an astrophysical context.