ELECTROMAGNETIC FIELDS IN A CYLINDRICAL INDUCTOR SYSTEM WITH AN EXTERNAL COAXIAL BIFILARY SOLENOID

Purpose. Bifilar structures are widely used in modern electrical devices for various purposes. The specific interest is the using of inductor systems with external bifilar coils in the elements of modern metalworking equipment. In particular, it is very important to study the possibility of using such devices as elements of equipment for magnetic-pulse processing of metals. The aim of this research is a derivation of design expressions for theoretical analysis and numerical estimates of the characteristics of electromagnetic processes in a cylindrical inductor system. The case when the inductor is located inside a coaxial solenoid, the winding of which is made in the form of a bifilar with oppositely directed currents is considered. Methodology. Maxwell’s equations with appropriate boundary conditions and Laplace transforms are used to solve this problem. This made it possible to determine the expression for the z-th component of the magnetic field intensity excited in the considered inductor system. Results. It was found that the excited magnetic fluxes are subtracted outside the bifilar coil windings, which leads to a decrease in the resulting field compared to the magnetic field of each of the currents separately. Thus, it is possible to reduce the inductance of the coil as an element of the electrical circuit. It is shown that the formulas obtained for the fields and currents remain valid for the case of unidirectional currents when the sign of the corresponding algebraic term changes. Numerical estimates for the experimental model of the inductor system showed that the induced current as a percentage of the value of the exciting current does not exceed ~ 6.3 %. Originality. The novelty of this work lies in proposing the idea of constructive execution of the inductor system itself, as well as in considering its physical and mathematical model and obtaining calculated expressions for analyzing the ongoing electromagnetic processes with numerical estimates of the characteristics of the excited fields. Practical value. The obtained time dependences for voltages and currents induced in the bifilar winding are applicable depending on the design conditions for various specific designs of the inductor system

Active sonic boom control

A theory and simulation code are developed to study non-steady sources as means to control sonic booms of supersonic aircraft. A key result is that the source of sonic boom pressure is not confined to the length of the aircraft but occupies an extensive segment of the flight path. An aircraft in non-steady flight functions as a synthetic aperture antenna, generating complex acoustic waves with no simple relation to instantaneous volume or lift distributions.The theory applies linear acoustics to slender non-steady sources but requires no far-field approximation. The solution for pressure contains a term not seen in Whitham's theory for sonic booms of distant supersonic aircraft. The term describes a pressure field that decays algebraically behind the Mach cone and, in the case of steady flight, integrates to a ground load equal to the weight of the aircraft. The algebraic term is separate from those that describe the sonic boom.Two non-steady source phenomena are evaluated: periodic velocity changes (surge), and periodic longitudinal lift redistribution (slosh). Surge can attenuate a sonic boom and covert it into prolonged weak reverberation, but accelerations needed to produce the phenomenon seem too large for practical use. Slosh may be practical and can alter sonic booms but does not, on average, result in boom attenuation. The conclusion is that active sonic boom abatement is possible in theory but maybe not practical.

On Monte Carlo algebra

A Monte Carlo method is proposed and demonstrated for obtaining an approximate algebraic solution to linear equations with algebraic coefficients arising from first order master equations at steady state. Exact solutions are hypothetically obtainable from the spanning trees of an associated graph, each tree contributing an algebraic term. The number of trees can be enormous. However, because of a high degeneracy, many trees yield the same algebraic term. Thus an approximate algebraic solution may be obtained by taking a Monte Carlo sampling of the trees, which yields an estimate of the frequency of each algebraic term. The accuracy of such solutions is discussed and algorithms are given for picking spanning trees of a graph with uniform probability. The argument is developed in terms of a lattice model for membrane transport, but should be generally applicable to problems in unimolecular kinetics and network analysis. The solution of partition functions and multivariable problems by analogous methods is discussed.

On Monte Carlo algebra

A Monte Carlo method is proposed and demonstrated for obtaining an approximate algebraic solution to linear equations with algebraic coefficients arising from first order master equations at steady state. Exact solutions are hypothetically obtainable from the spanning trees of an associated graph, each tree contributing an algebraic term. The number of trees can be enormous. However, because of a high degeneracy, many trees yield the same algebraic term. Thus an approximate algebraic solution may be obtained by taking a Monte Carlo sampling of the trees, which yields an estimate of the frequency of each algebraic term. The accuracy of such solutions is discussed and algorithms are given for picking spanning trees of a graph with uniform probability. The argument is developed in terms of a lattice model for membrane transport, but should be generally applicable to problems in unimolecular kinetics and network analysis. The solution of partition functions and multivariable problems by analogous methods is discussed.