Closed Electrical Transmission Line As A Ring Waveguide For Interacting Waves of Electron and Phonon Currents - Closed Electrical Transmission Line As A Ring Waveguide For Interacting Waves of Electron and Phonon Currents - Open Access Pub

As a result of mathematical modeling it has been shown that any closed electrical line can be interpreted as a ring waveguide where the Fermi-Pasta-Ulam recurrences of the electron and phonon currents interact with each other on the transversal and longitudinal periodical structures of the line conductor’s crystalline lattice as well as on the structures of the wire insulation. An electronic circuit simulating the mathematical model through the dynamics of magnons and phonons in a closed ferrite core with two different coils switched into the shoulders of a multivibrator has been developed. It has been demonstrated that the interacting ferromagnetic and ferroacoustic resonances excited simultaneously in a ferrite core qualitatively correspond to the dynamics of the electron and phonon currents interaction process in a closed electrical line. DOI10.14302/issn.2642-3146.jec-19-3049 In the earlier paper 1 there was discussed an idea that an electric current represents a quantum recurrence between the energies of its electron and phonon components. Similar hypothesis was put forward by British scientist Heaviside who supported a concept that the “energy current” propagates in an electrical line not along conductors but in the layers of their insulation 2, 3. The purpose of the study was to work out a mathematical model of an electric current in a transmission line as well as to elaborate a physical device that would support the developed theoretical notions. Theoretical Model of Electric Current in a Transmission Line First consider a closed electrical transmission line as a ring waveguide. We define the amplitude of electron current in the transversal plane of the waveguide as Ielectron and the amplitude of phonon current in the longitudinal plane of the waveguide as Iphonon. Using the results of the paper 1 we can describe the interaction process between the two currents within the framework of two parametrically coupled Hill’s type differential equations. Some properties of these equations including their ability to absorb the energy of a random perturbation force were discussed in 4: ………. (1) Where x -is the longitudinal coordinate along the waveguide and y –is the transversal coordinate across the waveguide, KII, K⊥ - are the longitudinal and transversal spatial frequencies. F1 and F1 - are the random functions reflecting the short and long wave heat oscillations along the conductor lattice correspondingly. The interaction process between the two currents takes place both on a quantum scale 1 and on a classical one. In order to unify the processes of