On the Violation of Ohm’s Law for Bounded Interactions: a One Dimensional System

We consider an infinite Hamiltonian system in one space dimension, given by a charged particle subjected to a constant electric field and interacting with an infinitely extended system of particles. We discuss conditions on the particle/medium interaction which are necessary for the charged particle to reach a finite limiting velocity. We assume that the background system is initially in an equilibrium Gibbs state and we prove that for bounded interactions the average velocity of the charged particle increases linearly in time. This statement holds for any positive intensity of the electric field, thus contradicting Ohms law.Work partially supported by the GNFM-INDAM and the Italian Ministry of the University.     

Electromagnetic radiation of a charged tachyon moving in a dispersive medium

At the present time a number of studies [1–6] have considered the possible properties of ultrarelativistic tachyon particles. In particular, [5, 6] were dedicated to analysis of the radiation of charged tachyons in a vacuum. The goal of the present study is to analyze the radiation emitted by charged tachyons in an immobile dispersive medium. We will consider the following problem: a charged particle moves with velocity v in an immobile dispersive medium and at time t=0 decays to neutral particles and a charged tachyon which moves at a velocity v₀. The tachyon in turn, because of collisions with neutral particles of the medium, at time t= forms a charged particle (electron) also moving with velocity v.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 130–134, June, 1978.In conclusion, the author expresses his sincere thanks to Professor Ya. P. Terletskii for his interest and aid in the study.     

On electromagnetic waves by an accelerated charged particle in medium

We have investigated the effects of acceleration of a charged particle on its Cerenkov emission and ionization-losses. We have considered the accelerated motion of a charged particle in an infinite medium with the acceleration parallel to the direction of its motion. We have used the method of Fourier transforms to solve the Maxwell's equations with appropriate current and charge-densities to find electromagnetic fields and hence the force experienced by the incident charge due to its interaction with the medium (dielectric or plasma). The results obtained are general and applicable to any acceleration. In the approximations of ‘small acceleration’ and ‘small interaction time’, we have solved the wave equations and determined electromagnetic potentials. It is found that the acceleration of the charged particle strongly changes both its ionization-loss and Cerenkov emission.     

Charged particle motion in a medium along an electromagnetic wave

The solution of the relativistic equation of motion is discussed for a charged particle interacting with an electromagnetic wave in a medium.     

On the Motion of a Charged Particle Interacting with an Infinitely Extended System

 We study the time evolution of a charged particle moving in a medium under the action of a constant electric field E. In the framework of fully Hamiltonian models, we discuss conditions on the particle/medium interaction which are necessary for the particle to reach a finite limit velocity. We first consider the case when the charged particle is confined in an unbounded tube of ℝ³. The electric field E is directed along the symmetry axis of the tube and the particle also interacts with an infinitely many particle system. The background system initial conditions are chosen in a set which is typical for any reasonable thermodynamic (equilibrium or non-equilibrium) state. We prove that, for large E and bounded interactions between the charged particle and the background, the velocity v(t) of the charged particle does not reach a finite limit velocity, but it increases to infinite as: |v(t)−Et|≤C ₀ (1+t), where C ₀ is a constant independent of E. As a corollary we obtain that, if the initial conditions of the background system are distributed according to any Gibbs state, then the average velocity of the charged particle diverges as time goes to infinite. This result is obtained for E large enough in comparison with the mean energy of the Gibbs state. We next study the one-dimensional case, in which the estimates can be improved. We finally discuss, at an heuristic level, the existence of a finite limit velocity for unbounded interactions, and give some suggestions about the case of small electric fields. Received: 7 March 2002 / Accepted: 23 September 2002 Published online: 8 January 2003 RID="*" ID="*" Work partially supported by the GNFM-INDAM and the Italian Ministry of the University. Communicated by J.L. Lebowitz     

Formation of particle tracks

Abstract

The formation of particle tracks, and such phenomena as the detection of charged particles, and the damage produced by charged particles, are intimately related to the spatial distribution of ionization energy deposited by δ-rays. Changes in the spectrum of δ-rays with the velocity of the primary particle, imply that linear measures of the interaction of the primary particle with the medium, such as specific energy loss, or primary ionization, are unsatisfactory measures of effects produced in the medium, for they contain no knowledge of the spatial deposition of the lost energy.     

The Faraday law of induction for an arbitrarily moving charge

The Faraday law of electromagnetic induction for an arbitrarily moving charge is generalized and the expression for the force acting on the charge in an alternating magnetic field is obtained. It is shown that besides the Lorentz force perpendicular to the velocity of the particle, the Faraday force parallel to the particle velocity and proportional to it is acting on the charge, too. The equations of motion of the charged particle and the magnetic moment are obtained in the time-varying magnetic field. The problems of induction acceleration of charged particles (betatron) and induction heating of medium (plasma, plasma betatron) are considered.     

Cherenkov-like mechanism of surface waves excitation

The theory of the excitation of surface waves by a fast charged particle moving though a thin homogeneous metal film surrounded by a dielectric medium is proposed. The Vavilov-Cherenkov effect is shown to occur for surface waves at the particle velocity one or two orders of magnitude lower than the corresponding velocities in a homogeneous medium.     

Self-consistent renormalized phonons in metallic and nonmetallic solids

The interaction of charged particle beam with non-linear “cubic” type media has been studied; the dielectric permeability of such media depends on the square strength of the electric field produced by the beam-excited wave. The processes of the Cherenkov excitation of the medium by a modulated definite current are investigated as well as the polarization of longitudinal oscillations of the medium excited by the current. The equations are obtained to determine the dependence of fields excited by the current on the amplitude of the exciting current. It is found that under certain circumstances (near the radiation cut-off) the conditions of Cherenkov radiation may be violated due to non-linearities of the medium and the particle radiation loss vanish. The amplification of longitudinal waves in an arbitrary isotropic medium with “cubic” non-linearity by a monoenergetic particle beam is studied when the frequencies of amplified oscillations are close to the resonance frequencies of the medium.     

A Charged Particle in an Electric Field in the Probability Representation of Quantum Mechanics

The Green's function and linear integrals of motion for a charged particle moving in an electric field are discussed. The Wigner functions and tomograms of the stationary states of the charged particle are obtained. The relationship between the quantum propagators for the Schrödinger evolution equation, the Moyal evolution equation, and the evolution equation in the tomographic-probability representation for a charged particle moving in an electric field is discussed.     

Resonant Interaction of the Transitional Radiation of Charged Particles with Anisotropic Magnetodielectric Filling of the Waveguide Periodically Modulated in Space

Optics and Spectroscopy - The features of the interaction of the transition radiation of a charged particle with an anisotropic magnetodielectric medium periodically modulated in the waveguide in...     

Detection of elementary charges on colloidal particles

We have succeeded in determining the charge of individual colloidal particles with resolution higher than the elementary charge. The number of elementary charges on a particle is obtained from the analysis of optical tracking data of weakly charged silica spheres in an electric field in a nonpolar medium. The analysis also yields an accurate value of the particle size. Measurement of the charge as a function of time reveals events in which the particle loses or gains an elementary charge due to ionization or recombination processes at the surface.     

Charged particles detection: The graft-and-dye method

Charged particles travelling through an organic medium leave a trail of highly concentrated active, stable chemical radicals. These functions are able to initiate copolymerization reactions of unsaturated molecules. Such a reagent is made to reach the trail; polymerization occurs. If the new polymer formed either absorbs or emits light the track of the charged particle is made visible. This technique and results are discussed: the efficiency of those detectors has been increased, they do not exhibit any critical dip angle for the registration of particle tracks, they may offer a way to reveal tracks originating in the detector itself.     

Mass Transfer in Free Convection Developing in a Magnetic Field

The interaction of a charged hydrated particle with an external magnetic field is analyzed under conditions of diffusion and convective mass transfer. A model of forming local space charge regions in the bulk of a solution is suggested. The model is used to study the feasibility of changing the velocity and redistribution of charged particles in an aqueous medium. The results of theoretical calculations are tested experimentally by quantitative estimation of the rate of the convective liquid flow developed in crossed electric and magnetic fields.     

Effective charge of a macroparticle in a non‐isothermal plasma within the Poisson–Boltzmann model

The electrostatic potential distribution around a charged, spherical, finite‐size macroparticle in a non‐isothermal plasma‐like medium is studied numerically within the Poisson–Boltzmann model. It is assumed that plasma consists of electrons and one species of singly charged ions. The effective charge of a macroparticle is calculated and its dependence on the electron to ion temperature ratio as well as on the particle radius and bare charge is considered. Numerical results for the effective charge in an isothermal plasma are compared with known analytical expressions.     

Polarization Bremsstrahlung at Atomic and Cerenkov Resonances

The polarization bremsstrahlung of a fast charged particle in a medium is considered for the case where the conditions for two resonances are satisfied simultaneously: the photon frequency is close to the frequency of one of the transitions of the medium atom, and the permittivity of the medium at this frequency meets the conditions of appearance of Cerenkov radiation. As this takes place, the radiation intensity becomes three or four orders of magnitude higher than that associated with the frequency band within which the bremsstrahlung photon energy exceeds the ionization energy of the atom. Estimates are made for an experiment performed on a gas atomic parahelium at frequencies close to that of the 1s-2p transition.     

Diffraction radiation of a dielectric wedge at the resonance frequency

The diffraction radiation at the frequency that is close to the natural resonance of the medium is considered for a fast charged particle that passes in the vicinity of a dielectric wedge. The dependence of the angular distribution of the diffraction radiation on the angle between the wedge faces and on the energy of the ultrarelativistic particle is analyzed.     

Cherenkov radiation: Electron self-energy approach

A short review is given of a previous paper on Cherenkov radiation (CR) by Fülöp and Biró (1992), together with some aspects of the collective dipole oscillations of atomic microclusters (atomic analog of the nuclear giant resonance). Finally, the CR energy loss of a relativistic charged particle in matter is obtained by evaluating the self-energy of the particle in the medium.