Behavior of a charged particle in a schwarzschild field

The influence of the De Witt self-action force on the motion of and electromagnetic emission from a charged particle in a Schwarzschild field is considered. It is shown that a charged particle in a Schwarzschild field is equivalent to a neutral particle of the same mass in a certain Reissner-Nordstrom field. A relationship is found between the power of the electromagnetic emission from an accelerated charge and the power of the thermal emission generated in a reference frame with the same acceleration at the event horizon. The quantum-mechanical problem of the motion of and emission from a charge in the field of a minihole is considered. Wave functions, the energy spectrum, and the widths of quasi-stationary levels are found with allowance for the De Witt self-action force. It is shown that the latter is important for large charges, when the solution becomes oscillatory. "Brainstorm" Little Science and Technology Enterprise. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 75–82, July, 1998.     

Brownian motion of a charged particle in a magnetic field

We develop and numerically illustrate an exact solution of the multivariate, stochastic, differential equations that govern the velocity and position of a charged particle in a plane normal to a uniform, stationary, magnetic field. The equations self-consistently incorporate the Lorentz force into an Ornstein-Uhlenbeck collision model. Properties of the solution in the infinite dissipation limit are explored and the spectral energy density function is found     

Propagator for a charged particle in a time-dependent electromagnetic field

We first show that the propagator of a charged particle in a time-dependent electromagnetic field, obtained by choosing the vector and scalar potentials to be in static symmetric gauge, is related to the propagator of a one-dimensional particle under a time-dependent perturbative force and with generalized memory. For the case of a constant magnetic field, the latter can then be evaluated exactly with the help of a gaussian integral. Our new results are in agreement with the well-known results of simpler cases.     

Motion of a charged particle in a uniform rotating magnetic field

The motion of a charged particle in a rotating, uniform magnetic field is investigated. Expressions are obtained for the domains of steady-state motion and for the particle trajectories. The investigation includes a treatment of conditions specifying the particle localization within the bounded space domain.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 7–11, December, 1976.     

Screening of a charged dust particle within a nonlocal charging theory

We study the influence of the nonlocality of the electron energy distribution function on the dust particle charge screening in a two-component plasma of various inert gases and nitrogen at atmospheric pressure. For our analytical and numerical calculations, we have chosen the point sink model in the diffusion-drift approximation, which, in addition to the bulk production and loss of electrons and ions, also includes the heterogeneous processes of their absorption by a dust particle. We have established that the dust particle potential distribution in the problem under consideration is a superposition of three Debye exponentials with three different screening constants. The first constant practically coincides with the inverse Debye length. The second constant is determined by the inverse length travelled by the electrons and ions in the ambipolar diffusion process in the characteristic recombination time. The third constant coincides with the inverse characteristic distance of electron energy transfer through heat conduction in the characteristic time of electron energy establishment in the processes of heating by a beam of fast electrons and energy losses in elastic and inelastic collisions. We compare our numerical calculations of the screening constants with the analytical estimates obtained in the ambipolar diffusion approximation.     

On the motion of a charged particle in a helical magnetic field

The rectilinear motion of a charged particle in a helical magnetic field is analyzed. Averaging methods are used as a device to study the equations of motion. The averaged system is constructed and analyzed to find the adiabatic invariants, from which the basic parameters of the focusing system can be calculated.     

Condensation mode instability in a heat-releasing weakly ionized gas in a magnetic field

Linear equations and dispersion relations describing the condensation mode in weakly ionized plasma with heat release, being in an external magnetic field, are derived. The conditions of the instability onset of the condensation mode of the ion component are found.     

Supersonic air-scoop flows of a weakly ionized gas in external electromagnetic field

Steady supersonic flows of a weakly ionized gas in external electric and magnetic fields computed for the problem of flow control in the air scoop of a supersonic vehicle. The numerical simulation was based on a second-order accurate marching scheme for the Euler equations. Effects of plasma and electromagnetic-field parameters on flow structure and distributions of flow variables are analyzed.     

Ion waves in a partially ionized gas in an external electric field

The propagation of longitudinal acoustic waves in the ion gas in an external electric field is studied theoretically. The results are compared with properties of waves in space without the external field. The phase velocities, damping factors and the influence of parameters of the gas on the properties of ion waves is discussed.In conclusion, the author would like to express his thanks to Prof. J. Kracík DrSc., for valuable advice and suggestions.     

Diffusion of nanoparticles in a rarefied gas

It is suggested to describe the diffusion of nanoparticles in rarefied gases in terms of the kinetic theory. For this purpose, the potential of interaction between a carrier gas molecule and a dispersed particle is constructed by summing the interactions of the given gas molecule with all atoms (molecules) of the dispersed particle. With this potential, a formula for the diffusion coefficient of the dispersed nanoparticle is derived. The dependence of the diffusion coefficient on the radius and temperature is studied. Analytical results are compared with experimental data. The well-known experimental Cunningham-Millikan correlation is shown to apply only in the range of near-room temperatures, for which the parameters of this correlation were determined.     

Motion of a charged particle in the field of a grounded conductive sphere

Motion of a charged particle in the field of a grounded conductive sphere is investigated. It is assumed that the field created by the sphere is quasi-static that implies limitation on particle velocities by nonrelativistic values and the possibility of neglecting magnetic interaction and heat losses. A classification is provided and possible particle trajectories are constructed in the examined case.     

Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

The classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.     

Degenerate Fermi gas of charged particles in a quantizing magnetic field

The strength at which a magnetic field has a quantizing effect on the particles of a degenerate ultrarelativistic electron gas is essentially the same as that for a nonrelativistic proton gas of the same density. Discrete field strengths at which the chemical potentials of these gases have fixed values are expressed in terms of the same index of the Landau quantum level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 5–9, September, 1991.     

Analytical solutions of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles

A two-stream Maxwellian distribution function with two unknown parameters corresponding to the mean velocity and the shear stress is used to obtained an approximate analytic solution of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles. For small magnetic field, solutions are presented for the four moments equations and the Maxwell's equations. The dynamical behaviour of the electron and ion gas is examined.     

Invariance operator groups for a charged particle in an external electromagnetic field

In this paper a general group theoretical approach is given for the problem of a charged particle moving in an external electromagnetic field F. From a knowledge of the symmetry transformations of the field (Galilean or Poincaré), it is possible to explicitly construct groups of operators which commute with the operators of the equations of motion (classical, quantum mechanical, Klein-Gordon or Dirac) using the concept of compensating gauge transformations together with a uniquely chosen map π: F → A fixing the gauge of the potential A. Other choices of gauges give rise to isomorphic operator groups. The general structure of the possible symmetry groups of the fields is discussed and the corresponding invariance operator groups are explicitly given for (almost) arbitrary fields. The structure of these groups is then investigated and it is shown in particular that a large class of fields give rise to non-Type I groups, i.e. to groups which have (unitary continuous) representations whose corresponding von Neumann algebras have non-discrete factors. A general criterion for these pathological cases is given. As an application, we study the problem of a Bloch electron in arbitrary constant uniform electric and magnetic fields.     

On the motion of a charged particle in the field of a magnetic monopole

A quantum mechanical treatment of the motion of a charged particle in the field of a fixed magnetic monopole is given, based on a representation of the corresponding vector potential by means of a distribution. The results are closely similar to those obtained in the work of Wu and Yang, which stems from ideas borrowed from mathematical fiber bundle theory. We believe that our method follows more closely the usual quantum mechanical procedures and provides an alternative approach to that of Wu and Yang. Although the present paper deals with non-relativistic problem, it is clear that the extension to the case of a Pauli or Dirac particle can be easily done using spinor monopole harmonics.