Theory of the drift motion of charged particles

A differential equation is derived for the time dependence of the average random-motion energy of a particle drifting in an electric field. There is a discussion of the various versions of this equation, the equation of motion which follows from it, and particular solutions. There is a discussion of topics associated with the time dependence of the coordinate of a drifting particle, the average drift velocity, and the current-voltage characteristic of the drift region for the case of a space-charge limitation on the current.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 8, pp. 119–125, August, 1969.     

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.     

The motion,in the drift approximation,of a relativistic charged particle in a strong magnetic field

The Witham's averaged Langrangian technique is applied to derive (in terms of drifts and transverse adiabetic invariant) the motion of a relativistic particle, in a strong magnetic field.     

Oscillations of charged particles in an external magnetic field about steady motion

We develop a Hamiltonian formalism that can be used to study the particle dynamics near stable equilibria. The construction of an original canonical transformation allowed us to prove the conservation of the linear momentum P₃, which permitted the expansion of the Hamiltonian about a fixed point. The definition of the rotational variable h whose Poisson algebra properties played the essential role in the diagonalization of the quadratic Hamiltonian yielding two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable near a fixed point that come to light Heisenberg's and Harmonic Oscillator equations of motion of the particles, leading thus the association of the fixed point trajectories with arbitrary trajectories in its immediate neighborhood. The present formalism succeeded to treat the problem of free-electron laser dynamics and may be applied to similar cases. Received 20 October 2001     

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.     

On the effect of a magnetic field on fast charged particles passing through a substance

A transport equation in the small-angle approximation is obtained for a curvilinear beam of fast charged particles passing through a substance in a nonuniform magnetic field. Green functions for this equation are found for an annular beam in a weak-focusing field and for a helical beam in the nonuniform magnetic field.     

On the motion of charged particles in an alternating nonuniform electric field

The equations of motion for a charged particle in an electric field featuring a stationary and an oscillating component are considered for the case where the force of friction is linear in the particle velocity. The averaging of these equations over the period of field oscillations is legitimate under some specific conditions. The most general expression for an additional stationary force acting on the particle under these conditions is derived, and the limiting values of this force are found. Applications of the results obtained in the present study are considered. Such applications include the use of pulsed currents in the electrochemical dimensional treatment of materials.     

Analytic treatment of the relativistic motion of charged particles in electric and magnetic field

Summary Using the Boris mover, or other standard methods, the error pile-up in the computation of the relativistic orbit of charged particles in electric and magnetic fields becomes quickly excessive, if one wants to keep reasonably limited the number of points employed to build the particle orbit. An analytical solution becomes, therefore, desirable and its construction is the subject of the present work.

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Riassunto Unsando il metodo di Boris, oppure altri metodi standard, l'accumulazione degli errori nella determinazione numerica delle orbite relativistiche di particelle cariche in campi elettrici e magnetici diventa intollerabile, se il numero dei punti impiegati per costruire le orbite stesse è mantenuto basso. Una soluzione analitica diviene quindi utile, e questa costituisce l'argomento del presente lavoro.

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Резюме В рамках стндартных методов погрешность при вычислении релятивистской орбиты заряженных частиц в электронном и магнитном полях становится чрезмерно большой, если для построения орбиты часицы используется ограниченное число точек. В связи с этим конструируется аналитическое решение.

     

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     

Retardation of charged particles by matter in a magnetic field

The Green's function of the steady transfer equation of charged particles in matter in the presence of a constant homogeneous magnetic field is found by the fifth-parameter method in the continuous-retardation approximation. The influence of the field on the particle penetration depth in matter is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 13–15, July, 1991.     

带电粒子在地磁场中的运动

用计算机模拟的方法研究了地磁场中带电粒子的运动特性,绘制了粒子轨迹曲线,对粒子运动进行了分析,解释了地磁场的磁瓶效应和辐射带.     

Dynamics of charged particles in the field of a spherical magnetic dipole

The results of numerical simulation of the dynamics of charged particles in the field of a spherical magnetic dipole are reported. Interesting features revealed in this dynamics can be used in analysis of near-Earth space with the help of charged particle beams.     

Analytical solutions for the energy distribution of charged particles in a weak electric field

The paper deals with the stationary distribution of charged particles moving in a material medium, having scattering and absorption properties, in which a uniform electric field is present. The purpose of the work is finding analytical solutions in simplified but physically significant situations and comparing different approximations based on a spherical-harmonics expansion of the velocity distribution. Received: 28 July 1998     

Transit of beams of charged particles through a non-adiabatic magnetic field

The possibility of obtaining beams of particles with high transverse energies in a strong magnetic field is discussed. The motion of particles in a weakly non-adiabatic field is described by a linear non-homogeneous equation. The non-adiabaticity of motion is caused, in the first approximation, by the curvature of the magnetic lines of force. The conditions for a small spread of magnetic moments of the beam particles are established by solving the equation of motion. The transverse energy of particles and its spread can be varied by varying the shape of the magnetic field and the initial radial velocities of the particles. As a result of the conditions for a small spread of magnetic moments, a beam traversing a steep magnetic field gains a smaller magnetic moment than a beam passing through a field with a lesser slope.The author is indebted to Dr M. Seidl, DrSc, for valuable discussions on the subject, and to Dr M. Ondráek, CSc for help in the computer calculations.     

Motion of bunches of charged particles in a transverse magnetic field

Gorizont Optical Construction Bureau. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 3, pp. 366–374, March, 1990.     

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.     

Equations of motion from field equations and a gauge-invariant variational principle for the motion of charged particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first-order Lagrangian by boundary terms only. A new method of deriving equations of motion from field equations is developed. When applied to classical electrodynamics, this method enables us to obtain unambiguously the above, second-order Lagrangian from the general energy-momentum conservation principle.     

The field of charged,spinning, magnetic particles

Stationary solutions of the Einstein-Maxwell equations have recently been given corresponding to charged, spinning magnetic matter. In this paper a solution for two particles of such matter is given. In general it contains a singularity between the particles.     

Deterministic chaos in the dynamics of charged particles near a magnetic field reversal

The charged particle motion near magnetic field reversals shows a miscellaneous picture, alternating between chaotic and regular trajectories. A general scheme for the different types of solutions in dependence on the initial phase space domain has been obtained as for as the chaotization thresshold and a velocity-space diffusion coefficient in strongly curved fields.