Charged Particle In Magnetic Field Research Articles

Energy transfer in binary collisions of two gyrating charged particles in a magnetic field

Binary collisions of the gyrating charged particles in an external magnetic field are considered within a classical second-order perturbation theory, i.e., up to contributions that are quadratic in the binary interaction, starting from the unperturbed helical motion of the particles. The calculations are done with the help of a binary collision treatment, which is valid for any strength of the magnetic field and involves all harmonics of the particles’ cyclotron motion. The energy transfer is explicitly calculated for a regularized and screened potential, which is both of finite range and nonsingular at the origin. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte Carlo (CTMC) calculations which also allow one to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities, on the other hand, only small velocity transfers occur. There the nonperturbative numerical CTMC results agree excellently with the predictions of the perturbative treatment.

Motion of charged particles in magnetic fields created by symmetric configurations of wires

In this paper we study the motion of a charged particle in the presence of a magnetic field created by three different systems of wires: an infinite rectilinear filament, a circular wire and the union of both. In the first case we prove that the equations of motion are Liouville integrable and we provide a complete description of the trajectories, which turn out to be of helicoidal type. In the case of the circular wire we study some restricted motions and we show that there is a trapping region similar to the Van Allen inner radiation belt in the Earth magnetosphere. We prove the existence of quasi-periodic orbits using Moser’s twist theorem, and the existence of scattering trajectories using differential inequalities. We also provide numerical evidence of Hamiltonian chaos and chaotic scattering by computing several Poincaré sections, Lyapunov exponents, fractal basins and their fractal dimensions. A similar study is done for the third system, although quasi-periodic orbits are proved to exist only under certain (perturbative) assumptions. From the viewpoint of the applications we propose a magnetic trap based on these configurations. Furthermore, the circular wire system can be interpreted as a simplified model of the levitated magnetic dipole–one of the recent proposals to confine a hot plasma for fusion power generation–and hence our work provides a verification of confinement and quasi-periodicity, beyond the adiabatic approximation, for this plasma system. Apart from contributing to the rigorous theory of the motion of charges in magnetic fields, this paper illustrates that very simple magnetic configurations can give rise to complicated, even chaotic trajectories, thus posing the question of how the complexity of magnetic lines affects the complexity of particle motions.

Binary collisions of charged particles in a magnetic field

Binary collisions between charged particles in an external magnetic field are considered within a classical second-order perturbation theory, i.e., up to contributions which are quadratic in the binary interaction, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an improved binary collisions treatment which is valid for any strength of the magnetic field, where the second-order energy and velocity transfers are represented in Fourier space for arbitrary interaction potentials. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and nonsingular at the origin, and which involves as limiting cases the Debye (i.e., screened) and Coulomb potential. Two distinct cases are considered in detail: (i) the collision of two identical (e.g., electron-electron) particles, and (ii) the collision between a magnetized electron and a uniformly moving heavy ion. The energy transfer involves all harmonics of the electron cyclotron motion. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte Carlo calculations which also allows to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the nonperturbative numerical classical trajectory Monte Carlo results agree excellently with the predictions of the perturbative treatment.

Exact Solution of Klein–Gordon Equation for Charged Particle in Magnetic Field with Shape Invariant Method

Based on the shape invariance property we obtain exact solutions of the three-dimensional relativistic Klein–Gordon equation for a charged particle moving in the presence of a certain varying magnetic field, and we also show its non-relativistic limit.

Classical statistical thermodynamics of a gas of charged particles in magnetic field

We will demonstrate that the paradox of classical statistical thermodynamics for a gas of charged particles in a magnetic field (GMF) has not yet been explained. The paradox lies in the statement that the average magnetic moment of a gas is zero, whereas the time-average magnetic moment of each particle is always negative. We consider a gas of charged particles moving in a plane perpendicular to a uniform magnetic field. The density of distribution of the ensemble describing statistical properties of the GMF is derived starting from the basics, with due regard for the specific character of dynamics of the charged particles in the magnetic field. It is emphasized that neither the imposition of a potential barrier restricting the existence region of the GMF, nor the introduction of a background neutralizing charge occupying a finite area, is a necessary condition for the stationary equilibrium state of the GMF to exist. We show that the reason for this fact is that the density of distribution of the ensemble is dependent, besides the Hamiltonian, on another positive definite integral of motion that is a linear combination of the Hamiltonian and the angular momentum of the GMF. Basic thermodynamic relations are deduced in terms of the new density of distribution, and it is demonstrated that the GMF has a magnetic moment whose magnitude and sign are determined by the external potential field. Particularly, the GMF is diamagnetic in the absence of the neutralizing background charge. Thus, the statement of the Bohr-van Leeuwen theorem, deduced using the ordinary Gibbs density of distribution depending on the Hamiltonian only, is wrong. It is noted that a great deal of works on the theory of electronic phenomena in magnetic field are based either on the same wrong density of distribution or on the formula for average occupation numbers depending on the energy of states, which follows from this density of distribution within quantum theory. These theories should be revised in view of the new form of the density of distribution.

On exponential localization of magnetic Wannier functions

A triple of quantum numbers of conventional zone theory, namely the quasi-momentum,described in terms of Bloch functions, the lattice coordinate, described in terms of Wannierfunctions, and the associated energy band index, are modified to describe the space ofstates of a charged particle in magnetic field, in a translation covariant manner.A quartet of Bloch functions that belong to an invariant subspace, and definean irreducible representation of an anticommutative subgroup of the magnetictranslation group, lead to Wannier function sets at a single Landau level thatsatisfy the exponential localization criterion. The degrees of freedom within theinvariant subspace of this physically irreducible representation match those of spin1/2. With a view to possible experimental studies, it is shown how a set of four regular arraysof connected wires or a similar quantum device may be used to access the pseudo-spindegree of freedom described, by observation of the effects of a controlled doubly periodicalelectric potential applied to a 2DEG in a strong and commensurate magnetic field.

Can branes travel beyond CTC horizon in Gödel universe?

Gödel universe in M-theory is a supersymmetric and homogeneous background with rotation and four-form magnetic flux. It is known that, as seen in inertial frame of comoving observer, all geodesics with zero orbital angular momentum orbit inside ‘surface of light velocity’ (CTC horizon). To learn if other probes can travel beyond the CTC horizon, we study dynamics of M-graviton and, in particular, M2-brane, whose motion is affected by Lorentz force exerted by the four-form magnetic flux and by nonzero orbital angular momentum. Classically, we find that both probes gyrate closed orbits, but diameter and center of gyration depends on sign and magnitude of probe's energy, charge and orbital angular momentum. For M2-brane, orbits in general travel outside the CTC horizon. Quantum-mechanically, we find that wave function and excitation energy levels are all self-similar. We draw analogy of probe's dynamics with Landau problem for charged particle in magnetic field.

Theory of synchrotron radiation: II. Backreaction in ensembles of particles

The standard calculations of the synchrotron emission from charged particles in magnetic fields does not apply when the energy losses of the particles are so severe that their energy is appreciably degraded during one Larmor rotation. In these conditions, the intensity and spectrum of the emitted radiation depend on the observation time T obs: the standard result is recovered only in the limit T obs≪ T loss, where T loss is the time for synchrotron losses. In this case the effects of the radiation backreaction cannot be detected by the observer. We calculate the emitted power of the radiation in the most general case, naturally including both the cases in which the backreaction is relevant and the standard case, where the usual result is recovered. Finally we propose several scenarios of astrophysical interest in which the effects of the backreaction cannot and should not be ignored.

L-DEPENDENCE OF PARTICLE RADIATION IN MAGNETIC-SOLENOID FIELD AS AHARONOV-BOHM EFFECT

Aharonov-Bohm solenoid changes the energy spectrum of charge particles in pure magnetic field. In particular, the degeneracy with respect to azimuthal quantum number l is partially lifted. In turn, this complicates the radiation spectrum of a charged particle in magnetic field in the presence of the solenoid (Aharonov-Bohm effect). In particular, the degeneracy of the radiation intensity with respect to the azimuthal quantum number is lifted completely. In the present work we study l-dependence (induced by Aharonov-Bohm solenoid) of synchrotron radiation intensity in semiclassical approximation.

Fundamentals on the Noncommutative Plane

We consider the addition of charged matter (``fundametals'') to noncommutative Yang-Mills theory and noncommutative QED, derive Feynman rules and tree-level potentials for them, and study the divergence structure of the theory. These particles behave very much as they do in the commutative theory, except that (1) they occupy bound-state wavefunctions which are essentially those of charged particles in magnetic fields, and (2) there is slight momentum nonconservation at vertices. There is no reduction in the degree of divergence of charged fermion loops like that which affects nonplanar noncommutative Yang-Mills diagrams.

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Trajectories of charged particles in Kähler magnetic fields

H-planar flows on Kähler manifolds are considered. All flowlines of such flows are H-planar curves (the complex analogues of geodesics). We investigate equations which the Hamiltonian of an H-planar flow has to obey. We also propose a method of finding a general solution of these equations. With the help of proposed approach, trajectories of charged particles in magnetic fields of special form on Kähler manifolds of constant holomorphic sectional curvature are studied. Using the fact that Kähler manifolds of constant holomorphic sectional curvature admit an H-projective mapping on a flat Kähler manifold, the equations of particle motion are reduced to one ordinary differential equation of the second order.

Low energy dynamics of

We apply the adiabatic approximation to investigate the low energy dynamics of vortices in the parity invariant double self-dual Higgs model with only mutual Chern-Simons interaction. When distances between solitons are large they are particles subject to the mutual interaction. The dual formulation of the model is derived to explain the sign of the statistical interaction. When vortices of different types pass one through another they behave like charged particles in magnetic field. They can form a bound state due to the mutual magnetic trapping. Vortices of the same type exhibit no statistical interaction. Their short range interactions are analysed. Possible quantum effects due to the finite width of vortices are discussed.

Green's Function of a Charged Particle in Magnetic Fields

It is shown that the Green function for a charged particle in a uniform magnetic field is resolved into the gauge dependent exponential factor which breaks the translational symmetry and the translationally symmetric gauge independent function even if the system contains periodic potential. In the absence of the periodic potential, several exact expression for the Green function is derived. The method for numerical calculation is presented as well as an example of application to a practical problem.

The radial force on a charged particle in superimposed magnetic fields on Schwarzschild spacetime

Following the approach of optical reference geometry we derive the expression for the total force in the radial direction acting on a charged particle in magnetic fields superimposed on the static Schwarzschild background and show the possible existence of bound orbits for particles in the field of ultra compact objects at distancesr⩽3m wherein the Lorentz force counterbalances both the gravitational and centrifugal forces.

Charged particle trajectories in simple nonuniform magnetic fields

The motion of charged particles in magnetic fields whose magnitude varies as a power of one of the coordinates in the plane of the motion is investigated. For interesting power laws, the parametric equations for the trajectory are expressible in terms of Jacobi elliptic functions. These represent a rather natural generalization of the elementary trigonometric solutions that are encountered in the case of a constant magnetic field.

Coherent states and accidental degeneracy for a charged particle in a magnetic field

The coherent state solution for a charged particle in a constant magnetic field and its implication for the accidental degeneracy present in the problem are discussed. Furthermore, a simple derivation is given for the density of electrons per unit area in the plane perpendicular to the magnetic field, which is required for the understanding of the quantum Hall effect.

Experimental difficulties in observing the effects of magnetic fields on biological and chemical processes

The effects of magnetic fields on biological and chemical processes are investigated. Time-varying magnetic fields produce eddy currents which stimulate excitable tissues at low frequencies and give rise to thermal effects at high frequencies. Biological and chemical effects of static magnetic fields are poorly understood. The effects of magnetic fields on combustion of alcohol and hydrocarbons are studied to simulate in part the oxidation of organic matter in the living body. The combustion temperature of alcohol with platinum catalysis decreases rapidly within a range 100-200°C when the place of combustion reaction is exposed to gradient magnetic fields (0.5-1.4T, 20- 200 T/m). To explain this phenomenon, an experiment is demonstrated where candle flames are exposed to gradient magnetic fields. The flames bend so as to escape from magnetic fields of higher intensities. The study is focused on the role of oxygen as a paramagnetic molecule and on the behavior of charged particles in magnetic fields. In contrast with the combustion experiments, no clear positive effects are observed in experiments of biochemical reactions and embryogenesis under magnetic fields of the same intensities.

Application of Particle Simulation Codes to Fusion Reactor Engineering

Particle simulation codes are useful for calculating the dynamics of systems of charged particles in magnetic fields. These codes can integrate ion and electron trajectories in applied or self-consistent electromagnetic fields. The codes have application to several areas of fusion reactor design, including plasma dynamic questions in the reactor plasma as well as in the design of devices for plasma heating. The central themes of plasma simulation, as well as several applications, are described.

Negative-energy states for charged particles in magnetic fields on the Kerr space-time

The possible existence of « negative-energy states » of positive-root solutions of the effective potential for a charged particle in an electromagnetic field superposed on black-hole space-times is presented. Though, in general, such states occur for particles contrarotating with respect to the black hole, indications are there that in some cases corotating particles also might show the existence of such states very close to the event horizon.