Charged Test Particles Research Articles

A pure geometric approach to the Aharonov–Bohm effect

This article represents a possible geometric interpretation of the Aharonov–Bohm (A–B) effect. We presented a new curve in the context of Einstein–Maxwell geometry, using the Bazanski approach. In the context of the geometrization philosophy, this curve can be used as an equation of motion of a charged test particle in a combined gravitational and electromagnetic field. The new equation of motion obtained contains two extra terms more than the geodesic equation. The first contains the electromagnetic field strength, while the second term gives rise to the electromagnetic potential. Both terms represent forces affecting the acceleration of the moving charged particle in the field mentioned above. The second term gives rise to the A–B effect. Linearization of the new equation gives more physical meaning to the extra terms obtained.

Алгебры операторов симметрии уравнения Клейна - Гордона - Фока для групп движений, действующих транзитивно на двумерных подпространствах пространственно-временного многообразия

All external electromagnetic fields are found in which the Klein-Gordon-Fock equation for a charged test particle admits first-order symmetry operators provided that the groups G 3, r £ 3, of motions act transitively on the two-dimensional subspace V 2.

Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb collisions.

The present paper considers the time evolution of a charged test particle of mass m in a constant temperature heat bath of a second charged particle of mass M. The time dependence of the distribution function of the test particles is given by a Fokker-Planck equation with a diffusion coefficient for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. For the mass ratio m/M→0, the steady distribution is a Kappa distribution which has been employed in space physics to fit observed particle energy spectra. The time dependence of the distribution functions with some initial value is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator and also interpreted with the transformation to a Schrödinger equation. We also consider the explicit time dependence of the distribution function with a discretization of the Fokker-Planck equation. We study the stability of the Kappa distribution to Coulomb collisions.

Complete separability of the Hamilton–Jacobi equation for the charged particle orbits in a Liénard–Wiechert field

We classify all orthogonal coordinate systems in M4, allowing complete additively separated solutions of the Hamilton–Jacobi equation for a charged test particle in the Liénard–Wiechert field generated by any possible given motion of a point-charge Q. We prove that only the Cavendish–Coulomb field, corresponding to the uniform motion of Q, admits separation of variables, precisely in cylindrical spherical and cylindrical conical-spherical coordinates. We show also that for some fields, the test particle with motion constrained into certain planes admits complete orthogonal separation, and we determine the separable coordinates.

Acceleration of charged particles from near-extremal rotating black holes embedded in magnetic fields

The aim of the present article is to evaluate the motion of neutral and charged test particles in the vicinity of a near-extremal rotating black hole (BH) in the presence of magnetic fields. Euler–Lagrange motion equations and effective potential methods are used to characterize the motion out of the equatorial plane. Such approach is of peculiar significance if it is considered, e.g., accretion processes onto rotating BHs. In general, investigations concerning accretion focus mostly on the simplest case of particles moving in the equatorial plane. Here it will be considered that particles initially moving around some particular orbit may be perturbed by a kick along the θ direction, giving rise to other possible orbits. We confirm the possibility that ultra high energy cosmic rays would be produced at the very center of AGNs, for a specific range of magnetic field magnitudes, since it is possible that ultra-high center-of-mass energies can be produced by particles colliding near the horizon of rotating BHs whose angular momentum tends to the Thorne limit.

Dynamics of test particles around a Bardeen black hole surrounded by perfect fluid dark matter

We study the dynamics of (i) neutral test particles, (ii) magnetically charged test particles, and (iii) test magnetic dipole around a regular Bardeen black hole surrounded by perfect fluid dark matter (PFDM). It has been shown how the magnetic charge of the black hole and the parameter of the surrounding PFDM can influence the innermost stable circular orbit (ISCO) radius of a test particle. We have found that the ISCO radius is strongly affected as a consequence of the combined effect of the magnetic charge parameter and the perfect fluid dark matter. The black hole magnetic charge parameter $g$ and the combined effect of perfect fluid dark matter can mimic the black hole rotation parameter up to $a/M\approx 0.9$. It has been observed that the ISCO for magnetic dipole disappears at the values exceeding the calculated upper value for the magnetic interaction parameter $\beta$. The upper limit decreases with the increase of both the dark matter and magnetic charge parameters. Finally, as an astrophysical application, we have analyzed degeneracy effects of spin of Kerr black holes and magnetic charge of regular Bardeen black holes for the different values of the dark matter parameter providing exactly the same value for ISCO radius of a magnetic dipole with the same value of the parameter $\beta=10.2$ of the magnetar called PSR J1745-2900 orbiting around supermassive black hole Sagittarius A*.

Charged fluids encircling compact objects: force representations and conformal geometries

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy–momentum conservation written in a standard representation. Here, we develop its interesting alternatives in terms of two covariant force representations, both based on a hypersurface projection of the energy–momentum conservation. In a proper hypersurface, space-like forces can be defined, following from a decomposition of the fluid four-acceleration. Each of the representations provides us with an insight into properties of the fluid flow, being well reflected in related conformal hypersurface geometries; we find behaviour of centrifugal forces directly related to geodesics of these conformal hypersurfaces and their embedding diagrams. We also reveal correspondence between the charged fluid flow world-lines from an ordinary spacetime, and world-lines determined by a charged test particles equation of motion in a conformal spacetime.

Separation of variables in Hamilton–Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

Weak cosmic censorship conjecture for the novel 4D charged Einstein\u2013Gauss\u2013Bonnet black hole with test scalar field and particle

Recent researches of the novel 4D Einstein–Gauss–Bonnet (EGB) gravity have attracted great attention. In this paper, we investigate the validity of the weak cosmic censorship conjecture for a novel 4D charged EGB black hole with test charged scalar field and test charged particle respectively. For the test charged field scattering process, we find that both extremal and near-extremal black holes cannot be overcharged. For the test charged particle injection, to first order, an extremal black hole cannot be overcharged while a near-extremal 4D charged EGB black hole can be destroyed. To second order, however, both extremal and near-extremal 4D charged EGB black holes can be overcharged for positive Gauss–Bonnet coupling constant; for negative Gauss–Bonnet coupling constant, an extremal black hole cannot be overcharged and the validity of the weak cosmic censorship conjecture for a near-extremal black hole depends on the Gauss–Bonnet coupling constant.

Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity.

Testing cosmic censorship conjecture for extremal and near-extremal (2 + 1)-dimensional MTZ black holes

We test the validity of the weak cosmic censorship conjecture for the (2 + 1)-dimensional charged anti-de Sitter black hole solution, which was derived by Martinez et al (MTZ). We first construct a thought experiment by throwing test charged particles on an extremal MTZ black hole. We derive that extremal (2 + 1) dimensional black holes can be overcharged by test particles, unlike their analogues in (3 + 1) and higher dimensions. Nearly-extremal MTZ black holes can also be overcharged, by a judicious choice of energy and charge for the test particles when the second order effects are ignored. We also incorporate the second order effects for nearly extremal MTZ black holes by adapting the method developed by Sorce and Wald. However it turns out that the second order effects cannot compensate for the overcharging of MTZ black holes.

Gravitational and electromagnetic memory

We present a unified investigation of memory effect in Einstein-Maxwell theory. We specify two types of memory effect, a velocity kick and a position displacement, by examining the motion of a single free falling charged test particle. Our result recovers the two known gravitational memory effect formulas and the two known electromagnetic memory effect formulas.

Hypocycloid motion in the Melvin magnetic universe

The trajectory of a charged test particle in the Melvin magnetic universe is shown to take the form of hypocycloids in two different regimes, first of which is the class of perturbed circular orbits, and secondly in the weak-field approximation. In the latter case we find a simple relation between the charge of the particle and the number of cusps. These two regimes are within a continuously connected family of deformed hypocycloid-like orbits parametrised by the magnetic flux strength of the Melvin spacetime.

The Lagrangian of charged test particle in Horava-Lifshitz black hole and deformed phase space

We use deformation approach and obtain Lagrangian of charged test particle. We show the effect of non-commutative parameters [Formula: see text] and [Formula: see text] on the Lagrangian of a test particle in Horava-Lifshitz background with charge and without charge and see in the case of [Formula: see text] and without charge, the deformed and non-deformed Lagrangian will be the same. In the case of [Formula: see text] and with charge will be the same but the charge or field need some scaling. Finally, results in the case of [Formula: see text] with charge are completely different. It means that we have other components in addition to having a time component of the field.

Overcharging higher curvature black holes

We examine the problem of overcharging extremal and near-extremal black hole solutions of Einstein-Gauss-Bonnet gravity in any dimension, generalizing the result in general relativity. We show that as in the case of general relativity, it is not possible to create a naked singularity by overcharging an extremal black hole in Einstein-Gauss-Bonnet gravity using a charged test particle. Our result suggests that the validity of the cosmic censorship hypothesis transcends beyond general relativity to well motivated higher curvature gravity.

Modelling the creation of surface nano-structures using test charge approach

Nowadays, surface nanostructures has become an important technological method that plays an important role in the electronic devices, as it has a very remarkable feature is that they are used in etching without using chemicals. Recently, the plasma expansion model was used to describe what happens in the creation of surface nanostructures in materials. In this paper, another model to describe the creation of surface materials like SiO2 has been introduced, using a test charge approach. The basic equations describe the SiO2 are reduced to one evolution equation characterize the wakefield electric potential of a moving test charged particle. The profile of the wakefield potential is examined with different plasma parameters. It has been found that the wakefield potential decreases for different values of negative and positive ions densities. Also, we deduced that the fast test charge creates high wakefield potential behind it. Thus, they drag more charges to follow it to create the surface nanostructure.

The Kerr–Newman–(anti-)de Sitter spacetime: Extremal configurations and electrogeodesics

We study motion of charged test particles, or electrogeodesics, in the Kerr–Newman–(anti-)de Sitter spacetime. We focus on the equatorial plane and the axis of symmetry where the analysis is considerably simpler. The electric charge opens up the possibility of new types of trajectories, particularly stationary points where the particle can remain indefinitely. It also influences the stability of the orbits, which can be interesting from the point of view of observations. We review the basic properties of the spacetime—the structure of its horizons, the extremal cases, the possibility of over-extreme rotation, regions admitting closed timelike curves, and the turnaround radius, among other.

Extraction of energy from an extremal rotating electrovacuum black hole: Particle collisions along the axis of symmetry

High-energy collisions can occur for radially moving charged test particles in the extremal Reissner-Nordstr\"om spacetime if one of the particles is fine-tuned and the collision point is taken close to the horizon. This is an analogy of the Banados-Silk-West (BSW) effect, first described for extremal Kerr black holes. However, it differs significantly in terms of energy extraction: unlike for the original BSW process, no unconditional upper bounds on mass and energy of an escaping test particle produced in the collision were found for the charged version. We show that these results can be replicated for the motion of charged test particles along the axis of a general extremal rotating electrovacuum black hole, also including the Schnittman-type process with reflected fine-tuned particles. This brings the possibility of high-energy extraction closer to astrophysical black holes, which can be fast spinning and have a small "Wald charge" due to interaction with external magnetic fields. Nevertheless, we find numerous caveats that can make the energy extraction unfeasible despite the lack of unconditional kinematic bounds.

On a possible quantum manifestation of the perihelion advance in a hydrogen-like atom

In a static and spherically symmetric case, by following an analog procedure for obtaining a Reissner–Nordstrom solution, thanks to the use of both the Einstein-type equation for an electromagnetic field as well as the Maxwell equation in curved space–time, we managed to find the Schwarzschild-like solution outside a charged sphere Q in interaction with a test charged particle q at an atomic scale where the gravitational force is negligibly small compared to the electrostatic force. Then, in the context of an extension of the equivalence principle to the electromagnetic interaction, we have studied the hydrogen atom. At the atomic scale, where quantum effects can no longer be ignored and the concept of trajectory is abandoned, the corrective terms derived from the geodesic equation for the electron are used within a perturbation theory. At the first order, these radial corrections of the Hamiltonian can partially remove the degeneracy of Bohr’s levels through a Lamb-like shift of the energy levels (2s) and (2p), estimated to E(2s) – E(2p) = 2.4595087102 × 10−4 eV. To match the experimental value of the Lamb shift, 4.372 × 10−6 eV, we have postulated the existence of an electromagnetic background that would describe statistically the vacuum energy by the introduction of a “cosmological”-like constant in the Einstein-like equation for electromagnetism. We have pointed out a divergence when n → +∞ in energy corrections due to a “cosmological” constant that technically could be overcome by the use of a cutoff as well as the renormalization of the electron’s mass.

A FRACTAL ACCELERATOR ON THE BASIS OF A CORRUGATED PLASMA WAVEGUIDE WITH SUPERCONDUCTING WALLS

The use of a two-stage mechanism for the acceleration of charged particles is proposed. The principle of acceleration is based on the use of the fractal properties of the wave spectrum of a corrugated plasma waveguide with superconducting walls. The first stage provides for the excitation of a corrugated plasma waveguide by short electron bunches in the direction of motion (the length of the bunch is significantly less than the period of the corrugation). On the second stage the test charged particles accelerates in an infinite number of harmonics of the electric field exited by an electron bunches. Calculations show that with the implementation of such an acceleration mechanism, the average speed of a non-relativistic test particle can increase several times, and its acceleration length can be up to one meter.