Motion Of Charged Particles Research Articles

Simulation study of motion of charged particles trapped in Earth’s magnetosphere

This article aims to understand the motion of the charged particles trapped in the Earth’s inner magnetosphere. The emphasis is on identifying the numerical scheme, which is appropriate to characterize the trajectories of the charged particles of different energies that enter the Earth’s magnetosphere and get trap along the magnetic field lines. These particles perform three different periodic motions, namely: gyration, bounce, and azimuthal drift. However, often, the gyration of the particle is ignored, and only the guiding center of the particle is traced to reduce the computational time. It is because the simulation of all three motions (gyro, bounce, and drift) together needed a robust numerical scheme, which has less numerical dissipation. We have developed a three-dimensional test particle simulation model in which the relativistic equation of motion is solved numerically using the fourth and sixth-order Runge-Kutta methods. The stability of the simulation model is verified by checking the conservation of total kinetic energy and adiabatic invariants linked with each type of motion. We found that the sixth-order Runge-Kutta method is suitable to trace the complete trajectories of both proton and electron of a wide energy range, 5 keV to 250 MeV for L = 2–6. We have estimated the bounce and drift periods from the simulations, and they are found to be in good agreement with the theory. The study implies that a simulation model with sixth-order Runge-Kutta method can be applied to the time-vary, non-analytical form of magnetic configuration in future studies to understand the dynamics of charged particles trapped in Earth’s magnetosphere.

Method of controlling the cyclotron motion of electron beams with a nonadiabatic magnetic field

This paper describes a method for reducing the energy of the cyclotron motion for charged particles in coherent beams using a nonadiabatic magnetic field. For the purpose of reducing the cyclotron motion, a local magnetic field reduction of the main guiding field should be situated in the region of the descending phase of the beam oscillation. The required local magnetic field depression can be produced with a soft iron ring or with a magnet coil. The nonadiabatic element can be positioned on the descending part of any period of the beam oscillation where the beam still remains sufficiently coherent. The effect of reducing the cyclotron motion with such nonadiabatic magnetic field is independent of the electric field of the cathode-anode gap and seems to be a universal method for the cyclotron motion control in coherent beams. Therefore, it can be used for reducing the cyclotron motion of electron beams produced with different kinds of guns with different perveances and sizes. For instance, the method is capable of creating ripple-free, laminar beams even for magneto-immersed guns positioned in a magnetic field of only a few hundred Gs and with a cathode emission current density exceeding $30\text{ }\text{ }\mathrm{A}/{\mathrm{cm}}^{2}$. It can also be applied for guns producing tubular beams, as demonstrated by our simulations. The results of computer simulations are presented, which demonstrate the capability of effective cyclotron motion control with nonadiabatic magnetic field.

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.

Generation of megatesla magnetic fields by intense-laser-driven microtube implosions

A microtube implosion driven by ultraintense laser pulses is used to produce ultrahigh magnetic fields. Due to the laser-produced hot electrons with energies of mega-electron volts, cold ions in the inner wall surface implode towards the central axis. By pre-seeding uniform magnetic fields on the kilotesla order, the Lorenz force induces the Larmor gyromotion of the imploding ions and electrons. Due to the resultant collective motion of relativistic charged particles around the central axis, strong spin current densities of sim peta-ampere/hbox {cm}^{2} are produced with a few tens of nm size, generating megatesla-order magnetic fields. The underlying physics and important scaling are revealed by particle simulations and a simple analytical model. The concept holds promise to open new frontiers in many branches of fundamental physics and applications in terms of ultrahigh magnetic fields.

Dynamics of test particles around renormalization group improved Schwarzschild black holes

In this paper we have investigated the dynamics of neutral, electrically charged and magnetized particles around renormalized group improved (RGI) Schwarzschild black hole in the presence of external asymptotically uniform magnetic field. We have analyzed the spacetime structure around RGI black hole by investigating Ricci, the square of Ricci tensor and Kretschmann curvature scalars and shown that only in the case when the parameter $\gamma=0$ the curvature becomes infinite at the center of the black hole, while for non-zero values of $\gamma$ parameter the black hole curvature reflects the properties of regular black hole. Analyzing the innermost stable circular orbits of test neutral particles around RGI black hole and comparing with the results for rotating Kerr black hole we have shown that RGI black hole parameters can mimic the rotation parameter of Kerr black hole upto $a/M \lesssim 0.31$ providing the same ISCO radius. Since according to the astronomical observations of the accretion disks confirm that the astrophysical black holes are rapidly rotating with the spin parameter upto $a/M \sim 0.99$ one may conclude that the effects of parameters of RGI Schwarzschild black hole on the circular orbits of the neutral particles can not mimic the Kerr black hole. Then the Hamilton-Jacobi equation has been used to analyze the charged and magnetized particles motion near the RGI black hole in the presence of the strong interaction between external asymptotically uniform magnetic (electromagnetic) field and magnetized (electrically charged) particle. We have shown that RGI black hole parameters quantitatively change the dynamics of the charged and magnetized particles, in particular ISCO radius of the particles decreases with increasing the parameter $\lambda$, while the increase of the parameter $\gamma$ causes to increase of it.

Electric field measurement in electric-field modified flames

The application of an electric field to a flame modifies the flame characteristics due to the collective motion of charged particles generated within the flame. The applied field mobilises electrons and ions depending on their polarity, leading to localised regions of space charge with sufficient density to either locally amplify or shield the applied electric field. A fundamental understanding of the local electric field is essential for both electrically and plasma-assisted combustion, because it determines electric body force as well as electron temperature. In this work, we propose a method, which is independent of gas composition and temperature, to measure the local electric field using electric field induced second harmonic generation (E-FISH). We successfully apply this method to a laminar nonpremixed counterflow flame by applying modulated direct current (DC) electric field with a microsecond duration zero volt pulse. Electric potential and space charge distribution are also deduced from the measured electric field. Furthermore, we show the importance of electron attachment to O2 forming O2− by changing the polarity of the applied DC electric field. When the anode is in the oxygen stream, a region of negative charge is obtained near the anode, whereas, when the anode is in the fuel stream, no region of negative charge is found. We also find the qualitative trends of the measured electric fields reasonably agree with previously reported one-dimensional modelling results. The limitations of the methodology are addressed, and we show that the ability to modulate the DC voltage on sub-microsecond timescales is required for accurate quantitative measurements.

Test particle motion around a black hole in Einstein-Maxwell-scalar theory

In this paper, we explore the test particle motion around a black hole in Einstein-Maxwell-scalar (EMS) theory using three different black hole solutions within this theory. We have first analyzed the spacetime curvature structure of these solutions and shown the existence of two singularities and the first one is at the center $r=0$. In black hole spacetime, there are two regions divided by the critical value of the cosmological parameter $\lambda_0$. The photon sphere around the black hole in EMS theory has also been studied and found that it does not depend on cosmological parameter $\lambda$. We have analyzed the innermost stable circular orbits (ISCO) around the black hole and shown that for all solutions ISCO radius for neutral particle decreases with the increase of black hole charge. We have also studied the charged particle motion around the black hole where charged particle motion is considered in the presence of the gravitational field and the Coulomb potential. It is shown that ISCO radius for charged particles increases depending on the selected value of the coupling parameter which is in contradiction with observations of the inner edge of the accretion disks of the astrophysical black holes and can be used as a powerful tool to rule out the EMS theory from consideration for the gravitational field theory. It is also studied the fundamental frequencies governed by test particle orbiting around the black hole in EMS theory. Finally, as a test of black hole solution in EMS theory ISCO radii is compared with that in Kerr black hole and found that the spin parameter of Kerr can be mimic up to $a/M\simeq 0.936$.

Kinetic Ballooning Instability of the Near‐Earth Magnetotail in Voigt Equilibrium

AbstractFor a long time, ballooning instabilities have been believed to be a possible triggering mechanism for the onset of substorm and current disruption initiation in the near‐Earth magnetotail. Yet the stability of the kinetic ballooning mode (KBM) in a global and realistic magnetotail configuration has not been well examined. In this paper, stability of the KBM is evaluated for the two‐dimensional Voigt equilibrium of the near‐Earth magnetotail based on an analytical kinetic theory of ballooning instability in the framework of kinetic magnetohydrodynamic (MHD) model, where the kinetic effects such as the finite gyroradius effect, wave‐particle resonances, and particle drifts motions are included usually through kinetic closures. The growth rate of the KBM strongly depends on the magnetic field line stiffening factor S, which is in turn determined by the effects of the trapped electrons, the finite ion gyroradius, and the magnetic drift motion of charged particles. The KBM is unstable in a finite intermediate range of equatorial βeq and only marginally unstable at higher βeq regime for higher Te/Ti values. The finite ion gyroradius and the trapped electron fraction enhance the stiffening factor that tends to stabilize the KBM in the magnetotail far away from Earth. On the other hand, the current sheet thinning destabilizes KBM in the lower βeq regime and stabilizes KBM in the higher βeq regime.

Hamiltonian in Guiding Center Theory: A Symplectic Structure Approach

The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on the conservation of an adiabatic invariant, the magnetic moment. Hamiltonian equations for the guiding center motion are traditionally introduced using a non-canonical symplectic structure. Under such an approach one has to apply the non-canonical Hamiltonian perturbation theory in order to calculate the magnetic moment corrections. In this study we present an alternative approach with canonical Hamiltonian equations for the guiding center motion in time-dependent electromagnetic fields. We show that the derived Hamiltonian decouples three types of motion (gyrorotation, field-aligned motion, and cross-field drifts), and each type is described by a pair of conjugate variables. This form of Hamiltonian and symplectic structure allows easy introduction of adiabatic invariants and can be useful for the analysis of various plasma systems.

The Polarity Reversal of Lightning‐Generated Sky Wave

AbstractThe polarity reversal of the lightning‐generated first sky wave as a function of the observation distance is studied using a novel approach combining the finite‐difference time domain (FDTD) method and the superposition principle of electromagnetic waves. In this method, the sky wave is generated by radiation from the induced current produced by the motion of charged particles driven by the lightning‐radiated electromagnetic waves in the ionosphere. The horizontal and vertical components of the induced current density under the daytime and nighttime ionospheric conditions are evaluated. Their different contributions to the sky wave at different observation distances are analyzed in detail. Furthermore, a physical explanation for the polarity reversal in the time domain is proposed. It is found that, for relatively short observation distances (within ~200 km), the first sky wave is dominated by the component generated by the horizontal equivalent current in the Fresnel zone, while for longer observation distances (larger than ~300 km), the first sky wave is dominated by the component generated by the vertical equivalent current in the Fresnel zone. Since the polarities of the sky wave components generated by the vertical current source and horizontal current source are opposite, the polarity of the sky wave will reverse when increasing the observation distance.

Drift Motion of Charged Particles in Inhomogeneous Magnetic and Strong Electric Fields

Distinctive features of the drift motion of a nonrelativistic charged particle in slowly varying magnetic and strong electric fields, for which the assumption that the electric drift velocity is small as compared to the total particle velocity is non-applicable, are studied. The variational principles of the drift motion are extended to the case of the strong electric field. The generalized Littlejohn’s Lagrangian is obtained and the extended set of drift equations is derived. The possibility of particle acceleration due to the drift motion along the strong electric field is demonstrated.

Model for Investigating the Physical Properties of a System of Charged Particles Taking into Account the External Magnetic Field and Friction Force

In the present work, a numerical modified Verlet scheme (MVS) is obtained. This scheme is intended to solve the equations of motion of charged particles immersed in an external stationary environment and a uniform magnetic field, for example, charged particles of a condensed substance in a buffer plasma (dusty plasma). The influence of the environment on the particle dynamics is described by the friction force. The particle dynamics are also affected by interparticle interaction and an external uniform magnetic field. To obtain the Verlet scheme (VS), the coordinates and velocities of the particles are decomposed into a Taylor series, taking into account the Lorentz force and the friction force. All Taylor series expansion terms that give the same order of accuracy are taken into account. In the obtained numerical scheme, the time step of modeling does not depend on the magnitude of the magnetic field but is determined only by the internal physical properties of the system under consideration, which is important when modeling an ensemble of charged particles taking electromagnetic fields into account. The paper solves a test problem for which particle trajectories obtained based on the conventional and modified VS for different values, both the friction parameter and the magnetic field parameter, are compared. Based on the analysis of the dependence of the maximum relative deviation of the coordinate on the time step, the time step is independent of the magnetic field in the Taylor expansion scheme, while in the inverse VS it is dependent.

Charged particle and epicyclic motions around 4D Einstein–Gauss–Bonnet black hole immersed in an external magnetic field

We investigate particle motion in the vicinity of a $4D$ Einstein-Gauss-Bonnet (EGB) black hole immersed in external asymptotically uniform magnetic field. It is well known that magnetic fields can strongly affect charged particle motion in the black hole vicinity due to the Lorenz force. We find that the presence of the Gauss-Bonnet (GB) coupling gives rise to a similar effect, reducing the radius of the innermost stable circular orbit (ISCO) with respect to the purely relativistic Schwarzschild black hole. Further, we consider particle collisions in the black hole vicinity to determine the center of mass energy and show that this energy increases with respect to the Schwarzschild case due to the effect of the GB term. Finally, we consider epicyclic motion and its frequencies and resonance as a mean to test the predictions of the model against astrophysical observations. In particular we test which values of the parameters of the theory best fit the 3:2 resonance of high-frequency quasi-periodic oscillations in three low-mass X-ray binaries.

Charged and magnetized particles motion in the field of generic singular black holes governed by general relativity coupled to nonlinear electrodynamics

We study spherically symmetric magnetically charged generic singular black hole solutions of general relativity coupled to nonlinear electrodynamics. For characteristic values of the generic spacetime parameters and the parameter characterizing the ratio of the gravitational and electromagnetic forces acting on an electrically charged particle we study the circular orbits and related epicyclic motion and its frequencies. We demonstrate that the equatorial circular orbits are forbidden in such situations, but off-equatorial circular orbits are possible. We give dependence of the stable circular orbit on the spacetime parameters and intensity of the electromagnetic interaction of the charged particles with magnetically charged black holes. We study the possible resonance phenomena of the epicyclic frequencies and the orbital frequency of the electrically charged particles in order to fit the data of the twin high-frequency quasiperiodic oscillations of x rays observed in microquasars. Moreover, the dynamics of magnetized particles around the magnetically charged generic black hole have also been explored and it is shown that as increasing magnetic charge and magnetic moment parameters, the innermost stable circular orbit (ISCO) radius decreases and disappears at some value of the magnetic moment parameter, inversely proportional to the magnetic charge of black hole. As an astrophysical application we treated the magnetar PSR J1745--2900 orbiting around Sagittarius (Sgr) A* as a magnetized particle and showed that the magnetic charge of black hole can mimic black hole spin up to $a/M=0.865694$ at $\ensuremath{\nu}=2$, and the spin parameter can mimic the magnetic charge parameter up to $q/M=0.578575$ at $\ensuremath{\nu}=1$, providing exactly the same value of the ISCO radius. Finally, we predict that no magnetar with the surface magnetic field of the order of ${10}^{14}--1{0}^{15}\text{ }\text{ }\mathrm{G}$ can follow stable orbits, but it is possible to observe ordinary neutron stars as recycled radio pulsars in the close environment of Sgr A*.

Quasiharmonic oscillations of charged particles in static axially symmetric space-times immersed in a uniform magnetic field

In continuation of our previous study [Phys. Rev. D 99 (2019) 4, 044012], we investigate the motion of charged particles in the $\gamma$-metric. We provide some examples of curled trajectories in the equatorial plane and escape trajectories outside the equatorial plane. Finally, we consider harmonic oscillations due to small displacements from stable circular orbits on the equatorial plane and compute the epicyclic frequencies for different values of deformation parameter and magnetic field.

Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials

We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass M, described by the Klein-Fock-Gordon equation with equal scalar Sr→ and vector Vr→ Coulomb plus ring-shaped potentials. It is shown that the system under consideration has both a discrete at E<Mc2 and a continuous at E>Mc2 energy spectra. We find the analytical expressions for the corresponding complete wave functions. A dynamical symmetry group SU1,1 for the radial wave equation of motion is constructed. The algebra of generators of this group makes it possible to find energy spectra in a purely algebraic way. It is also shown that relativistic expressions for wave functions, energy spectra, and group generators in the limit c⟶∞ go over into the corresponding expressions for the nonrelativistic problem.

General relativistic manifestations of orbital angular and intrinsic hyperbolic momentum in electromagnetic radiation

General relativistic effects in the weak field approximation are calculated for electromagnetic Laguerre–Gaussian beams. The current work is an extension of previous work on the precession of a spinning neutral particle in the weak gravitational field of an optical vortex. In the current work, the metric perturbation is extended to all coordinate configurations and includes gravitational effects from circular polarization and intrinsic hyperbolic momentum. The final metric reveals frame-dragging effects due to intrinsic spin angular momentum (SAM), orbital angular momentum (OAM), and spin–orbit coupling. When investigating the acceleration of test particles in this metric, an unreported gravitational phenomenon was found. This effect is analogous to the motion of charged particles in the magnetic field produced by a current-carrying wire. It was found that the gravitational influence of SAM and OAM affects test-rays traveling perpendicular to the intense beam and from this a gravitational Aharonov–Bohm analog is pursued.

Motion of Charged Particle in a Class of Homogeneous Spaces

We study the motion of charged particle under a natural choice of electromagnetic field in a general class of compact homogeneous spaces. As a special case we describe the motion in homogeneous Riemannian spaces $(G/H,g)$, where $g$ is any deformation of a normal metric along the fibers of a homogeneous fibration $K/H\rightarrow G/H \rightarrow G/K$.

Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle

We show that nontrivial topologies of the spatial section of Minkowski space–time allow for motion of a charged particle under quantum vacuum fluctuations of the electromagnetic field. This is a potentially observable effect of these fluctuations. We derive the mean squared velocity dispersion when the charged particle lies in Minkowski space–time with compact spatial sections in one, two and/or three directions. We concretely examine the details of these stochastic motions when the spatial section is endowed with different globally homogeneous and inhomogeneous topologies. We also show that compactification in just one direction of the spatial section of Minkowski space–time is sufficient to give rise to velocity dispersion components in the compact and noncompact directions. The question as to whether these stochastic motions under vacuum fluctuations can locally be used to unveil global (topological) homogeneity and inhomogeneity is discussed. In globally homogeneous space topologically induced velocity dispersion of a charged particle is the same regardless of the particle’s position, whereas in globally inhomogeneous the time-evolution of the velocity depends on the particle’s position. Finally, by using the Minkowskian topological limit of globally homogeneous spaces we show that the greater is the value of the compact topological length the longer is the time interval within which the velocity dispersion of a charged particle is negligible. This means that no motion of a charged particle under electromagnetic quantum fluctuations is allowed when Minkowski space–time is endowed with the simply-connected spatial topology. The ultimate ground for such stochastic motion of charged particle under electromagnetic quantum vacuum fluctuations is a nontrivial space topology.

Test particle orbits around regular black holes in general relativity combined with nonlinear electrodynamics

We provide detailed analysis of the curvature structure of the spacetime around regular black holes (RBHs) governed by general relativity (GR) combined with nonlinear electrodynamics (NED), characterized by electric charge $Q$, and degree of nonlinearity $n$. We consider special class of the backgrounds introduced by Toshmatov et al. [Phys. Rev. D 98, 028501 (2018)] that have proper Maxwell weak-field limit of the NED sector. We also study the motion of uncharged and charged particles in the RBH background. We determine shadows of such black holes (BHs) using the effective geometry governing motion of photons in the background of NED RBHs. The analysis of circular motion enables to determine innermost stable circular orbits (ISCO) and marginally bound orbits (MBO). We show that the radius of ISCO and MBO for neutral particles decreases as the parameters of the RBH $Q$ and $n$ increase for the fixed value of the BH mass. We demonstrate that for the electrically charged particles properties of the circular orbits strongly depend on their Coulomb interaction with the RBH charge. The dependence of the ISCO radius on the particle specific charge $q$ and the RBH parameters is rather complex, but for the attractive Coulomb interaction there is a general feature (independent of $n$) giving a limiting value of the intensity of this interaction $q{Q}_{\mathrm{max}}$ behind which no stable circular orbits are allowed around the RBH. Comparison of the RBH with Reissner-Nordstr\"om black holes (RNBH) shows that for the same electric charges of these backgrounds the location of the relevant orbits is at substantially smaller radii for the RBH, demonstrating thus a strong influence of the NED effects. The analysis of ISCO radius of test particles has shown that the charge of RBH $Q$ can mimic the rotation parameter of Kerr BH up to the value $a=0.8M$. We have also shown that the RN BH charge can mimic the rotation parameter up to $a=0.5M$ and the RBH charge up to $Q=0.2M$. Applications from observational data to the parameters of the supermassive black holes (SMBHs) at the galactic center Messier 87 (M87) and Milky Way so called Sagittarius ${\mathrm{A}}^{*}$ (${\mathrm{Sgr}\text{ }A}^{*}$) give the mimic value for the RBH charge parameter for the rotation parameter of M87 to be ${10}^{3}Q\ensuremath{\approx}277.5{6}_{\ensuremath{-}1.26}^{+3.82}$, while for ${\mathrm{Sgr}\text{ }A}^{*}$ there is ${10}^{3}Q\ensuremath{\approx}187.3{3}_{\ensuremath{-}26.4}^{+27.6}$. Moreover, it is shown that the RN BH charge cannot mimic the rotation parameter of the SMBH M87, however, it can mimic the spin parameter of ${\mathrm{Sgr}\text{ }A}^{*}$ at ${10}^{3}{Q}_{\mathrm{RN}}/M=828.7{1}_{\ensuremath{-}60.94}^{+70.58}$.