Motion Of Charged Particles Research Articles

Circular motion and chaos bound of a charged particle near charged 4D Einstein–Gauss–Bonnet-AdS black holes

The circular motion and chaos bound of one charged particle near 4D charged AdS black holes in the Einstein–Gauss–Bonnet gravity theory are analytically investigated. With the help of the Jacobian matrix, we construct the actual formula of the Lyapunov exponent for the charged particle, which satisfies the upper bound when it is localized at the event horizon. Further considering the Lyapunov exponent in the vicinity of the horizon and studying the 4D charged Einstein–Gauss–Bonnet-AdS black hole with different Gauss–Bonnet coupling coefficients, it is found that it has some specific values to determine whether a violation of chaos bound. The Lyapunov exponent for the circular motion of charged test particle is larger than the static equilibrium because of the appearance of angular momentum. We find that, with the increase of the Gauss–Bonnet coupling coefficient, the black hole gets closer to the extremal state and the bound is more easily violated. For various Gauss–Bonnet coupling coefficients, we obtain a corresponding range of the particle charge, in which the chaos bound is violated. Our results indicate that, as the Gauss–Bonnet coupling coefficient increases, the value of the particle charge violating the chaos bound is even smaller.

Long time gyrokinetic equations

The aim of this text is to elucidate the oscillating patterns (see C. Cheverry [Res. Rep. Math. (2018)]) which are generated in a toroidal plasma by a strong external magnetic field and a nonzero electric field. It is also to justify and then study new modulation equations which are valid for longer times than before. Oscillating coherent structures are induced by the collective motions of charged particles which satisfy a system of ODEs implying a large parameter, the gyrofrequency ε − 1 ≫ 1 \varepsilon ^{-1} \gg 1 . By exploiting the properties of underlying integrable systems, we can complement the KAM picture (see G. Benettin and P. Sempio [Nonlinearity 7 (1994), pp. 281–303]; M. Braun [SIAM Rev. 23 (1981), pp. 61–93]) and go beyond the classical results about gyrokinetics (see M. Bostan [Multiscale Model. Simul. 8 (2010), pp. 1923–1957]; A. J. Brizard and T. S. Hahm [Rev. Modern Phys. 79 (2007), pp. 421–468]). The purely magnetic situation was addressed by C. Cheverry [Comm. Math. Phys. 338 (2015), pp. 641–703; J. Differential Equations 262 (2017), pp. 2987–3033]. We are concerned here with the numerous additional difficulties due to the influence of a nonzero electric field.

Electromagnetic effects on charged particles in a near-horizon-extreme-Kerr geometry

We investigate the motions of charged particles in the near horizon region of an extreme Kerr black hole with weak electromagnetic fields. There is an enhanced symmetry in the near-horizon-extreme-Kerr geometry. We find that when the electromagnetic field respects this enhanced symmetry, which we refer to as the maximally symmetric electromagnetic field, the equations of motion of charged particles get simplified into a set of decoupled first-order differential equations. We discuss the motions of charged particles in two maximally symmetric electromagnetic fields, one being the force-free field and the other being the vacuum fields. Even though the radial motions are similar to the geodesics in near-horizon-extreme-Kerr geometry, the angular motions could be affected by the electromagnetic field significantly. In particular, for the vacuum solution that is produced by a weakly charged black hole, there exist stable vortical motions if the electromagnetic parameter is above the critical value ${\mathfrak{B}}_{c}=\sqrt{3}$. These vortical motions do not cross the equatorial planes, and the charged particles in them radiate nonthermally. We discuss the corresponding astrophysical implications.

Plasmoid Instability in the Multiphase Interstellar Medium

The processes controlling the complex clump structure, phase distribution, and magnetic field geometry that develop across a broad range of scales in the turbulent interstellar medium (ISM) remain unclear. Using unprecedentedly high-resolution 3D magnetohydrodynamic simulations of thermally unstable turbulent systems, we show that large current sheets unstable to plasmoid-mediated reconnection form regularly throughout the volume. The plasmoids form in three distinct environments: (i) within cold clumps, (ii) at the asymmetric interface of the cold and warm phases, and (iii) within the warm, volume-filling phase. We then show that the complex magnetothermal phase structure is characterized by a predominantly highly magnetized cold phase, but that regions of high magnetic curvature, which are the sites of reconnection, span a broad range in temperature. Furthermore, we show that thermal instabilities change the scale-dependent anisotropy of the turbulent magnetic field, reducing the increase in eddy elongation at smaller scales. Finally, we show that most of the mass is contained in one contiguous cold structure surrounded by smaller clumps that follow a scale-free mass distribution. These clumps tend to be highly elongated and exhibit a size versus internal velocity relation consistent with supersonic turbulence and a relative clump distance–velocity scaling consistent with subsonic motion. We discuss the striking similarity of cold plasmoids to observed tiny-scale atomic and ionized structures and H i fibers and consider how the presence of plasmoids will modify the motion of charged particles, thereby impacting cosmic-ray transport and thermal conduction in the ISM and other similar systems.

Motion of charged and magnetized particles around regular black holes immersed in an external magnetic field in modified gravity

Motion of charged and magnetized particles around regular black holes immersed in an external magnetic field in modified gravity

Particle motion in the Einstein-Euler-Heisenberg rotating black hole spacetime

We study the motion of charged test particles and photons in the gravitational field of the rotating electrically charged Einstein-Euler-Heisenberg black hole solution. This describes a nonlinear electromagnetic generalization of the Kerr-Newman solution, which endows the vacuum with an effective dielectric constant. The orbits of photons are analyzed by means of the effective Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski pseudometric related to the geometrical metric and to the electromagnetic energy-momentum tensor. The QED induced modifications of the shape of the shadow are presented and discussed.

Новая схема интегрирования уравнений движения частиц в методе “частиц-в-ячейках” для задач физики плазмы

Представлен новый метод решения релятивистских уравнений движения заряженных частиц в электромагнитных полях, учитывающий условие постоянства их значений на каждом временном шаге. Проведено сравнение точности и эффективности вычислений при решении тестовых задач в дву- и трехмерной постановках на основе нового метода, метода Бориса и его модификаций. В каждом случае рассматривались варианты аналитически и дискретно заданных значений электрического и магнитного полей. At present, the Boris method is mostly common for the numerical solution of problems of the dynamics of charged particles in electromagnetic fields. In recent years, new modifications of the Boris method have appeared that are capable to simplify, refine, or speed up calculations. However, despite the rather large number of publications which consider algorithms for calculating the trajectories of charged particles, new, more accurate and high-performance algorithms are desired. The article presents a detailed analysis of some explicit methods for solving the problem of the motion of charged particles in electromagnetic fields, which differ in how they set the average values of velocities. A new scheme based on an analytical solution, which has not been studied before, is proposed. For the Boris, Vay, Higuera – Cary schemes and the new VD1 scheme, a comparative analysis of the accuracy, convergence and counting time for the relativistic and nonrelativistic cases is carried out. In the nonrelativistic case, the new scheme allows accurate solving of the equations for motion of charged particles, and in the relativistic case, the accuracy of the new scheme remains higher compared to other schemes. As the relativistic factor increases, the accuracy of all considered schemes for calculating the trajectory of particles in an electromagnetic field decreases. For large values of the relativistic parameter, the new scheme is more accurate than the other schemes and retains the second order. In practical calculations, when particles can have different speeds, the scheme automatically adjusts to the given speed of the particle. The presented new scheme for calculating trajectories can be important for solving a wide range of problems in astrophysics and thermonuclear fusion, where high accuracy in determining particle trajectories in inhomogeneous fields for large moments of time is required.

Neuronal cable equations derived from the hydrodynamic motion of charged particles

Neuronal cable theory is usually derived from an electric analogue of the membrane, which contrasts with the slow movement of ions in aqueous media. We show here that it is possible to derive neuronal cable equations from a different perspective, based on the laws of hydrodynamic motion of charged particles (Navier–Stokes equations). This results in similar cable equations, but with additional contributions arising from nonlinear interactions inherent to fluid dynamics, and which may shape the integrative properties of the neurons. The model recovers the classic cable equations as a particular case, when the fluid is assumed to be linear.

Particle motion around Schwarzschild-MOG black hole

In this paper, we present an analysis of the circular motion of test particles around a Schwarzschild-MOG black hole. Initially, our focus lies on studying the shadow cast by the spherically symmetric black hole within the framework of MOG gravity. Notably, we observe that the presence of MOG influences both the photon-sphere and the black hole’s shadow, causing them to increase in size. Furthermore, our research reveals that the characteristic radii of massive particles in circular orbits around the Schwarzschild-MOG black hole, specifically the innermost stable circular orbits (ISCO) and marginally bound orbits, are greater than those observed in the Schwarzschild metric alone. Additionally, we examine the electromagnetic field structure when a black hole is subjected to an external uniform magnetic field. Our findings demonstrate that in the vicinity of the Schwarzschild-MOG black hole, the magnetic field exhibits non-uniform behavior, with field lines becoming more densely distributed. Lastly, we delve into the motion of charged particles around the Schwarzschild-MOG black hole in the presence of an external magnetic field. Our investigation highlights that the ISCO position for charged particles is consistently less than that for neutral particles, indicating a significant distinction between the two scenarios.

Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field

It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering difference between the temporal variation of gyrophase and that of the other phase space coordinates needs to be taken into account. Second, it is also important to note that the parametric limit of the derivative of a function is not equivalent to the derivative of the limit function. When these facts are taken into account, the near identity transformation rule for one form related to the Lagrangian is modified. With the modified near identity transformation rule, the drift motion of charged particles can be described in the first order, instead of the second order and beyond through a tedious expansion process as in the conventional formulation. This resolves the discrepancy between the direct and Lie transform treatments in the Lagrangian perturbation theory for charged particle motion in a magnetic field.

Particle and guiding-center orbits in crossed electric and magnetic fields

The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, and the validity of the guiding-center representation is assessed in comparison with the exact particle dynamics. While the magnetic field is considered to be straight and uniform, the (perpendicular) radial electric field is nonuniform. The Hamiltonian guiding-center theory of charged-particle motion is presented for arbitrary radial electric fields, and explicit examples are provided for the case of a linear radial electric field.

Faithful guiding-center orbits in an axisymmetric magnetic field

The problem of the charged-particle motion in an axisymmetric magnetic geometry is used to assess the validity of higher-order Hamiltonian guiding-center theory, which includes higher-order corrections associated with gyrogauge invariance as well as guiding-center polarization induced by magnetic-field non-uniformity. Two axisymmetric magnetic geometries are considered: a magnetic mirror geometry and a simple tokamak geometry. When a magnetically confined charged-particle orbit is regular (i.e., its guiding-center magnetic moment is adiabatically invariant), the guiding-center approximation, which conserves both energy and azimuthal canonical angular momentum, is shown to be faithful to the particle orbit when higher-order corrections are taken into account.

Role of the overshoot in the shock self-organization

A collisionless shock is a self-organized structure where fields and particle distributions are mutually adjusted to ensure a stable mass, momentum and energy transfer from the upstream to the downstream region. This adjustment may involve rippling, reformation or whatever else is needed to maintain the shock. The fields inside the shock front are produced due to the motion of charged particles, which is in turn governed by the fields. The overshoot arises due to the deceleration of the ion flow by the increasing magnetic field, so that the drop of the dynamic pressure should be compensated by the increase of the magnetic pressure. The role of the overshoot is to regulate ion reflection, thus properly adjusting the downstream ion temperature and kinetic pressure and also speeding up the collisionless relaxation and reducing the anisotropy of the eventually gyrotropized distributions.

Magnetic-field-dependent electric-charge transport in hadronic medium at finite temperature

Electric charge transport of hadronic matter at finite temperature and magnetic field is studied within the linear sigma model. Anisotropic transport coefficients associated with the charge transport are estimated both in the weak and strong regimes of the magnetic field using the transport theory approach. In a weakly magnetized medium, the magnetic field effects are incorporated through the Lorentz force term in the Boltzmann equation. Strong magnetic field puts further constraints on the motion of charged particles through Landau quantization. Magnetic field-dependent thermal relaxation time is obtained from interaction rates of hadrons with the S-matrix approach by considering the Landau level kinematics of the charged hadrons. Mean-field effects are embedded in the analysis through the temperature-dependent hadron masses. Further, the hadronic medium response to a time-varying external electric field is studied in weak and strong magnetic field regimes. It is seen that electromagnetic responses of the hadronic matter have a strong dependence on the mean-field effects, sigma mass, the strength of the external fields, and its evolution in the medium.

Plasma poration: Transdermal electric fields, conduction currents, and reactive species transport.

Radical species and electric fields produced by gas plasmas are increasingly used in dermatology. Plasma-poration is the key basis for the efficient plasma skin treatment, which involves the plasma electric field, the directional motion of charged particles, and the transport of reactive particles. However, the enabling mechanisms of the plasma-poration remain unclear and require urgent attention. Here, the plasma-induced electric fields in each skin layer are accurately measured for the first time. The maximum electric field in the stratum corneum is 43kV/cm, while the electric field in the active epidermis and dermis is about 1.8kV/cm. This electric field strength is in the range of strength required for electroporation. Different from traditional electroporation treatments, the plasma-poration mainly relies on the effects of strong electric fields and the conductive current. The active power of the plasma-poration up to 18.5kW/cm3 in the stratum corneum can rapidly change the structure of the skin. At the same time, reactive oxygen and nitrogen species also pass through the stratum corneum and effectively interact with the skin tissue. The plasma-poration does not cause any pain, which is an inevitable side effect of common electroporation.

Comparative Study of the Geodesic Structure of Time-Conformal Quantum-Corrected AdS–Schwarzschild Black Hole

This manuscript reports the dynamics of a time-conformal quantum-corrected AdS–Schwarzschild black hole. The quantum-corrected parameter and the time-conformal factors are inserted in the AdS–Schwarzschild black. These insertions in the said space- time are taken to study and understand the phenomena of the formation of gravitational waves and Hawking radiations. The Hawking temperature distributions and Bekenstein–Hawking entropy for the inner and outer horizon of the new developed black hole solution are calculated and discussed. The motion of neutral and charged particles in the orbits of the said black hole is discussed under the influence of effective potential and effective force in the new development of the black hole solution. The escape velocity for the time-conformal black hole is obtained and compared with the escape velocity of the exact black hole. The roles of the quantum-corrected parameter and the effect of the time-conformal factor are high- lighted, and their influences are discussed in different situations. Einstein’s field equations are also obtained for the time-conformal quantum-corrected AdS–Schwarzschild black hole. The Lyapunov exponent is used for the stability of the said black hole spacetime. The effects of different parameters on different dynamical aspects of the black hole are explored.

Investigation of heat and mass transfer of flow structures generated by a pulsed surface arc discharge actuator in quiescent air

Pulsed Surface Arc Discharge (PSAD) actuators can improve the aerodynamic performance of aircraft due to their fast response speed and wide frequency band. Understanding the flow structure induced by arc discharge and its transfer process is the key to the sensible use of plasma excitation for flow control. This paper has investigated the dynamic heat and mass transfer process of charged particle clusters generated by arc discharge theoretically and experimentally. The results show that the clusters are composed of charged particles, and the thermal effect is the macroscopic manifestation of the thermal motion of charged particles. The heat and mass transfer processes of charged particle clusters can be expressed as a function of temperature. During heat and mass transfer, the transfer mode of the plasma cluster composed of charged particles will change. The plasma cluster will change from forced convection in the initial stage to natural convection in the final stage, and the Richardson number is different in different stages. The heat released by the gas discharge and the heat released by the plasma mass transfer will form accumulated heat in the space and change the temperature difference, thereby affecting the process of heat and mass transfer. This paper has constructed a model describing pulsed plasma clusters' dynamic heat and mass transfer. Furthermore, the dynamic mode decomposition results of the theoretical model function show that plasma clusters mainly conduct the mass transfer through low-frequency and heat transfer through high-frequency modes.

Locally-symplectic neural networks for learning volume-preserving dynamics

We propose locally-symplectic neural networks LocSympNets for learning the flow of phase volume-preserving dynamics. The construction of LocSympNets stems from the theorem of the local Hamiltonian description of the divergence-free vector field and the splitting methods based on symplectic integrators. Symplectic gradient modules of the recently proposed symplecticity-preserving neural networks SympNets are used to construct invertible locally-symplectic modules, which compositions result in volume-preserving neural networks LocSympNets. To further preserve properties of the flow of a dynamical system LocSympNets are extended to symmetric locally-symplectic neural networks SymLocSympNets, such that the inverse of SymLocSympNets is equal to the feed-forward propagation of SymLocSympNets with the negative time step, which is a general property of the flow of a dynamical system. LocSympNets and SymLocSympNets are studied numerically considering learning linear and nonlinear volume-preserving dynamics. In particular, we demonstrate learning of linear traveling wave solutions to the semi-discretized advection equation, periodic trajectories of the Euler equations of the motion of a free rigid body, and quasi-periodic solutions of the charged particle motion in an electromagnetic field. LocSympNets and SymLocSympNets can learn linear and nonlinear dynamics to a high degree of accuracy even when random noise is added to the training data. In all numerical experiments, SymLocSympNets have produced smaller errors in long-time predictions compared to the LocSympNets. When learning a single trajectory of the rigid body dynamics locally-symplectic neural networks can learn both quadratic invariants of the system with absolute relative errors below 1%. In addition, SymLocSympNets produce qualitatively good long-time predictions, when the learning of the whole system from randomly sampled data is considered. LocSympNets and SymLocSympNets can produce accurate short-time predictions of quasi-periodic solutions, which is illustrated in the example of the charged particle motion in an electromagnetic field.

Physics education using beams of ions and electrons

Physics education and public outreach are becoming increasingly important in the activities of physics departments in universities and research centers. In this contribution, we would like to illustrate some didactic paths focused on Ion and electron beam technologies, developed in our research group to create connections with nearby secondary schools. These didactic paths connect curricular topics, like for example the motion of charged particles within electric and magnetic fields, with the production and the use of beams of ions and electrons in several branches of both basic and applied research.

Трехмерная ловушка с возбуждением колебаний ионов на границе устойчивости диаграммы Матье

Vibrations of charged particles in compositions of three-dimensional high-frequency quadrupole and static homogeneous electric fields in the stable region and in the vicinity of the stability boundary of the Mathieu diagram are investigated. Using a pseudopotential model of a rapidly oscillating field, it is shown that the motion of charged particles during linear scanning of a secular frequency is described by the Airy differential equation. Based on the properties of solutions of the Airy equation, a method of ion mass separation with resonant excitation of oscillations at the stability boundary of the Mathieu diagram has been developed. To implement the method, the ion-optical system of the three-dimensional trap is supplemented with corrective electrodes. Computer modeling has determined the optimal potentials of the correcting electrodes, at which the errors of the distributions of quadrupole and homogeneous fields do not exceed 10E-4 and 2·10E-3. Keywords: superposition of quadrupole and homogeneous fields, Airy differential equation, mode of resonant excitation of oscillations, three-dimensional ion trap with correcting electrodes.