Uniform Magnetic Field Parallel Research Articles

Dynamics of charged and magnetized particles around cylindrical black holes immersed in external magnetic field

The motion and acceleration of an electrically charged and magnetized particle around a cylindrical black hole in the presence of an external asymptotically uniform magnetic field parallel to the [Formula: see text]-axis are investigated. We look at circular orbits around a central object and study the dependence of the most internal stable circular orbits (ISCO) on the so-called magnetic coupling parameters, which are responsible for the interaction between the external magnetic field and magnetized and charged particles. It is shown that the ISCO radius decreases with increasing magnetized interaction parameter. Therefore, we also studied collisions of magnetized particles around a cylindrical black hole immersed in an external magnetic field, and showed that the magnetic field can act as a particle accelerator near nonrotating cylindrical black holes.

Long-Term Electrodeposition under a Uniform Parallel Magnetic Field. 2. Flow-Mode Transition from Laminar MHD Flow to Convection Cells with Two-Dimensional (2D) Nucleation.

Following the analysis of the self-organization of two-dimensional (2D) nuclei in Part 1, the flow-mode transition from laminar magnetohydrodynamics (MHD) flow to convection cells accompanied by 2D nucleation under a uniform parallel magnetic field was theoretically examined using the statistical mechanics of nonequilibrium fluctuation. As a result, it was clarified that secondary nodules of 2D nuclei develop with multiple nucleations during the transition, forming a one-upon-another structure. Then, the evolution of the convection cells as well as the secondary nodules requires unstable growth of the asymmetrical fluctuations by the specific adsorption of an ion. As predicted by the theory, the electrolytic current in copper deposition with specific adsorption of hydrogen ions under a parallel magnetic field developed with time, resulting in a nonlinear steplike curve in a 1200 s deposition time.

Long-Term Electrodeposition under a Uniform Parallel Magnetic Field. 1. Instability of Two-Dimensional Nucleation in an Electric Double Layer.

Under a parallel magnetic field, after long-term copper deposition from an acidic copper sulfate solution, numerous spherical secondary nodules of 10 to 100 μm diameters were formed one upon another in dendritic mode. This is a new type of micro-magnetohydrodynamic (MHD) effect arising from the unstable growth of three-dimensional (3D) and two-dimensional (2D) nuclei by specific adsorption of hydrogen ions (second micro-MHD effect). From the viewpoint of instability in electrodeposition, though 3D nucleation in the diffusion layer is always unstable, with ionic specific adsorption such as hydrogen ions, stable 2D nucleation turns unstable after long-term deposition. The resultant competitive growth of 3D and 2D nuclei produces spherical nodules as their composite, leading to their dendritic growth. Furthermore, though negligibly small, nonequilibrium fluctuations occurring in 2D nucleation migrate with the laminar solution flow caused by Lorentz force (MHD flow). Depending on whether the ionic adsorption is specific or nonspecific, the traveling asymmetrical fluctuation changes the direction to the upstream or downstream side, respectively.

Electron power absorption dynamics in magnetized capacitively coupled radio frequency oxygen discharges

The influence of a uniform magnetic field parallel to the electrodes on radio frequency capacitively coupled oxygen discharges driven at 13.56 MHz at a pressure of 100 mTorr is investigated by one-dimensional particle-in-cell/Monte Carlo collision (1D PIC/MCC) simulations. Increasing the magnetic field from 0 to 200 G is found to result in a drastic enhancement of the electron and the ion density due to the enhanced confinement of electrons by the magnetic field. The time and space averaged O− ion density, however, is found to remain almost constant, since both the dissociative electron attachment (production channel of O−) and the associative electron detachment rate due to the collisions of negative ions with oxygen metastables (main loss channel of O−) are enhanced simultaneously. This is understood based on a detailed analysis of the spatio-temporal electron dynamics. The nearly constant O− density in conjunction with the increased electron density causes a significant reduction of the electronegativity and a pronounced change of the electron power absorption dynamics as a function of the externally applied magnetic field. While at low magnetic fields the discharge is operated in the electronegative drift-ambipolar mode, a transition to the electropositive α-mode is induced by increasing the magnetic field. Meanwhile, a strong electric field reversal is generated near each electrode during the local sheath collapse at high magnetic fields, which locally enhances the electron power absorption. A model of the electric field generation reveals that the reversed electric field is caused by the reduction of the electron flux to the electrodes due to their trapping by the magnetic field. The consequent changes of the plasma properties are expected to affect the applications of such discharges in etching, deposition and other semiconductor processing technologies.

Combined effects of Forchheimer, Soret and Dufour on MHD mixed convective dusty viscoelastic Couette flow in an irregular channel

PurposeA study on convective aspects was carried out on a Couette flow in an irregular channel by applying a constant uniform magnetic field parallel to the channel flow.Design/methodology/approachThe dynamic study of such a flow resulted in highly nonlinear coupled partial differential equations. To solve these partial differential equations analytically, regular perturbation method was invoked for velocity, temperature and concentration with a combined parameter of Soret and Forchheimer. The numerical computational results have been extracted for various nondimensional parameters with regard to fluid and particle flow as well as for temperature and solute concentration.FindingsThe current article presents a novel approach to assess the effects of drag force as well as the diffusion-based interactions between the velocity, temperature and concentrations with the aid of Soret and Dufour on two-dimensional MHD mixed with a dusty viscoelastic fluid.Originality/valueThe results found are in good agreement with the earlier studies in the absence of nonlinear effect of Forchheimer model.

Theory of microscopic electrodeposition under a uniform parallel magnetic field - 1. Nonequilibrium fluctuations of magnetohydrodynamic (MHD) flow

Nonequilibrium fluctuations of concentration, velocity and so on are formulated for electrode reactions including electrodeposition under a uniform magnetic field parallel to electrode surface. In electrodeposition, nonequilibrium fluctuations occur on the both sides of the electrode surface and solution; on the electrode-surface side, three-dimensional (3D) and two-dimensional (2D) nucleation proceed under the control of symmetrical and asymmetrical nonequilibrium fluctuations, respectively. On the solution side, a characteristic laminar flow called magnetohydrodynamic (MHD) flow with microscopic convection flows called micro-MHD flows are induced, so that the fluctuations on the solution side are described as Fourier components of complex 2D plane waves traveling with the MHD flow. The fluctuations on the electrode-surface side are interfered with the micro-MHD flows, yielding characteristic 3D and 2D nuclei. In Part 1 of the present paper, the amplitudes of the micro-MHD flows and concentration fluctuation on the solution side are first established independent of the fluctuations on the electrode-surface side.

Theory of microscopic electrodeposition under a uniform parallel magnetic field - 2. Suppression of 3D nucleation by micro-MHD flow

In electrodeposition under a uniform parallel magnetic field, the suppression of three-dimensional (3D) nucleation by microscopic magnetohydrodynamic flow (micro-MHD flow) and formation of stream pattern of macroscopic MHD flow by the multiple nucleation of 3D nuclei are theoretically clarified. The interference of micro-MHD flow with concentration fluctuation generally results in the suppression of 3D nucleation (1st micro-MHD effect). However, due to the small scale of length of 3D nucleus, the effective viscosity is too high for micro-MHD flow to sufficiently work on individual 3D nuclei, so that the suppression is not so obvious. On the other hand, for 3D nucleus groups after multiple nucleation, due to larger scale of length, effective viscosity decreases, so that micro-MHD flow easily interacts with the corresponding concentration fluctuation, which gives rise to a striped pattern reflecting macroscopic MHD flow.

Landau levels in the presence of a cosmic string in rainbow gravity

In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schrödinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein–Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity.

Klein–Gordon oscillator with position-dependent mass in the rotating cosmic string spacetime

A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein–Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein–Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein–Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

On Tomonaga’s theory of split-anode magnetrons

This article is meant to formulate the equations of motion of an electron in a cavity magnetron using action-angle variables. This means following the electron's path on its way from a cylindrical cathode moving toward a co-axial cylindrical anode in presence of a uniform magnetic field parallel to the common axis. After analyzing the situation without coupling to an external oscillatory electric field, we employ methods of canonical perturbation theory to find the resonance condition between the frequencies of the free theory w_r, w_phi and the applied perturbing oscillatory frequency w. A long-time averaging process will then eliminate the periodic terms in the equation for the now time-dependent action-angle variables. The terms that are no longer periodic will cause secular changes so that the canonical action-angle variables (J, delta) change in a way that the path of the electron will deform gradually so that it can reach the anode. How the ensemble of the initially randomly distributed electrons forms spokes and how their energy is conveyed to the cavity-field oscillation is the main focus of this article. Some remarks concerning the importance of results in QED and the invention of radar theory and application conclude the article.

Landau quantization in the spinning cosmic string spacetime

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e., having a finite width and uniformly filled with both material and vacuum energies.

Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers

The flow of steady, incompressible, viscous, electrically conducting fluid past a sphere in the presence of an uniform magnetic field parallel to the undisturbed flow is investigated using the finite difference method. The multigrid method with defect correction technique is used to achieve the second order accurate solution. The Hartmann number, M is used as the perturbation parameter. It is found that the increase of magnetic field decreases the wake length and increases the drag coefficient. The graphs of streamlines, vorticity lines, drag coefficient, surface pressure and surface vorticity are presented and discussed. Keywords: Navier-Stokes equations, MHD, Hartmann number, Multigrid method, Defect correctionInternational Journal of Engineering, Science and Technology, Vol. 6, No. 1, 2014, pp

Six-Beam Gun Design for a High Power Multiple-Beam Klystron

This paper presents the detailed design of a six-beam gun for use in an L-band 10-MW multiple-beam klystron. To facilitate the gun simulation, we developed a joint design methodology with 2-D and 3-D simulation codes. The six-beam gun is designed to produce a total current of 132 A divided equally among the six beams at an accelerating potential of 115 kV. For the design of the gun, special emphasis is placed on the geometric layout of the electrodes to ensure moderate voltage gradient, accurate beam perveance and reasonable cathode loading. The magnetic circuit consists of solenoid magnet structures. Special coils and iron shells are set to ensure a uniform parallel magnetic field in the region between the cathode and the anode. Two set of amendatory coils and shield irons are set in the transition region to optimize the beam radius. Special coils are set in the both ends of the interaction region to trim the radial magnetic fields. The gun design is accomplished with EGUN and CST codes. Simulation results show that the joint design methodology is effective and the magnetic circuit has an excellent flexibility. The final gun has a cathode loading lower than 2.1 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and excellent beam transport characteristics. The dependency relationship between the beam off-centering and the asymmetry radial magnetic fields is analyzed.

On some consequences of an external magnetic field applied to HTS coils

A computational model which enables to evaluate the distribution of the critical currents, electric fields and the voltage in the winding of a solenoidal high temperature superconducting (HTS) magnets subjected to an external magnetic field parallel with the magnet axis, was developed. The model comes out from the well-known power law between the electric field and the transport current of the HTS tape short sample. It allows to predict the voltage–current V( I) characteristics of both the pancake coils and the complete magnet. The model was applied to the magnet system consisting of 22 pancake coils made of multifilamentary Bi(2223)/Ag tape at 20 K, which is subjected to an external uniform magnetic field parallel with the coil axis. A rather unexpected behavior of the magnet at different operating conditions (operating current and external magnetic field strength) is predicted, analyzed and reported together with a theoretical explanation. On one hand, the external uniform magnetic field parallel with the coil axis increases the resulting magnetic field strength, however, on the other hand it simultaneously decreases the angle between the resulting magnetic field and the tape surface. Thus, the effect of higher magnetic loading caused by the presence of an external magnetic field strength which is acting on individual turns located close to the coil’s flanges is compensated by more favorable orientation of the tape with respect to the resulting magnetic field. As a result, increase in the critical currents of these turns is expected. Further, the results indicate, that in case of the high field HTS insert coils the anisotropy in the I c ( B) characteristic does not play a substantial role. As a consequence, the technology of the production of the tapes for high field insert HTS coils should concentrate rather on the tapes having the current carrying capacity as high as possible, than on the attempt how to decrease the anisotropy in the I c ( B) by changing the architecture of the filaments in the tape.

Radiation from relativistic shocks in turbulent magnetic fields

Using our new 3-D relativistic particle-in-cell (PIC) code parallelized with MPI, we investigated long-term particle acceleration associated with a relativistic electron–positron jet propagating in an unmagnetized ambient electron–positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value as predicted by hydrodynamic shock compression. In the jet (reverse) shock behind the bow (forward) shock the strongest electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. In order to calculate radiation from first principles that goes beyond the standard synchrotron model used in astrophysical objects we have used PIC simulations. Initially we calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We then used the technique to calculate emission from electrons in a small simulation system. From these simulations we obtained spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields with red noise. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger simulation system may generate a jitter/synchrotron spectrum.

RADIATION FROM RELATIVISTIC SHOCKS WITH TURBULENT MAGNETIC FIELDS

Using our new 3D relativistic electromagnetic particle (REMP) code parallelized with MPI, we investigated long-term particle acceleration associated with a relativistic electron–positron jet propagating in an unmagnetized ambient electron–positron plasma. We have also performed simulations with electron-ion jets. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability for electron–positron jets and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks for pair plasma case. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value for pair plasmas. Behind the bow shock in the jet shock strong electromagnetic fields are generated. These fields may lead to time-dependent afterglow emission. We calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We also used the new technique to calculate emission from electrons based on simulations with a small system with two different cases for Lorentz factors (15 and 100). We obtained spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields with red noise. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability.

Magnetometric Demagnetizing Factors for Various Shapes of Rotational Symmetry

We have investigated the magnetometric demagnetizing factors of rotation-symmetrical magnetic bodies of relative permeability mu placed in a uniform magnetic field parallel to the axis of rotation. The bodies we considered include a cylinder, a sphere, a bicone, and a rotating astroid. We numerically calculated the magnetometric demagnetizing factors from the surface magnetic charge densities sigma obtained by the surface magnetic charge simulation method. We show that the magnetometric demagnetizing factors for various shapes of rotation-symmetrical bodies are significantly different from those of a sphere. We have determined the shape producing the largest demagnetizing field in ferromagnetic bodies with sufficiently large relative permeability mu . We report the magnetometric demagnetizing factors for uniformly magnetized bodies (mu = 1 , i.e., susceptibility chi = 0 ) of various shapes.

DC and AC Shielding Properties of Bulk High-Tc Superconducting Tubes

We have studied numerically and experimentally the magnetic flux penetration in high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tc</i> superconducting tube subjected to a uniform magnetic field parallel to its long axis. This study is carried in view of designing low-frequency magnetic shields by exploiting the diamagnetic properties of high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tc</i> superconducting ceramics. We have measured the field attenuation for applied magnetic fields in the frequency range 5 mHz-0.1 Hz by Hall probe measurements and at audio frequencies using a sensing coil. A simple 1D analysis using the Kim critical state model was found to be able to reproduce the experimental data satisfactorily. We have also determined the phase shift between the internal and the applied field both experimentally and numerically. Finally, we have studied the sweep rate dependence of the magnetic shielding properties, using data recorded either at several constant sweep rates d <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> /d <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> or at several AC fields of various amplitudes and frequencies. Both methods agree with each other and lead to a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -value of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> ~ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> law equal to ~ 40 at 77 K.

The Influence of a Longitudinal Magnetic Fields on a Non‐Uniform Positive Column

AbstractThe variations of plasma parameters of a dc discharge in a non‐uniform magnetized plasma were measured using fast floating double Langmuir probes. A solenoid is used to produce a uniform magnetic field parallel to the discharge axis. The axial changes of the plasma parameters are presented in the range of longitudinal magnetic fields 200 to 600 Gauss at the pressure range 0.3 to 2.1 Torr and discharge currents 5 and 15 mA in argon gas. The experimental results indicate that, as a consequence of the axial magnetic.eld and the variations in the discharge tube radii, the plasma parameters at small radius exhibit obvious changes in their distributions along the axis compared to the situation of unmagnetized plasma. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Interaction of a magnetic vortex with the probe field of a magnetic force microscope

The interaction of a magnetic vortex in a circular ferromagnetic nanoparticle with the probe field of a magnetic force microscope (MFM) is theoretically investigated. In the calculations, the probe field is approximated by the point dipole field. The rigid magnetic vortex model is used to describe the vortex state of magnetization. It is found that the effect of the probe field on the rigid magnetic vortex shell is similar to the effect of a uniform magnetic field parallel to the particle plane. The effect of the Z component of the probe field on the core of the vortex results in mutual probe-vortex attraction or repulsion. It is shown that the magnetization direction of the core of the vortex in the MFM probe field can be changed without a change in the shell vorticity direction.