Equations Of Motion For Particles Research Articles

External magnetic field effect on the growth rate of a plasma-loaded free-electron laser

In order to extend the production of intense coherent radiation to angstrom wavelengths, a laser wave is employed as a laser wiggler which propagates through a magnetized plasma channel. The plasma-loaded laser wigglers increase the ability of laser guidance and electron bunching process compared to the counterpropagating laser wigglers in vacuum. The presence of the plasma medium can make it possible to propagate the laser wiggler and the electron beam parallel to each other so that the focusing of the pulse will be saved. In addition, employing an external guide magnetic field can confine both the ambient plasma and the transverse motions of the electron beam, therefore, improving the free-electron lasers’ efficiency, properly. Electron trajectories have been obtained by solving the steady state equations of motion for a single particle and the fourth-order Runge-Kutta method has been used to simulate the electron orbits. To study the growth rate of a laser-pumped free-electron laser in the presence of a plasma medium, perturbation analysis has been performed to combine the momentum transfer, continuity, and wave equations, respectively. Numerical calculations indicate that by increasing the guide magnetic field frequency, the growth rate for group I orbits increases, while for group II and III orbits decreases.

Estimation of Acoustic Energy and Performance Characterization of Acoustic Concentrator

Among many methods of particle concentration in liquid, acoustic concentrator uses ultrasonic standing wave to concentrate microparticles in liquid. In order to determine its performance on particle concentration, estimation of acoustic energy density inside the concentrator is important since energy density is the main contributing factor in calculating the primary acoustic radiation force acting on the particles. The balance between the primary radiation force and hydrodynamic force acting on the particles inside the acoustic concentrator determine the performance of the acoustic concentrator. Therefore, this study focuses on the measurement of acoustic energy density inside the h-shaped acoustic concentrator and characterization of performance of the concentrator. First, energy density is estimated by curve-fitting the experimental particle position in the ultrasonic field with one-dimensional theoretical position. Second, two-dimensional acoustic and hydrodynamic fields are determined using two-dimensional simulation model in COMSOL Multiphysics. Integrating the governing equation for particle motion in the balance of acoustic and hydrodynamic forces result in the particle trajectory and it is compared with the experimental observation. The results would provide deeper insight into the operation of acoustic concentrator and the detailed phenomenon of particle motions inside the concentrator.

Drift approximation and ideal MHD of cold relativistic winds

A critical revision of the essential principles of the physics of relativistic flows of cold plasma is given. We prove that the approximation of ideal magnetic hydrodynamics of the cold plasma is equivalent to the drift approximation of motion of charged particles in an electromagnetic field. The equations of magnetohydrodynamics are obtained from equations for the drift motion of the charged particles. The conditions of application of the equations of ideal magnetohydrodynamics are obtained. In the case of the Crab pulsar the violation of the frozen-in condition can happen at a distance that well exceeds the distance to the termination shock. One fluid MHD can be incorrect at the light cylinder provided that the Lorentz factor of the plasma exceeds $10^{4}$ and the curvature radius of the flow line is comparable with the light cylinder. It is shown that the electric currents in the cold plasma are the result of the inertial drift motion of the charged particles in the crossed electric and magnetic fields.

Investigation of the particle capture of elliptic cross-sectional matrix for high gradient magnetic separation

High gradient magnetic separation (HGMS) is an effective method to recover fine weakly magnetic particles from a suspension. Magnetic matrices are the crucial components of the HGMS system. The most commonly used matrices in HGMS are cylinder matrices of high magnetic permeability. Special cross-section shape matrix may have better magnetic characteristics and show better performance than circular cross-section matrix in HGMS. The particle capture of elliptic cross-section matrix in the three configurations of HGMS are modeled and investigated, aiming at revealing the application possibility of elliptic cross-section matrix in HGMS and providing a research clue for the development of novel high efficiency magnetic matrix for scientific researchers. The magnetic field and the flow field around the elliptic matrix are analytically calculated. The particle motion equations in the three configurations of HGMS are derived. The particle motion trajectories around the elliptic matrices are plotted. The particle capture radius and efficiency of the elliptic matrix are calculated and compared with those of the circular matrix, providing that the diameter of the circular matrix is equal to the short axis of the elliptic matrix. In the three configurations, the elliptic matrix can present higher particle efficiency than the circular matrix under some circumstances. The results indicate the promising application prospect of elliptic cross-section matrix in HGMS. The particle capture efficiency is influenced by many factors. In the development of novel high efficiency magnetic matrix, the magnetic characteristics, the flow characteristics and the arrangement of the matrix should all be taken into consideration.

Gravitational deflection of light and massive particles by a moving Kerr–Newman black hole

The gravitational deflection of test particles including light, due to a radially moving Kerr–Newman (KN) black hole with an arbitrary constant velocity that is perpendicular to its angular momentum, is investigated. In harmonic coordinates, we derive the second post-Minkowskian (2PM) equations of motion for test particles, and solve them by high-accuracy numerical calculations. We then concentrate on discussing the kinematical corrections caused by the motion of the gravitational source to second-order deflection. The analytical formula of the light-deflection angle up to the second order by a moving lens is obtained. For a massive particle moving with a relativistic velocity, there are two different analytical results for the Schwarzschild deflection angle up to the second order reported in the previous works, i.e. and , where and w are the mass of the lens, the impact parameter, and the particle’s initial velocity, respectively. Our numerical result is in perfect agreement with the former result. Furthermore, the analytical formula for massive particle deflection up to the second order in the Kerr geometry is achieved. Finally, the possibilities of detecting the motion effects on the second-order deflection are also analyzed.

A Dusty Plasma in a Non‐Self‐Sustained Gas Discharge at Atmospheric Pressure

AbstractA non‐self‐sustained (NSS) discharge at atmospheric gas pressure containing dust particles is studied. The NSS discharge was controlled by a stationary electron beam with energy up to 120 keV. A numerical model of the NSS discharge is based on the drift‐diffusion approach for electrons and ions and self‐consistently takes into account effects of the dust particles on the electron and ion densities. The dusty component is described by the number balance equation and the equation of motion for dust particles with allowance for the Stokes force, gravity force and electric force in the cathode sheath. Interaction between dust particles is described in the self‐consistent field approximation. It is established that, at a given gas ionization rate and given applied voltage, there is a critical dust particle size above which the levitation condition in the cathode sheath cannot be satisfied. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analysis of the Hydrogen Reduction Rate of Magnetite Concentrate Particles in a Drop Tube Reactor Through CFD Modeling

A computational fluid dynamics (CFD) approach, coupled with experimental results, was developed to accurately evaluate the kinetic parameters of iron oxide particle reduction. Hydrogen reduction of magnetite concentrate particles was used as a sample case. A detailed evaluation of the particle residence time and temperature profile inside the reactor is presented. This approach eliminates the errors associated with assumptions like constant particle temperature and velocity while the particles travel down a drop tube reactor. The gas phase was treated as a continuum in the Eulerian frame of reference, and the particles are tracked using a Lagrangian approach in which the trajectory and velocity are determined by integrating the equation of particle motion. In addition, a heat balance on the particle that relates the particle temperature to convection and radiation was also applied. An iterative algorithm that numerically solves the governing coupled ordinary differential equations was developed to determine the pre-exponential factor and activation energy that best fit the experimental data.

Intrinsic gravitomagnetism and non-commutative effects

We give a demonstration that gravito-magnetism and non-commutative geometry predict an orbit precession for a test particle moving in the central force obeying the inverse-square law. To this end, the two equations of motion for a test particle are compared with each other, one in the non-commutative space involving a static solid sphere and the other in the usual space involving a slowly rotating sphere. The comparison indicates that the non-commutative effect is similar to the intrinsic gravitomagnetic contribution to the orbit precession.

Grain size distribution uncertainty quantification in volcanic ash dispersal and deposition from weak plumes

AbstractWe present the results of uncertainty quantification and sensitivity analysis applied to volcanic ash dispersal from weak plumes with focus on the uncertainties associated to the original grain size distribution of the mixture. The Lagrangian particle model Lagrangian Particles Advection Code is used to simulate the transport of inertial particles under the action of realistic atmospheric conditions. The particle motion equations are derived by expressing the particle acceleration as the sum of forces acting along its trajectory, with the drag force calculated as a function of particle diameter, density, shape, and Reynolds number. Simulations are representative of a weak plume event of Mount Etna (Italy) and aimed at quantifying the effect on the dispersal process of the uncertainty in the mean and standard deviation of a lognormal function describing the initial grain size distribution and in particle sphericity. In order to analyze the sensitivity of particle dispersal to these uncertain variables with a reasonable number of simulations, response surfaces in the parameter space are built by using the generalized polynomial chaos expansion technique. The mean diameter and standard deviation of particle size distribution, and their probability density functions, at various distances from the source, both airborne and on ground, are quantified. Results highlight that uncertainty ranges in these quantities are drastically reduced with distance from source, making them largely dependent just on the location. Moreover, at a given distance from source, the distribution is mostly controlled by particle sphericity, particularly on the ground, whereas in air also mean diameter and sorting play a main role.

A Chebyshev expansion of hydrodynamical fields for ultrafast vibrational wave packet dynamics

A computational method based on the Chebyshev polynomial expansion of the hydrodynamical fields is applied to the quantum trajectory modeling of the one-dimensional vibrational dynamics. The spatial derivatives of the fields are computed using the Chebyshev polynomial recursion, and they are subsequently used to numerically integrate the equations of motion for the fluid particles. The performance of the proposed algorithm is assessed via the comparison with the analytical solutions for the time evolution of a Gaussian wave packet on harmonic potential, and with the results of quantum wave packet propagation on an anharmonic potential. The scheme is found to provide an accurate representation of both the molecular density and the quantum potential, even if low-order truncated expansions are used. The quantum trajectory propagation using the Chebyshev expansion method yields results in close agreement with the corresponding benchmarks, regarding both the time-dependent molecular distributions and the computed observables.

Particle capture of elliptic cross-section matrices for parallel stream high gradient magnetic separation

Purpose – The purpose of this paper is to model the particle capture of elliptic magnetic matrices for parallel stream type high magnetic separation, which can be a guidance for the development of novel elliptic cylinder matrices for high-gradient magnetic separation (HGMS). Design/methodology/approach – The magnetic field distribution around the elliptic matrices is investigated quantitatively and the magnetic field and gradient were calculated. The motion equations of the magnetic particles around the matrices were derived and the particle capture cross-section of elliptic matrices was studied and was compared with that of the conventional circular matrices. Findings – Elliptic matrices can present larger particle capture cross-section than the conventional circular matrices and can be a kind of promising matrices to be applied to HGMS. Originality/value – There is little literature investigating the magnetic characteristics and the particle capture of the elliptic matrices in HGMS, the study is of great significance for the development of novel elliptic magnetic matrices in HGMS.

Effective Perihelion Advance and Potentials in a Conformastatic Background with Magnetic Field

Exact solutions of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources are investigated. In this context, effective potentials are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of the equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the solar system and the Moon (EPM2011). In general, we show that the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein’s gravity alone.

Establishment and analysis of erosion depth model for impeller material FV520B

The multifactorial erosion was conducted in this paper to test the compressor impeller material FV520B using high-speed gas-solid two phase flow erosion tester and surface morphology analysis method. Based on the particle motion and collision energy equation as well as regression analysis of multi-factor orthogonal experiment, a phenomenological erosion depth model which captures the effects of impact velocity, angle and particle size, has been developed. The model includes removal of material due to both deformation damage and micro-cutting. Results show that the peak of experiment depth and the maximum calculated depth all appeared at near 45°, rather than near 24° where the maximum erosion rate appeared. Comparing the calculated values and the results of each single factor experiment, the errors are within 15%. The predictions of the simplified version of the model were in good agreement with the results of single factor experiments. Also, the reliability of the assessment formula was verified to assess the impeller erosion life, which indicated that this calculation model could be used to estimate the erosion depth of compressor impeller material FV520B.

A new method to analyze the velocity spectrograms of photonic Doppler velocimetry

Ejecta mixing takes place at the interface between metal and gas under shock loading, i.e., the transport process of ejecta from metal surface happens in gas. Ejecta production and transport processes in gas are the focuses and key problems of shock wave physics at present. So far, extensive investigations have been devoted mainly to the ejecta formation from metal surface under shock-loaded conditions, and many experimental measurement techniques have been developed, such as the Asay foil, high-speed camera and holography technique. As a newly developed instrument, photon Doppler velocitymetry (PDV) which allows the simultaneous detection of velocities of multiple particles has been widely used in the dynamic impact areas, especially in micro-jetting and ejecta mixing experiments. Although PDV spectrogram includes abundant information about ejecta particles, it seems to be too hard to obtain the particle velocity history, which embarrasses the analysis and application of PDV spectrogram. In this paper, the equation of particle motion including the effects of aerodynamic damping force, pressure gradient force, and additional mass force is established, and the analytical solutions of the particle position and velocity are derived in the conditions of planar constant flow, constant flow, and constant acceleration flow. According to the analytical solutions, the characteristics of particle movement are analyzed. A simplified formulation of the relaxation time of the particle velocity, which reflects the particle decelerated speed, is given. And it is found that the relaxation time is proportional to the four-thirds power of particle diameter. Based on the characteristics of particle motion in the planar constant flow, a new method is proposed to analyze the spectrogram of PDV. The fastest velocity of particle in the mixing zone is obtained by extracting the upper part of PDV spectrogram. By integrating the fastest velocity, the time evolution of the head of mixing zone is deduced approximately. The thickness of the mixing zone can be obtained by subtracting the free surface position from the head of mixing zone. The relaxation time of particle velocity is inferred by the exponential fitting of the fastest velocity based on the motion equation of the particle in the planar constant flow. Furthermore, the equivalent diameter of the mixing zone head can also be obtained through the relaxation time. Based on the above methods, the spectrograms of various ejection mixing experiments under different shock-loaded conditions and gas environments are analyzed. The time evolutions of the mixing zone and equivalent diameter are presented, and the effects of shock loading strength and post-shock gas temperature on the mixing zone are analyzed. It is found that the deduced equivalent diameter in gas is smaller than that in vacuum, validating the pneumatic breakup of liquid metal particles in gas.

Spin-axion coupling

We establish a new covariant phenomenological model, which describes an influence of pseudoscalar (axion) field on spins of test massive particles. The model includes general relativistic equations of particle motion and spin evolution in background pseudoscalar (axion), electromagnetic and gravitational fields. It describes both the direct spin-axion coupling of the gradient type and indirect spin-axion interaction mediated by electromagnetic fields. Special attention is paid to the direct spin-axion coupling caused by the gradient of the pseudoscalar (axion) field. We show that it describes a spin precession, when the pseudoscalar (axion) field is inhomogeneous and/or non-stationary. Applications of the model, which correspond to the three types of four-vectors attributed to the gradient of the pseudoscalar (axion) field (time-like, space-like, and null), are considered in detail. These are the spin precessions induced by relic cosmological axions, axions distributed around spherically symmetric static objects, and axions in a gravitational wave field, respectively. We discuss features of the obtained exact solutions and some general properties of the axionically induced spin rotation.

Heat transfer enhancement in a gas–solid suspension flow by applying electric field

Enhancing convective heat transfer is important for improving performance of heat exchangers. We studied the enhancement of heat transfer in a gas–solid suspension flow wherein the solid particle motions were controlled using an electric field. In the experiments, hollow glass particles suspended in air flowed vertically upward in a channel confined by parallel-plate electrodes, one of which served as a heat transfer surface. Particle trajectories, temperature profiles in the airflow, and heat transfer rates were measured. A theoretical study was also performed by considering the particle equations of motion, electric charge transfer at the walls, and heat exchange between particles and the gas phase using the particle source in cell model. As the results, we found that Coulomb forces acting on particles caused alternating one-sided motion in the flow direction through contact charging on the wall electrodes. Thus, particles repeatedly collided with both channel walls. Hence, heat transfer was enhanced, primarily due to heat transport by particles across thermal boundary layer at the heated wall. The simulation results of heat transfer rates were compared with the experimental results, and show quantitatively good agreement. On the basis of the results, the optimum particle diameter for enhancing heat transfer was determined by imposing the condition that the thermal relaxation time of a particle is equal to the contact-charging time of the particle on the wall.

Simulation of Particle Trajectory in the Head–Disk Interface

This paper presents a numerical method to simulate the particle trajectory in the head–disk interface (HDI). The simulator solves the reduced Navier–Stokes equation with the second-slip boundary conditions to get the air velocity distribution, then solves the motion equations of particles and obtains the trajectories of the particles in the HDI using the binary Lagrange interpolation and the fourth-order Runge–Kutta method. The calculated trajectories of particles follow well with the air streamlines in the recessed regions. The particle density, diameter, and initial entering velocity have different effects on particle movement. Furthermore, particle velocity behaviors in the recessed regions are investigated for the first time. The particle is accelerated or decelerated by the action of the drag force and becomes close to the velocity of local air flow. Such effects are more obvious for small particles than large particles. The particle velocity becomes very small when it is close to the leading edge of the trailing pad. The numerical results also show that the particle goes up when it crosses the transition regions, and the particle moves upward more sharply with higher initial entrance height due to the larger vertical velocity of the local air flow.

The effects of near wall corrections to hydrodynamic forces on particle deposition and transport in vertical turbulent boundary layers

In a previous paper we presented a model for the transport and deposition of particles in a turbulent boundary layer which involved tracking individual particles via their interactions with a succession of random eddies found in each quadrant of the fluid Reynolds shear stress domain. Using drag forces based on unbounded flow, the model in common with other stochastic models significantly underestimated the deposition rates for small particles with particle relaxation times (in wall units) St < 5. Here, using the same model we consider the influence on the transport and deposition of corrections to the drag and lift force in the near wall region utilizing the composite correlations proposed by Zeng et al. for a rigid spherical particle. As far as deposition rates are concerned, the inclusion of near wall effects and lift forces are unable to explain the underestimate in deposition for low inertial particles compared to the benchmark experimental measurements of Liu et al. More specifically, the overall effect of near-wall corrections to the drag is found to decrease deposition rates for small particles and to increase them for large particles. The inclusion of a Saffman lift force into the particle equation of motion (for a uniform bounded shear flow) reduced the deposition rates of the particles considered but the change was not significant (unlike previous predictions). The inclusion of a lift force based on Zeng et al.’s formula (Zeng et al., 2009) which accounts for both wall and Reynolds number effects was little different to that based on Saffman’s formula. In contrast, the corrected drag does yield significant differences between the particle and carrier flow streamwise velocities for large particles (St ∼ 20) in the near wall region. Given all the results obtained, whether the wall effects on the hydrodynamic forces should be included or not depends on specific applications.

Modeling of the charge-state separation at ITEP experimental facility for material science based on a Bernas ion source.

The experiment automation system is supposed to be developed for experimental facility for material science at ITEP, based on a Bernas ion source. The program CAMFT is assumed to be involved into the program of the experiment automation. CAMFT is developed to simulate the intense charged particle bunch motion in the external magnetic fields with arbitrary geometry by means of the accurate solution of the particle motion equation. Program allows the consideration of the bunch intensity up to 10(10) ppb. Preliminary calculations are performed at ITEP supercomputer. The results of the simulation of the beam pre-acceleration and following turn in magnetic field are presented for different initial conditions.

Numerical study of sensitivity enhancement in a photonic crystal microcavity biosensor due to optical forces.

Photonic crystal microcavity biosensors can detect single biomolecules, but reliance on diffusion from microfluidic flow for particle delivery limits the minimum detectable particle concentration. Here the particle equation of motion is solved to find the sensitivity enhancement due to optical forces. The enhancement is examined for a range of parameters, including input optical power, fluid flow rate, device quality factor, and particle size.