Oblique External Magnetic Field Research Articles

Density polarization effect of spin-up and spin-down electrons on magnetosonic solitons in a dense plasma with oblique magnetic field

Nonlinear wave propagation of fast and slow magnetosonic waves is investigated in a magnetized quantum plasma with spin polarization effects of degenerate electrons. The multi-fluid quantum magnetohydrodynamic model is considered and two separate fluid dynamic equations for degenerate electrons i.e. spin-up and spin-down states (Pauli paramagnetism) with their different Fermi pressures. The ions are assumed to be classical and external magnetic field lies in a plane. The magnetization energy and current density of electrons due to the spin-1/2 effects are included in the momentum equation of the degenerate electrons and Maxwell equations, respectively. A Korteweg-de-Vries (KdV) equation is derived for nonlinear magnetosonic waves in a dense magnetized plasma with the inclusion of electron spin effects and oblique external magnetic field. The electron inertial effect (which causes wave dispersion) of both spin-up and spin-down state electrons is also included in the model. It is found that electron spin polarization density has significant effects on the phase speed and soliton structures (i.e. its width and amplitude) of fast (hump) and slow (dip) magnetosonic waves in a dense magnetized plasma. The present theoretical study along with the obtained numerical results may have possible applications towards many realistic astrophysical scenarios.

Study of two-electron temperature plasma sheath using non-extensive electron distribution in presence of an external magnetic field

In this study, the physics of sheath formation in a collisional two-electron temperature plasma in the presence of an oblique external magnetic field has been investigated. At first, a comparative study among the fluid electron model, Boltzmann electron model, and the non-extensive electron model has been carried out and a suitable range of non-extensive parameter q has been predicted. In the latter part, a collisional two-electron temperature plasma is considered. Both the hot and cold electron densities are described using the non-extensive distribution, whereas cold ions are described by the fluid equations. The properties of the sheath are investigated in different collisional regimes by varying the non-extensive parameter (q) and the hot to cold electron densities and temperatures. The magnetic field inclination angle is varied in the limit 1° ≤ α ≤ 5°. It is observed that electron distribution significantly deviates from Boltzmann distribution for nearly parallel magnetic field. Moreover, collision enhanced flux deposition for highly magnetized case is a significant finding of the study. The results obtained in this study can enhance the understanding of plasma–matter interaction processes where multiple electron groups with near parallel magnetic field are found.

Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation

In this paper, the numerical solution of the fully developed liquid–metal magnetohydrodynamic (MHD) flow is given in a rectangular duct under an external oblique magnetic field with no-slip and insulated walls containing crack regions. The coupled MHD flow equations are transformed first into decoupled convection–diffusion equations in terms of the velocity and induced magnetic field. Thus, we apply the SUPG stabilization in the finite element method (FEM) solution procedure for high values of Hartmann number which determine the convection dominant case. Numerical solutions for high values of Hartmann number and several orientation angles of external magnetic field as well as different crack configurations depict the effects of these parameters on the flow, flowrate and induced current. The SUPG in the FEM solution of MHD equations enables one to display the well-known characteristics of MHD pipe flow for large values of Hartmann number in which wall insulation is faced to several cracks. It is found that, the flowrate drops with an increase in the Hartmann number, and the increase in the number and lengths of the cracks which are located on one Hartmann wall. The flowrate is minimum if the crack is located at the center of the Hartmann wall. If the crack is located on the side layer, it does not significantly affect the flowrate. The case of each Hartmann wall contains one crack, significantly drops the flowrate compared to two cracks on the same Hartmann wall. Also, the breakdowns and peaks are sharpened when the Hartmann wall is a curved boundary. The FEM with SUPG stabilization is capable of capturing flow changes for high values of Hartmann number even in the vicinity of small-sized crack regions.

Nonlinear Propagation of Gaussian Laser Beam in Magnetized Plasma: Effect of Oblique Magnetic Field

In this paper, the propagation of Gaussian laser beam in underdense and magnetized plasma has been studied. The effect of oblique external magnetic field on self-focusing of laser is specifically explored. An envelope equation governing dependence of beam-width parameter with dimensionless distance of propagation of laser is derived by adopting parabolic equation approach under WKB and paraxial approximations. It is found that increasing the angle between the laser beam magnetic field and external magnetic field decreases the self-focusing of laser propagating through plasma.

Temporal Ion Velocity Variation with Obliqueness in Magnetized Plasma Sheath

A narrow region having sharp gradients in physical parameters is formed whenever plasma comes into contact with a material wall. In this work, the temporal velocity variation of ions in such a sheath has been studied in the presence of an external oblique magnetic field. The Lorentz force equation has been solved for the given boundary conditions using Runge-Kutta method. In order to satisfy the Bohm criterion, ions enter the sheath region with ion acoustic velocity. It is observed that all components of the velocity waves are damped in plasma in the time scale of one second. The computed oscillatory part of ion velocity match with the equation of the damped harmonic oscillator. Thus obtained damping constants as well as the frequency of all three components are nearly equal for obliqueness less than 600 after which they are distinctly different. This is due to the fact that the magnetic field becomes almost parallel to the wall. In earlier studies, only the final velocity profiles are reported and hence this study is useful in understanding how the ion velocities evolve in time as they move from sheath entrance towards the wall.

Chebyshev wavelet collocation method for magnetohydrodynamic flow equations

This study proposes Chebyshev wavelet collocation method for partial differential equation and applies to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Approximate solutions of velocity and induced magnetic field are obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. Numerical results of the MHD flow problem show that the accuracy of proposed method is quite good even in the case of a small number of grid points. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number Ha ≤ 1000.

Relativistic electron dynamics in ion channel guiding in the presence of a helical ‎wiggler and an external oblique magnetic field ‎

In this paper, the electron acceleration and its relativistic dynamics in an ion-channel formed due to the laser pulse propagation through the plasma and under influence of the ion channel space-charge and a heliacal wiggler as well as the oblique magnetic field have been investigated. The equations for investigation of the electron dynamics are the tree-dimension Lorentz equations. For analytical analysis of the obtained equations, a three-dimension single particle code and forth order Runge-Kutta method is used as well. The electron energy gain and the relativistic electron dynamics drastically are affected by the ion-channel potential and the helical wiggler and also the external oblique magnetic field. The results of this paper can be significant in the selection of the appropriate parameters for plasma-based accelerators design.

NUMERICAL SOLUTION OF MAGNETOHYDRODYNAMIC FLOW PROBLEM USING RADIAL BASIS FUNCTION BASED FINITE DIFFERENCE METHOD

This paper focuses on the application of Radial Basis Function generated Finite Difference Method (RBF-FD) to solve Magnetohydrodynamic (MHD) flow equation in a rectangular duct in the presence of the transverse external oblique magnetic field. Multiquadric (MQ) Radial Basis Function is used to obtain the numerical solution of the MHD flow problem. Accuracy of the solution can be improved by varying the shape parameter in MQ function. The solution obtained from RBF-FD method is compared with the analytical solution and classical Finite Difference solution. Contours are presented for various Hartmann numbers with different grid sizes and directions of the applied magnetic field. The behaviour of velocity and the magnetic field of the MHD flow have been studied using the contours.

Linear analysis of the dispersion relation of surface waves of a magnetic fluid in a square container under an external oblique magnetic field

In this study, free surface evolution of a magnetic fluid in a finite size tank which is subjected to an external magnetic field was investigated. The physical problem and equations governing fluid motion and magnetic field were given with boundary conditions. Using proper selection of variables, dimensionless equation system governing magnetic fluid sloshing were written. Resolution method based on multiple scale variables was presented and solution of the linear problem was given. The dispersion relation obtained in the finite depth case was compared with that corresponding to an infinite depth calculated with the same assumptions. Direction and magnitude of the external magnetic field, magnetic permeability ratio and surface tension effects on magnetic fluid free surface stability were analysed and important results were discussed.

Genesis of non-uniformity of plasma fluxes over emissive wall in low-temperature plasmas

Origins of spatial modulation of stationary electron and ion currents to the wall in discharge plasma with/without magnetic field at low gas pressure are studied in the experiments and 2D PIC MCC simulations. It is shown that a non-uniformity of ion and electron fluxes to the wall is induced by (a) a non-planar topology on the emissive wall, (b) a difference in the secondary electron emission yields of materials in segmented wall or (c) an inclination of the external magnetic field. The transition in the sheath structure over the grooved emissive surface from a developed sheath to a collapsed one caused by the increase of electron energy enlarges the alteration of the ion and electron currents over the grooved or segmented surfaces. The experimental study of the plasma-emissive wall sheath transition was carried out with hexagonal boron nitride wall samples grooved with the characteristic size of 1 mm and 5 mm, which is about of the Debye length. In kinetic simulations, this phenomenon is analyzed in terms of the electron and ion energy distribution functions. An external oblique magnetic field applyed to the dc discharge is found to redistribute the plasma and the periodical structure with the spikes of electron and ion densities forms This phenomena causes the non-uniform spatial distribution of electron and ion currents to the wall. The spikes in electron and ion densities became more pronounced with an increase of magnetic field incidence angle.

Effect of an Oblique Magnetic Field Applied to the Sloshing of Free Surface Waves in the Magnetic Fluid

In this paper, linear theory of magnetic fluid sloshing in a rectangular tank subjected to an external oblique magnetic field was studied. Historic of subject as well his importance for fluid mechanics, technology and industrial applications. Magnetic fluid was considered perfect, incompressible and irrotational. Surface tension, gravity and magnetic permeability were taken into account. Linear equations are solved with linear boundary conditions. In the framework of the linear theory, variable separation method makes it possible to construct solutions and obtain eigenfrequencies and the eigen modes. The linear theory is still valid for a very small amplitude of sloshing. The direction and amplitude effects of the external oblique magnetic field on the free surface evolution were analyzed and main results were synthesized. The stability criteria are discussed theoretically and graphically illustrated.

Effects of magnetic fields on capillary-gravity waves in the presence of magnetic surfactants

The stability of capillary-gravity wave motion on horizontal free surface of viscous noncompressible fluid in the presence of magnetic surfactant in an external magnetic field was studied. It is shown that for normal as well as for tangential external magnetic field the horizontal free liquid surface is unstable for field strength exceeding some critical value that does not depend on the elastic constant of the surfactant film. However, for oblique external magnetic field the stability of the free surface depends not only on the field value but also on the surfactant elastic constant.

Nonlinear interaction of intense left- and right-hand polarized laser pulse with hot magnetized plasma

In this article, self-focusing of an intense circularly polarized laser pulse in the presence of an external oblique magnetic field in hot magnetized plasma, using Maxwell’s equations and the relativistic fluid momentum equation, is studied. An envelope equation governing the spot size of the laser beam for both of left- and right-hand polarizations has been derived and the effects of the plasma temperature and oblique magnetic field on the electron density distribution of hot plasma with respect to variation of the normalized laser spot size has been investigated. Numerical results depict that in right-hand polarization, self-focusing of the laser pulse along the propagation direction in hot magnetized plasma becomes better and more compressed with increasing $\unicode[STIX]{x1D703}$. Inversely, in left-hand polarization, increase of $\unicode[STIX]{x1D703}$ in an oblique magnetic field leads to enhancement of the spot size and reduction self-focusing. Besides, in the plasma density profile, self-focusing of the laser pulse improves in comparison with no oblique magnetic field. Also it is shown that plasma temperature has a key role in the laser spot size, normalized laser output power and the variation of plasma density.

A mathematical description for the scattering phenomena of plane wave from elliptical plasma antenna located in oblique static magnetic field

The problem of electromagnetic wave scattering from an elliptical plasma cylinder in the presence of an external oblique magnetic field is investigated. The electromagnetic waves are landed obliquely on the plasma column. Knowing the dielectric permittivity tensor of the plasma column, the electric potential and the electric field inside and outside the plasma column are obtained for the long-wavelength waves. The graphs of the electric field profile and pattern scattering are presented. Also, the dependence of those graphs on the incident angle, the geometrical dimensions of the plasma column and the magnetic field angle are analyzed. The physical justifications based on the theory of Fresnel’s transmission coefficients for describing the graphs, have been presented. Moreover, the effective factors on the shift of the resonance frequency are investigated. Finally, to verify the accuracy of the obtained results, some limiting cases are discussed.

Laser-Plasma Interaction in Presence of an Obliquely External Magnetic Field: Application to Laser Fusion without Radioactivity

In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic Geld has been studied. Imposing an external magnetic Geld on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen-Boron (HB) fuel, the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle (from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.

Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic field

The stability of base gravitational convection in a layer of ferrofluid confined between two vertical wide and tall non-magnetic plates, heated from one side, cooled from the other and placed in a uniform oblique external magnetic field is studied. Two distinct mechanisms, thermo-gravitational and thermo-magnetic, are found to be responsible for the appearance of various stationary and wave-like instability modes. The characteristics of all instability modes are investigated as functions of the orientation angles of the applied magnetic field and its magnitude for various values of magnetic parameters when both the thermo-magnetic and gravitational buoyancy mechanisms are active. The original three-dimensional problem is cast in an equivalent two-dimensional form using generalised Squire’s transformations, which significantly reduces a computational cost. Subsequently, full three-dimensional instability patterns are recovered using the inverse Squire’s transformation, and the optimal field and pattern orientations are determined.

Theoretical studies to elucidate the influence of magnetic dipolar interactions occurring in the magnetic nanoparticle systems, for biomedical applications

In recent years, the study of magnetic nanoparticles has been intensively developed not only for their fundamental theoretical interest, but also for their many technological applications, especially biomedical applications, ranging from contrast agents for magnetic resonance imaging to the deterioration of cancer cells via hyperthermia treatment. The theoretical and experimental research has shown until now that the magnetic dipolar interactions between nanoparticles can have a significant influence on the magnetic behaviour of the system. But, this influence is not well understood. It is clear that the magnetic dipolar interaction intensity is correlated with the nanoparticle concentration, volume fraction and magnetic moment orientations. In this paper, we try to understand the influence of magnetic dipolar interactions on the behaviour of magnetic nanoparticle systems, for biomedical applications. For the model, we considered spherical nanoparticles with uniaxial anisotropy and lognormal distribution of the sizes. The model involves a simulation stage of the spatial distribution and orientation of the nanoparticles and their easy axes of magnetic anisotropy, and an evaluation stage of the Néel relaxation time. To assess the Néel relaxation time, we are going to discretise and adapt, to the local magnetic field, the Coffey analytical solution for the equation Fokker-Planck describing the dynamics of magnetic moments of nanoparticles in oblique external magnetic field. There are three fundamental aspects of interest in our studies on the magnetic nanoparticles: their spatial & orientational distributions, concentrations and sizes.

Thermomagnetic convection in a layer of ferrofluid placed in a uniform oblique external magnetic field

AbstractLinear stability of magnetoconvection of a ferromagnetic fluid contained between two infinite differentially heated non-magnetic plates in the presence of an oblique uniform external magnetic field is studied in zero gravity conditions. The thermomagnetic convection that arises is caused by the spatial variation of magnetisation occurring due to its dependence on the temperature. The critical values of the governing parameters at which the transition between motionless and convective states is observed are determined for various field inclination angles and for fluid magnetic parameters that are consistently chosen from a realistic experimental range. It is shown that, similar to natural paramagnetic fluids, the most prominent convection patterns align with the in-layer component of the applied magnetic field but in contrast to such paramagnetic fluids the instability patterns detected in ferrofluids can be oscillatory. It is also found that, contrary to paramagnetic fluids, the stability characteristics of magnetoconvection in ferrofluids depend on the magnitude of the applied field which becomes an additional parameter of the problem. This is shown to be due to the nonlinearity of the magnetic field distribution within the ferrofluid.

Haar wavelet approximation for magnetohydrodynamic flow equations

This study proposes Haar wavelet (HW) approximation method for solving magnetohydrodynamic flow equations in a rectangular duct in presence of transverse external oblique magnetic field. The method is based on approximating the truncated double Haar wavelets series. Numerical solution of velocity and induced magnetic field is obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. The calculations show that the accuracy of the Haar wavelet solutions is quite good even in the case of a small number of grid points. The HW approximation method may be used in a wide variety of high-order linear partial differential equations. Application of the HW approximation method showed that it is reliable, simple, fast, least computation at costs and flexible.

Solution of Magnetohydrodynamic Flow in a Rectangular Duct by Chebyshev Polynomial Method

In this study, Chebyshev polynomial method is applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. In present method, approximate solution is taken as truncated Chebyshev series. The MHD equations are decoupled first and then present method is used to solve for positive and negative Hartmann numbers. Numerical solutions of velocity and induced magnetic field are obtained for steady-state, fully developed, incompressible flow for a conducting fluid inside the duct. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann numbers .