NUMERICAL INVESTIGATION OF SILICON MELT FLOW IN A SHALLOW ANNULAR POOL UNDER AN AXIAL MAGNETIC FIELD

We present a set of equations modelling a low-pressure plasma column sustained by a travelling electromagnetic wave in the dipolar mode in the presence of a constant external magnetic field. It is shown that, from a practical point of view, only the m = 1 mode (the right-hand-polarized wave) can sustain plasma columns in a wide region of gas-discharge conditions: plasma radius R, wave frequency ωo, magnetic field Bo and low pressures, irrespective of the nature of the gas. We have examined two gas-discharge regimes: freefall/diffusion and recombination respectively. For a given gas-discharge regime the axial column structure and wave-field characteristics are specified by two numerical parameters: σ = ωR/c and ω = ωc/ω, where c is the speed of light and ωc the electron-cyclotron frequency. The main result of our study is that the magnetic field-makes it possible to sustain a plasma column for values of σ smaller than σcr = 0.3726, below which, in the absence of a magnetic field, the dipolar wave cannot produce a plasma. Moreover, at a fixed wave power, the magnetic field – in contrast with the case of plasma columns sustained by azimuthally symmetric waves – increases the plasma density and its axial gradient. The limit of an infinite external magnetic field (Ω → ∞) is also considered. A three-dimensional wave structure is obtained, and it indicates that the wave can be a generalized surface mode, a pure surface or a pseudosurface one.

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Three-Dimensional Flow of Silicon Melt in a Rotating Shallow Annular Pool

Heat Transfer, Volume 2 ◽

10.1115/imece2004-60640 ◽

2004 ◽

Author(s):

You-Rong Li ◽

Lan Peng ◽

Shuang-Ying Wu ◽

Dan-Ling Zeng ◽

Nobuyuki Imaishi

Keyword(s):

Rotation Rate ◽

Three Dimensional ◽

Outer Wall ◽

Annular Pool ◽

Rotation Rates ◽

Melt Pool ◽

Silicon Melt ◽

Surface Patterns ◽

Micro Gravity ◽

Direction Opposite

In order to understand the mechanism of the surface patterns on silicon melt in Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a rotating shallow annular pool in the counter-clockwise direction under micro-gravity. The pool is heated from the outer cylindrical wall and cooled at the bottom of an inner cylinder. The temperature differences between the vertical outer wall and the inner wall are 16 K, 21 K, 26 K and 32 K. Bottom and top surfaces of the melt pool are adiabatic. When the rotation rate is very slow, the hydrothermal waves are dominant in the pool and propagate in a direction opposite to the pool rotation. When the rotation rate exceeds the first critical value, the phase velocity of the hydrothermal waves increases rapidly and its propagating direction becomes same as that of the pool rotation. With much larger rotation rate, the flow becomes an axisymmetric steady flow. Details of the flow and temperature disturbances are discussed and the critical rotation rates are determined.

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Nonlinear evolution of a wave packet propagating along a hot magnetoplasma column

Journal of Plasma Physics ◽

10.1017/s0022377800012022 ◽

1987 ◽

Vol 37 (1) ◽

pp. 107-115

Author(s):

B. Ghosh ◽

K. P. Das

Keyword(s):

Magnetic Field ◽

Multiple Scales ◽

Nonlinear Evolution ◽

Axial Magnetic Field ◽

Modulational Instability ◽

Wave Train ◽

Dielectric Medium ◽

Ion Effects ◽

The Magnetic Field ◽

Uniform Plasma

The method of multiple scales is used to derive a nonlinear Schrödinger equation, which describes the nonlinear evolution of electron plasma ‘slow waves’ propagating along a hot cylindrical plasma column, surrounded by a dielectric medium and immersed in an essentially infinite axial magnetic field. The temperature is included as well as mobile ion effects for ail possible modes of propagation along the magnetic field. From this equation the condition for modulational instability for a uniform plasma wave train is determined.

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Thermalization of synchrotron radiation from field-aligned currents

Laser and Particle Beams ◽

10.1017/s0263034600005413 ◽

1988 ◽

Vol 6 (3) ◽

pp. 493-501 ◽

Cited By ~ 8

Author(s):

William Peter ◽

Anthony L. Peratt

Keyword(s):

Magnetic Field ◽

Synchrotron Radiation ◽

Energy Density ◽

Radiation Spectrum ◽

Axial Magnetic Field ◽

Three Dimensional ◽

Synchrotron Emission ◽

Microwave Background ◽

Strong Function ◽

Current Filaments

Three-dimensional plasma simulations of interacting galactic-dimensioned current filaments show bursts of synchroton radiation of energy density 1·2 ×10−13 erg/cm3 which can be compared with the measured cosmic microwave background energy density of 1·5 × 10−13 erg/cm3. However, the synchrotron emission observed in the simulations is not blackbody. In this paper, we analyze the absorption of the synchrotron emission by the current filaments themselves (i.e., self-absorption) in order to investigate the thermalization of the emitted radiation. It is found that a large number of current filaments (>1031) are needed to make the radiation spectrum blackbody up to the observed measured frequency of 100 GHz. The radiation spectrum and the required number of current filaments is a strong function of the axial magnetic field in the filaments.

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Magnetic Field Structure of Star Forming Regions: VLBI Spectral Line Results

Symposium - International Astronomical Union ◽

10.1017/s0074180900078426 ◽

1984 ◽

Vol 110 ◽

pp. 333-334

Author(s):

J.A. Garcia-Barreto ◽

B. F. Burke ◽

M. J. Reid ◽

J. M. Moran ◽

A. D. Haschick

Keyword(s):

Magnetic Field ◽

Three Dimensional ◽

Aperture Synthesis ◽

Stokes Parameters ◽

Hii Region ◽

Star Forming ◽

Star Forming Regions ◽

Vlbi Observations ◽

The Magnetic Field ◽

Synthesis Experiment

Magnetic fields play a major role in the general dynamics of astronomical phenomena and particularly in the process of star formation. The magnetic field strength in galactic molecular clouds is of the order of few tens of μG. On a smaller scale, OH masers exhibit fields of the order of mG and these can probably be taken as representative of the magnetic field in the dense regions surrounding protostars. The OH molecule has been shown to emit highly circular and linearly polarized radiation. That it was indeed the action of the magnetic field that would give rise to the highly polarized spectrum of OH has been shown by the VLBI observations of Zeeman pairs of the 1720 and 6035 MHz by Lo et. al. and Moran et. al. VLBI observations of W3 (OH) revealed that the OH emission was coming from numerous discrete locations and that all spots fell within the continuum contours of the compact HII region. The most detailed VLBI aperture synthesis experiment of the 1665 MHz emission from W3 (OH) was carried out by Reid et. al. who found several Zeeman pairs and a characteristic maser clump size of 30 mas. In this work, we report the results of a 5 station VLBI aperture synthesis experiment of the 1665 MHz OH emission from W3 (OH) with full polarization information. We produced VLBI synthesis maps of all Stokes parameters of 16 spectral features that showed elliptical polarization. The magnitude and direction of the magnetic field have been obtained by the detection of 7 Zeeman pairs. The three dimensional orientation of the magnetic field can be obtained, following the theoretical arguments of Goldreich et. al., from the observation of π and σ components.

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DC Glow Discharge in Axial Magnetic Field at Low Pressures

Advances in Mathematical Physics ◽

10.1155/2017/9193149 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Shen Gao ◽

Shixiu Chen ◽

Zengchao Ji ◽

Wei Tian ◽

Jun Chen

Keyword(s):

Magnetic Field ◽

Glow Discharge ◽

Differential Equations ◽

Axial Magnetic Field ◽

Glow Discharge Plasma ◽

Dc Glow Discharge ◽

Fluid Approximation ◽

Low Pressures ◽

Physical Quantities ◽

The Magnetic Field

On the basis of fluid approximation, an improved version of the model for the description of dc glow discharge plasma in the axial magnetic field was successfully developed. The model has yielded a set of analytic formulas for the physical quantities concerned from the electron and ion fluids equations and Poisson equation. The calculated results satisfy the practical boundary conditions. Results obtained from the model reveal that although the differential equations under the condition of axial magnetic field are consistent with the differential equations without considering the magnetic field, the solution of the equations is not completely consistent. The results show that the stronger the magnetic field, the greater the plasma density.

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INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

EUREKA Physics and Engineering ◽

10.21303/2461-4262.2021.001713 ◽

2021 ◽

Author(s):

Jasim Mohmed Jasim Jasim ◽

Iryna Shvedchykova ◽

Igor Panasiuk ◽

Julia Romanchenko ◽

Inna Melkonova

Keyword(s):

Magnetic Field ◽

Field Distribution ◽

Three Dimensional ◽

Magnetic Potential ◽

Geometric Parameters ◽

Two Dimensional ◽

Air Gaps ◽

Vector Magnetic Potential ◽

Electromagnetic Separator ◽

The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

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Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

10.32920/ryerson.14657451 ◽

2021 ◽

Author(s):

Leily Abidi

Keyword(s):

Magnetic Field ◽

Stokes Equations ◽

Axial Magnetic Field ◽

Three Dimensional ◽

Maximum Velocity ◽

Navier Stokes ◽

Growth Interface ◽

Navier Stokes Equations ◽

Solvent Method ◽

Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

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Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

10.32920/ryerson.14657451.v1 ◽

2021 ◽

Author(s):

Leily Abidi

Keyword(s):

Magnetic Field ◽

Stokes Equations ◽

Axial Magnetic Field ◽

Three Dimensional ◽

Maximum Velocity ◽

Navier Stokes ◽

Growth Interface ◽

Navier Stokes Equations ◽

Solvent Method ◽

Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

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