scholarly journals Zur Theorie der Verteilungen von Potential, elektrischer Feldstärke und Stromdichte in einem Lichtbogen endlicher Länge im starken axialen Magnetfeld

1969 ◽  
Vol 24 (10) ◽  
pp. 1433-1448
Author(s):  
J. Raeder ◽  
S. Wirtz
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Potential Distribution ◽  
Axial Magnetic Field ◽  
Temperature Profiles ◽  
Arc Length ◽  
Relaxation Methods ◽  
Radial Temperature ◽  
Potential Equation ◽  
Hall Parameter

Abstract A partial differential equation for the electric potential in an arc with an applied axial magnetic field is derived by using Ohm's law and the equations ∇·j=0 and ∇XE=0. To clarify the physics the potential equation is solved for two simple cases where the plasma is assumed to be homogeneous. The solutions reveal that the Hall parameter ωe τe and the arc length strongly influence the potential distribution. The dependence of the potential on the axial and radial temperature profiles is studied numerically by relaxation methods.

scholarly journals Saturation of the magnetorotational instability by stable magnetoacoustic modes

2012 ◽  
Vol 8 (S294) ◽  
pp. 365-366
Author(s):  
Edward Liverts ◽  
Yuri Shtemler ◽  
Michael Mond ◽  
Orkan M. Umurhan ◽  
Dmitry V. Bisikalo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Axial Magnetic Field ◽  
Nonlinear Ordinary Differential Equation ◽  
Amplitude Equation ◽  
Magnetorotational Instability ◽  
Zero Eigenvalue ◽  
Magnetoacoustic Waves ◽  
Linearized System

AbstractThe magnetorotational instability (MRI) of thin, vertically-isothermal Keplerian discs, under the influence of an axial magnetic field is investigated near the instability threshold. The nonlinear interaction of Alfven-Coriolis (MRI) modes with stable magnetoacoustic waves is considered. The transition of the Alfven-Coriolis modes to instability occurs when the linearized system has zero eigenvalue of multiplicity two. As a result the nonlinear ordinary differential equation that describes the evolution of the amplitude of the MRI mode near the threshold is of second order. Solutions of that amplitude equation reveal that the MRI is saturated to bursty periodical oscillations due to the transfer of energy to the stable magnetosonic modes.

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

2007 ◽  
Vol 21 (18n19) ◽  
pp. 3486-3488
Author(s):  
YOU-RONG LI ◽  
DONG-MING MO ◽  
LAN PENG ◽  
SHUANG-YING WU
Keyword(s):  
Magnetic Field ◽  
Steady Flow ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Melt Flow ◽  
Radial Temperature ◽  
Annular Pool ◽  
Silicon Melt ◽  
Surface Patterns ◽  
The Magnetic Field

In order to understand the effect of the magnetic field on surface patterns on semi-conducting silicon melt in industrial Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a shallow annular pool under the axial magnetic field for the magnetic field strength from 0 to 0.1T. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. When the magnetic field is weak, the simulation can predict various three-dimensional oscillatory flows depending on the radial temperature difference. With the much larger magnetic field, three-dimensional flow becomes axisymmetric steady flow. Details of flow and temperature disturbances are discussed and the critical magnetic field strengths for the onset of axisymmetric steady flow are determined.

Experimentelle Untersuchungen an einem Wasserstoff-Lichtbogen im achsenparallelen Magnetfeld. I.

1968 ◽  
Vol 23 (6) ◽  
pp. 867-873 ◽  
Author(s):  
C. Mahn ◽  
H. Ringler ◽  
G. Zankl
Keyword(s):  
Magnetic Field ◽  
Heat Conduction ◽  
Field Strength ◽  
Radial Direction ◽  
Axial Magnetic Field ◽  
Hydrogen Plasma ◽  
Power Input ◽  
Measured Temperature ◽  
Radial Temperature ◽  
Theoretical Predictions

In a stationary high density d. c. arc, the electric power input is balanced essentially by heat conduction losses in radial direction. These losses increase greatly with temperature and thus they limit the axial temperatures attainable with reasonable power input.An experiment is described in which considerably higher plasma temperatures have been obtained by reducing the coefficient of heat conduction with a superimposed axial magnetic field. At arc currents of about 2 kA and a magnetic field of 10 kG temperatures in the middle of the arc of the order of 10 eV were reached.The measured temperature, pressure and power input of the hydrogen plasma are compared with calculated values. In particular, the coefficient of heat conduction perpendicular to a magnetic field has been determined by measuring the radial temperature profile and the electric field strength. The results agree with theoretical predictions.

Die Energiebilanz eines Wasserstoffbogens in axialem Magnetfeld

1965 ◽  
Vol 20 (3) ◽  
pp. 475-484 ◽  
Author(s):  
Udo Heidrich
Keyword(s):  
Magnetic Field ◽  
Electrical Power ◽  
Homogeneous Magnetic Field ◽  
Hydrogen Atmosphere ◽  
Arc Length ◽  
Radial Temperature ◽  
Cylindrically Symmetric ◽  
Radiation Losses ◽  
Current Voltage ◽  
The Magnetic Field

The numerical solution of the energy balance of a cylindrically symmetric hydrogen arc immersed in an axial, strong, homogeneous magnetic field led to the current-voltage-characteristic and the radial temperature distribution. Three types of arc models were used, each with different assumptions on radiation losses. The results show that, by the reduction of the thermal conductivity perpendicular to the magnetic field for a fully ionized plasma, the necessary electrical power is diminished for temperatures along the axis higher than about 2·104°K. For example, an arc with 1 cm radius in a hydrogen atmosphere of 5 · 104 dyne/cm2, in an external magnetic field of 20 kGauss, a temperature along the axis of 105°K requires about 3,5 kW per cm arc length. Of this, radiation losses account for about 0,5 kW per cm. However, without a superimposed magnetic field the electrical power is about 200 kW per cm.

scholarly journals Oscillatory Flow of LDL-C and Blood Fluid through a Slanted Channel with Heat within the Sight of Magnetic Field

2021 ◽  
Vol 3 (5) ◽  
pp. 37-44
Author(s):  
K. W. Bunonyo ◽  
I. C. Eli
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Oscillatory Flow ◽  
Blood Stream ◽  
Temperature Profiles ◽  
Undetermined Coefficient ◽  
Dimensionless Variables ◽  
Perturbation Parameters ◽  
The Impact ◽  
It Controlling

In this research, we investigated LDL-C and blood movement through a slanted channel with heat within the sight of magnetic field. In the evaluation, mathematical models for the LDL-C and blood stream and energy transfer were developed  as partially coupled arrangement of partial differential equation (PDEs), the PDEs were scaled utilizing the dimensionless variables to dimensionless ordinary differential equation, they are further reduced to perturbed differential equations (ODEs) utilizing the perturbation parameters including the oscillatory term, where the non-homogenous equation and  conditions are solved straightforwardly utilizing the technique for undetermined coefficient. The velocity and temperature profiles are gotten for certain overseeing boundaries included, and Mathematica codes were created utilizing simulate the impact of entering parameters on the profile. It is seen that the overseeing boundaries impacted that the entering pertinent parameters influences blood flow and it helps it controlling the LDL-C concentration, aiding treatment of atherosclerosis.

EXPANSION OF LASER-PRODUCED ION BEAMS IN AN AXIAL MAGNETIC FIELD

2002 ◽  
Vol 6 (4) ◽  
pp. 8
Author(s):  
J. Wolowski ◽  
J. Badziak ◽  
P. Parys ◽  
E. Woryna ◽  
J. Krasa ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Ion Beams

A Slotless PM Variable Reluctance Resolver with Axial Magnetic Field

2021 ◽  
pp. 1-1
Author(s):  
Le Sun ◽  
Zhejun Luo ◽  
Jun Hang ◽  
Shichuan Ding ◽  
Wei Wang
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Variable Reluctance

scholarly journals Solitons of the midpoint mapping and affine curvature

2021 ◽  
Vol 112 (1) ◽  
Author(s):  
Christine Rademacher ◽  
Hans-Bert Rademacher
Keyword(s):  
Differential Equation ◽  
Large Class ◽  
Affine Group ◽  
Arc Length ◽  
Smooth Curves ◽  
Affine Map ◽  
Affine Curvature

AbstractFor a polygon $$x=(x_j)_{j\in \mathbb {Z}}$$ x = ( x j ) j ∈ Z in $$\mathbb {R}^n$$ R n we consider the midpoints polygon $$(M(x))_j=\left( x_j+x_{j+1}\right) /2.$$ ( M ( x ) ) j = x j + x j + 1 / 2 . We call a polygon a soliton of the midpoints mapping M if its midpoints polygon is the image of the polygon under an invertible affine map. We show that a large class of these polygons lie on an orbit of a one-parameter subgroup of the affine group acting on $$\mathbb {R}^n.$$ R n . These smooth curves are also characterized as solutions of the differential equation $$\dot{c}(t)=Bc (t)+d$$ c ˙ ( t ) = B c ( t ) + d for a matrix B and a vector d. For $$n=2$$ n = 2 these curves are curves of constant generalized-affine curvature $$k_{ga}=k_{ga}(B)$$ k ga = k ga ( B ) depending on B parametrized by generalized-affine arc length unless they are parametrizations of a parabola, an ellipse, or a hyperbola.

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