scholarly journals 5. The axisymmetric case in hydromagnetics

1958 ◽  
Vol 6 ◽  
pp. 46-49
Author(s):  
S. Chandrasekhar ◽  
Kevin H. Prendergast
Keyword(s):  
Magnetic Field ◽  
Recent Work ◽  
Hydrodynamic Equation ◽  
Azimuthal Angle ◽  
Unit Vector ◽  
Velocity Fields ◽  
Laplacian Operator ◽  
Axis Of Symmetry ◽  
Image Position ◽  
The Magnetic Field

Recent work at the Yerkes Observatory has been concerned with the study of configurations in which the magnetic and velocity fields possess a common axis of symmetry. In those cases where the density ρ may be assumed constant, it has proved advantageous to employ a representation suggested by Lüst and Schlüter[1]: in cylindrical co-ordinates (ω, ϕ, z) let and where is a unit vector and T, P, V, and U are independent of the azimuthal angle Φ. The hydrodynamic equation may then be replaced by the pair of equations (cf. Ghandrasekhar [2]) and where Δ5 is the Laplacian operator in 5 dimensions. The equation for the magnetic field, may similarly be replaced by the pair of equations and

scholarly journals Study of the Magnetic Field of the Galaxy using Correlation Functions of the Intensity of Synchrotron Background Radio Emission

1996 ◽  
Vol 169 ◽  
pp. 615-616
Author(s):  
V.R. Shoutenkov
Keyword(s):  
Magnetic Field ◽  
Radio Emission ◽  
Correlation Functions ◽  
Theoretical Calculations ◽  
Angular Separation ◽  
Field Studies ◽  
Position Angle ◽  
The Galaxy ◽  
Image Position ◽  
The Magnetic Field

The possibility to study magnetic field of the Galaxy calculating correlation or structure functions of synchrotron background radio emission have been known long ago (Kaplan and Pikel'ner (1963); Getmantsev (1958)). But this method had not been as popular as other methods of magnetic field studies. However theoretical calculations made by Chibisov and Ptuskin (1981) showed that correlation functions of intensity of synchrotron background radio emission can give a lot of valuable information about galactic magnetic fields because of the intensity of synchrotron background radio emission depends on H⊥. According to this theory correlation C(θ, φ) and structure S(θ, φ) functions of intensity, as functions of angular separation θ between two lines of sight and position angle φ on the sky between this two lines of sight, can be presented as a sum of isotropic (not dependent from angle φ) and anisotropic parts:

A Discussion on solar studies with special reference to space observations - The manifold structure of the chromosphere and corona

1971 ◽  
Vol 270 (1202) ◽  
pp. 77-80 ◽  
Keyword(s):  
Magnetic Field ◽  
Fine Structure ◽  
High Resolution ◽  
Field Strength ◽  
Special Reference ◽  
Velocity Fields ◽  
Field Patterns ◽  
Uniform Region ◽  
Determining Factor ◽  
The Magnetic Field

Although the photosphere is a uniform region for scales greater than the granulation, the fact that the magnetic field strength falls off less sharply than the gas pressure leads to strong magnetic influence at greater heights in the solar atmosphere. This magnetic influence leads to non-uniformity and fine structure in the chromosphere and corona. The existence of such structure has been deduced mostly from measurements of photospheric phenomena; in particular, from measurements of photospheric velocity fields (Leighton, Noyes & Simon 1962) and of photospheric magnetic fields (Bumba & Howard 1965). The determining factor would thus appear to be in the photosphere; but visible effects only are produced in the chromosphere and corona. In recent years, high resolution filter photography has enabled us to recognize different regions of the chromosphere, where qualitatively different structure is associated with distinct magnetic field patterns. This progress has been possible because of better Lyot filters, better films and better observing sites; the spectroheliograph has always been limited for high resolution work by the finite slit width and the difficulty of accurate guiding during the long exposures.

Considerations of the effect of space-charge in the magnetron

1940 ◽  
Vol 36 (1) ◽  
pp. 94-100 ◽  
Author(s):  
E. B. Moullin
Keyword(s):  
Magnetic Field ◽  
Space Charge ◽  
Cylindrical Symmetry ◽  
Potential Difference ◽  
Anode Current ◽  
Pronounced Decrease ◽  
Field Parallel ◽  
Image Position ◽  
The Magnetic Field

When a diode thermionic tube, having cylindrical symmetry, is placed in a magnetic field parallel to its axis it is commonly called a magnetron. If there is a given potential difference between the anode and cathode of the tube, and if the magnetic field is steadily increased, a sharp and pronounced decrease of anode current occurs when the field reaches a certain value. It is easy to show that, if electrons leave without velocity from a cathode of radius b, they will just graze a concentric anode of radius a at potential V when the magnetic field H has the value given by

An experimental study of transverse ionizing MHD shock waves

1968 ◽  
Vol 2 (4) ◽  
pp. 633-652 ◽  
Author(s):  
Charlles F. Stebbins ◽  
George C. Vlases
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
High Speed ◽  
Initial Conditions ◽  
Easy Access ◽  
Low Speed ◽  
Wide Range ◽  
Image Position ◽  
Shock Jump Relations ◽  
The Magnetic Field

The jump conditions across a transverse ionizing MHD shock wave, where the magnetic field is in the plane of the shock, are examined. The conservation laws, in conjunction with Maxwell's laws and the equation of state, yield three jump equations in four unknowns. To uniquely describe jumps across an ionizing wave requires an additional descriptive relationship. The theory of Kulikovskii & Lyubimov and, later, Chu, in which the internal structure of the shock itself supplies the missing relationship, is examined. In particular, Kulikovskii & Lyubimov show, for appropriate ratios of thermal to magnetic diffusivities, that for low-speed waves the magnetic field compression across the shock is unity and the jump equations reduce to the ordinary Rankine—Hugoniot relations. For high-speed shock waves, the magnetic field compression, B2/B1, equals the gas compression across the wave, p2/p1, and the jump equations become the magnetohydrodynamic shock jump relations. Furthermore, intermediate speed shocks induce magnetic field compressions between 1 and p2/p1. An experiment was performed in an inverse pinch where E behind the shock, the shock and piston velocities, and the magnetic field compression across the shock, were measured over a wide range of initial conditions and shock velocities in hydrogen. The jump relations were written with B2/B1 as a parameter and programmed into a digital computer. The program was written for real, equilibrium hydrogen. The program provided easy access to a unique solution of the jump equations for any B2/B1. The experiment tends to confirm the Kulikovskii—Lyubimov—Chu theory. Ordinary shock waves were observed at low speeds and near-MilD shocks were observed at high speeds. Further, the relation was verified for the plasma behind the shock for low-speed shock waves, and was verified to within experimental accuracy for the intermediate class of shock waves.

scholarly journals A Storage Process of the Magnetic Energy in the Space Active Regions and Stellar Atmosphere

1990 ◽  
Vol 140 ◽  
pp. 17-19
Author(s):  
Li Zhongyuan
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Free Field ◽  
Stellar Atmosphere ◽  
Mhd Equations ◽  
Static Force ◽  
Specific Expression ◽  
Image Position ◽  
The Magnetic Field ◽  
Force Free Field

A few authors (Barnes and Sturrock, 1972; Ma, 1977; Svestka, 1977) have calculated the quantitative relationship between the static force-free field connecting the magnetic field and the twisting processes. They pointed out that the potential magnetic field without the current may be twisted into the force-free field with the enhanced current produced by the plasma rotation. Li et al. (1982) and Li and Hu (1984) have stated that the processes should be unsteady, and especially that they should not be static. The magnetic Reynold number is usually much larger than 100 in stellar atmosphere (Li et al., 1982). We adopt the following MHD equations: where the force - free factor α (t, r) depends on both, t and r. According to t h e kinematical momentum conservation, the following constraint is easily obtained: where V = (u, v, w) is the velocity field in the cylindrical coordinates. When studying the evolution of the kinematical force - free field, the in fluence of a reasonable flow on the variations of the magnetic field should be taken into account. After some reasonable simplification we deduce the specific expression of the variation law of the toroidal magnetic energy where J1 is the Bessel function of the first order. In the active region, magnetic energy including the term of a twisted effect f(t) is larger than that of the static force - free field.

Plane MHD Steady Flows with Constantly Inclined Magnetic and Velocity Fields

1975 ◽  
Vol 53 (23) ◽  
pp. 2613-2616 ◽  
Author(s):  
O. P. Chandna ◽  
H. Toews ◽  
V. I. Nath
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Velocity Field ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Steady Flows ◽  
Physical Conditions ◽  
Zero Current ◽  
Necessary And Sufficient ◽  
The Magnetic Field

Plane steady state viscous fluid flows, in which the magnetic field and velocity field are constantly inclined to one another, are considered. Necessary and sufficient physical conditions have been derived for flows with zero current density and the general solutions for these flows are obtained. Irrotational flows and flows with straight streamlines are also studied.

scholarly journals MFV: Application software for the visualization and characterization of the DC magnetic field distribution in circular coil systems

2020 ◽  
pp. 1-9
Author(s):  
J. Torres-Osorio ◽  
D. Sabogal-Suárez ◽  
J.D. Alzate-Cardona ◽  
E. Restrepo-Parra
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Magnetic Field Distribution ◽  
Magnetic Flux Density ◽  
Application Software ◽  
Circular Coil ◽  
Density Values ◽  
Axis Of Symmetry ◽  
The Magnetic Field

The characterization of the magnetic field distribution is essential in experiments and devices that use magnetic field coil systems. We present an open-source application software, MFV (Magnetic Field Visualizer), for the visualization of the distribution of the magnetic field produced by circular coil systems. MFV models, simulates, and plots the magnetic field of coil systems composed by any number of circular coils of any size placed symmetrically along the same axis. Therefore, any new design or well-known coil system, such as the Helmholtz or the Maxwell coil, can be easily modeled and simulated using MFV. A graph of the homogeneity of the magnetic field can be also produced, showing the work region where the magnetic field is homogeneous according to a percentage of homogeneity given by the user. A standardized input and output file format are employed to facilitate the exchange and archiving of data. We include some results obtained using MFV, showing its applicability to characterize the magnetic field in different coil systems. Furthermore, the magnetic field results provided by MFV were validated by comparing them with results obtained experimentally in a commercial Helmholtz coil. Obtaining the maximum variability between the experimental and simulation magnetic flux density values along the axis of symmetry is 0.87%.

Small, cool lenses

1989 ◽  
Vol 47 ◽  
pp. 96-97
Author(s):  
Albert V. Crewe
Keyword(s):  
Magnetic Field ◽  
Power Consumption ◽  
Focal Length ◽  
Thin Lens ◽  
Image Position ◽  
The Magnetic Field ◽  
Simple Integration ◽  
Excellent Article

The potential advantages of small magnetic lenses are well-known and obvious and many attempts have been made to make such lenses. Previous work has been adequately summarized in an excellent article by Mulvey who covered most of the ground. This paper can be considered to be just a small addendum to that publication. As often happens surprises occur when we combine two different concepts.If we consider an annular shaped coil (Fig. 1a) we can easily relate the power consumption to the ampere turns by a simple integration. Inserting some practical values, we obtainand we see that the power consumption does not depend upon the radius directly, only by virtue of the ratio r2/r1.We can make the coil into a lens very simply by wrapping it in iron (Fig. 1b). In the case of a thin lens (e.g. for an SEM) the focal length depends upon the value of s and the magnetic field and it is possible to combine these expressions to obtain

Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung

1966 ◽  
Vol 21 (4) ◽  
pp. 369-376 ◽  
Author(s):  
M. Steenbeck ◽  
F. Krause ◽  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Velocity Fields ◽  
Rotating Stars ◽  
Correlation Tensor ◽  
Coriolis Forces ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
The Magnetic Field ◽  
Component Parallel

A turbulent, electrically conducting fluid containing a magnetic field with non-vanishing meanvalue is investigated. The magnetic field strength and the conductivity may be so small that the turbulence is not influenced by the action of the LORENTZ force.The average of the crossproduct of velocity and magnetic field is calculated in a second approximation. It contains the averages of the products of two components of the velocity field, i. e. the components of the correlation tensor.Here the structure of the correlation tensor is determined for a medium with gradients of density and/or turbulence intensity, furthermore the turbulent motion is influenced by CORIOLIS forces.As the main result is shown that in those turbulent velocity fields the average crossproduct of velocity and magnetic field generally has a non-vanishing component parallel to the average magnetic field.Such a turbulence may be present in rotating stars. Consequences concerning the selfexcited build up of steller magnetic fields are discussed in a following paper.

scholarly journals ON MAGNETIC FIELDS IN ROTATING NUCLEAR MATTER CORES OF STELLAR DIMENSIONS

2012 ◽  
Vol 12 ◽  
pp. 58-67 ◽  
Author(s):  
KUANTAY BOSHKAYEV ◽  
MICHAEL ROTONDO ◽  
REMO RUFFINI
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Charge Distribution ◽  
Constant Angular Velocity ◽  
Classical Electrodynamics ◽  
Neutral System ◽  
Nuclear Density ◽  
Axis Of Symmetry ◽  
A Charge ◽  
The Magnetic Field

We consider a degenerate globally neutral system of stellar dimensions consisting of Nn neutrons, Np protons and Ne electrons in beta equilibrium. Such a system at nuclear density having mass numbers A ≈ 1057 can exhibit a charge distribution different from zero. We present the analysis in the framework of classical electrodynamics to investigate the magnetic field induced by this charge distribution when the system is allowed to rotate as a whole rigid body with constant angular velocity around the axis of symmetry.

Sign in / Sign up

Export Citation Format

Share Document