The Hooke and Jeeves method applied to the study of the focusing properties of charged particles in an axially symmetric magnetic field

1974 ◽  
Vol 7 (6) ◽  
pp. 793-804 ◽  
Author(s):  
A H Greenaway ◽  
D Michelson
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Axially Symmetric ◽  
Focusing Properties

scholarly journals Two-fluid simulations of the magnetic field evolution in neutron star cores in the weak-coupling regime

2020 ◽  
Vol 498 (2) ◽  
pp. 3000-3012 ◽  
Author(s):  
F Castillo ◽  
A Reisenegger ◽  
J A Valdivia
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Charged Particles ◽  
Stable Stratification ◽  
Composition Gradient ◽  
Axially Symmetric ◽  
Drag Forces ◽  
Degeneracy Pressure ◽  
The Magnetic Field ◽  
Two Fluid

ABSTRACT In a previous paper, we reported simulations of the evolution of the magnetic field in neutron star (NS) cores through ambipolar diffusion, taking the neutrons as a motionless uniform background. However, in real NSs, neutrons are free to move, and a strong composition gradient leads to stable stratification (stability against convective motions) both of which might impact on the time-scales of evolution. Here, we address these issues by providing the first long-term two-fluid simulations of the evolution of an axially symmetric magnetic field in a neutron star core composed of neutrons, protons, and electrons with density and composition gradients. Again, we find that the magnetic field evolves towards barotropic ‘Grad–Shafranov equillibria’, in which the magnetic force is balanced by the degeneracy pressure gradient and gravitational force of the charged particles. However, the evolution is found to be faster than in the case of motionless neutrons, as the movement of charged particles (which are coupled to the magnetic field, but are also limited by the collisional drag forces exerted by neutrons) is less constrained, since neutrons are now allowed to move. The possible impact of non-axisymmetric instabilities on these equilibria, as well as beta decays, proton superconductivity, and neutron superfluidity, are left for future work.

I.—Focusing of Electron Beams in Crossed Static Electric and Magnetic Fields

1962 ◽  
Vol 66 (1) ◽  
pp. 1-19
Author(s):  
P. S. Farago
Keyword(s):  
Magnetic Field ◽  
Electric Fields ◽  
Solid Angle ◽  
Scalar Potential ◽  
Charged Particles ◽  
Direction Parallel ◽  
Electric And Magnetic Fields ◽  
Double Focusing ◽  
The Magnetic Field ◽  
Focusing Properties

SynopsisIn a crossed static homogeneous electric and magnetic field charged particles describing trochoidal orbits in a plane perpendicular to the direction of the magnetic field are focused, but a beam emitted by a point source in a finite solid angle spreads out indefinitely in the direction parallel to the magnetic field. The essential characteristics of trochoidal orbits can be preserved if the superimposed magnetic and electric fields are two-dimensional and orthogonal, such as derived from a vector potential, say, Ax = A(y, z), Av = Az = O, and a scalar potential Ф(y, z)= const. A(y, z). The focusing properties of such a field combination depend on the distribution of the magnetic field only. Following some general considerations, specific examples of double focusing field distributions are given, and the electron motion in one of them is treated in detail.

scholarly journals Quasiharmonic oscillations of charged particles in static axially symmetric space-times immersed in a uniform magnetic field

2020 ◽  
Vol 101 (12) ◽  
Author(s):  
Carlos A. Benavides-Gallego ◽  
Ahmadjon Abdujabbarov ◽  
Daniele Malafarina ◽  
Cosimo Bambi
Keyword(s):  
Magnetic Field ◽  
Symmetric Space ◽  
Uniform Magnetic Field ◽  
Charged Particles ◽  
Axially Symmetric

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

scholarly journals 46. The störmertron

1958 ◽  
Vol 6 ◽  
pp. 446-447
Author(s):  
Willard H. Bennett
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Mercury Vapor ◽  
Electron Gun ◽  
Conducting Film ◽  
New Developments ◽  
Electrically Conducting ◽  
The Earth ◽  
Magnetic Dipole Field ◽  
Glass Tubes

A tube has been developed in which the shapes of streams of charged particles moving in the earth's magnetic field can be produced accurately to scale. The tube has been named the Störmertron in honor of Carl Störmer who calculated many such orbits. New developments which have made this tube possible include a method for coating the inside of large glass tubes with a transparent electrically conducting film, and an electron gun producing gas-focused streams in less than ½ micron of mercury vapor, a nearly vapor-free grease joint, and a nearly vapor-free carbon black. The magnetic dipole field of the earth is simulated with an Alnico magnet capped with properly shaped soft iron caps. The stream is deflected using two pairs of yoke coils near the gun.

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