Axially symmetric solutions to the force-free magnetic-field equations in spherical and cylindrical coordinates

1992 ◽  
Vol 45 (10) ◽  
pp. 7520-7525 ◽  
Author(s):  
Gerald E. Marsh
Keyword(s):  
Magnetic Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Cylindrical Coordinates

scholarly journals Charged Particle Motion in a Time?Dependent Axially Symmetric Magnetic Field

1965 ◽  
Vol 18 (6) ◽  
pp. 553 ◽  
Author(s):  
PW Seymour ◽  
RB Leipnik ◽  
AF Nicholson
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Constant Velocity ◽  
Short Review ◽  
Time Dependent ◽  
Radial Compression ◽  
Axially Symmetric ◽  
Cylindrical Coordinates ◽  
Drift Theory ◽  
The Magnetic Field

Following a short review of the drift theory of plasma radial compression, an exact solution for the motion of a charged particle in an axially symmetric time-dependent magnetic field is� obtained. The method gives forms for the cylindrical coordinates rand B of the charged particle that have a simple interpretation, the z-motion being of constant velocity. As examples, the exact results are discussed for a simple power law and an exponential time dependence of the magnetic field and, using the latter results, the drift theory of plasma radial compression is qualitatively verified.

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.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

1969 ◽  
Vol 3 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. P. Srivastava ◽  
P. K. Bhat
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Neutral Point ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Hybrid Type

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

scholarly journals ECsim-CYL: Energy Conserving Semi-Implicit particle in cell simulation in axially symmetric cylindrical coordinates

2019 ◽  
Vol 236 ◽  
pp. 153-163 ◽  
Author(s):  
Diego Gonzalez-Herrero ◽  
Alfredo Micera ◽  
Elisabetta Boella ◽  
Jaeyoung Park ◽  
Giovanni Lapenta
Keyword(s):  
Axially Symmetric ◽  
Cylindrical Coordinates ◽  
Particle In Cell ◽  
Energy Conserving ◽  
Cell Simulation
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