Electronic Resource
Springer
The European physical journal
159 (1960), S. 194-211
ISSN:
1434-601X
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Force-free magnetic fields are defined by the equation rot $$\mathfrak{H} = \alpha \mathfrak{H}$$ . Making use of a moving Frenet coordinate system $$(\mathfrak{t} = tangential, \mathfrak{n} = normal, \mathfrak{b} = binormal unit vector)$$ we find the following general features of these fields: 1. grad $$\left| \mathfrak{H} \right|$$ is always parallel to the osculating plane of the $$\mathfrak{H}$$ -lines. 2. If the lines of force are rectilinear within a finite region of space, the component of grad $$\left| \mathfrak{H} \right|$$ along $$\left| \mathfrak{H} \right|$$ must be zero for a force-free field with rot . 3. The factor of proportionality $$\alpha = \alpha (\mathfrak{r})$$ and $$\mathfrak{H}$$ can be calculated by means of two equations involving only the direction of $$\left| \mathfrak{H} \right|$$ . For several models of force-free fields the effect of symmetry assumptions on $$\alpha = \alpha (\mathfrak{r})$$ is discussed using special coordinate systems. In the appendix it is pointed out that a particle drift arises in magnetic fields with .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01338347
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