Abstract
A brief discussion of second-order tensorial objects such as dyads and dyadics is necessary in a comprehensive treatment of flux coordinates. The reason is twofold. Firstly, we regularly deal with dyadic objects in studying plasma equilibrium, even in scalar pressure cases. We frequently come across expressions such as A · BC or A · ▽B, where BC and ▽B are dyads. An important example is the curvature along a magnetic-field line: \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{B} \cdot \nabla \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{B} \) Secondly, tensor analysis in curvilinear coordinates is merely an extension of vector analysis; more accurately, vectors are a special case of tensors: vectors are first-order tensors.
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© 1991 Springer-Verlag Berlin Heidelberg
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D’haeseleer, W.D., Hitchon, W.N.G., Callen, J.D., Shohet, J.L. (1991). Tensorial Objects. In: Flux Coordinates and Magnetic Field Structure. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75595-8_3
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DOI: https://doi.org/10.1007/978-3-642-75595-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75597-2
Online ISBN: 978-3-642-75595-8
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