L - Scalars, Vectors, Dyadics and Tensors

Summary

Plasma physics is a subject where advanced mathematical techniques are frequently required to gain an understanding of the physical phenomena under consideration. This is particularly true in studies involving kinetic theory and plasma transport effects, where scalars, vectors, and multi-order tensors are needed (Chapters 3 and 4). Therefore, it is useful to briefly review some of the required mathematics.

A scalar is a single number that is useful for describing, say, the temperature of a gas. However, in order to describe the velocity of the gas, both a magnitude and direction are required (e.g., a vector). A vector is defined relative to some orthogonal coordinate system and three numbers, corresponding to the components of the vector, are required to define the vector. In a Cartesian coordinate system, the vector a is given

where e₁, e₂, and e₃ are unit vectors along the x, y, and z axes, respectively. In index notation, the vector a is simply represented by a_α where α varies from 1 to 3.