Using the Maxwell equation (1.5.3) (Eq. 5.3 in Chapter 1) and the equation (3.34) which defines the plasma conductivity dyad S, and considering the time variation indicated in (3.1), show that

where ε is the plasma electric permittivity dyad given by

where 1 denotes the unit dyad, which in Cartesian coordinates can be written as

Maxwell equation 5.3 Chapter 1

Equation 3.1, 3.34.

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V x B = -ίωμο Ε. Ε