2.2 Constitutive relation

Maxwell equations (??) are a closed system only if the charge and the current densities are known. In a plasma ρ(X,t) and J(X, t) are functions of E(X, t) and B(X, t). The expression of J(X, t) as a function of E(X, t) is called the constitutive relation. For linearized fields, this relation can be expressed in general as

(3)

where S(X, X ′,t,t′) is the conductivity tensor, which depends upon the plasma equilibrium.