SYMMETRY PROPERTIES OF NONLINEAR RESPONSES IN A PLASMA

Abstract-The symmetry properties of tensors describing the nonlinear responses of a collisionless magnetoactive plasma are discussed, concentrating on the generalization of the Onsager relations. The Onsager relations generalize into two sets of relations called time-reversal-invariance relations and crossing symmetries. For the parts of the tensors of practical relevance the following properties are found. The tensor describing the relation between the induced current and a product of n vector potentials changes sign by (-).+l under reversal of the signs of the frequencies and of the sense of the background magnetic field, and is completely symmetric under permutations of the indices with associated permutations of the arguments. These symmetry properties underlie the reciprocal and crossing symmetries of coefficients describing the consequent nonlinear process