On the Nonlinear Conductivity Tensor for an Unmagnetized Relativistic Turbulent Plasma.

The symmetry properties of the second-order nonlinear conductivity tensor for an unmagnetized, relativistic, and weakly turbulent plasma are important in the analysis of the collective bremsstrahlung instability. This tensor has some exact symmetries that, if resonant wave-particle interactions are neglected, become the widely known symmetry related to the Manley-Rowe relations, crossing symmetry, and the nondissipative nature of the nonlinear current. Using the well-known expression for the conductivity from plasma turbulence theory, a polynomial representation for the tensor is obtained in which all derivatives are removed and the pole structure is clearly exhibited. The exact symmetries are obtained by a lengthy algebraic reduction using this representation. Author