Conductivity Tensor of a Collisional Plasma in a Magnetic Field

A general method is developed for the calculation of the conductivity tensor, collisional contribution included, associated with a wave in a plasma in a magnetic field. The method is based on an iterative procedure and is applicable to any kinetic equation. With the Landau collision term a result valid to all orders in $k^2\lambda _D^{}{}_{}{}^2$ is given in integral form, and the electron current contribution is calculated explicitly to order $k^2\lambda _D^{}{}_{}{}^2$. The leading contributions resulting from the ion motion are also obtained.