Eigenfunctions and eigenvalues of the Dougherty collision operator

The Dougherty collision operator is a simplified Fokker-Planck collision operator that conserves particle number, momentum, and energy. In this paper, a complete set of orthogonal eigenfunctions of the linearized Dougherty operator is obtained. Five of the eigenfunctions have zero eigenvalue and correspond to the five conserved quantities (particle number, three components of momentum, and energy). The connection between the eigenfunctions and fluid modes in the limit of strong collisionality is demonstrated; in particular, the sound speed, thermal conductivity, and viscosity predicted by the Dougherty operator are identified. (C) 2007 American Institute of Physics.