A New Method of Analyzing Eigenvalues and Eigenfunctions of Linearized Rosenbluth Collision Operator

Abstract

Eigenvalue spectrum has been a long term unsolved problem for plasma physicists. In this paper, some numerical calculations are conducted about the minimum eigenvalues of the linearized Rosenbluth collision operator and the differential part of the whole operator. Similarities of the two operator lead to further discussions about the differential operator. Completeness and orthogonality are rigorously proved. Moreover, the continuum of the whole operator is indicated.