The Discrete Eigenvalue Problem for Azimuthally Dependent Transport Theory

The discrete eigenvalue problem associated with the one-speed azimuthal Fourier harmonics in plane geometry is discussed. An explicit expression, well-suited to numerical evaluation, is given for the dispersion function, and the reality and maximum number of discrete eigenvalues are demonstrated. From numerical examples, it is found that quite often there are no discrete eigenvalues, particularly for the higher harmonics.