Solution of the Integral Equations

As pointed out before, Eqs. (3.20a) and (3.22a) are of the standard type of linear integral equations encountered in the kinetic theory of neutral systems so we need not worry about their solutions at all. We shall give a summary of their main properties in Appendix C. Here we wish to deal with Eqs. (3.20b) and (3.20b) whose structure becomes quite complicated due to the presence of the three magnetic field dependent terms appearing in their right hand side. Since they essentially differ only in structure by their inhomogeneous term, let us fix our attention to one of them namely, Eq. (3.20b) whose solution will yield the values of the “a” coefficients required to compute the three thermal conductivities. We shall seek a solution to this equation using a variational method.