An electromagnetic integral equation: Application to microtearing modes

The integral equation technique previously developed for electrostatic drift waves to study low-frequency electromagnetic perturbation is extended. When σe≫σi (as is the case for tearing modes) the problem can be reduced to the simultaneous solution of an integral and a differential equation. Using a Fourier representation for φ̃(x), a differential equation is derived from Ampere’s law for a modified Green’s function that contains the magnetic effects. This equation is solved simultaneously with an integral equation (corresponding to the quasineutrality condition in k space) to obtain the eigenvalues and corresponding eigenfunctions. When applied to the study of microtearing modes this method gave, for the same values of the parameters, larger growth rates than those of the usual differential approximation.