VALIDITY OF THE FIELD LINE RESONANCE EXPANSION - COMMENT

In a recent paper Hansen and Goertz (hereafter HG) [Phys. Fluids B 4, 2713 (1992)] considered the coupling between fast and Alfven modes in a cold plasma containing a uniform magnetic field (B0x) extending betw een two perfectly reflecting plane boundaries at constant x. The equil ibrium medium is invariant in only one direction (y), and (importantly ) the density may vary along the equilibrium field lines, rho0(x,z). H G sought solutions of the coupled governing PDEs (partial differential equations) for linear perturbations of the form exp i(k(y)y-omegat). The solution has been studied previously [Planet. Space Sci. 22, 483 ( 1974); J. Geophys. Res. 79, 1024 (1974)] in the case when rho0 does no t vary along the background field lines, when each Fourier mode in x d ecouples from the others and may be considered separately-reducing the problem to an ODE (ordinary differential equation). In this case a lo garithmic singularity exists at the resonant field line where omega2 = k(x)2V(A)2(z), V(A) being the Alfven speed (V(A)2 = B-0(2)/4pirho0). HG claim the introduction of density variation along the equilibrium f ield causes the modes in x to become coupled resulting in the singular ODE solution becoming a nonsingular solution in the PDE case. If this conclusion is true it is of great importance for researchers in many areas such as solar corona and laboratory plasma heating, and magnetos pheric pulsations. Indeed, it suggests that a large portion of the exi sting literature in these fields is wrong. Clearly it is important to decide whether the calculation of HG is correct or not. In this Commen t the equations they set up are analyzed and are solved in a different fashion to HG. The solution found is different from that of HG and in agreement with the existing body of literature. Some sources of error in HG's analysis are pointed out.