ISSN:
1089-7674
Source:
AIP Digital Archive
Topics:
Physics
Notes:
In a recent paper Hansen and Goertz (hereafter HG) [Phys. Fluids B 4, 2713 (1992)] considered the coupling between fast and Alfvén modes in a cold plasma containing a uniform magnetic field (B0xˆ) extending between two perfectly reflecting plane boundaries at constant x. The equilibrium medium is invariant in only one direction (yˆ), and (importantly) the density may vary along the equilibrium field lines, ρ0(x,z). HG sought solutions of the coupled governing PDEs (partial differential equations) for linear perturbations of the form exp i(kyy−ωt). The solution has been studied previously [Planet. Space Sci. 22, 483 (1974); J. Geophys. Res. 79, 1024 (1974)] in the case when ρ0 does not vary along the background field lines, when each Fourier mode in x decouples from the others and may be considered separately—reducing the problem to an ODE (ordinary differential equation). In this case a logarithmic singularity exists at the resonant field line where ω2=k2xV2A(z), VA being the Alfvén speed (V2A=B20/4πρ0). HG claim the introduction of density variation along the equilibrium field 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 magnetospheric pulsations. Indeed, it suggests that a large portion of the existing literature in these fields is wrong. Clearly it is important to decide whether the calculation of HG is correct or not. In this Comment 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.870789
