Nonlinear magnetosonic waves propagating perpendicular to a magnetic neutral sheet

Abstract

Nonlinear magnetosonic waves propagating in a magnetic neutral sheet are investigated within the framework of a fluid model. It is shown that the behavior of the magnetosonic waves is governed by a ‘modified Burgers equation’ with an additional termc(η)ϕ due to the relevant slowly varying background plasma parameter (density or magnetic field), $$\frac{{\partial \phi }}{{\partial \eta }}$$ where ϕ(ξ, η) is the amplitude of the wave,\(\xi = \int {k_x } {\text{d}}x + k_y y - \omega t\), and η=ex is the coordinate stretched by a smallness parameter e. When we consider fast magnetosonic waves propagating toward the neutral region across the magnetic field, they grow and undergo rapid steepening after passing through the neutral region; i.e., shock formation is promoted by the background inhomogeneity. By the numerical computation of the above equation, the time evolution is examined for two initial disturbances, the pulse type (gaussian) and the wave train type (sinusoidal wave).