Effect of viscosity on the current layers emerging upon propagation of the Alfvén pulse in a hyperbolic magnetic field

The propagation of the Alfvén pulse in the vicinity of the X-point in the presence of viscosity is studied for the first time. It is shown that, in contrast to the case of magnetosonic perturbation, where the dynamic viscosity $\eta$ (the point is that we are dealing with dimensionless quantities), which is small compared to the magnetic plasma viscosity $\nu$, does not affect the flow, this influence is of primary importance in the Alfvén case. The magnitude of the steady-state current density is proportional to $(\nu\eta)^{-1/4}$. It is also shown that at large times the distribution of the $z$-component of a magnetic field that is close to the distribution obtained in solving a linear problem is established in this significantly nonlinear problem. The effect of the heat conduction on this process is studied.