The tearing instability of resistive magnetohydrodynamics

In this chapter we explore the linear onset of one of the most important instabilities of resistive magnetohydrodynamics, the tearing instability. In particular, we focus on two important aspects of the onset of tearing: asymptotic (modal) stability and transient (non-modal) stability. We discuss the theory required to understand these two aspects of stability, both of which have undergone significant development in recent years

Viscous normal-modes on coronal inhomogeneities and their role as a heating mechanism

Viscous damping of Alfvén surface waves is examined both analytically and numerically using incompressible MHD. Normal modes are shown to exist on discontinuous as well as continuously varying interfaces in Alfvén speed. The waves experience negligible decay below the transition zone. High-frequency waves damp just above the transition region, while those of lower frequency lose energy further out. A comparison of dissipative decay rates shows that wave damping by viscosity proceeds approximately two orders of magnitude faster than by resistivity.status: publishe

Anomalously small magnetic field in the local interstellar cloud

The solar wind carves out a cavity, known as the heliosphere, in the warm local interstellar cloud, which is itself embedded in a larger hot cloud. It is generally assumed that there is an overall pressure balance between these three regions. Thermal pressure and magnetic field pressure in the local interstellar cloud should therefore balance the inward pressure from the hot cloud(1-3), and determine the size of the heliosphere. Here we present direct measurements of the density and speed of interstellar hydrogen and helium ions deep inside the Solar System, from which we derive the thermal pressure in the local interstellar cloud. Combined with the fact that the magnetic field strength in the local cloud is constrained to be less than 4.3 mu G (to be compatible with the fact that the Voyager I spacecraft has yet to encounter the heliosphere termination shock), the total pressure that we infer is insufficient to balance the inward pressure from the hot cloud. We conclude that either the magnetic field in the local cloud is inhomogeneous, or there is a significant, as yet undetected, non-thermal component to the pressure in the local cloud.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62497/1/386374a0.pd