Resistive Magnetohydrodynamics

Abstract

Although the plasma relevant to fusion research can normally be treated as being collisionless, the collisional resistivity, however small, often plays a crucial role in the macroscopic processes of MHD plasmas. Indeed, the resistivity causes a “reconnection” of different magnetic field lines, which never happens in an ideal MHD plasma because of the “frozen-in” condition of the fluid, and results in a topological change of the magnetic configuration accompanied by magnetic energy dissipation. Magnetic field line reconnection takes place in a very thin layer where the resistivity cannot be ignored because the parallel electric field locally vanishes, i.e., E • B = 0. In this chapter, we shall be concerned mainly with this problem. First in Sect. 11.1, we derive the reduced MHD equations [11.1–5] which describe the plasma in the presence of a strong longitudinal magnetic field with shear. Then the tearing mode instability that occurs in a local resistive layer and the resulting magnetic island formation are described in Sect 11.2. The next section is devoted to the resistive modification of the kink instability discussed in Sect. 10.5 [11.4]. Ballooning instability, which is a localized Rayleigh-Taylor instability [11.6], and resistive modification of the interchange instability are described in Sects. 11.4,5 [11.1,3.4]. Disruptive instabilities observed in tokamaks are briefly explained in Sect. 11.6. Section 11.7 deals with the nonlinear magnetic reconnection driven by an external plasma flow. The final section is devoted to the description of the plasma self-organization process due to the topological change via magnetic reconnection.