S. Chandrasekhar and magnetohydrodynamics

Abstract

This chapter summarizes the many fundamental contributions of Chandrasekhar to the subject of hydromagnetics or magnetohydrodynamics (MHD) with particular attention to the generation, static equilibrium, and dynamical stability-instability of magnetic field in various idealized settings with conceptual application to astronomical problems. His interest in MHD seems to have arisen first in connection with the turbulence of electrically conducting fluid in the presence of a magnetic field, sparked by Heisenberg's (1948a,b) formulation of an equation for the energy spectrum function F(k) of statistically isotropic homogeneous hydrodynamic turbulence. From there Chandrasekhar's attention moved to the nature of the magnetic field along the spiral arm of the Galaxy (with E. Fermi), inferred from the polarization of starlight then recently discovered by Hall (1949) and Hiltner (1949, 1951). The polarization implied a magnetic field along the galactic arm, which played a key role in understanding the confinement of cosmic rays to the Galaxy. The detection and measurement of the longitudinal Zeeman effect in the spectra of several stars (Babcock and Babcock 1955) suggested the next phase of Chandrasekhar's investigations, in which he explored the combined effects of magnetic field, internal motion, and overall rotation on the figure of a star in stationary ( ∂/∂t = 0) equilibrium. Chandrasekhar and his students did some of the first work in formulating the quasi-linear field equations for the pressure, fluid velocity, and magnetic field in axisymmetric gravitating bodies. From there his thinking turned to the generation of the magnetic fields of planets and stars by the convective motions of the electrically conducting fluid in their interiors. Now the outer atmosphere of planets, stars, and galaxies are so tenuous that in most cases the atmospheres do not exert significant forces on the strong external magnetic fields of these objects, so that the external magnetic field is “force-free”, i.e., the Lorentz force, given by the divergence ∂Tij / ∂xj of the Maxwell stress tensor T ij, is negligible. The special properties of these force-free fields provide a particularly elegant mathematical formalism in the axisymmetric case. Subsequently the challenging problem of laboratory plasmas confined in strong magnetic fields attracted Chandrasekhar's interest and, with A. N. Kaufman and K. M. Watson, he developed a perturbation solution to the collisionless Boltzmann