Hydrodynamics, magnetohydrodynamics, and astrophysical plasmas

1 Introduction It is not uncommon to encounter the assertion that the dynamical evolution of the large-scale bulk velocity v of a collisionless gas is not described by the hydrodynamic (HD) equations. A favorite " reason " is the statement that pressure cannot be defined in the absence of collisions. Then in some quarters it is believed that the large-scale bulk dynamics of a swirling magnetized ionized gas must be described in terms of the electric current density j and the electric field E rather than B and v, thereby rejecting magnetohydrodynamics (MHD). This point of view arises from the conviction that j is the cause of B, and, therefore, the more fundamental field variable. As a matter of fact, HD is based on the concepts of conservation of particles, momentum and energy, so HD cannot be avoided whether there are interparticle collisions (which conserve particles, momentum and energy) or not. So the basic HD equations cannot be avoided. The dynamics of a swirling magnetized plasma follows from the equations of Newton, Maxwell, Lorentz, etc., from which one discovers that the dynamical theory cannot be formulated in terms of j and E in tractable form. The dynamical equations become nonlinear global integro-differential equations, of little use in a time varying system. Unfortunately the response often is to maintain the supremacy of j and E and turn away from Newton and Maxwell to seemingly plausible, but largely false, concepts. The standard textbooks of HD and MHD are generally correct in their derivation of the dynamical equations from Newton, Maxwell, and Lorentz, but they do not address the popular misunderstandings and the rejection of HD and MHD. In fact, the basic equations of HD and MHD are simply derived and cannot be avoided in the large-scale bulk dynamics of a collisionless gas, with or without a magnetic field. The purpose of this article is to show that Newton, Maxwell, and Lorentz constrain the theory to HD and MHD and exclude the aforementioned misconceptions.