The Physics of Partially Ionized Gas with Applications to Processes in the Interstellar Medium
The dynamical equations for a partially ionized plasma are a matter of some recent controversy. Understanding this problem is important in understanding the interaction of the interstellar medium with the heliosphere and for understanding the spectrum of interstellar turbulence. If collision scales are much smaller than the internal interaction scales such as the ion gyroradius, the fluid approximation may be used. The analysis then must deal with at least three fluids (protons, electrons, and neutrals) which are coupled to each other by collisions and/or electromagnetic fields. Often, the proton and electron gyro-radii are much smaller than the collision length scales, so the electric and magnetic fields dominate the motions of the electrons and protons. In this case, the only important particle-particle collisions are those of the electrons and protons with the neutral atoms. Since the three species have, in general, different velocities, it is not immediately clear which fluid velocity to use. This ambiguity in the choice of fluid velocity has led to recent confusion regarding the physics of partially ionized plasmas. If the neutrals have a significant fraction of the mass, working in the center-of-mass coordinate frame can result in dynamical equations that differ greatly from those of ideal MHD. This is because the magnetic field is not frozen into the frame moving at the center-of-mass velocity, which leads to additional effects on the magnetic field that can be difficult to understand intuitively. To the extent that the electron mass is negligible, the magnetic field is actually found to be frozen into the frame moving with the electron bulk velocity. If we then take U to be the bulk velocity of the proton fluid the resulting dynamical equations closely resemble those of ideal MHD with the exception of the Hall term in the induction equation. Similarly, the frequently used Cowling conductivity also depends on the choice of coordinate frame. These conclusions address directly the recent controversy regarding the interaction of the interstellar medium with the heliosphere and also impact our understanding of interstellar turbulence.