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Hydromagnetic equations for collisionless plasmas in strong magnetic fields

The Chew, Goldberger & Low equations are a one-fluid system for the thermodynamic variables of the ions that are coupled to the electrons only through the electromagnetic variables. The magnitude of these variables in a collisionless plasma is re-examined in the present paper and it is found that, in the limit in which the Larmor radius and the electron-to-ion mass ratio are both zero, the current, in the plane normal to the magnetic field, is entirely transported by the electrons in the reference frame that moves with the bulk velocity. The first-order electric field contributes to the ion equation of motion with a zero-order term that couples the thermodynamic variables of both species. So the energy equation of the electrons must now be included in the equation set; to close this equation, a simple mathematical representation of the measured quasi-stationary velocity distribution function of this species is used. A two-fluid equation system in the limit in which the Larmor radius and the electron-to-ion mass ratio are both zero is then found.