Grad's 20-moment set of transport equations has been examined in the limit of strong external magnetic fields. In this approximation, transport perpendicular to field lines is assumed to follow E¿B convection paths, and the original 20-moment set of equations reduces to a set of six partial differential equations. This simplified set of equations describes the transport of mass and parallel momentum as well as the transport of parallel and perpendicular energy and heat flow in the magnetic field direction. However, since convection perpendicular to field lines is consistently carried throughout the derivation of the reduced 20-moment set, the transport of mass, momentum, energy, and heat flow perpendicular to the magnetic field is also explicitly maintained in this formulation. The effect of collisions was calculated assuming a modified relaxation model. Wave speeds and normal modes of the simplified set of equations were examined for an ion and electron gas. It was found that four of the 10 normal modes are electron thermal-heat waves which approximately decouple from the six ion waves in the system. When low-frequency waves are considered (slow-wave approximation), this allows the electron energy and heat flow equations to be solved separately from the ion equations and in a time-independent fashion.

When this was done, it was found that under certain conditions these equations predict an infinite electron perpendicular temperature, Te⊥, in the collisionless regime. This occurs whenever Te⊥ is greater than the parallel temperature, Te∥ at any point along collisionless and diverging magnetic field lines. This nonphysical result calls into question the validity of generalized transport equations in the collisionless regime whenever Te⊥ is greater than Te∥. However, when applied appropriately, the significantly simplified set of equations derived here are well suited for application to a large variety of problems in planetary ionospheres and magnetospheres. We have also demonstrated that the heat flow must be limited to values smaller than the pressure times the thermal speed or otherwise the fundamental assumptions of the 20-moment truncation are violated. The double adiabatic approximation for hypersonic situations in the presence of heat flow was also examined. ¿1991 American Geophysical Union