Effect of ion–neutral collision on the deduction of Mach number in collisional plasmas

A new unmagnetized collisional Mach probe theory is developed in order to resolve the collisional effect on Mach probe analysis by including ionization, charge and momentum transfer of ions in the perturbation region of a Mach probe. A fluid model is established by assuming Boltzmann electrons and taking the moments of the one-dimensional Boltzmann transport equation, which contains the two-dimensional transport information as a source, after adding a collisional term. A new relation between the flow velocity and the ratio of the ion sheath current densities is obtained, and is compared with those by a collisionless kinetic theory and a particle-in-cell simulation in the applicable range of these theories. A new relation between flow velocity and the ratio of the ion sheath current densities shows that ion-neutral collisions have a very strong effect to produce much smaller Mach numbers from the same ratio than those by collisionless models.